Probabilistic hazard assessment for skin sensitization potency by dose–response modeling using feature elimination instead of quantitative structure–activity relationships

PubMed Central

McKim, James M.; Hartung, Thomas; Kleensang, Andre; Sá-Rocha, Vanessa

2016-01-01

Supervised learning methods promise to improve integrated testing strategies (ITS), but must be adjusted to handle high dimensionality and dose–response data. ITS approaches are currently fueled by the increasing mechanistic understanding of adverse outcome pathways (AOP) and the development of tests reflecting these mechanisms. Simple approaches to combine skin sensitization data sets, such as weight of evidence, fail due to problems in information redundancy and high dimension-ality. The problem is further amplified when potency information (dose/response) of hazards would be estimated. Skin sensitization currently serves as the foster child for AOP and ITS development, as legislative pressures combined with a very good mechanistic understanding of contact dermatitis have led to test development and relatively large high-quality data sets. We curated such a data set and combined a recursive variable selection algorithm to evaluate the information available through in silico, in chemico and in vitro assays. Chemical similarity alone could not cluster chemicals’ potency, and in vitro models consistently ranked high in recursive feature elimination. This allows reducing the number of tests included in an ITS. Next, we analyzed with a hidden Markov model that takes advantage of an intrinsic inter-relationship among the local lymph node assay classes, i.e. the monotonous connection between local lymph node assay and dose. The dose-informed random forest/hidden Markov model was superior to the dose-naive random forest model on all data sets. Although balanced accuracy improvement may seem small, this obscures the actual improvement in misclassifications as the dose-informed hidden Markov model strongly reduced "false-negatives" (i.e. extreme sensitizers as non-sensitizer) on all data sets. PMID:26046447

Probabilistic hazard assessment for skin sensitization potency by dose-response modeling using feature elimination instead of quantitative structure-activity relationships.

PubMed

Luechtefeld, Thomas; Maertens, Alexandra; McKim, James M; Hartung, Thomas; Kleensang, Andre; Sá-Rocha, Vanessa

2015-11-01

Supervised learning methods promise to improve integrated testing strategies (ITS), but must be adjusted to handle high dimensionality and dose-response data. ITS approaches are currently fueled by the increasing mechanistic understanding of adverse outcome pathways (AOP) and the development of tests reflecting these mechanisms. Simple approaches to combine skin sensitization data sets, such as weight of evidence, fail due to problems in information redundancy and high dimensionality. The problem is further amplified when potency information (dose/response) of hazards would be estimated. Skin sensitization currently serves as the foster child for AOP and ITS development, as legislative pressures combined with a very good mechanistic understanding of contact dermatitis have led to test development and relatively large high-quality data sets. We curated such a data set and combined a recursive variable selection algorithm to evaluate the information available through in silico, in chemico and in vitro assays. Chemical similarity alone could not cluster chemicals' potency, and in vitro models consistently ranked high in recursive feature elimination. This allows reducing the number of tests included in an ITS. Next, we analyzed with a hidden Markov model that takes advantage of an intrinsic inter-relationship among the local lymph node assay classes, i.e. the monotonous connection between local lymph node assay and dose. The dose-informed random forest/hidden Markov model was superior to the dose-naive random forest model on all data sets. Although balanced accuracy improvement may seem small, this obscures the actual improvement in misclassifications as the dose-informed hidden Markov model strongly reduced " false-negatives" (i.e. extreme sensitizers as non-sensitizer) on all data sets. Copyright © 2015 John Wiley & Sons, Ltd.

Probability distributions for Markov chain based quantum walks

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

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

NASA Astrophysics Data System (ADS)

Nickelsen, Daniel

2017-07-01

The statistics of velocity increments in homogeneous and isotropic turbulence exhibit universal features in the limit of infinite Reynolds numbers. After Kolmogorov’s scaling law from 1941, many turbulence models aim for capturing these universal features, some are known to have an equivalent formulation in terms of Markov processes. We derive the Markov process equivalent to the particularly successful scaling law postulated by She and Leveque. The Markov process is a jump process for velocity increments u(r) in scale r in which the jumps occur randomly but with deterministic width in u. From its master equation we establish a prescription to simulate the She-Leveque process and compare it with Kolmogorov scaling. To put the She-Leveque process into the context of other established turbulence models on the Markov level, we derive a diffusion process for u(r) using two properties of the Navier-Stokes equation. This diffusion process already includes Kolmogorov scaling, extended self-similarity and a class of random cascade models. The fluctuation theorem of this Markov process implies a ‘second law’ that puts a loose bound on the multipliers of the random cascade models. This bound explicitly allows for instances of inverse cascades, which are necessary to satisfy the fluctuation theorem. By adding a jump process to the diffusion process, we go beyond Kolmogorov scaling and formulate the most general scaling law for the class of Markov processes having both diffusion and jump parts. This Markov scaling law includes She-Leveque scaling and a scaling law derived by Yakhot.

Skin cancer texture analysis of OCT images based on Haralick, fractal dimension, Markov random field features, and the complex directional field features

NASA Astrophysics Data System (ADS)

Raupov, Dmitry S.; Myakinin, Oleg O.; Bratchenko, Ivan A.; Zakharov, Valery P.; Khramov, Alexander G.

2016-10-01

In this paper, we propose a report about our examining of the validity of OCT in identifying changes using a skin cancer texture analysis compiled from Haralick texture features, fractal dimension, Markov random field method and the complex directional features from different tissues. Described features have been used to detect specific spatial characteristics, which can differentiate healthy tissue from diverse skin cancers in cross-section OCT images (B- and/or C-scans). In this work, we used an interval type-II fuzzy anisotropic diffusion algorithm for speckle noise reduction in OCT images. The Haralick texture features as contrast, correlation, energy, and homogeneity have been calculated in various directions. A box-counting method is performed to evaluate fractal dimension of skin probes. Markov random field have been used for the quality enhancing of the classifying. Additionally, we used the complex directional field calculated by the local gradient methodology to increase of the assessment quality of the diagnosis method. Our results demonstrate that these texture features may present helpful information to discriminate tumor from healthy tissue. The experimental data set contains 488 OCT-images with normal skin and tumors as Basal Cell Carcinoma (BCC), Malignant Melanoma (MM) and Nevus. All images were acquired from our laboratory SD-OCT setup based on broadband light source, delivering an output power of 20 mW at the central wavelength of 840 nm with a bandwidth of 25 nm. We obtained sensitivity about 97% and specificity about 73% for a task of discrimination between MM and Nevus.

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

NASA Astrophysics Data System (ADS)

Sughiyama, Yuki; Kobayashi, Testuya J.

2018-03-01

We derive the explicit form of the rate function for semi-Markov processes. Here, the ‘random time change trick’ plays an essential role. Also, by exploiting the contraction principle of large deviation theory to the explicit form, we show that the fluctuation theorem (Gallavotti-Cohen symmetry) holds for semi-Markov cases. Furthermore, we elucidate that our rate function is an extension of the level 2.5 rate function for Markov processes to semi-Markov cases.

Markov Random Fields, Stochastic Quantization and Image Analysis

DTIC Science & Technology

1990-01-01

Markov random fields based on the lattice Z2 have been extensively used in image analysis in a Bayesian framework as a-priori models for the...of Image Analysis can be given some fundamental justification then there is a remarkable connection between Probabilistic Image Analysis , Statistical Mechanics and Lattice-based Euclidean Quantum Field Theory.

A Fast Variational Approach for Learning Markov Random Field Language Models

DTIC Science & Technology

2015-01-01

the same distribution as n- gram models, but utilize a non-linear neural network pa- rameterization. NLMs have been shown to produce com- petitive...to either resort to local optimiza- tion methods, such as those used in neural lan- guage models, or work with heavily constrained distributions. In...embeddings learned through neural language models. Central to the language modelling problem is the challenge Proceedings of the 32nd International

Markov-random-field-based super-resolution mapping for identification of urban trees in VHR images

NASA Astrophysics Data System (ADS)

Ardila, Juan P.; Tolpekin, Valentyn A.; Bijker, Wietske; Stein, Alfred

2011-11-01

Identification of tree crowns from remote sensing requires detailed spectral information and submeter spatial resolution imagery. Traditional pixel-based classification techniques do not fully exploit the spatial and spectral characteristics of remote sensing datasets. We propose a contextual and probabilistic method for detection of tree crowns in urban areas using a Markov random field based super resolution mapping (SRM) approach in very high resolution images. Our method defines an objective energy function in terms of the conditional probabilities of panchromatic and multispectral images and it locally optimizes the labeling of tree crown pixels. Energy and model parameter values are estimated from multiple implementations of SRM in tuning areas and the method is applied in QuickBird images to produce a 0.6 m tree crown map in a city of The Netherlands. The SRM output shows an identification rate of 66% and commission and omission errors in small trees and shrub areas. The method outperforms tree crown identification results obtained with maximum likelihood, support vector machines and SRM at nominal resolution (2.4 m) approaches.

Stability of the Markov operator and synchronization of Markovian random products

NASA Astrophysics Data System (ADS)

Díaz, Lorenzo J.; Matias, Edgar

2018-05-01

We study Markovian random products on a large class of ‘m-dimensional’ connected compact metric spaces (including products of closed intervals and trees). We introduce a splitting condition, generalizing the classical one by Dubins and Freedman, and prove that this condition implies the asymptotic stability of the corresponding Markov operator and (exponentially fast) synchronization.

Markov Chain Monte Carlo Bayesian Learning for Neural Networks

NASA Technical Reports Server (NTRS)

Goodrich, Michael S.

2011-01-01

Conventional training methods for neural networks involve starting al a random location in the solution space of the network weights, navigating an error hyper surface to reach a minimum, and sometime stochastic based techniques (e.g., genetic algorithms) to avoid entrapment in a local minimum. It is further typically necessary to preprocess the data (e.g., normalization) to keep the training algorithm on course. Conversely, Bayesian based learning is an epistemological approach concerned with formally updating the plausibility of competing candidate hypotheses thereby obtaining a posterior distribution for the network weights conditioned on the available data and a prior distribution. In this paper, we developed a powerful methodology for estimating the full residual uncertainty in network weights and therefore network predictions by using a modified Jeffery's prior combined with a Metropolis Markov Chain Monte Carlo method.

RANDOM EVOLUTIONS, MARKOV CHAINS, AND SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS

PubMed Central

Griego, R. J.; Hersh, R.

1969-01-01

Several authors have considered Markov processes defined by the motion of a particle on a fixed line with a random velocity1, 6, 8, 10 or a random diffusivity.5, 12 A “random evolution” is a natural but apparently new generalization of this notion. In this note we hope to show that this concept leads to simple and powerful applications of probabilistic tools to initial-value problems of both parabolic and hyperbolic type. We obtain existence theorems, representation theorems, and asymptotic formulas, both old and new. PMID:16578690

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

NASA Astrophysics Data System (ADS)

Saakian, David B.

2012-03-01

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

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

NASA Astrophysics Data System (ADS)

Sargolzahi, Iman

2018-06-01

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

Local Random Quantum Circuits are Approximate Polynomial-Designs

NASA Astrophysics Data System (ADS)

Brandão, Fernando G. S. L.; Harrow, Aram W.; Horodecki, Michał

2016-09-01

We prove that local random quantum circuits acting on n qubits composed of O( t 10 n 2) many nearest neighbor two-qubit gates form an approximate unitary t-design. Previously it was unknown whether random quantum circuits were a t-design for any t > 3. The proof is based on an interplay of techniques from quantum many-body theory, representation theory, and the theory of Markov chains. In particular we employ a result of Nachtergaele for lower bounding the spectral gap of frustration-free quantum local Hamiltonians; a quasi-orthogonality property of permutation matrices; a result of Oliveira which extends to the unitary group the path-coupling method for bounding the mixing time of random walks; and a result of Bourgain and Gamburd showing that dense subgroups of the special unitary group, composed of elements with algebraic entries, are ∞-copy tensor-product expanders. We also consider pseudo-randomness properties of local random quantum circuits of small depth and prove that circuits of depth O( t 10 n) constitute a quantum t-copy tensor-product expander. The proof also rests on techniques from quantum many-body theory, in particular on the detectability lemma of Aharonov, Arad, Landau, and Vazirani. We give applications of the results to cryptography, equilibration of closed quantum dynamics, and the generation of topological order. In particular we show the following pseudo-randomness property of generic quantum circuits: Almost every circuit U of size O( n k ) on n qubits cannot be distinguished from a Haar uniform unitary by circuits of size O( n ( k-9)/11) that are given oracle access to U.

Decomposition of conditional probability for high-order symbolic Markov chains.

PubMed

Melnik, S S; Usatenko, O V

2017-07-01

The main goal of this paper is to develop an estimate for the conditional probability function of random stationary ergodic symbolic sequences with elements belonging to a finite alphabet. We elaborate on a decomposition procedure for the conditional probability function of sequences considered to be high-order Markov chains. We represent the conditional probability function as the sum of multilinear memory function monomials of different orders (from zero up to the chain order). This allows us to introduce a family of Markov chain models and to construct artificial sequences via a method of successive iterations, taking into account at each step increasingly high correlations among random elements. At weak correlations, the memory functions are uniquely expressed in terms of the high-order symbolic correlation functions. The proposed method fills the gap between two approaches, namely the likelihood estimation and the additive Markov chains. The obtained results may have applications for sequential approximation of artificial neural network training.

Decomposition of conditional probability for high-order symbolic Markov chains

NASA Astrophysics Data System (ADS)

Melnik, S. S.; Usatenko, O. V.

2017-07-01

The main goal of this paper is to develop an estimate for the conditional probability function of random stationary ergodic symbolic sequences with elements belonging to a finite alphabet. We elaborate on a decomposition procedure for the conditional probability function of sequences considered to be high-order Markov chains. We represent the conditional probability function as the sum of multilinear memory function monomials of different orders (from zero up to the chain order). This allows us to introduce a family of Markov chain models and to construct artificial sequences via a method of successive iterations, taking into account at each step increasingly high correlations among random elements. At weak correlations, the memory functions are uniquely expressed in terms of the high-order symbolic correlation functions. The proposed method fills the gap between two approaches, namely the likelihood estimation and the additive Markov chains. The obtained results may have applications for sequential approximation of artificial neural network training.

Sub- and super-diffusion on Cantor sets: Beyond the paradox

NASA Astrophysics Data System (ADS)

K. Golmankhaneh, Alireza; Balankin, Alexander S.

2018-04-01

There is no way to build a nontrivial Markov process having continuous trajectories on a totally disconnected fractal embedded in the Euclidean space. Accordingly, in order to delineate the diffusion process on the totally disconnected fractal, one needs to relax the continuum requirement. Consequently, a diffusion process depends on how the continuum requirement is handled. This explains the emergence of different types of anomalous diffusion on the same totally disconnected set. In this regard, we argue that the number of effective spatial degrees of freedom of a random walker on the totally disconnected Cantor set is equal to nsp = [ D ] + 1, where [ D ] is the integer part of the Hausdorff dimension of the Cantor set. Conversely, the number of effective dynamical degrees of freedom (ds) depends on the definition of a Markov process on the totally disconnected Cantor set embedded in the Euclidean space En (n ≥nsp). This allows us to deduce the equation of diffusion by employing the local differential operators on the Fα-support. The exact solutions of this equation are obtained on the middle-ɛ Cantor sets for different kinds of the Markovian random processes. The relation of our findings to physical phenomena observed in complex systems is highlighted.

Fuzzy Markov random fields versus chains for multispectral image segmentation.

PubMed

Salzenstein, Fabien; Collet, Christophe

2006-11-01

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

Handling target obscuration through Markov chain observations

NASA Astrophysics Data System (ADS)

Kouritzin, Michael A.; Wu, Biao

2008-04-01

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

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

NASA Astrophysics Data System (ADS)

Marzen, Sarah E.; Crutchfield, James P.

2017-10-01

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

Scan Order in Gibbs Sampling: Models in Which it Matters and Bounds on How Much.

PubMed

He, Bryan; De Sa, Christopher; Mitliagkas, Ioannis; Ré, Christopher

2016-01-01

Gibbs sampling is a Markov Chain Monte Carlo sampling technique that iteratively samples variables from their conditional distributions. There are two common scan orders for the variables: random scan and systematic scan. Due to the benefits of locality in hardware, systematic scan is commonly used, even though most statistical guarantees are only for random scan. While it has been conjectured that the mixing times of random scan and systematic scan do not differ by more than a logarithmic factor, we show by counterexample that this is not the case, and we prove that that the mixing times do not differ by more than a polynomial factor under mild conditions. To prove these relative bounds, we introduce a method of augmenting the state space to study systematic scan using conductance.

Scan Order in Gibbs Sampling: Models in Which it Matters and Bounds on How Much

PubMed Central

He, Bryan; De Sa, Christopher; Mitliagkas, Ioannis; Ré, Christopher

2016-01-01

Gibbs sampling is a Markov Chain Monte Carlo sampling technique that iteratively samples variables from their conditional distributions. There are two common scan orders for the variables: random scan and systematic scan. Due to the benefits of locality in hardware, systematic scan is commonly used, even though most statistical guarantees are only for random scan. While it has been conjectured that the mixing times of random scan and systematic scan do not differ by more than a logarithmic factor, we show by counterexample that this is not the case, and we prove that that the mixing times do not differ by more than a polynomial factor under mild conditions. To prove these relative bounds, we introduce a method of augmenting the state space to study systematic scan using conductance. PMID:28344429

Large deviations and mixing for dissipative PDEs with unbounded random kicks

NASA Astrophysics Data System (ADS)

Jakšić, V.; Nersesyan, V.; Pillet, C.-A.; Shirikyan, A.

2018-02-01

We study the problem of exponential mixing and large deviations for discrete-time Markov processes associated with a class of random dynamical systems. Under some dissipativity and regularisation hypotheses for the underlying deterministic dynamics and a non-degeneracy condition for the driving random force, we discuss the existence and uniqueness of a stationary measure and its exponential stability in the Kantorovich-Wasserstein metric. We next turn to the large deviations principle (LDP) and establish its validity for the occupation measures of the Markov processes in question. The proof is based on Kifer’s criterion for non-compact spaces, a result on large-time asymptotics for generalised Markov semigroup, and a coupling argument. These tools combined together constitute a new approach to LDP for infinite-dimensional processes without strong Feller property in a non-compact space. The results obtained can be applied to the two-dimensional Navier-Stokes system in a bounded domain and to the complex Ginzburg-Landau equation.

Assessing significance in a Markov chain without mixing.

PubMed

Chikina, Maria; Frieze, Alan; Pegden, Wesley

2017-03-14

We present a statistical test to detect that a presented state of a reversible Markov chain was not chosen from a stationary distribution. In particular, given a value function for the states of the Markov chain, we would like to show rigorously that the presented state is an outlier with respect to the values, by establishing a [Formula: see text] value under the null hypothesis that it was chosen from a stationary distribution of the chain. A simple heuristic used in practice is to sample ranks of states from long random trajectories on the Markov chain and compare these with the rank of the presented state; if the presented state is a [Formula: see text] outlier compared with the sampled ranks (its rank is in the bottom [Formula: see text] of sampled ranks), then this observation should correspond to a [Formula: see text] value of [Formula: see text] This significance is not rigorous, however, without good bounds on the mixing time of the Markov chain. Our test is the following: Given the presented state in the Markov chain, take a random walk from the presented state for any number of steps. We prove that observing that the presented state is an [Formula: see text]-outlier on the walk is significant at [Formula: see text] under the null hypothesis that the state was chosen from a stationary distribution. We assume nothing about the Markov chain beyond reversibility and show that significance at [Formula: see text] is best possible in general. We illustrate the use of our test with a potential application to the rigorous detection of gerrymandering in Congressional districting.

Assessing significance in a Markov chain without mixing

PubMed Central

Chikina, Maria; Frieze, Alan; Pegden, Wesley

2017-01-01

We present a statistical test to detect that a presented state of a reversible Markov chain was not chosen from a stationary distribution. In particular, given a value function for the states of the Markov chain, we would like to show rigorously that the presented state is an outlier with respect to the values, by establishing a p value under the null hypothesis that it was chosen from a stationary distribution of the chain. A simple heuristic used in practice is to sample ranks of states from long random trajectories on the Markov chain and compare these with the rank of the presented state; if the presented state is a 0.1% outlier compared with the sampled ranks (its rank is in the bottom 0.1% of sampled ranks), then this observation should correspond to a p value of 0.001. This significance is not rigorous, however, without good bounds on the mixing time of the Markov chain. Our test is the following: Given the presented state in the Markov chain, take a random walk from the presented state for any number of steps. We prove that observing that the presented state is an ε-outlier on the walk is significant at p=2ε under the null hypothesis that the state was chosen from a stationary distribution. We assume nothing about the Markov chain beyond reversibility and show that significance at p≈ε is best possible in general. We illustrate the use of our test with a potential application to the rigorous detection of gerrymandering in Congressional districting. PMID:28246331

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

PubMed

Punzo, Antonio; Ingrassia, Salvatore; Maruotti, Antonello

2018-04-22

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

Inferring animal densities from tracking data using Markov chains.

PubMed

Whitehead, Hal; Jonsen, Ian D

2013-01-01

The distributions and relative densities of species are keys to ecology. Large amounts of tracking data are being collected on a wide variety of animal species using several methods, especially electronic tags that record location. These tracking data are effectively used for many purposes, but generally provide biased measures of distribution, because the starts of the tracks are not randomly distributed among the locations used by the animals. We introduce a simple Markov-chain method that produces unbiased measures of relative density from tracking data. The density estimates can be over a geographical grid, and/or relative to environmental measures. The method assumes that the tracked animals are a random subset of the population in respect to how they move through the habitat cells, and that the movements of the animals among the habitat cells form a time-homogenous Markov chain. We illustrate the method using simulated data as well as real data on the movements of sperm whales. The simulations illustrate the bias introduced when the initial tracking locations are not randomly distributed, as well as the lack of bias when the Markov method is used. We believe that this method will be important in giving unbiased estimates of density from the growing corpus of animal tracking data.

Modelling Evolutionary Algorithms with Stochastic Differential Equations.

PubMed

Heredia, Jorge Pérez

2017-11-20

There has been renewed interest in modelling the behaviour of evolutionary algorithms (EAs) by more traditional mathematical objects, such as ordinary differential equations or Markov chains. The advantage is that the analysis becomes greatly facilitated due to the existence of well established methods. However, this typically comes at the cost of disregarding information about the process. Here, we introduce the use of stochastic differential equations (SDEs) for the study of EAs. SDEs can produce simple analytical results for the dynamics of stochastic processes, unlike Markov chains which can produce rigorous but unwieldy expressions about the dynamics. On the other hand, unlike ordinary differential equations (ODEs), they do not discard information about the stochasticity of the process. We show that these are especially suitable for the analysis of fixed budget scenarios and present analogues of the additive and multiplicative drift theorems from runtime analysis. In addition, we derive a new more general multiplicative drift theorem that also covers non-elitist EAs. This theorem simultaneously allows for positive and negative results, providing information on the algorithm's progress even when the problem cannot be optimised efficiently. Finally, we provide results for some well-known heuristics namely Random Walk (RW), Random Local Search (RLS), the (1+1) EA, the Metropolis Algorithm (MA), and the Strong Selection Weak Mutation (SSWM) algorithm.

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

The generalization ability of online SVM classification based on Markov sampling.

PubMed

Xu, Jie; Yan Tang, Yuan; Zou, Bin; Xu, Zongben; Li, Luoqing; Lu, Yang

2015-03-01

In this paper, we consider online support vector machine (SVM) classification learning algorithms with uniformly ergodic Markov chain (u.e.M.c.) samples. We establish the bound on the misclassification error of an online SVM classification algorithm with u.e.M.c. samples based on reproducing kernel Hilbert spaces and obtain a satisfactory convergence rate. We also introduce a novel online SVM classification algorithm based on Markov sampling, and present the numerical studies on the learning ability of online SVM classification based on Markov sampling for benchmark repository. The numerical studies show that the learning performance of the online SVM classification algorithm based on Markov sampling is better than that of classical online SVM classification based on random sampling as the size of training samples is larger.

Comparison of estimation methods for creating small area rates of acute myocardial infarction among Medicare beneficiaries in California.

PubMed

Yasaitis, Laura C; Arcaya, Mariana C; Subramanian, S V

2015-09-01

Creating local population health measures from administrative data would be useful for health policy and public health monitoring purposes. While a wide range of options--from simple spatial smoothers to model-based methods--for estimating such rates exists, there are relatively few side-by-side comparisons, especially not with real-world data. In this paper, we compare methods for creating local estimates of acute myocardial infarction rates from Medicare claims data. A Bayesian Monte Carlo Markov Chain estimator that incorporated spatial and local random effects performed best, followed by a method-of-moments spatial Empirical Bayes estimator. As the former is more complicated and time-consuming, spatial linear Empirical Bayes methods may represent a good alternative for non-specialist investigators. Copyright © 2015 Elsevier Ltd. All rights reserved.

Local Composite Quantile Regression Smoothing for Harris Recurrent Markov Processes

PubMed Central

Li, Degui; Li, Runze

2016-01-01

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

Hyper-Spectral Image Analysis With Partially Latent Regression and Spatial Markov Dependencies

NASA Astrophysics Data System (ADS)

Deleforge, Antoine; Forbes, Florence; Ba, Sileye; Horaud, Radu

2015-09-01

Hyper-spectral data can be analyzed to recover physical properties at large planetary scales. This involves resolving inverse problems which can be addressed within machine learning, with the advantage that, once a relationship between physical parameters and spectra has been established in a data-driven fashion, the learned relationship can be used to estimate physical parameters for new hyper-spectral observations. Within this framework, we propose a spatially-constrained and partially-latent regression method which maps high-dimensional inputs (hyper-spectral images) onto low-dimensional responses (physical parameters such as the local chemical composition of the soil). The proposed regression model comprises two key features. Firstly, it combines a Gaussian mixture of locally-linear mappings (GLLiM) with a partially-latent response model. While the former makes high-dimensional regression tractable, the latter enables to deal with physical parameters that cannot be observed or, more generally, with data contaminated by experimental artifacts that cannot be explained with noise models. Secondly, spatial constraints are introduced in the model through a Markov random field (MRF) prior which provides a spatial structure to the Gaussian-mixture hidden variables. Experiments conducted on a database composed of remotely sensed observations collected from the Mars planet by the Mars Express orbiter demonstrate the effectiveness of the proposed model.

Exact Markov chains versus diffusion theory for haploid random mating.

PubMed

Tyvand, Peder A; Thorvaldsen, Steinar

2010-05-01

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

Single-image super-resolution based on Markov random field and contourlet transform

NASA Astrophysics Data System (ADS)

Wu, Wei; Liu, Zheng; Gueaieb, Wail; He, Xiaohai

2011-04-01

Learning-based methods are well adopted in image super-resolution. In this paper, we propose a new learning-based approach using contourlet transform and Markov random field. The proposed algorithm employs contourlet transform rather than the conventional wavelet to represent image features and takes into account the correlation between adjacent pixels or image patches through the Markov random field (MRF) model. The input low-resolution (LR) image is decomposed with the contourlet transform and fed to the MRF model together with the contourlet transform coefficients from the low- and high-resolution image pairs in the training set. The unknown high-frequency components/coefficients for the input low-resolution image are inferred by a belief propagation algorithm. Finally, the inverse contourlet transform converts the LR input and the inferred high-frequency coefficients into the super-resolved image. The effectiveness of the proposed method is demonstrated with the experiments on facial, vehicle plate, and real scene images. A better visual quality is achieved in terms of peak signal to noise ratio and the image structural similarity measurement.

Bayesian prestack seismic inversion with a self-adaptive Huber-Markov random-field edge protection scheme

NASA Astrophysics Data System (ADS)

Tian, Yu-Kun; Zhou, Hui; Chen, Han-Ming; Zou, Ya-Ming; Guan, Shou-Jun

2013-12-01

Seismic inversion is a highly ill-posed problem, due to many factors such as the limited seismic frequency bandwidth and inappropriate forward modeling. To obtain a unique solution, some smoothing constraints, e.g., the Tikhonov regularization are usually applied. The Tikhonov method can maintain a global smooth solution, but cause a fuzzy structure edge. In this paper we use Huber-Markov random-field edge protection method in the procedure of inverting three parameters, P-velocity, S-velocity and density. The method can avoid blurring the structure edge and resist noise. For the parameter to be inverted, the Huber-Markov random-field constructs a neighborhood system, which further acts as the vertical and lateral constraints. We use a quadratic Huber edge penalty function within the layer to suppress noise and a linear one on the edges to avoid a fuzzy result. The effectiveness of our method is proved by inverting the synthetic data without and with noises. The relationship between the adopted constraints and the inversion results is analyzed as well.

Markov models of genome segmentation

NASA Astrophysics Data System (ADS)

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

2007-01-01

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

Gossip and Distributed Kalman Filtering: Weak Consensus Under Weak Detectability

NASA Astrophysics Data System (ADS)

Kar, Soummya; Moura, José M. F.

2011-04-01

The paper presents the gossip interactive Kalman filter (GIKF) for distributed Kalman filtering for networked systems and sensor networks, where inter-sensor communication and observations occur at the same time-scale. The communication among sensors is random; each sensor occasionally exchanges its filtering state information with a neighbor depending on the availability of the appropriate network link. We show that under a weak distributed detectability condition: 1. the GIKF error process remains stochastically bounded, irrespective of the instability properties of the random process dynamics; and 2. the network achieves \\emph{weak consensus}, i.e., the conditional estimation error covariance at a (uniformly) randomly selected sensor converges in distribution to a unique invariant measure on the space of positive semi-definite matrices (independent of the initial state.) To prove these results, we interpret the filtered states (estimates and error covariances) at each node in the GIKF as stochastic particles with local interactions. We analyze the asymptotic properties of the error process by studying as a random dynamical system the associated switched (random) Riccati equation, the switching being dictated by a non-stationary Markov chain on the network graph.

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

NASA Astrophysics Data System (ADS)

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

1999-12-01

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

Counting of oligomers in sequences generated by markov chains for DNA motif discovery.

PubMed

Shan, Gao; Zheng, Wei-Mou

2009-02-01

By means of the technique of the imbedded Markov chain, an efficient algorithm is proposed to exactly calculate first, second moments of word counts and the probability for a word to occur at least once in random texts generated by a Markov chain. A generating function is introduced directly from the imbedded Markov chain to derive asymptotic approximations for the problem. Two Z-scores, one based on the number of sequences with hits and the other on the total number of word hits in a set of sequences, are examined for discovery of motifs on a set of promoter sequences extracted from A. thaliana genome. Source code is available at http://www.itp.ac.cn/zheng/oligo.c.

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

PubMed

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

1988-04-22

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

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.

Generating intrinsically disordered protein conformational ensembles from a Markov chain

NASA Astrophysics Data System (ADS)

Cukier, Robert I.

2018-03-01

Intrinsically disordered proteins (IDPs) sample a diverse conformational space. They are important to signaling and regulatory pathways in cells. An entropy penalty must be payed when an IDP becomes ordered upon interaction with another protein or a ligand. Thus, the degree of conformational disorder of an IDP is of interest. We create a dichotomic Markov model that can explore entropic features of an IDP. The Markov condition introduces local (neighbor residues in a protein sequence) rotamer dependences that arise from van der Waals and other chemical constraints. A protein sequence of length N is characterized by its (information) entropy and mutual information, MIMC, the latter providing a measure of the dependence among the random variables describing the rotamer probabilities of the residues that comprise the sequence. For a Markov chain, the MIMC is proportional to the pair mutual information MI which depends on the singlet and pair probabilities of neighbor residue rotamer sampling. All 2N sequence states are generated, along with their probabilities, and contrasted with the probabilities under the assumption of independent residues. An efficient method to generate realizations of the chain is also provided. The chain entropy, MIMC, and state probabilities provide the ingredients to distinguish different scenarios using the terminologies: MoRF (molecular recognition feature), not-MoRF, and not-IDP. A MoRF corresponds to large entropy and large MIMC (strong dependence among the residues' rotamer sampling), a not-MoRF corresponds to large entropy but small MIMC, and not-IDP corresponds to low entropy irrespective of the MIMC. We show that MorFs are most appropriate as descriptors of IDPs. They provide a reasonable number of high-population states that reflect the dependences between neighbor residues, thus classifying them as IDPs, yet without very large entropy that might lead to a too high entropy penalty.

The Markov blankets of life: autonomy, active inference and the free energy principle

PubMed Central

Palacios, Ensor; Friston, Karl; Kiverstein, Julian

2018-01-01

This work addresses the autonomous organization of biological systems. It does so by considering the boundaries of biological systems, from individual cells to Home sapiens, in terms of the presence of Markov blankets under the active inference scheme—a corollary of the free energy principle. A Markov blanket defines the boundaries of a system in a statistical sense. Here we consider how a collective of Markov blankets can self-assemble into a global system that itself has a Markov blanket; thereby providing an illustration of how autonomous systems can be understood as having layers of nested and self-sustaining boundaries. This allows us to show that: (i) any living system is a Markov blanketed system and (ii) the boundaries of such systems need not be co-extensive with the biophysical boundaries of a living organism. In other words, autonomous systems are hierarchically composed of Markov blankets of Markov blankets—all the way down to individual cells, all the way up to you and me, and all the way out to include elements of the local environment. PMID:29343629

Auto-biometric for M-mode echocardiography

NASA Astrophysics Data System (ADS)

Zhang, Wei; Park, Jinhyong; Zhou, S. Kevin

2010-03-01

In this paper we present a system for fast and accurate detection of anatomical structures (calipers) in M-mode images. The task is challenging because of dramatic variations in their appearances. We propose to solve the problem in a progressive manner, which ensures both robustness and efficiency. It first obtains rough caliper localization using the intensity profile image. Then run a constrained search for accurate caliper positions. Markov Random Field (MRF) and warping image detectors are used for jointly considering appearance information and the geometric relationship between calipers. Extensive experiments show that our system achieves more accurate results and uses less time in comparison with previously reported work.

Semantic segmentation of 3D textured meshes for urban scene analysis

NASA Astrophysics Data System (ADS)

Rouhani, Mohammad; Lafarge, Florent; Alliez, Pierre

2017-01-01

Classifying 3D measurement data has become a core problem in photogrammetry and 3D computer vision, since the rise of modern multiview geometry techniques, combined with affordable range sensors. We introduce a Markov Random Field-based approach for segmenting textured meshes generated via multi-view stereo into urban classes of interest. The input mesh is first partitioned into small clusters, referred to as superfacets, from which geometric and photometric features are computed. A random forest is then trained to predict the class of each superfacet as well as its similarity with the neighboring superfacets. Similarity is used to assign the weights of the Markov Random Field pairwise-potential and to account for contextual information between the classes. The experimental results illustrate the efficacy and accuracy of the proposed framework.

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

A new test statistic for climate models that includes field and spatial dependencies using Gaussian Markov random fields

DOE PAGES

Nosedal-Sanchez, Alvaro; Jackson, Charles S.; Huerta, Gabriel

2016-07-20

A new test statistic for climate model evaluation has been developed that potentially mitigates some of the limitations that exist for observing and representing field and space dependencies of climate phenomena. Traditionally such dependencies have been ignored when climate models have been evaluated against observational data, which makes it difficult to assess whether any given model is simulating observed climate for the right reasons. The new statistic uses Gaussian Markov random fields for estimating field and space dependencies within a first-order grid point neighborhood structure. We illustrate the ability of Gaussian Markov random fields to represent empirical estimates of fieldmore » and space covariances using "witch hat" graphs. We further use the new statistic to evaluate the tropical response of a climate model (CAM3.1) to changes in two parameters important to its representation of cloud and precipitation physics. Overall, the inclusion of dependency information did not alter significantly the recognition of those regions of parameter space that best approximated observations. However, there were some qualitative differences in the shape of the response surface that suggest how such a measure could affect estimates of model uncertainty.« less

A new test statistic for climate models that includes field and spatial dependencies using Gaussian Markov random fields

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

Nosedal-Sanchez, Alvaro; Jackson, Charles S.; Huerta, Gabriel

A new test statistic for climate model evaluation has been developed that potentially mitigates some of the limitations that exist for observing and representing field and space dependencies of climate phenomena. Traditionally such dependencies have been ignored when climate models have been evaluated against observational data, which makes it difficult to assess whether any given model is simulating observed climate for the right reasons. The new statistic uses Gaussian Markov random fields for estimating field and space dependencies within a first-order grid point neighborhood structure. We illustrate the ability of Gaussian Markov random fields to represent empirical estimates of fieldmore » and space covariances using "witch hat" graphs. We further use the new statistic to evaluate the tropical response of a climate model (CAM3.1) to changes in two parameters important to its representation of cloud and precipitation physics. Overall, the inclusion of dependency information did not alter significantly the recognition of those regions of parameter space that best approximated observations. However, there were some qualitative differences in the shape of the response surface that suggest how such a measure could affect estimates of model uncertainty.« less

A Markov model for blind image separation by a mean-field EM algorithm.

PubMed

Tonazzini, Anna; Bedini, Luigi; Salerno, Emanuele

2006-02-01

This paper deals with blind separation of images from noisy linear mixtures with unknown coefficients, formulated as a Bayesian estimation problem. This is a flexible framework, where any kind of prior knowledge about the source images and the mixing matrix can be accounted for. In particular, we describe local correlation within the individual images through the use of Markov random field (MRF) image models. These are naturally suited to express the joint pdf of the sources in a factorized form, so that the statistical independence requirements of most independent component analysis approaches to blind source separation are retained. Our model also includes edge variables to preserve intensity discontinuities. MRF models have been proved to be very efficient in many visual reconstruction problems, such as blind image restoration, and allow separation and edge detection to be performed simultaneously. We propose an expectation-maximization algorithm with the mean field approximation to derive a procedure for estimating the mixing matrix, the sources, and their edge maps. We tested this procedure on both synthetic and real images, in the fully blind case (i.e., no prior information on mixing is exploited) and found that a source model accounting for local autocorrelation is able to increase robustness against noise, even space variant. Furthermore, when the model closely fits the source characteristics, independence is no longer a strict requirement, and cross-correlated sources can be separated, as well.

Searching Remote Homology with Spectral Clustering with Symmetry in Neighborhood Cluster Kernels

PubMed Central

Maulik, Ujjwal; Sarkar, Anasua

2013-01-01

Remote homology detection among proteins utilizing only the unlabelled sequences is a central problem in comparative genomics. The existing cluster kernel methods based on neighborhoods and profiles and the Markov clustering algorithms are currently the most popular methods for protein family recognition. The deviation from random walks with inflation or dependency on hard threshold in similarity measure in those methods requires an enhancement for homology detection among multi-domain proteins. We propose to combine spectral clustering with neighborhood kernels in Markov similarity for enhancing sensitivity in detecting homology independent of “recent” paralogs. The spectral clustering approach with new combined local alignment kernels more effectively exploits the unsupervised protein sequences globally reducing inter-cluster walks. When combined with the corrections based on modified symmetry based proximity norm deemphasizing outliers, the technique proposed in this article outperforms other state-of-the-art cluster kernels among all twelve implemented kernels. The comparison with the state-of-the-art string and mismatch kernels also show the superior performance scores provided by the proposed kernels. Similar performance improvement also is found over an existing large dataset. Therefore the proposed spectral clustering framework over combined local alignment kernels with modified symmetry based correction achieves superior performance for unsupervised remote homolog detection even in multi-domain and promiscuous domain proteins from Genolevures database families with better biological relevance. Source code available upon request. Contact: sarkar@labri.fr. PMID:23457439

Searching remote homology with spectral clustering with symmetry in neighborhood cluster kernels.

PubMed

Maulik, Ujjwal; Sarkar, Anasua

2013-01-01

Remote homology detection among proteins utilizing only the unlabelled sequences is a central problem in comparative genomics. The existing cluster kernel methods based on neighborhoods and profiles and the Markov clustering algorithms are currently the most popular methods for protein family recognition. The deviation from random walks with inflation or dependency on hard threshold in similarity measure in those methods requires an enhancement for homology detection among multi-domain proteins. We propose to combine spectral clustering with neighborhood kernels in Markov similarity for enhancing sensitivity in detecting homology independent of "recent" paralogs. The spectral clustering approach with new combined local alignment kernels more effectively exploits the unsupervised protein sequences globally reducing inter-cluster walks. When combined with the corrections based on modified symmetry based proximity norm deemphasizing outliers, the technique proposed in this article outperforms other state-of-the-art cluster kernels among all twelve implemented kernels. The comparison with the state-of-the-art string and mismatch kernels also show the superior performance scores provided by the proposed kernels. Similar performance improvement also is found over an existing large dataset. Therefore the proposed spectral clustering framework over combined local alignment kernels with modified symmetry based correction achieves superior performance for unsupervised remote homolog detection even in multi-domain and promiscuous domain proteins from Genolevures database families with better biological relevance. Source code available upon request. sarkar@labri.fr.

Algorithms for Discovery of Multiple Markov Boundaries

PubMed Central

Statnikov, Alexander; Lytkin, Nikita I.; Lemeire, Jan; Aliferis, Constantin F.

2013-01-01

Algorithms for Markov boundary discovery from data constitute an important recent development in machine learning, primarily because they offer a principled solution to the variable/feature selection problem and give insight on local causal structure. Over the last decade many sound algorithms have been proposed to identify a single Markov boundary of the response variable. Even though faithful distributions and, more broadly, distributions that satisfy the intersection property always have a single Markov boundary, other distributions/data sets may have multiple Markov boundaries of the response variable. The latter distributions/data sets are common in practical data-analytic applications, and there are several reasons why it is important to induce multiple Markov boundaries from such data. However, there are currently no sound and efficient algorithms that can accomplish this task. This paper describes a family of algorithms TIE* that can discover all Markov boundaries in a distribution. The broad applicability as well as efficiency of the new algorithmic family is demonstrated in an extensive benchmarking study that involved comparison with 26 state-of-the-art algorithms/variants in 15 data sets from a diversity of application domains. PMID:25285052

Stochastic-shielding approximation of Markov chains and its application to efficiently simulate random ion-channel gating.

PubMed

Schmandt, Nicolaus T; Galán, Roberto F

2012-09-14

Markov chains provide realistic models of numerous stochastic processes in nature. We demonstrate that in any Markov chain, the change in occupation number in state A is correlated to the change in occupation number in state B if and only if A and B are directly connected. This implies that if we are only interested in state A, fluctuations in B may be replaced with their mean if state B is not directly connected to A, which shortens computing time considerably. We show the accuracy and efficacy of our approximation theoretically and in simulations of stochastic ion-channel gating in neurons.

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

PubMed

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

2012-02-01

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

Semi-Markov Models for Degradation-Based Reliability

DTIC Science & Technology

2010-01-01

standard analysis techniques for Markov processes can be employed (cf. Whitt (1984), Altiok (1985), Perros (1994), and Osogami and Harchol-Balter...We want to approximate X by a PH random variable, sayY, with c.d.f. Ĥ. Marie (1980), Altiok (1985), Johnson (1993), Perros (1994), and Osogami and...provides a minimal representation when matching only two moments. By considering the guidance provided by Marie (1980), Whitt (1984), Altiok (1985), Perros

Poisson-Box Sampling algorithms for three-dimensional Markov binary mixtures

NASA Astrophysics Data System (ADS)

Larmier, Coline; Zoia, Andrea; Malvagi, Fausto; Dumonteil, Eric; Mazzolo, Alain

2018-02-01

Particle transport in Markov mixtures can be addressed by the so-called Chord Length Sampling (CLS) methods, a family of Monte Carlo algorithms taking into account the effects of stochastic media on particle propagation by generating on-the-fly the material interfaces crossed by the random walkers during their trajectories. Such methods enable a significant reduction of computational resources as opposed to reference solutions obtained by solving the Boltzmann equation for a large number of realizations of random media. CLS solutions, which neglect correlations induced by the spatial disorder, are faster albeit approximate, and might thus show discrepancies with respect to reference solutions. In this work we propose a new family of algorithms (called 'Poisson Box Sampling', PBS) aimed at improving the accuracy of the CLS approach for transport in d-dimensional binary Markov mixtures. In order to probe the features of PBS methods, we will focus on three-dimensional Markov media and revisit the benchmark problem originally proposed by Adams, Larsen and Pomraning [1] and extended by Brantley [2]: for these configurations we will compare reference solutions, standard CLS solutions and the new PBS solutions for scalar particle flux, transmission and reflection coefficients. PBS will be shown to perform better than CLS at the expense of a reasonable increase in computational time.

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

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

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

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

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

PubMed

Engin, Ozge; Sayar, Mehmet; Erman, Burak

2009-01-13

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

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

NASA Astrophysics Data System (ADS)

Engin, Ozge; Sayar, Mehmet; Erman, Burak

2009-03-01

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

Stochastically gated local and occupation times of a Brownian particle

NASA Astrophysics Data System (ADS)

Bressloff, Paul C.

2017-01-01

We generalize the Feynman-Kac formula to analyze the local and occupation times of a Brownian particle moving in a stochastically gated one-dimensional domain. (i) The gated local time is defined as the amount of time spent by the particle in the neighborhood of a point in space where there is some target that only receives resources from (or detects) the particle when the gate is open; the target does not interfere with the motion of the Brownian particle. (ii) The gated occupation time is defined as the amount of time spent by the particle in the positive half of the real line, given that it can only cross the origin when a gate placed at the origin is open; in the closed state the particle is reflected. In both scenarios, the gate randomly switches between the open and closed states according to a two-state Markov process. We derive a stochastic, backward Fokker-Planck equation (FPE) for the moment-generating function of the two types of gated Brownian functional, given a particular realization of the stochastic gate, and analyze the resulting stochastic FPE using a moments method recently developed for diffusion processes in randomly switching environments. In particular, we obtain dynamical equations for the moment-generating function, averaged with respect to realizations of the stochastic gate.

Effective comparative analysis of protein-protein interaction networks by measuring the steady-state network flow using a Markov model.

PubMed

Jeong, Hyundoo; Qian, Xiaoning; Yoon, Byung-Jun

2016-10-06

Comparative analysis of protein-protein interaction (PPI) networks provides an effective means of detecting conserved functional network modules across different species. Such modules typically consist of orthologous proteins with conserved interactions, which can be exploited to computationally predict the modules through network comparison. In this work, we propose a novel probabilistic framework for comparing PPI networks and effectively predicting the correspondence between proteins, represented as network nodes, that belong to conserved functional modules across the given PPI networks. The basic idea is to estimate the steady-state network flow between nodes that belong to different PPI networks based on a Markov random walk model. The random walker is designed to make random moves to adjacent nodes within a PPI network as well as cross-network moves between potential orthologous nodes with high sequence similarity. Based on this Markov random walk model, we estimate the steady-state network flow - or the long-term relative frequency of the transitions that the random walker makes - between nodes in different PPI networks, which can be used as a probabilistic score measuring their potential correspondence. Subsequently, the estimated scores can be used for detecting orthologous proteins in conserved functional modules through network alignment. Through evaluations based on multiple real PPI networks, we demonstrate that the proposed scheme leads to improved alignment results that are biologically more meaningful at reduced computational cost, outperforming the current state-of-the-art algorithms. The source code and datasets can be downloaded from http://www.ece.tamu.edu/~bjyoon/CUFID .

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

NASA Astrophysics Data System (ADS)

Hersvik, K.; Endrerud, O.-E. V.

2017-12-01

A method is developed for generating a set of unique weather time-series based on an existing weather series. The method allows statistically valid weather variations to take place within repeated simulations of offshore operations. The numerous generated time series need to share the same statistical qualities as the original time series. Statistical qualities here refer mainly to the distribution of weather windows available for work, including durations and frequencies of such weather windows, and seasonal characteristics. The method is based on the Markov chain process. The core new development lies in how the Markov Process is used, specifically by joining small pieces of random length time series together rather than joining individual weather states, each from a single time step, which is a common solution found in the literature. This new Markov model shows favorable characteristics with respect to the requirements set forth and all aspects of the validation performed.

Multiscale hidden Markov models for photon-limited imaging

NASA Astrophysics Data System (ADS)

Nowak, Robert D.

1999-06-01

Photon-limited image analysis is often hindered by low signal-to-noise ratios. A novel Bayesian multiscale modeling and analysis method is developed in this paper to assist in these challenging situations. In addition to providing a very natural and useful framework for modeling an d processing images, Bayesian multiscale analysis is often much less computationally demanding compared to classical Markov random field models. This paper focuses on a probabilistic graph model called the multiscale hidden Markov model (MHMM), which captures the key inter-scale dependencies present in natural image intensities. The MHMM framework presented here is specifically designed for photon-limited imagin applications involving Poisson statistics, and applications to image intensity analysis are examined.

An adaptive random search for short term generation scheduling with network constraints.

PubMed

Marmolejo, J A; Velasco, Jonás; Selley, Héctor J

2017-01-01

This paper presents an adaptive random search approach to address a short term generation scheduling with network constraints, which determines the startup and shutdown schedules of thermal units over a given planning horizon. In this model, we consider the transmission network through capacity limits and line losses. The mathematical model is stated in the form of a Mixed Integer Non Linear Problem with binary variables. The proposed heuristic is a population-based method that generates a set of new potential solutions via a random search strategy. The random search is based on the Markov Chain Monte Carlo method. The main key of the proposed method is that the noise level of the random search is adaptively controlled in order to exploring and exploiting the entire search space. In order to improve the solutions, we consider coupling a local search into random search process. Several test systems are presented to evaluate the performance of the proposed heuristic. We use a commercial optimizer to compare the quality of the solutions provided by the proposed method. The solution of the proposed algorithm showed a significant reduction in computational effort with respect to the full-scale outer approximation commercial solver. Numerical results show the potential and robustness of our approach.

A Perron-Frobenius Type of Theorem for Quantum Operations

NASA Astrophysics Data System (ADS)

Lagro, Matthew; Yang, Wei-Shih; Xiong, Sheng

2017-10-01

We define a special class of quantum operations we call Markovian and show that it has the same spectral properties as a corresponding Markov chain. We then consider a convex combination of a quantum operation and a Markovian quantum operation and show that under a norm condition its spectrum has the same properties as in the conclusion of the Perron-Frobenius theorem if its Markovian part does. Moreover, under a compatibility condition of the two operations, we show that its limiting distribution is the same as the corresponding Markov chain. We apply our general results to partially decoherent quantum random walks with decoherence strength 0 ≤ p ≤ 1. We obtain a quantum ergodic theorem for partially decoherent processes. We show that for 0 < p ≤ 1, the limiting distribution of a partially decoherent quantum random walk is the same as the limiting distribution for the classical random walk.

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.

PubMed

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.

Eternal non-Markovianity: from random unitary to Markov chain realisations.

PubMed

Megier, Nina; Chruściński, Dariusz; Piilo, Jyrki; Strunz, Walter T

2017-07-25

The theoretical description of quantum dynamics in an intriguing way does not necessarily imply the underlying dynamics is indeed intriguing. Here we show how a known very interesting master equation with an always negative decay rate [eternal non-Markovianity (ENM)] arises from simple stochastic Schrödinger dynamics (random unitary dynamics). Equivalently, it may be seen as arising from a mixture of Markov (semi-group) open system dynamics. Both these approaches lead to a more general family of CPT maps, characterized by a point within a parameter triangle. Our results show how ENM quantum dynamics can be realised easily in the laboratory. Moreover, we find a quantum time-continuously measured (quantum trajectory) realisation of the dynamics of the ENM master equation based on unitary transformations and projective measurements in an extended Hilbert space, guided by a classical Markov process. Furthermore, a Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) representation of the dynamics in an extended Hilbert space can be found, with a remarkable property: there is no dynamics in the ancilla state. Finally, analogous constructions for two qubits extend these results from non-CP-divisible to non-P-divisible dynamics.

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

PubMed Central

Chevalier, Michael W.; El-Samad, Hana

2014-01-01

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

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

NASA Astrophysics Data System (ADS)

Chevalier, Michael W.; El-Samad, Hana

2014-12-01

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

Cover estimation and payload location using Markov random fields

NASA Astrophysics Data System (ADS)

Quach, Tu-Thach

2014-02-01

Payload location is an approach to find the message bits hidden in steganographic images, but not necessarily their logical order. Its success relies primarily on the accuracy of the underlying cover estimators and can be improved if more estimators are used. This paper presents an approach based on Markov random field to estimate the cover image given a stego image. It uses pairwise constraints to capture the natural two-dimensional statistics of cover images and forms a basis for more sophisticated models. Experimental results show that it is competitive against current state-of-the-art estimators and can locate payload embedded by simple LSB steganography and group-parity steganography. Furthermore, when combined with existing estimators, payload location accuracy improves significantly.

Stochastic interpretation of the advection-diffusion equation and its relevance to bed load transport

NASA Astrophysics Data System (ADS)

Ancey, C.; Bohorquez, P.; Heyman, J.

2015-12-01

The advection-diffusion equation is one of the most widespread equations in physics. It arises quite often in the context of sediment transport, e.g., for describing time and space variations in the particle activity (the solid volume of particles in motion per unit streambed area). Phenomenological laws are usually sufficient to derive this equation and interpret its terms. Stochastic models can also be used to derive it, with the significant advantage that they provide information on the statistical properties of particle activity. These models are quite useful when sediment transport exhibits large fluctuations (typically at low transport rates), making the measurement of mean values difficult. Among these stochastic models, the most common approach consists of random walk models. For instance, they have been used to model the random displacement of tracers in rivers. Here we explore an alternative approach, which involves monitoring the evolution of the number of particles moving within an array of cells of finite length. Birth-death Markov processes are well suited to this objective. While the topic has been explored in detail for diffusion-reaction systems, the treatment of advection has received no attention. We therefore look into the possibility of deriving the advection-diffusion equation (with a source term) within the framework of birth-death Markov processes. We show that in the continuum limit (when the cell size becomes vanishingly small), we can derive an advection-diffusion equation for particle activity. Yet while this derivation is formally valid in the continuum limit, it runs into difficulty in practical applications involving cells or meshes of finite length. Indeed, within our stochastic framework, particle advection produces nonlocal effects, which are more or less significant depending on the cell size and particle velocity. Albeit nonlocal, these effects look like (local) diffusion and add to the intrinsic particle diffusion (dispersal due to velocity fluctuations), with the important consequence that local measurements depend on both the intrinsic properties of particle displacement and the dimensions of the measurement system.

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

RRW: repeated random walks on genome-scale protein networks for local cluster discovery

PubMed Central

Macropol, Kathy; Can, Tolga; Singh, Ambuj K

2009-01-01

Background We propose an efficient and biologically sensitive algorithm based on repeated random walks (RRW) for discovering functional modules, e.g., complexes and pathways, within large-scale protein networks. Compared to existing cluster identification techniques, RRW implicitly makes use of network topology, edge weights, and long range interactions between proteins. Results We apply the proposed technique on a functional network of yeast genes and accurately identify statistically significant clusters of proteins. We validate the biological significance of the results using known complexes in the MIPS complex catalogue database and well-characterized biological processes. We find that 90% of the created clusters have the majority of their catalogued proteins belonging to the same MIPS complex, and about 80% have the majority of their proteins involved in the same biological process. We compare our method to various other clustering techniques, such as the Markov Clustering Algorithm (MCL), and find a significant improvement in the RRW clusters' precision and accuracy values. Conclusion RRW, which is a technique that exploits the topology of the network, is more precise and robust in finding local clusters. In addition, it has the added flexibility of being able to find multi-functional proteins by allowing overlapping clusters. PMID:19740439

Stochastic Calculus and Differential Equations for Physics and Finance

NASA Astrophysics Data System (ADS)

McCauley, Joseph L.

2013-02-01

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

On the mixing time in the Wang-Landau algorithm

NASA Astrophysics Data System (ADS)

Fadeeva, Marina; Shchur, Lev

2018-01-01

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

Power spectral ensity of markov texture fields

NASA Technical Reports Server (NTRS)

Shanmugan, K. S.; Holtzman, J. C.

1984-01-01

Texture is an important image characteristic. A variety of spatial domain techniques were proposed for extracting and utilizing textural features for segmenting and classifying images. for the most part, these spatial domain techniques are ad hos in nature. A markov random field model for image texture is discussed. A frequency domain description of image texture is derived in terms of the power spectral density. This model is used for designing optimum frequency domain filters for enhancing, restoring and segmenting images based on their textural properties.

Honest Importance Sampling with Multiple Markov Chains

PubMed Central

Tan, Aixin; Doss, Hani; Hobert, James P.

2017-01-01

Importance sampling is a classical Monte Carlo technique in which a random sample from one probability density, π1, is used to estimate an expectation with respect to another, π. The importance sampling estimator is strongly consistent and, as long as two simple moment conditions are satisfied, it obeys a central limit theorem (CLT). Moreover, there is a simple consistent estimator for the asymptotic variance in the CLT, which makes for routine computation of standard errors. Importance sampling can also be used in the Markov chain Monte Carlo (MCMC) context. Indeed, if the random sample from π1 is replaced by a Harris ergodic Markov chain with invariant density π1, then the resulting estimator remains strongly consistent. There is a price to be paid however, as the computation of standard errors becomes more complicated. First, the two simple moment conditions that guarantee a CLT in the iid case are not enough in the MCMC context. Second, even when a CLT does hold, the asymptotic variance has a complex form and is difficult to estimate consistently. In this paper, we explain how to use regenerative simulation to overcome these problems. Actually, we consider a more general set up, where we assume that Markov chain samples from several probability densities, π1, …, πk, are available. We construct multiple-chain importance sampling estimators for which we obtain a CLT based on regeneration. We show that if the Markov chains converge to their respective target distributions at a geometric rate, then under moment conditions similar to those required in the iid case, the MCMC-based importance sampling estimator obeys a CLT. Furthermore, because the CLT is based on a regenerative process, there is a simple consistent estimator of the asymptotic variance. We illustrate the method with two applications in Bayesian sensitivity analysis. The first concerns one-way random effects models under different priors. The second involves Bayesian variable selection in linear regression, and for this application, importance sampling based on multiple chains enables an empirical Bayes approach to variable selection. PMID:28701855

Honest Importance Sampling with Multiple Markov Chains.

PubMed

Tan, Aixin; Doss, Hani; Hobert, James P

2015-01-01

Importance sampling is a classical Monte Carlo technique in which a random sample from one probability density, π 1 , is used to estimate an expectation with respect to another, π . The importance sampling estimator is strongly consistent and, as long as two simple moment conditions are satisfied, it obeys a central limit theorem (CLT). Moreover, there is a simple consistent estimator for the asymptotic variance in the CLT, which makes for routine computation of standard errors. Importance sampling can also be used in the Markov chain Monte Carlo (MCMC) context. Indeed, if the random sample from π 1 is replaced by a Harris ergodic Markov chain with invariant density π 1 , then the resulting estimator remains strongly consistent. There is a price to be paid however, as the computation of standard errors becomes more complicated. First, the two simple moment conditions that guarantee a CLT in the iid case are not enough in the MCMC context. Second, even when a CLT does hold, the asymptotic variance has a complex form and is difficult to estimate consistently. In this paper, we explain how to use regenerative simulation to overcome these problems. Actually, we consider a more general set up, where we assume that Markov chain samples from several probability densities, π 1 , …, π k , are available. We construct multiple-chain importance sampling estimators for which we obtain a CLT based on regeneration. We show that if the Markov chains converge to their respective target distributions at a geometric rate, then under moment conditions similar to those required in the iid case, the MCMC-based importance sampling estimator obeys a CLT. Furthermore, because the CLT is based on a regenerative process, there is a simple consistent estimator of the asymptotic variance. We illustrate the method with two applications in Bayesian sensitivity analysis. The first concerns one-way random effects models under different priors. The second involves Bayesian variable selection in linear regression, and for this application, importance sampling based on multiple chains enables an empirical Bayes approach to variable selection.

Automated brain tumor segmentation using spatial accuracy-weighted hidden Markov Random Field.

PubMed

Nie, Jingxin; Xue, Zhong; Liu, Tianming; Young, Geoffrey S; Setayesh, Kian; Guo, Lei; Wong, Stephen T C

2009-09-01

A variety of algorithms have been proposed for brain tumor segmentation from multi-channel sequences, however, most of them require isotropic or pseudo-isotropic resolution of the MR images. Although co-registration and interpolation of low-resolution sequences, such as T2-weighted images, onto the space of the high-resolution image, such as T1-weighted image, can be performed prior to the segmentation, the results are usually limited by partial volume effects due to interpolation of low-resolution images. To improve the quality of tumor segmentation in clinical applications where low-resolution sequences are commonly used together with high-resolution images, we propose the algorithm based on Spatial accuracy-weighted Hidden Markov random field and Expectation maximization (SHE) approach for both automated tumor and enhanced-tumor segmentation. SHE incorporates the spatial interpolation accuracy of low-resolution images into the optimization procedure of the Hidden Markov Random Field (HMRF) to segment tumor using multi-channel MR images with different resolutions, e.g., high-resolution T1-weighted and low-resolution T2-weighted images. In experiments, we evaluated this algorithm using a set of simulated multi-channel brain MR images with known ground-truth tissue segmentation and also applied it to a dataset of MR images obtained during clinical trials of brain tumor chemotherapy. The results show that more accurate tumor segmentation results can be obtained by comparing with conventional multi-channel segmentation algorithms.

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

PubMed

Numazawa, Satoshi; Smith, Roger

2011-10-01

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

Complete Scene Recovery and Terrain Classification in Textured Terrain Meshes

PubMed Central

Song, Wei; Cho, Kyungeun; Um, Kyhyun; Won, Chee Sun; Sim, Sungdae

2012-01-01

Terrain classification allows a mobile robot to create an annotated map of its local environment from the three-dimensional (3D) and two-dimensional (2D) datasets collected by its array of sensors, including a GPS receiver, gyroscope, video camera, and range sensor. However, parts of objects that are outside the measurement range of the range sensor will not be detected. To overcome this problem, this paper describes an edge estimation method for complete scene recovery and complete terrain reconstruction. Here, the Gibbs-Markov random field is used to segment the ground from 2D videos and 3D point clouds. Further, a masking method is proposed to classify buildings and trees in a terrain mesh. PMID:23112653

Surgical gesture segmentation and recognition.

PubMed

Tao, Lingling; Zappella, Luca; Hager, Gregory D; Vidal, René

2013-01-01

Automatic surgical gesture segmentation and recognition can provide useful feedback for surgical training in robotic surgery. Most prior work in this field relies on the robot's kinematic data. Although recent work [1,2] shows that the robot's video data can be equally effective for surgical gesture recognition, the segmentation of the video into gestures is assumed to be known. In this paper, we propose a framework for joint segmentation and recognition of surgical gestures from kinematic and video data. Unlike prior work that relies on either frame-level kinematic cues, or segment-level kinematic or video cues, our approach exploits both cues by using a combined Markov/semi-Markov conditional random field (MsM-CRF) model. Our experiments show that the proposed model improves over a Markov or semi-Markov CRF when using video data alone, gives results that are comparable to state-of-the-art methods on kinematic data alone, and improves over state-of-the-art methods when combining kinematic and video data.

Quantum Markov chains

NASA Astrophysics Data System (ADS)

Gudder, Stanley

2008-07-01

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

Random Breakage of a Rod into Unit Lengths

ERIC Educational Resources Information Center

Gani, Joe; Swift, Randall

2011-01-01

In this article we consider the random breakage of a rod into "L" unit elements and present a Markov chain based method that tracks intermediate breakage configurations. The probability of the time to final breakage for L = 3, 4, 5 is obtained and the method is shown to extend in principle, beyond L = 5.

Quantum speedup of Monte Carlo methods.

PubMed

Montanaro, Ashley

2015-09-08

Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition functions. In this work, we describe a quantum algorithm which can accelerate Monte Carlo methods in a very general setting. The algorithm estimates the expected output value of an arbitrary randomized or quantum subroutine with bounded variance, achieving a near-quadratic speedup over the best possible classical algorithm. Combining the algorithm with the use of quantum walks gives a quantum speedup of the fastest known classical algorithms with rigorous performance bounds for computing partition functions, which use multiple-stage Markov chain Monte Carlo techniques. The quantum algorithm can also be used to estimate the total variation distance between probability distributions efficiently.

Quantum speedup of Monte Carlo methods

PubMed Central

Montanaro, Ashley

2015-01-01

Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition functions. In this work, we describe a quantum algorithm which can accelerate Monte Carlo methods in a very general setting. The algorithm estimates the expected output value of an arbitrary randomized or quantum subroutine with bounded variance, achieving a near-quadratic speedup over the best possible classical algorithm. Combining the algorithm with the use of quantum walks gives a quantum speedup of the fastest known classical algorithms with rigorous performance bounds for computing partition functions, which use multiple-stage Markov chain Monte Carlo techniques. The quantum algorithm can also be used to estimate the total variation distance between probability distributions efficiently. PMID:26528079

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

PubMed

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

2006-03-01

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

Discriminative motif discovery via simulated evolution and random under-sampling.

PubMed

Song, Tao; Gu, Hong

2014-01-01

Conserved motifs in biological sequences are closely related to their structure and functions. Recently, discriminative motif discovery methods have attracted more and more attention. However, little attention has been devoted to the data imbalance problem, which is one of the main reasons affecting the performance of the discriminative models. In this article, a simulated evolution method is applied to solve the multi-class imbalance problem at the stage of data preprocessing, and at the stage of Hidden Markov Models (HMMs) training, a random under-sampling method is introduced for the imbalance between the positive and negative datasets. It is shown that, in the task of discovering targeting motifs of nine subcellular compartments, the motifs found by our method are more conserved than the methods without considering data imbalance problem and recover the most known targeting motifs from Minimotif Miner and InterPro. Meanwhile, we use the found motifs to predict protein subcellular localization and achieve higher prediction precision and recall for the minority classes.

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

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

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

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

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

Bayesian Analysis for Exponential Random Graph Models Using the Adaptive Exchange Sampler.

PubMed

Jin, Ick Hoon; Yuan, Ying; Liang, Faming

2013-10-01

Exponential random graph models have been widely used in social network analysis. However, these models are extremely difficult to handle from a statistical viewpoint, because of the intractable normalizing constant and model degeneracy. In this paper, we consider a fully Bayesian analysis for exponential random graph models using the adaptive exchange sampler, which solves the intractable normalizing constant and model degeneracy issues encountered in Markov chain Monte Carlo (MCMC) simulations. The adaptive exchange sampler can be viewed as a MCMC extension of the exchange algorithm, and it generates auxiliary networks via an importance sampling procedure from an auxiliary Markov chain running in parallel. The convergence of this algorithm is established under mild conditions. The adaptive exchange sampler is illustrated using a few social networks, including the Florentine business network, molecule synthetic network, and dolphins network. The results indicate that the adaptive exchange algorithm can produce more accurate estimates than approximate exchange algorithms, while maintaining the same computational efficiency.

Locally adaptive MR intensity models and MRF-based segmentation of multiple sclerosis lesions

NASA Astrophysics Data System (ADS)

Galimzianova, Alfiia; Lesjak, Žiga; Likar, Boštjan; Pernuš, Franjo; Špiclin, Žiga

2015-03-01

Neuroimaging biomarkers are an important paraclinical tool used to characterize a number of neurological diseases, however, their extraction requires accurate and reliable segmentation of normal and pathological brain structures. For MR images of healthy brains the intensity models of normal-appearing brain tissue (NABT) in combination with Markov random field (MRF) models are known to give reliable and smooth NABT segmentation. However, the presence of pathology, MR intensity bias and natural tissue-dependent intensity variability altogether represent difficult challenges for a reliable estimation of NABT intensity model based on MR images. In this paper, we propose a novel method for segmentation of normal and pathological structures in brain MR images of multiple sclerosis (MS) patients that is based on locally-adaptive NABT model, a robust method for the estimation of model parameters and a MRF-based segmentation framework. Experiments on multi-sequence brain MR images of 27 MS patients show that, compared to whole-brain model and compared to the widely used Expectation-Maximization Segmentation (EMS) method, the locally-adaptive NABT model increases the accuracy of MS lesion segmentation.

Bayesian random local clocks, or one rate to rule them all

PubMed Central

2010-01-01

Background Relaxed molecular clock models allow divergence time dating and "relaxed phylogenetic" inference, in which a time tree is estimated in the face of unequal rates across lineages. We present a new method for relaxing the assumption of a strict molecular clock using Markov chain Monte Carlo to implement Bayesian modeling averaging over random local molecular clocks. The new method approaches the problem of rate variation among lineages by proposing a series of local molecular clocks, each extending over a subregion of the full phylogeny. Each branch in a phylogeny (subtending a clade) is a possible location for a change of rate from one local clock to a new one. Thus, including both the global molecular clock and the unconstrained model results, there are a total of 22n-2 possible rate models available for averaging with 1, 2, ..., 2n - 2 different rate categories. Results We propose an efficient method to sample this model space while simultaneously estimating the phylogeny. The new method conveniently allows a direct test of the strict molecular clock, in which one rate rules them all, against a large array of alternative local molecular clock models. We illustrate the method's utility on three example data sets involving mammal, primate and influenza evolution. Finally, we explore methods to visualize the complex posterior distribution that results from inference under such models. Conclusions The examples suggest that large sequence datasets may only require a small number of local molecular clocks to reconcile their branch lengths with a time scale. All of the analyses described here are implemented in the open access software package BEAST 1.5.4 (http://beast-mcmc.googlecode.com/). PMID:20807414

Robust Dehaze Algorithm for Degraded Image of CMOS Image Sensors.

PubMed

Qu, Chen; Bi, Du-Yan; Sui, Ping; Chao, Ai-Nong; Wang, Yun-Fei

2017-09-22

The CMOS (Complementary Metal-Oxide-Semiconductor) is a new type of solid image sensor device widely used in object tracking, object recognition, intelligent navigation fields, and so on. However, images captured by outdoor CMOS sensor devices are usually affected by suspended atmospheric particles (such as haze), causing a reduction in image contrast, color distortion problems, and so on. In view of this, we propose a novel dehazing approach based on a local consistent Markov random field (MRF) framework. The neighboring clique in traditional MRF is extended to the non-neighboring clique, which is defined on local consistent blocks based on two clues, where both the atmospheric light and transmission map satisfy the character of local consistency. In this framework, our model can strengthen the restriction of the whole image while incorporating more sophisticated statistical priors, resulting in more expressive power of modeling, thus, solving inadequate detail recovery effectively and alleviating color distortion. Moreover, the local consistent MRF framework can obtain details while maintaining better results for dehazing, which effectively improves the image quality captured by the CMOS image sensor. Experimental results verified that the method proposed has the combined advantages of detail recovery and color preservation.

The fusion of large scale classified side-scan sonar image mosaics.

PubMed

Reed, Scott; Tena, Ruiz Ioseba; Capus, Chris; Petillot, Yvan

2006-07-01

This paper presents a unified framework for the creation of classified maps of the seafloor from sonar imagery. Significant challenges in photometric correction, classification, navigation and registration, and image fusion are addressed. The techniques described are directly applicable to a range of remote sensing problems. Recent advances in side-scan data correction are incorporated to compensate for the sonar beam pattern and motion of the acquisition platform. The corrected images are segmented using pixel-based textural features and standard classifiers. In parallel, the navigation of the sonar device is processed using Kalman filtering techniques. A simultaneous localization and mapping framework is adopted to improve the navigation accuracy and produce georeferenced mosaics of the segmented side-scan data. These are fused within a Markovian framework and two fusion models are presented. The first uses a voting scheme regularized by an isotropic Markov random field and is applicable when the reliability of each information source is unknown. The Markov model is also used to inpaint regions where no final classification decision can be reached using pixel level fusion. The second model formally introduces the reliability of each information source into a probabilistic model. Evaluation of the two models using both synthetic images and real data from a large scale survey shows significant quantitative and qualitative improvement using the fusion approach.

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

PubMed Central

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

2012-01-01

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

Identifying differentially expressed genes in cancer patients using a non-parameter Ising model.

PubMed

Li, Xumeng; Feltus, Frank A; Sun, Xiaoqian; Wang, James Z; Luo, Feng

2011-10-01

Identification of genes and pathways involved in diseases and physiological conditions is a major task in systems biology. In this study, we developed a novel non-parameter Ising model to integrate protein-protein interaction network and microarray data for identifying differentially expressed (DE) genes. We also proposed a simulated annealing algorithm to find the optimal configuration of the Ising model. The Ising model was applied to two breast cancer microarray data sets. The results showed that more cancer-related DE sub-networks and genes were identified by the Ising model than those by the Markov random field model. Furthermore, cross-validation experiments showed that DE genes identified by Ising model can improve classification performance compared with DE genes identified by Markov random field model. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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

NASA Astrophysics Data System (ADS)

Lu, Jianbo; Li, Dewei; Xi, Yugeng

2013-07-01

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

Phase unwrapping using region-based markov random field model.

PubMed

Dong, Ying; Ji, Jim

2010-01-01

Phase unwrapping is a classical problem in Magnetic Resonance Imaging (MRI), Interferometric Synthetic Aperture Radar and Sonar (InSAR/InSAS), fringe pattern analysis, and spectroscopy. Although many methods have been proposed to address this problem, robust and effective phase unwrapping remains a challenge. This paper presents a novel phase unwrapping method using a region-based Markov Random Field (MRF) model. Specifically, the phase image is segmented into regions within which the phase is not wrapped. Then, the phase image is unwrapped between different regions using an improved Highest Confidence First (HCF) algorithm to optimize the MRF model. The proposed method has desirable theoretical properties as well as an efficient implementation. Simulations and experimental results on MRI images show that the proposed method provides similar or improved phase unwrapping than Phase Unwrapping MAx-flow/min-cut (PUMA) method and ZpM method.

Markov switching of the electricity supply curve and power prices dynamics

NASA Astrophysics Data System (ADS)

Mari, Carlo; Cananà, Lucianna

2012-02-01

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

Modeling sediment transport as a spatio-temporal Markov process.

NASA Astrophysics Data System (ADS)

Heyman, Joris; Ancey, Christophe

2014-05-01

Despite a century of research about sediment transport by bedload occuring in rivers, its constitutive laws remain largely unknown. The proof being that our ability to predict mid-to-long term transported volumes within reasonable confidence interval is almost null. The intrinsic fluctuating nature of bedload transport may be one of the most important reasons why classical approaches fail. Microscopic probabilistic framework has the advantage of taking into account these fluctuations at the particle scale, to understand their effect on the macroscopic variables such as sediment flux. In this framework, bedload transport is seen as the random motion of particles (sand, gravel, pebbles...) over a two-dimensional surface (the river bed). The number of particles in motion, as well as their velocities, are random variables. In this talk, we show how a simple birth-death Markov model governing particle motion on a regular lattice accurately reproduces the spatio-temporal correlations observed at the macroscopic level. Entrainment, deposition and transport of particles by the turbulent fluid (air or water) are supposed to be independent and memoryless processes that modify the number of particles in motion. By means of the Poisson representation, we obtained a Fokker-Planck equation that is exactly equivalent to the master equation and thus valid for all cell sizes. The analysis shows that the number of moving particles evolves locally far from thermodynamic equilibrium. Several analytical results are presented and compared to experimental data. The index of dispersion (or variance over mean ratio) is proved to grow from unity at small scales to larger values at larger scales confirming the non Poisonnian behavior of bedload transport. Also, we study the one and two dimensional K-function, which gives the average number of moving particles located in a ball centered at a particle centroid function of the ball's radius.

Pervasive randomness in physics: an introduction to its modelling and spectral characterisation

NASA Astrophysics Data System (ADS)

Howard, Roy

2017-10-01

An introduction to the modelling and spectral characterisation of random phenomena is detailed at a level consistent with a first exposure to the subject at an undergraduate level. A signal framework for defining a random process is provided and this underpins an introduction to common random processes including the Poisson point process, the random walk, the random telegraph signal, shot noise, information signalling random processes, jittered pulse trains, birth-death random processes and Markov chains. An introduction to the spectral characterisation of signals and random processes, via either an energy spectral density or a power spectral density, is detailed. The important case of defining a white noise random process concludes the paper.

Evaluation of the path integral for flow through random porous media

NASA Astrophysics Data System (ADS)

Westbroek, Marise J. E.; Coche, Gil-Arnaud; King, Peter R.; Vvedensky, Dimitri D.

2018-04-01

We present a path integral formulation of Darcy's equation in one dimension with random permeability described by a correlated multivariate lognormal distribution. This path integral is evaluated with the Markov chain Monte Carlo method to obtain pressure distributions, which are shown to agree with the solutions of the corresponding stochastic differential equation for Dirichlet and Neumann boundary conditions. The extension of our approach to flow through random media in two and three dimensions is discussed.

Multilayer Markov Random Field models for change detection in optical remote sensing images

NASA Astrophysics Data System (ADS)

Benedek, Csaba; Shadaydeh, Maha; Kato, Zoltan; Szirányi, Tamás; Zerubia, Josiane

2015-09-01

In this paper, we give a comparative study on three Multilayer Markov Random Field (MRF) based solutions proposed for change detection in optical remote sensing images, called Multicue MRF, Conditional Mixed Markov model, and Fusion MRF. Our purposes are twofold. On one hand, we highlight the significance of the focused model family and we set them against various state-of-the-art approaches through a thematic analysis and quantitative tests. We discuss the advantages and drawbacks of class comparison vs. direct approaches, usage of training data, various targeted application fields and different ways of Ground Truth generation, meantime informing the Reader in which roles the Multilayer MRFs can be efficiently applied. On the other hand we also emphasize the differences between the three focused models at various levels, considering the model structures, feature extraction, layer interpretation, change concept definition, parameter tuning and performance. We provide qualitative and quantitative comparison results using principally a publicly available change detection database which contains aerial image pairs and Ground Truth change masks. We conclude that the discussed models are competitive against alternative state-of-the-art solutions, if one uses them as pre-processing filters in multitemporal optical image analysis. In addition, they cover together a large range of applications, considering the different usage options of the three approaches.

Modelling past land use using archaeological and pollen data

NASA Astrophysics Data System (ADS)

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

2016-04-01

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

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

NASA Astrophysics Data System (ADS)

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

2014-11-01

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

Adaptive Markov Random Fields for Example-Based Super-resolution of Faces

NASA Astrophysics Data System (ADS)

Stephenson, Todd A.; Chen, Tsuhan

2006-12-01

Image enhancement of low-resolution images can be done through methods such as interpolation, super-resolution using multiple video frames, and example-based super-resolution. Example-based super-resolution, in particular, is suited to images that have a strong prior (for those frameworks that work on only a single image, it is more like image restoration than traditional, multiframe super-resolution). For example, hallucination and Markov random field (MRF) methods use examples drawn from the same domain as the image being enhanced to determine what the missing high-frequency information is likely to be. We propose to use even stronger prior information by extending MRF-based super-resolution to use adaptive observation and transition functions, that is, to make these functions region-dependent. We show with face images how we can adapt the modeling for each image patch so as to improve the resolution.

Active classifier selection for RGB-D object categorization using a Markov random field ensemble method

NASA Astrophysics Data System (ADS)

Durner, Maximilian; Márton, Zoltán.; Hillenbrand, Ulrich; Ali, Haider; Kleinsteuber, Martin

2017-03-01

In this work, a new ensemble method for the task of category recognition in different environments is presented. The focus is on service robotic perception in an open environment, where the robot's task is to recognize previously unseen objects of predefined categories, based on training on a public dataset. We propose an ensemble learning approach to be able to flexibly combine complementary sources of information (different state-of-the-art descriptors computed on color and depth images), based on a Markov Random Field (MRF). By exploiting its specific characteristics, the MRF ensemble method can also be executed as a Dynamic Classifier Selection (DCS) system. In the experiments, the committee- and topology-dependent performance boost of our ensemble is shown. Despite reduced computational costs and using less information, our strategy performs on the same level as common ensemble approaches. Finally, the impact of large differences between datasets is analyzed.

Auxiliary Parameter MCMC for Exponential Random Graph Models

NASA Astrophysics Data System (ADS)

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

2016-11-01

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

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.

Markov Chain Analysis of Musical Dice Games

NASA Astrophysics Data System (ADS)

Volchenkov, D.; Dawin, J. R.

2012-07-01

A system for using dice to compose music randomly is known as the musical dice game. The discrete time MIDI models of 804 pieces of classical music written by 29 composers have been encoded into the transition matrices and studied by Markov chains. Contrary to human languages, entropy dominates over redundancy, in the musical dice games based on the compositions of classical music. The maximum complexity is achieved on the blocks consisting of just a few notes (8 notes, for the musical dice games generated over Bach's compositions). First passage times to notes can be used to resolve tonality and feature a composer.

Musical Markov Chains

NASA Astrophysics Data System (ADS)

Volchenkov, Dima; Dawin, Jean René

A system for using dice to compose music randomly is known as the musical dice game. The discrete time MIDI models of 804 pieces of classical music written by 29 composers have been encoded into the transition matrices and studied by Markov chains. Contrary to human languages, entropy dominates over redundancy, in the musical dice games based on the compositions of classical music. The maximum complexity is achieved on the blocks consisting of just a few notes (8 notes, for the musical dice games generated over Bach's compositions). First passage times to notes can be used to resolve tonality and feature a composer.

Feynman-Kac formula for stochastic hybrid systems.

PubMed

Bressloff, Paul C

2017-01-01

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

Multivariate longitudinal data analysis with mixed effects hidden Markov models.

PubMed

Raffa, Jesse D; Dubin, Joel A

2015-09-01

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

Stochastic Dynamics through Hierarchically Embedded Markov Chains

NASA Astrophysics Data System (ADS)

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

2017-02-01

Studying dynamical phenomena in finite populations often involves Markov processes of significant mathematical and/or computational complexity, which rapidly becomes prohibitive with increasing population size or an increasing number of individual configuration states. Here, we develop a framework that allows us to define a hierarchy of approximations to the stationary distribution of general systems that can be described as discrete Markov processes with time invariant transition probabilities and (possibly) a large number of states. This results in an efficient method for studying social and biological communities in the presence of stochastic effects—such as mutations in evolutionary dynamics and a random exploration of choices in social systems—including situations where the dynamics encompasses the existence of stable polymorphic configurations, thus overcoming the limitations of existing methods. The present formalism is shown to be general in scope, widely applicable, and of relevance to a variety of interdisciplinary problems.

Constructing 1/omegaalpha noise from reversible Markov chains.

PubMed

Erland, Sveinung; Greenwood, Priscilla E

2007-09-01

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

Stochastic Dynamics through Hierarchically Embedded Markov Chains.

PubMed

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

2017-02-03

Studying dynamical phenomena in finite populations often involves Markov processes of significant mathematical and/or computational complexity, which rapidly becomes prohibitive with increasing population size or an increasing number of individual configuration states. Here, we develop a framework that allows us to define a hierarchy of approximations to the stationary distribution of general systems that can be described as discrete Markov processes with time invariant transition probabilities and (possibly) a large number of states. This results in an efficient method for studying social and biological communities in the presence of stochastic effects-such as mutations in evolutionary dynamics and a random exploration of choices in social systems-including situations where the dynamics encompasses the existence of stable polymorphic configurations, thus overcoming the limitations of existing methods. The present formalism is shown to be general in scope, widely applicable, and of relevance to a variety of interdisciplinary problems.

Exact solution of the hidden Markov processes.

PubMed

Saakian, David B

2017-11-01

We write a master equation for the distributions related to hidden Markov processes (HMPs) and solve it using a functional equation. Thus the solution of HMPs is mapped exactly to the solution of the functional equation. For a general case the latter can be solved only numerically. We derive an exact expression for the entropy of HMPs. Our expression for the entropy is an alternative to the ones given before by the solution of integral equations. The exact solution is possible because actually the model can be considered as a generalized random walk on a one-dimensional strip. While we give the solution for the two second-order matrices, our solution can be easily generalized for the L values of the Markov process and M values of observables: We should be able to solve a system of L functional equations in the space of dimension M-1.

Exact solution of the hidden Markov processes

NASA Astrophysics Data System (ADS)

Saakian, David B.

2017-11-01

We write a master equation for the distributions related to hidden Markov processes (HMPs) and solve it using a functional equation. Thus the solution of HMPs is mapped exactly to the solution of the functional equation. For a general case the latter can be solved only numerically. We derive an exact expression for the entropy of HMPs. Our expression for the entropy is an alternative to the ones given before by the solution of integral equations. The exact solution is possible because actually the model can be considered as a generalized random walk on a one-dimensional strip. While we give the solution for the two second-order matrices, our solution can be easily generalized for the L values of the Markov process and M values of observables: We should be able to solve a system of L functional equations in the space of dimension M -1 .

Hidden Markov model-derived structural alphabet for proteins: the learning of protein local shapes captures sequence specificity.

PubMed

Camproux, A C; Tufféry, P

2005-08-05

Understanding and predicting protein structures depend on the complexity and the accuracy of the models used to represent them. We have recently set up a Hidden Markov Model to optimally compress protein three-dimensional conformations into a one-dimensional series of letters of a structural alphabet. Such a model learns simultaneously the shape of representative structural letters describing the local conformation and the logic of their connections, i.e. the transition matrix between the letters. Here, we move one step further and report some evidence that such a model of protein local architecture also captures some accurate amino acid features. All the letters have specific and distinct amino acid distributions. Moreover, we show that words of amino acids can have significant propensities for some letters. Perspectives point towards the prediction of the series of letters describing the structure of a protein from its amino acid sequence.

A class of generalized Ginzburg-Landau equations with random switching

NASA Astrophysics Data System (ADS)

Wu, Zheng; Yin, George; Lei, Dongxia

2018-09-01

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

S-SPatt: simple statistics for patterns on Markov chains.

PubMed

Nuel, Grégory

2005-07-01

S-SPatt allows the counting of patterns occurrences in text files and, assuming these texts are generated from a random Markovian source, the computation of the P-value of a given observation using a simple binomial approximation.

Surgical motion characterization in simulated needle insertion procedures

NASA Astrophysics Data System (ADS)

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

2012-02-01

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

Detecting structure of haplotypes and local ancestry

USDA-ARS?s Scientific Manuscript database

We present a two-layer hidden Markov model to detect the structure of haplotypes for unrelated individuals. This allows us to model two scales of linkage disequilibrium (one within a group of haplotypes and one between groups), thereby taking advantage of rich haplotype information to infer local an...

Detecting targets hidden in random forests

NASA Astrophysics Data System (ADS)

Kouritzin, Michael A.; Luo, Dandan; Newton, Fraser; Wu, Biao

2009-05-01

Military tanks, cargo or troop carriers, missile carriers or rocket launchers often hide themselves from detection in the forests. This plagues the detection problem of locating these hidden targets. An electro-optic camera mounted on a surveillance aircraft or unmanned aerial vehicle is used to capture the images of the forests with possible hidden targets, e.g., rocket launchers. We consider random forests of longitudinal and latitudinal correlations. Specifically, foliage coverage is encoded with a binary representation (i.e., foliage or no foliage), and is correlated in adjacent regions. We address the detection problem of camouflaged targets hidden in random forests by building memory into the observations. In particular, we propose an efficient algorithm to generate random forests, ground, and camouflage of hidden targets with two dimensional correlations. The observations are a sequence of snapshots consisting of foliage-obscured ground or target. Theoretically, detection is possible because there are subtle differences in the correlations of the ground and camouflage of the rocket launcher. However, these differences are well beyond human perception. To detect the presence of hidden targets automatically, we develop a Markov representation for these sequences and modify the classical filtering equations to allow the Markov chain observation. Particle filters are used to estimate the position of the targets in combination with a novel random weighting technique. Furthermore, we give positive proof-of-concept simulations.

Multi-Robot FastSLAM for Large Domains

DTIC Science & Technology

2007-03-01

Derr, D. Fox, A.B. Cremers , Integrating global position estimation and position tracking for mobile robots: The dynamic markov localization approach...Intelligence (AAAI), 2000. 53. Andrew J. Davison and David W. Murray. Simultaneous Localization and Map- Building Using Active Vision. IEEE...Wyeth, Michael Milford and David Prasser. A Modified Particle Filter for Simultaneous Robot Localization and Landmark Tracking in an Indoor

Slow diffusion by Markov random flights

NASA Astrophysics Data System (ADS)

Kolesnik, Alexander D.

2018-06-01

We present a conception of the slow diffusion processes in the Euclidean spaces Rm , m ≥ 1, based on the theory of random flights with small constant speed that are driven by a homogeneous Poisson process of small rate. The slow diffusion condition that, on long time intervals, leads to the stationary distributions, is given. The stationary distributions of slow diffusion processes in some Euclidean spaces of low dimensions, are presented.

The Spectrum of the Billiard Laplacian of a Family of Random Billiards

NASA Astrophysics Data System (ADS)

Feres, Renato; Zhang, Hong-Kun

2010-12-01

Random billiards are billiard dynamical systems for which the reflection law giving the post-collision direction of a billiard particle as a function of the pre-collision direction is specified by a Markov (scattering) operator P. Billiards with microstructure are random billiards whose Markov operator is derived from a "microscopic surface structure" on the boundary of the billiard table. The microstructure in turn is defined in terms of what we call a billiard cellQ, the shape of which completely determines the operator P. This operator, defined on an appropriate Hilbert space, is bounded self-adjoint and, for the examples considered here, a Hilbert-Schmidt operator. A central problem in the statistical theory of such random billiards is to relate the geometric characteristics of Q and the spectrum of P. We show, for a particular family of billiard cell shapes parametrized by a scale invariant curvature K (Fig. 2), that the billiard Laplacian P- I is closely related to the ordinary spherical Laplacian, and indicate, by partly analytical and partly numerical means, how this provides asymptotic information about the spectrum of P for small values of K. It is shown, in particular, that the second moment of scattering about the incidence angle closely approximates the spectral gap of P.

A descriptive model of resting-state networks using Markov chains.

PubMed

Xie, H; Pal, R; Mitra, S

2016-08-01

Resting-state functional connectivity (RSFC) studies considering pairwise linear correlations have attracted great interests while the underlying functional network structure still remains poorly understood. To further our understanding of RSFC, this paper presents an analysis of the resting-state networks (RSNs) based on the steady-state distributions and provides a novel angle to investigate the RSFC of multiple functional nodes. This paper evaluates the consistency of two networks based on the Hellinger distance between the steady-state distributions of the inferred Markov chain models. The results show that generated steady-state distributions of default mode network have higher consistency across subjects than random nodes from various RSNs.

Vulnerability of networks of interacting Markov chains.

PubMed

Kocarev, L; Zlatanov, N; Trajanov, D

2010-05-13

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

A novel image encryption algorithm based on chaos maps with Markov properties

NASA Astrophysics Data System (ADS)

Liu, Quan; Li, Pei-yue; Zhang, Ming-chao; Sui, Yong-xin; Yang, Huai-jiang

2015-02-01

In order to construct high complexity, secure and low cost image encryption algorithm, a class of chaos with Markov properties was researched and such algorithm was also proposed. The kind of chaos has higher complexity than the Logistic map and Tent map, which keeps the uniformity and low autocorrelation. An improved couple map lattice based on the chaos with Markov properties is also employed to cover the phase space of the chaos and enlarge the key space, which has better performance than the original one. A novel image encryption algorithm is constructed on the new couple map lattice, which is used as a key stream generator. A true random number is used to disturb the key which can dynamically change the permutation matrix and the key stream. From the experiments, it is known that the key stream can pass SP800-22 test. The novel image encryption can resist CPA and CCA attack and differential attack. The algorithm is sensitive to the initial key and can change the distribution the pixel values of the image. The correlation of the adjacent pixels can also be eliminated. When compared with the algorithm based on Logistic map, it has higher complexity and better uniformity, which is nearer to the true random number. It is also efficient to realize which showed its value in common use.

Large Deviations for Stationary Probabilities of a Family of Continuous Time Markov Chains via Aubry-Mather Theory

NASA Astrophysics Data System (ADS)

Lopes, Artur O.; Neumann, Adriana

2015-05-01

In the present paper, we consider a family of continuous time symmetric random walks indexed by , . For each the matching random walk take values in the finite set of states ; notice that is a subset of , where is the unitary circle. The infinitesimal generator of such chain is denoted by . The stationary probability for such process converges to the uniform distribution on the circle, when . Here we want to study other natural measures, obtained via a limit on , that are concentrated on some points of . We will disturb this process by a potential and study for each the perturbed stationary measures of this new process when . We disturb the system considering a fixed potential and we will denote by the restriction of to . Then, we define a non-stochastic semigroup generated by the matrix , where is the infinifesimal generator of . From the continuous time Perron's Theorem one can normalized such semigroup, and, then we get another stochastic semigroup which generates a continuous time Markov Chain taking values on . This new chain is called the continuous time Gibbs state associated to the potential , see (Lopes et al. in J Stat Phys 152:894-933, 2013). The stationary probability vector for such Markov Chain is denoted by . We assume that the maximum of is attained in a unique point of , and from this will follow that . Thus, here, our main goal is to analyze the large deviation principle for the family , when . The deviation function , which is defined on , will be obtained from a procedure based on fixed points of the Lax-Oleinik operator and Aubry-Mather theory. In order to obtain the associated Lax-Oleinik operator we use the Varadhan's Lemma for the process . For a careful analysis of the problem we present full details of the proof of the Large Deviation Principle, in the Skorohod space, for such family of Markov Chains, when . Finally, we compute the entropy of the invariant probabilities on the Skorohod space associated to the Markov Chains we analyze.

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

PubMed

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

2012-01-01

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

Spatiotemporal progression of metastatic breast cancer: a Markov chain model highlighting the role of early metastatic sites

PubMed Central

Newton, Paul K; Mason, Jeremy; Venkatappa, Neethi; Jochelson, Maxine S; Hurt, Brian; Nieva, Jorge; Comen, Elizabeth; Norton, Larry; Kuhn, Peter

2015-01-01

Background: Cancer cell migration patterns are critical for understanding metastases and clinical evolution. Breast cancer spreads from one organ system to another via hematogenous and lymphatic routes. Although patterns of spread may superficially seem random and unpredictable, we explored the possibility that this is not the case. Aims: Develop a Markov based model of breast cancer progression that has predictive capability. Methods: On the basis of a longitudinal data set of 446 breast cancer patients, we created a Markov chain model of metastasis that describes the probabilities of metastasis occurring at a given anatomic site together with the probability of spread to additional sites. Progression is modeled as a random walk on a directed graph, where nodes represent anatomical sites where tumors can develop. Results: We quantify how survival depends on the location of the first metastatic site for different patient subcategories. In addition, we classify metastatic sites as “sponges” or “spreaders” with implications regarding anatomical pathway prediction and long-term survival. As metastatic tumors to the bone (main spreader) are most prominent, we focus in more detail on differences between groups of patients who form subsequent metastases to the lung as compared with the liver. Conclusions: We have found that spatiotemporal patterns of metastatic spread in breast cancer are neither random nor unpredictable. Furthermore, the novel concept of classifying organ sites as sponges or spreaders may motivate experiments seeking a biological basis for these phenomena and allow us to quantify the potential consequences of therapeutic targeting of sites in the oligometastatic setting and shed light on organotropic aspects of the disease. PMID:28721371

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

PubMed

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

2016-09-21

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

Probabilistic generation of random networks taking into account information on motifs occurrence.

PubMed

Bois, Frederic Y; Gayraud, Ghislaine

2015-01-01

Because of the huge number of graphs possible even with a small number of nodes, inference on network structure is known to be a challenging problem. Generating large random directed graphs with prescribed probabilities of occurrences of some meaningful patterns (motifs) is also difficult. We show how to generate such random graphs according to a formal probabilistic representation, using fast Markov chain Monte Carlo methods to sample them. As an illustration, we generate realistic graphs with several hundred nodes mimicking a gene transcription interaction network in Escherichia coli.

Probabilistic Generation of Random Networks Taking into Account Information on Motifs Occurrence

PubMed Central

Bois, Frederic Y.

2015-01-01

Abstract Because of the huge number of graphs possible even with a small number of nodes, inference on network structure is known to be a challenging problem. Generating large random directed graphs with prescribed probabilities of occurrences of some meaningful patterns (motifs) is also difficult. We show how to generate such random graphs according to a formal probabilistic representation, using fast Markov chain Monte Carlo methods to sample them. As an illustration, we generate realistic graphs with several hundred nodes mimicking a gene transcription interaction network in Escherichia coli. PMID:25493547

RSAT: regulatory sequence analysis tools.

PubMed

Thomas-Chollier, Morgane; Sand, Olivier; Turatsinze, Jean-Valéry; Janky, Rekin's; Defrance, Matthieu; Vervisch, Eric; Brohée, Sylvain; van Helden, Jacques

2008-07-01

The regulatory sequence analysis tools (RSAT, http://rsat.ulb.ac.be/rsat/) is a software suite that integrates a wide collection of modular tools for the detection of cis-regulatory elements in genome sequences. The suite includes programs for sequence retrieval, pattern discovery, phylogenetic footprint detection, pattern matching, genome scanning and feature map drawing. Random controls can be performed with random gene selections or by generating random sequences according to a variety of background models (Bernoulli, Markov). Beyond the original word-based pattern-discovery tools (oligo-analysis and dyad-analysis), we recently added a battery of tools for matrix-based detection of cis-acting elements, with some original features (adaptive background models, Markov-chain estimation of P-values) that do not exist in other matrix-based scanning tools. The web server offers an intuitive interface, where each program can be accessed either separately or connected to the other tools. In addition, the tools are now available as web services, enabling their integration in programmatic workflows. Genomes are regularly updated from various genome repositories (NCBI and EnsEMBL) and 682 organisms are currently supported. Since 1998, the tools have been used by several hundreds of researchers from all over the world. Several predictions made with RSAT were validated experimentally and published.

Random walk on p-adics and hierarchical systems

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

Lukierska-Walasek, K.; Topolski, K.; Institute of Mathematics, Wroclaw University, pl. Grunwaldzki 2/4, 50-384 Wroclaw

2006-02-01

We show that p-adic analysis provides a quite natural basis for the description of relaxation in hierarchical systems. For our purposes, we specify the Markov stochastic process considered by Albeverio and Karwowski. As a result we have obtained a random walk on the p-adic integer numbers, which provides the generalization of Cayley tree proposed by Ogielski and Stein. The temperature-dependent power-law decay and the Kohlrausch law are derived.

SAR Image Change Detection Based on Fuzzy Markov Random Field Model

NASA Astrophysics Data System (ADS)

Zhao, J.; Huang, G.; Zhao, Z.

2018-04-01

Most existing SAR image change detection algorithms only consider single pixel information of different images, and not consider the spatial dependencies of image pixels. So the change detection results are susceptible to image noise, and the detection effect is not ideal. Markov Random Field (MRF) can make full use of the spatial dependence of image pixels and improve detection accuracy. When segmenting the difference image, different categories of regions have a high degree of similarity at the junction of them. It is difficult to clearly distinguish the labels of the pixels near the boundaries of the judgment area. In the traditional MRF method, each pixel is given a hard label during iteration. So MRF is a hard decision in the process, and it will cause loss of information. This paper applies the combination of fuzzy theory and MRF to the change detection of SAR images. The experimental results show that the proposed method has better detection effect than the traditional MRF method.

Tumor angiogenesis assessment using multi-fluorescent scans on murine slices by Markov random field framework

NASA Astrophysics Data System (ADS)

Laifa, Oumeima; Le Guillou-Buffello, Delphine; Racoceanu, Daniel

2017-11-01

The fundamental role of vascular supply in tumor growth makes the evaluation of the angiogenesis crucial in assessing effect of anti-angiogenic therapies. Since many years, such therapies are designed to inhibit the vascular endothelial growth factor (VEGF). To contribute to the assessment of anti-angiogenic agent (Pazopanib) effect on vascular and cellular structures, we acquired data from tumors extracted from a murine tumor model using Multi- Fluorescence Scanning. In this paper, we implemented an unsupervised algorithm combining the Watershed segmentation and Markov Random Field model (MRF). This algorithm allowed us to quantify the proportion of apoptotic endothelial cells and to generate maps according to cell density. Stronger association between apoptosis and endothelial cells was revealed in the tumors receiving anti-angiogenic therapy (n = 4) as compared to those receiving placebo (n = 4). A high percentage of apoptotic cells in the tumor area are endothelial. Lower density cells were detected in tumor slices presenting higher apoptotic endothelial areas.

A multiscale Markov random field model in wavelet domain for image segmentation

NASA Astrophysics Data System (ADS)

Dai, Peng; Cheng, Yu; Wang, Shengchun; Du, Xinyu; Wu, Dan

2017-07-01

The human vision system has abilities for feature detection, learning and selective attention with some properties of hierarchy and bidirectional connection in the form of neural population. In this paper, a multiscale Markov random field model in the wavelet domain is proposed by mimicking some image processing functions of vision system. For an input scene, our model provides its sparse representations using wavelet transforms and extracts its topological organization using MRF. In addition, the hierarchy property of vision system is simulated using a pyramid framework in our model. There are two information flows in our model, i.e., a bottom-up procedure to extract input features and a top-down procedure to provide feedback controls. The two procedures are controlled simply by two pyramidal parameters, and some Gestalt laws are also integrated implicitly. Equipped with such biological inspired properties, our model can be used to accomplish different image segmentation tasks, such as edge detection and region segmentation.

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

NASA Astrophysics Data System (ADS)

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

2015-11-01

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

A Heavy Tailed Expectation Maximization Hidden Markov Random Field Model with Applications to Segmentation of MRI

PubMed Central

Castillo-Barnes, Diego; Peis, Ignacio; Martínez-Murcia, Francisco J.; Segovia, Fermín; Illán, Ignacio A.; Górriz, Juan M.; Ramírez, Javier; Salas-Gonzalez, Diego

2017-01-01

A wide range of segmentation approaches assumes that intensity histograms extracted from magnetic resonance images (MRI) have a distribution for each brain tissue that can be modeled by a Gaussian distribution or a mixture of them. Nevertheless, intensity histograms of White Matter and Gray Matter are not symmetric and they exhibit heavy tails. In this work, we present a hidden Markov random field model with expectation maximization (EM-HMRF) modeling the components using the α-stable distribution. The proposed model is a generalization of the widely used EM-HMRF algorithm with Gaussian distributions. We test the α-stable EM-HMRF model in synthetic data and brain MRI data. The proposed methodology presents two main advantages: Firstly, it is more robust to outliers. Secondly, we obtain similar results than using Gaussian when the Gaussian assumption holds. This approach is able to model the spatial dependence between neighboring voxels in tomographic brain MRI. PMID:29209194

Constructing 1/ωα noise from reversible Markov chains

NASA Astrophysics Data System (ADS)

Erland, Sveinung; Greenwood, Priscilla E.

2007-09-01

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

An open Markov chain scheme model for a credit consumption portfolio fed by ARIMA and SARMA processes

NASA Astrophysics Data System (ADS)

Esquível, Manuel L.; Fernandes, José Moniz; Guerreiro, Gracinda R.

2016-06-01

We introduce a schematic formalism for the time evolution of a random population entering some set of classes and such that each member of the population evolves among these classes according to a scheme based on a Markov chain model. We consider that the flow of incoming members is modeled by a time series and we detail the time series structure of the elements in each of the classes. We present a practical application to data from a credit portfolio of a Cape Verdian bank; after modeling the entering population in two different ways - namely as an ARIMA process and as a deterministic sigmoid type trend plus a SARMA process for the residues - we simulate the behavior of the population and compare the results. We get that the second method is more accurate in describing the behavior of the populations when compared to the observed values in a direct simulation of the Markov chain.

Optimal Linear Responses for Markov Chains and Stochastically Perturbed Dynamical Systems

NASA Astrophysics Data System (ADS)

Antown, Fadi; Dragičević, Davor; Froyland, Gary

2018-03-01

The linear response of a dynamical system refers to changes to properties of the system when small external perturbations are applied. We consider the little-studied question of selecting an optimal perturbation so as to (i) maximise the linear response of the equilibrium distribution of the system, (ii) maximise the linear response of the expectation of a specified observable, and (iii) maximise the linear response of the rate of convergence of the system to the equilibrium distribution. We also consider the inhomogeneous, sequential, or time-dependent situation where the governing dynamics is not stationary and one wishes to select a sequence of small perturbations so as to maximise the overall linear response at some terminal time. We develop the theory for finite-state Markov chains, provide explicit solutions for some illustrative examples, and numerically apply our theory to stochastically perturbed dynamical systems, where the Markov chain is replaced by a matrix representation of an approximate annealed transfer operator for the random dynamical system.

The Fisher-Markov selector: fast selecting maximally separable feature subset for multiclass classification with applications to high-dimensional data.

PubMed

Cheng, Qiang; Zhou, Hongbo; Cheng, Jie

2011-06-01

Selecting features for multiclass classification is a critically important task for pattern recognition and machine learning applications. Especially challenging is selecting an optimal subset of features from high-dimensional data, which typically have many more variables than observations and contain significant noise, missing components, or outliers. Existing methods either cannot handle high-dimensional data efficiently or scalably, or can only obtain local optimum instead of global optimum. Toward the selection of the globally optimal subset of features efficiently, we introduce a new selector--which we call the Fisher-Markov selector--to identify those features that are the most useful in describing essential differences among the possible groups. In particular, in this paper we present a way to represent essential discriminating characteristics together with the sparsity as an optimization objective. With properly identified measures for the sparseness and discriminativeness in possibly high-dimensional settings, we take a systematic approach for optimizing the measures to choose the best feature subset. We use Markov random field optimization techniques to solve the formulated objective functions for simultaneous feature selection. Our results are noncombinatorial, and they can achieve the exact global optimum of the objective function for some special kernels. The method is fast; in particular, it can be linear in the number of features and quadratic in the number of observations. We apply our procedure to a variety of real-world data, including mid--dimensional optical handwritten digit data set and high-dimensional microarray gene expression data sets. The effectiveness of our method is confirmed by experimental results. In pattern recognition and from a model selection viewpoint, our procedure says that it is possible to select the most discriminating subset of variables by solving a very simple unconstrained objective function which in fact can be obtained with an explicit expression.

Modular Hamiltonians on the null plane and the Markov property of the vacuum state

NASA Astrophysics Data System (ADS)

Casini, Horacio; Testé, Eduardo; Torroba, Gonzalo

2017-09-01

We compute the modular Hamiltonians of regions having the future horizon lying on a null plane. For a CFT this is equivalent to regions with a boundary of arbitrary shape lying on the null cone. These Hamiltonians have a local expression on the horizon formed by integrals of the stress tensor. We prove this result in two different ways, and show that the modular Hamiltonians of these regions form an infinite dimensional Lie algebra. The corresponding group of unitary transformations moves the fields on the null surface locally along the null generators with arbitrary null line dependent velocities, but act non-locally outside the null plane. We regain this result in greater generality using more abstract tools on the algebraic quantum field theory. Finally, we show that modular Hamiltonians on the null surface satisfy a Markov property that leads to the saturation of the strong sub-additive inequality for the entropies and to the strong super-additivity of the relative entropy.

The collection of images of an insulator taken outdoors in varying lighting conditions with additional laser spots.

PubMed

Tomaszewski, Michał; Ruszczak, Bogdan; Michalski, Paweł

2018-06-01

Electrical insulators are elements of power lines that require periodical diagnostics. Due to their location on the components of high-voltage power lines, their imaging can be cumbersome and time-consuming, especially under varying lighting conditions. Insulator diagnostics with the use of visual methods may require localizing insulators in the scene. Studies focused on insulator localization in the scene apply a number of methods, including: texture analysis, MRF (Markov Random Field), Gabor filters or GLCM (Gray Level Co-Occurrence Matrix) [1], [2]. Some methods, e.g. those which localize insulators based on colour analysis [3], rely on object and scene illumination, which is why the images from the dataset are taken under varying lighting conditions. The dataset may also be used to compare the effectiveness of different methods of localizing insulators in images. This article presents high-resolution images depicting a long rod electrical insulator under varying lighting conditions and against different backgrounds: crops, forest and grass. The dataset contains images with visible laser spots (generated by a device emitting light at the wavelength of 532 nm) and images without such spots, as well as complementary data concerning the illumination level and insulator position in the scene, the number of registered laser spots, and their coordinates in the image. The laser spots may be used to support object-localizing algorithms, while the images without spots may serve as a source of information for those algorithms which do not need spots to localize an insulator.

Image texture segmentation using a neural network

NASA Astrophysics Data System (ADS)

Sayeh, Mohammed R.; Athinarayanan, Ragu; Dhali, Pushpuak

1992-09-01

In this paper we use a neural network called the Lyapunov associative memory (LYAM) system to segment image texture into different categories or clusters. The LYAM system is constructed by a set of ordinary differential equations which are simulated on a digital computer. The clustering can be achieved by using a single tuning parameter in the simplest model. Pattern classes are represented by the stable equilibrium states of the system. Design of the system is based on synthesizing two local energy functions, namely, the learning and recall energy functions. Before the implementation of the segmentation process, a Gauss-Markov random field (GMRF) model is applied to the raw image. This application suitably reduces the image data and prepares the texture information for the neural network process. We give a simple image example illustrating the capability of the technique. The GMRF-generated features are also used for a clustering, based on the Euclidean distance.

Infrared Ship Target Segmentation Based on Spatial Information Improved FCM.

PubMed

Bai, Xiangzhi; Chen, Zhiguo; Zhang, Yu; Liu, Zhaoying; Lu, Yi

2016-12-01

Segmentation of infrared (IR) ship images is always a challenging task, because of the intensity inhomogeneity and noise. The fuzzy C-means (FCM) clustering is a classical method widely used in image segmentation. However, it has some shortcomings, like not considering the spatial information or being sensitive to noise. In this paper, an improved FCM method based on the spatial information is proposed for IR ship target segmentation. The improvements include two parts: 1) adding the nonlocal spatial information based on the ship target and 2) using the spatial shape information of the contour of the ship target to refine the local spatial constraint by Markov random field. In addition, the results of K -means are used to initialize the improved FCM method. Experimental results show that the improved method is effective and performs better than the existing methods, including the existing FCM methods, for segmentation of the IR ship images.

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

PubMed

Chattopadhyay, Ishanu; Ray, Asok

2009-12-01

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

Teaching Probability in Intermediate Grades

ERIC Educational Resources Information Center

Engel, Arthur

1971-01-01

A discussion of the importance and procedures for including probability in the elementary through secondary mathematics curriculum is presented. Many examples and problems are presented which the author feels students can understand and will be motivated to do. Random digits, Monte Carlo methods, combinatorial theory, and Markov chains are…

Dimensional Reduction for the General Markov Model on Phylogenetic Trees.

PubMed

Sumner, Jeremy G

2017-03-01

We present a method of dimensional reduction for the general Markov model of sequence evolution on a phylogenetic tree. We show that taking certain linear combinations of the associated random variables (site pattern counts) reduces the dimensionality of the model from exponential in the number of extant taxa, to quadratic in the number of taxa, while retaining the ability to statistically identify phylogenetic divergence events. A key feature is the identification of an invariant subspace which depends only bilinearly on the model parameters, in contrast to the usual multi-linear dependence in the full space. We discuss potential applications including the computation of split (edge) weights on phylogenetic trees from observed sequence data.

Scaling Limit of Symmetric Random Walk in High-Contrast Periodic Environment

NASA Astrophysics Data System (ADS)

Piatnitski, A.; Zhizhina, E.

2017-11-01

The paper deals with the asymptotic properties of a symmetric random walk in a high contrast periodic medium in Z^d, d≥1. From the existing homogenization results it follows that under diffusive scaling the limit behaviour of this random walk need not be Markovian. The goal of this work is to show that if in addition to the coordinate of the random walk in Z^d we introduce an extra variable that characterizes the position of the random walk inside the period then the limit dynamics of this two-component process is Markov. We describe the limit process and observe that the components of the limit process are coupled. We also prove the convergence in the path space for the said random walk.

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

PubMed

Bacaër, Nicolas

2016-10-01

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

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.

Remote Sensing Image Change Detection Based on NSCT-HMT Model and Its Application.

PubMed

Chen, Pengyun; Zhang, Yichen; Jia, Zhenhong; Yang, Jie; Kasabov, Nikola

2017-06-06

Traditional image change detection based on a non-subsampled contourlet transform always ignores the neighborhood information's relationship to the non-subsampled contourlet coefficients, and the detection results are susceptible to noise interference. To address these disadvantages, we propose a denoising method based on the non-subsampled contourlet transform domain that uses the Hidden Markov Tree model (NSCT-HMT) for change detection of remote sensing images. First, the ENVI software is used to calibrate the original remote sensing images. After that, the mean-ratio operation is adopted to obtain the difference image that will be denoised by the NSCT-HMT model. Then, using the Fuzzy Local Information C-means (FLICM) algorithm, the difference image is divided into the change area and unchanged area. The proposed algorithm is applied to a real remote sensing data set. The application results show that the proposed algorithm can effectively suppress clutter noise, and retain more detailed information from the original images. The proposed algorithm has higher detection accuracy than the Markov Random Field-Fuzzy C-means (MRF-FCM), the non-subsampled contourlet transform-Fuzzy C-means clustering (NSCT-FCM), the pointwise approach and graph theory (PA-GT), and the Principal Component Analysis-Nonlocal Means (PCA-NLM) denosing algorithm. Finally, the five algorithms are used to detect the southern boundary of the Gurbantunggut Desert in Xinjiang Uygur Autonomous Region of China, and the results show that the proposed algorithm has the best effect on real remote sensing image change detection.

Remote Sensing Image Change Detection Based on NSCT-HMT Model and Its Application

PubMed Central

Chen, Pengyun; Zhang, Yichen; Jia, Zhenhong; Yang, Jie; Kasabov, Nikola

2017-01-01

Traditional image change detection based on a non-subsampled contourlet transform always ignores the neighborhood information’s relationship to the non-subsampled contourlet coefficients, and the detection results are susceptible to noise interference. To address these disadvantages, we propose a denoising method based on the non-subsampled contourlet transform domain that uses the Hidden Markov Tree model (NSCT-HMT) for change detection of remote sensing images. First, the ENVI software is used to calibrate the original remote sensing images. After that, the mean-ratio operation is adopted to obtain the difference image that will be denoised by the NSCT-HMT model. Then, using the Fuzzy Local Information C-means (FLICM) algorithm, the difference image is divided into the change area and unchanged area. The proposed algorithm is applied to a real remote sensing data set. The application results show that the proposed algorithm can effectively suppress clutter noise, and retain more detailed information from the original images. The proposed algorithm has higher detection accuracy than the Markov Random Field-Fuzzy C-means (MRF-FCM), the non-subsampled contourlet transform-Fuzzy C-means clustering (NSCT-FCM), the pointwise approach and graph theory (PA-GT), and the Principal Component Analysis-Nonlocal Means (PCA-NLM) denosing algorithm. Finally, the five algorithms are used to detect the southern boundary of the Gurbantunggut Desert in Xinjiang Uygur Autonomous Region of China, and the results show that the proposed algorithm has the best effect on real remote sensing image change detection. PMID:28587299

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

NASA Astrophysics Data System (ADS)

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

2017-08-01

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

Bayesian multiple-source localization in an uncertain ocean environment.

PubMed

Dosso, Stan E; Wilmut, Michael J

2011-06-01

This paper considers simultaneous localization of multiple acoustic sources when properties of the ocean environment (water column and seabed) are poorly known. A Bayesian formulation is developed in which the environmental parameters, noise statistics, and locations and complex strengths (amplitudes and phases) of multiple sources are considered to be unknown random variables constrained by acoustic data and prior information. Two approaches are considered for estimating source parameters. Focalization maximizes the posterior probability density (PPD) over all parameters using adaptive hybrid optimization. Marginalization integrates the PPD using efficient Markov-chain Monte Carlo methods to produce joint marginal probability distributions for source ranges and depths, from which source locations are obtained. This approach also provides quantitative uncertainty analysis for all parameters, which can aid in understanding of the inverse problem and may be of practical interest (e.g., source-strength probability distributions). In both approaches, closed-form maximum-likelihood expressions for source strengths and noise variance at each frequency allow these parameters to be sampled implicitly, substantially reducing the dimensionality and difficulty of the inversion. Examples are presented of both approaches applied to single- and multi-frequency localization of multiple sources in an uncertain shallow-water environment, and a Monte Carlo performance evaluation study is carried out. © 2011 Acoustical Society of America

Iterative normalization method for improved prostate cancer localization with multispectral magnetic resonance imaging

NASA Astrophysics Data System (ADS)

Liu, Xin; Samil Yetik, Imam

2012-04-01

Use of multispectral magnetic resonance imaging has received a great interest for prostate cancer localization in research and clinical studies. Manual extraction of prostate tumors from multispectral magnetic resonance imaging is inefficient and subjective, while automated segmentation is objective and reproducible. For supervised, automated segmentation approaches, learning is essential to obtain the information from training dataset. However, in this procedure, all patients are assumed to have similar properties for the tumor and normal tissues, and the segmentation performance suffers since the variations across patients are ignored. To conquer this difficulty, we propose a new iterative normalization method based on relative intensity values of tumor and normal tissues to normalize multispectral magnetic resonance images and improve segmentation performance. The idea of relative intensity mimics the manual segmentation performed by human readers, who compare the contrast between regions without knowing the actual intensity values. We compare the segmentation performance of the proposed method with that of z-score normalization followed by support vector machine, local active contours, and fuzzy Markov random field. Our experimental results demonstrate that our method outperforms the three other state-of-the-art algorithms, and was found to have specificity of 0.73, sensitivity of 0.69, and accuracy of 0.79, significantly better than alternative methods.

Saliency Detection via Absorbing Markov Chain With Learnt Transition Probability.

PubMed

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

2018-02-01

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

Markov chain decision model for urinary incontinence procedures.

PubMed

Kumar, Sameer; Ghildayal, Nidhi; Ghildayal, Neha

2017-03-13

Purpose Urinary incontinence (UI) is a common chronic health condition, a problem specifically among elderly women that impacts quality of life negatively. However, UI is usually viewed as likely result of old age, and as such is generally not evaluated or even managed appropriately. Many treatments are available to manage incontinence, such as bladder training and numerous surgical procedures such as Burch colposuspension and Sling for UI which have high success rates. The purpose of this paper is to analyze which of these popular surgical procedures for UI is effective. Design/methodology/approach This research employs randomized, prospective studies to obtain robust cost and utility data used in the Markov chain decision model for examining which of these surgical interventions is more effective in treating women with stress UI based on two measures: number of quality adjusted life years (QALY) and cost per QALY. Treeage Pro Healthcare software was employed in Markov decision analysis. Findings Results showed the Sling procedure is a more effective surgical intervention than the Burch. However, if a utility greater than certain utility value, for which both procedures are equally effective, is assigned to persistent incontinence, the Burch procedure is more effective than the Sling procedure. Originality/value This paper demonstrates the efficacy of a Markov chain decision modeling approach to study the comparative effectiveness analysis of available treatments for patients with UI, an important public health issue, widely prevalent among elderly women in developed and developing countries. This research also improves upon other analyses using a Markov chain decision modeling process to analyze various strategies for treating UI.

Hybrid simulated annealing and its application to optimization of hidden Markov models for visual speech recognition.

PubMed

Lee, Jong-Seok; Park, Cheol Hoon

2010-08-01

We propose a novel stochastic optimization algorithm, hybrid simulated annealing (SA), to train hidden Markov models (HMMs) for visual speech recognition. In our algorithm, SA is combined with a local optimization operator that substitutes a better solution for the current one to improve the convergence speed and the quality of solutions. We mathematically prove that the sequence of the objective values converges in probability to the global optimum in the algorithm. The algorithm is applied to train HMMs that are used as visual speech recognizers. While the popular training method of HMMs, the expectation-maximization algorithm, achieves only local optima in the parameter space, the proposed method can perform global optimization of the parameters of HMMs and thereby obtain solutions yielding improved recognition performance. The superiority of the proposed algorithm to the conventional ones is demonstrated via isolated word recognition experiments.

Mathematic Model of Digital Control System with PID Regulator and Regular Step of Quantization with Information Transfer via the Channel of Plural Access

NASA Astrophysics Data System (ADS)

Abramov, G. V.; Emeljanov, A. E.; Ivashin, A. L.

Theoretical bases for modeling a digital control system with information transfer via the channel of plural access and a regular quantization cycle are submitted. The theory of dynamic systems with random changes of the structure including elements of the Markov random processes theory is used for a mathematical description of a network control system. The characteristics of similar control systems are received. Experimental research of the given control systems is carried out.

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

NASA Astrophysics Data System (ADS)

Mitsutake, Ayori; Takano, Hiroshi

2015-09-01

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

Unravelling changing interspecific interactions across environmental gradients using Markov random fields.

PubMed

Clark, Nicholas J; Wells, Konstans; Lindberg, Oscar

2018-05-16

Inferring interactions between co-occurring species is key to identify processes governing community assembly. Incorporating interspecific interactions in predictive models is common in ecology, yet most methods do not adequately account for indirect interactions (where an interaction between two species is masked by their shared interactions with a third) and assume interactions do not vary along environmental gradients. Markov random fields (MRF) overcome these limitations by estimating interspecific interactions, while controlling for indirect interactions, from multispecies occurrence data. We illustrate the utility of MRFs for ecologists interested in interspecific interactions, and demonstrate how covariates can be included (a set of models known as Conditional Random Fields, CRF) to infer how interactions vary along environmental gradients. We apply CRFs to two data sets of presence-absence data. The first illustrates how blood parasite (Haemoproteus, Plasmodium, and nematode microfilaria spp.) co-infection probabilities covary with relative abundance of their avian hosts. The second shows that co-occurrences between mosquito larvae and predatory insects vary along water temperature gradients. Other applications are discussed, including the potential to identify replacement or shifting impacts of highly connected species along climate or land-use gradients. We provide tools for building CRFs and plotting/interpreting results as an R package. © 2018 by the Ecological Society of America.

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

PubMed Central

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

2016-01-01

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

Resolvent-Techniques for Multiple Exercise Problems

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

Christensen, Sören, E-mail: christensen@math.uni-kiel.de; Lempa, Jukka, E-mail: jukka.lempa@hioa.no

2015-02-15

We study optimal multiple stopping of strong Markov processes with random refraction periods. The refraction periods are assumed to be exponentially distributed with a common rate and independent of the underlying dynamics. Our main tool is using the resolvent operator. In the first part, we reduce infinite stopping problems to ordinary ones in a general strong Markov setting. This leads to explicit solutions for wide classes of such problems. Starting from this result, we analyze problems with finitely many exercise rights and explain solution methods for some classes of problems with underlying Lévy and diffusion processes, where the optimal characteristicsmore » of the problems can be identified more explicitly. We illustrate the main results with explicit examples.« less

Quantum Graphical Models and Belief Propagation

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

Leifer, M.S.; Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo Ont., N2L 2Y5; Poulin, D.

Belief Propagation algorithms acting on Graphical Models of classical probability distributions, such as Markov Networks, Factor Graphs and Bayesian Networks, are amongst the most powerful known methods for deriving probabilistic inferences amongst large numbers of random variables. This paper presents a generalization of these concepts and methods to the quantum case, based on the idea that quantum theory can be thought of as a noncommutative, operator-valued, generalization of classical probability theory. Some novel characterizations of quantum conditional independence are derived, and definitions of Quantum n-Bifactor Networks, Markov Networks, Factor Graphs and Bayesian Networks are proposed. The structure of Quantum Markovmore » Networks is investigated and some partial characterization results are obtained, along the lines of the Hammersley-Clifford theorem. A Quantum Belief Propagation algorithm is presented and is shown to converge on 1-Bifactor Networks and Markov Networks when the underlying graph is a tree. The use of Quantum Belief Propagation as a heuristic algorithm in cases where it is not known to converge is discussed. Applications to decoding quantum error correcting codes and to the simulation of many-body quantum systems are described.« less

Extreme event statistics in a drifting Markov chain

NASA Astrophysics Data System (ADS)

Kindermann, Farina; Hohmann, Michael; Lausch, Tobias; Mayer, Daniel; Schmidt, Felix; Widera, Artur

2017-07-01

We analyze extreme event statistics of experimentally realized Markov chains with various drifts. Our Markov chains are individual trajectories of a single atom diffusing in a one-dimensional periodic potential. Based on more than 500 individual atomic traces we verify the applicability of the Sparre Andersen theorem to our system despite the presence of a drift. We present detailed analysis of four different rare-event statistics for our system: the distributions of extreme values, of record values, of extreme value occurrence in the chain, and of the number of records in the chain. We observe that, for our data, the shape of the extreme event distributions is dominated by the underlying exponential distance distribution extracted from the atomic traces. Furthermore, we find that even small drifts influence the statistics of extreme events and record values, which is supported by numerical simulations, and we identify cases in which the drift can be determined without information about the underlying random variable distributions. Our results facilitate the use of extreme event statistics as a signal for small drifts in correlated trajectories.

Using hidden Markov models to align multiple sequences.

PubMed

Mount, David W

2009-07-01

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

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

NASA Astrophysics Data System (ADS)

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

2014-09-01

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

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

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

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

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

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

PubMed Central

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

2014-01-01

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

BMRF-Net: a software tool for identification of protein interaction subnetworks by a bagging Markov random field-based method.

PubMed

Shi, Xu; Barnes, Robert O; Chen, Li; Shajahan-Haq, Ayesha N; Hilakivi-Clarke, Leena; Clarke, Robert; Wang, Yue; Xuan, Jianhua

2015-07-15

Identification of protein interaction subnetworks is an important step to help us understand complex molecular mechanisms in cancer. In this paper, we develop a BMRF-Net package, implemented in Java and C++, to identify protein interaction subnetworks based on a bagging Markov random field (BMRF) framework. By integrating gene expression data and protein-protein interaction data, this software tool can be used to identify biologically meaningful subnetworks. A user friendly graphic user interface is developed as a Cytoscape plugin for the BMRF-Net software to deal with the input/output interface. The detailed structure of the identified networks can be visualized in Cytoscape conveniently. The BMRF-Net package has been applied to breast cancer data to identify significant subnetworks related to breast cancer recurrence. The BMRF-Net package is available at http://sourceforge.net/projects/bmrfcjava/. The package is tested under Ubuntu 12.04 (64-bit), Java 7, glibc 2.15 and Cytoscape 3.1.0. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Detecting brain tumor in computed tomography images using Markov random fields and fuzzy C-means clustering techniques

NASA Astrophysics Data System (ADS)

Abdulbaqi, Hayder Saad; Jafri, Mohd Zubir Mat; Omar, Ahmad Fairuz; Mustafa, Iskandar Shahrim Bin; Abood, Loay Kadom

2015-04-01

Brain tumors, are an abnormal growth of tissues in the brain. They may arise in people of any age. They must be detected early, diagnosed accurately, monitored carefully, and treated effectively in order to optimize patient outcomes regarding both survival and quality of life. Manual segmentation of brain tumors from CT scan images is a challenging and time consuming task. Size and location accurate detection of brain tumor plays a vital role in the successful diagnosis and treatment of tumors. Brain tumor detection is considered a challenging mission in medical image processing. The aim of this paper is to introduce a scheme for tumor detection in CT scan images using two different techniques Hidden Markov Random Fields (HMRF) and Fuzzy C-means (FCM). The proposed method has been developed in this research in order to construct hybrid method between (HMRF) and threshold. These methods have been applied on 4 different patient data sets. The result of comparison among these methods shows that the proposed method gives good results for brain tissue detection, and is more robust and effective compared with (FCM) techniques.

Fluctuation theorems for discrete kinetic models of molecular motors

NASA Astrophysics Data System (ADS)

Faggionato, Alessandra; Silvestri, Vittoria

2017-04-01

Motivated by discrete kinetic models for non-cooperative molecular motors on periodic tracks, we consider random walks (also not Markov) on quasi one dimensional (1d) lattices, obtained by gluing several copies of a fundamental graph in a linear fashion. We show that, for a suitable class of quasi-1d lattices, the large deviation rate function associated to the position of the walker satisfies a Gallavotti-Cohen symmetry for any choice of the dynamical parameters defining the stochastic walk. This class includes the linear model considered in Lacoste et al (2008 Phys. Rev. E 78 011915). We also derive fluctuation theorems for the time-integrated cycle currents and discuss how the matrix approach of Lacoste et al (2008 Phys. Rev. E 78 011915) can be extended to derive the above Gallavotti-Cohen symmetry for any Markov random walk on {Z} with periodic jump rates. Finally, we review in the present context some large deviation results of Faggionato and Silvestri (2017 Ann. Inst. Henri Poincaré 53 46-78) and give some specific examples with explicit computations.

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

PubMed

Reich, W; Scheuermann, G

2012-12-01

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

A New Framework for Analysis of Coevolutionary Systems-Directed Graph Representation and Random Walks.

PubMed

Chong, Siang Yew; Tiňo, Peter; He, Jun; Yao, Xin

2017-11-20

Studying coevolutionary systems in the context of simplified models (i.e., games with pairwise interactions between coevolving solutions modeled as self plays) remains an open challenge since the rich underlying structures associated with pairwise-comparison-based fitness measures are often not taken fully into account. Although cyclic dynamics have been demonstrated in several contexts (such as intransitivity in coevolutionary problems), there is no complete characterization of cycle structures and their effects on coevolutionary search. We develop a new framework to address this issue. At the core of our approach is the directed graph (digraph) representation of coevolutionary problems that fully captures structures in the relations between candidate solutions. Coevolutionary processes are modeled as a specific type of Markov chains-random walks on digraphs. Using this framework, we show that coevolutionary problems admit a qualitative characterization: a coevolutionary problem is either solvable (there is a subset of solutions that dominates the remaining candidate solutions) or not. This has an implication on coevolutionary search. We further develop our framework that provides the means to construct quantitative tools for analysis of coevolutionary processes and demonstrate their applications through case studies. We show that coevolution of solvable problems corresponds to an absorbing Markov chain for which we can compute the expected hitting time of the absorbing class. Otherwise, coevolution will cycle indefinitely and the quantity of interest will be the limiting invariant distribution of the Markov chain. We also provide an index for characterizing complexity in coevolutionary problems and show how they can be generated in a controlled manner.

Electronic Noise and Fluctuations in Solids

NASA Astrophysics Data System (ADS)

Kogan, Sh.

2008-07-01

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

The Embedding Problem for Markov Models of Nucleotide Substitution

PubMed Central

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

2013-01-01

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

Efficient Inference for Trees and Alignments: Modeling Monolingual and Bilingual Syntax with Hard and Soft Constraints and Latent Variables

ERIC Educational Resources Information Center

Smith, David Arthur

2010-01-01

Much recent work in natural language processing treats linguistic analysis as an inference problem over graphs. This development opens up useful connections between machine learning, graph theory, and linguistics. The first part of this dissertation formulates syntactic dependency parsing as a dynamic Markov random field with the novel…

A Hierarchical and Contextual Model for Learning and Recognizing Highly Variant Visual Categories

DTIC Science & Technology

2010-01-01

neighboring pattern primitives, to create our model. We also present a minimax entropy framework for automatically learning which contextual constraints are...Grammars . . . . . . . . . . . . . . . . . . 19 3.2 Markov Random Fields . . . . . . . . . . . . . . . . . . . . . . . . 23 3.3 Creating a Contextual...Compositional Boosting. . . . . 119 7.8 Top-down hallucinations of missing objects. . . . . . . . . . . . . . . 121 7.9 The bottom-up to top-down

Bayesian spatial transformation models with applications in neuroimaging data

PubMed Central

Miranda, Michelle F.; Zhu, Hongtu; Ibrahim, Joseph G.

2013-01-01

Summary The aim of this paper is to develop a class of spatial transformation models (STM) to spatially model the varying association between imaging measures in a three-dimensional (3D) volume (or 2D surface) and a set of covariates. Our STMs include a varying Box-Cox transformation model for dealing with the issue of non-Gaussian distributed imaging data and a Gaussian Markov Random Field model for incorporating spatial smoothness of the imaging data. Posterior computation proceeds via an efficient Markov chain Monte Carlo algorithm. Simulations and real data analysis demonstrate that the STM significantly outperforms the voxel-wise linear model with Gaussian noise in recovering meaningful geometric patterns. Our STM is able to reveal important brain regions with morphological changes in children with attention deficit hyperactivity disorder. PMID:24128143

An analytic technique for statistically modeling random atomic clock errors in estimation

NASA Technical Reports Server (NTRS)

Fell, P. J.

1981-01-01

Minimum variance estimation requires that the statistics of random observation errors be modeled properly. If measurements are derived through the use of atomic frequency standards, then one source of error affecting the observable is random fluctuation in frequency. This is the case, for example, with range and integrated Doppler measurements from satellites of the Global Positioning and baseline determination for geodynamic applications. An analytic method is presented which approximates the statistics of this random process. The procedure starts with a model of the Allan variance for a particular oscillator and develops the statistics of range and integrated Doppler measurements. A series of five first order Markov processes is used to approximate the power spectral density obtained from the Allan variance.

Optically phase-locked electronic speckle pattern interferometer system performance for vibration measurement in random displacement fields

NASA Astrophysics Data System (ADS)

Moran, Steve E.; Lugannani, Robert; Craig, Peter N.; Law, Robert L.

1989-02-01

An analysis is made of the performance of an optically phase-locked electronic speckle pattern interferometer in the presence of random noise displacements. Expressions for the phase-locked speckle contrast for single-frame imagery and the composite rms exposure for two sequentially subtracted frames are obtained in terms of the phase-locked composite and single-frame fringe functions. The noise fringe functions are evaluated for stationary, coherence-separable noise displacements obeying Gauss-Markov temporal statistics. The theoretical findings presented here are qualitatively supported by experimental results.

Kullback-Leibler Divergence-Based Differential Evolution Markov Chain Filter for Global Localization of Mobile Robots.

PubMed

Martín, Fernando; Moreno, Luis; Garrido, Santiago; Blanco, Dolores

2015-09-16

One of the most important skills desired for a mobile robot is the ability to obtain its own location even in challenging environments. The information provided by the sensing system is used here to solve the global localization problem. In our previous work, we designed different algorithms founded on evolutionary strategies in order to solve the aforementioned task. The latest developments are presented in this paper. The engine of the localization module is a combination of the Markov chain Monte Carlo sampling technique and the Differential Evolution method, which results in a particle filter based on the minimization of a fitness function. The robot's pose is estimated from a set of possible locations weighted by a cost value. The measurements of the perceptive sensors are used together with the predicted ones in a known map to define a cost function to optimize. Although most localization methods rely on quadratic fitness functions, the sensed information is processed asymmetrically in this filter. The Kullback-Leibler divergence is the basis of a cost function that makes it possible to deal with different types of occlusions. The algorithm performance has been checked in a real map. The results are excellent in environments with dynamic and unmodeled obstacles, a fact that causes occlusions in the sensing area.

Kullback-Leibler Divergence-Based Differential Evolution Markov Chain Filter for Global Localization of Mobile Robots

PubMed Central

Martín, Fernando; Moreno, Luis; Garrido, Santiago; Blanco, Dolores

2015-01-01

One of the most important skills desired for a mobile robot is the ability to obtain its own location even in challenging environments. The information provided by the sensing system is used here to solve the global localization problem. In our previous work, we designed different algorithms founded on evolutionary strategies in order to solve the aforementioned task. The latest developments are presented in this paper. The engine of the localization module is a combination of the Markov chain Monte Carlo sampling technique and the Differential Evolution method, which results in a particle filter based on the minimization of a fitness function. The robot’s pose is estimated from a set of possible locations weighted by a cost value. The measurements of the perceptive sensors are used together with the predicted ones in a known map to define a cost function to optimize. Although most localization methods rely on quadratic fitness functions, the sensed information is processed asymmetrically in this filter. The Kullback-Leibler divergence is the basis of a cost function that makes it possible to deal with different types of occlusions. The algorithm performance has been checked in a real map. The results are excellent in environments with dynamic and unmodeled obstacles, a fact that causes occlusions in the sensing area. PMID:26389914

Blind Bayesian restoration of adaptive optics telescope images using generalized Gaussian Markov random field models

NASA Astrophysics Data System (ADS)

Jeffs, Brian D.; Christou, Julian C.

1998-09-01

This paper addresses post processing for resolution enhancement of sequences of short exposure adaptive optics (AO) images of space objects. The unknown residual blur is removed using Bayesian maximum a posteriori blind image restoration techniques. In the problem formulation, both the true image and the unknown blur psf's are represented by the flexible generalized Gaussian Markov random field (GGMRF) model. The GGMRF probability density function provides a natural mechanism for expressing available prior information about the image and blur. Incorporating such prior knowledge in the deconvolution optimization is crucial for the success of blind restoration algorithms. For example, space objects often contain sharp edge boundaries and geometric structures, while the residual blur psf in the corresponding partially corrected AO image is spectrally band limited, and exhibits while the residual blur psf in the corresponding partially corrected AO image is spectrally band limited, and exhibits smoothed, random , texture-like features on a peaked central core. By properly choosing parameters, GGMRF models can accurately represent both the blur psf and the object, and serve to regularize the deconvolution problem. These two GGMRF models also serve as discriminator functions to separate blur and object in the solution. Algorithm performance is demonstrated with examples from synthetic AO images. Results indicate significant resolution enhancement when applied to partially corrected AO images. An efficient computational algorithm is described.

Comparing efficacy of reduced-toxicity allogeneic hematopoietic cell transplantation with conventional chemo-(immuno) therapy in patients with relapsed or refractory CLL: a Markov decision analysis.

PubMed

Kharfan-Dabaja, M A; Pidala, J; Kumar, A; Terasawa, T; Djulbegovic, B

2012-09-01

Despite therapeutic advances, relapsed/refractory CLL, particularly after fludarabine-based regimens, remains a major challenge for which optimal therapy is undefined. No randomized comparative data exist to suggest the superiority of reduced-toxicity allogeneic hematopoietic cell transplantation (RT-allo-HCT) over conventional chemo-(immuno) therapy (CCIT). By using estimates from a systematic review and by meta-analysis of available published evidence, we constructed a Markov decision model to examine these competing modalities. Cohort analysis demonstrated superior outcome for RT-allo-HCT, with a 10-month overall life expectancy (and 6-month quality-adjusted life expectancy (QALE)) advantage over CCIT. Although the model was sensitive to changes in base-case assumptions and transition probabilities, RT-allo-HCT provided superior overall life expectancy through a range of values supported by the meta-analysis. QALE was superior for RT-allo-HCT compared with CCIT. This conclusion was sensitive to change in the anticipated state utility associated with the post-allogeneic HCT state; however, RT-allo-HCT remained the optimal strategy for values supported by existing literature. This analysis provides a quantitative comparison of outcomes between RT-allo-HCT and CCIT for relapsed/refractory CLL in the absence of randomized comparative trials. Confirmation of these findings requires a prospective randomized trial, which compares the most effective RT-allo-HCT and CCIT regimens for relapsed/refractory CLL.

SfM with MRFs: discrete-continuous optimization for large-scale structure from motion.

PubMed

Crandall, David J; Owens, Andrew; Snavely, Noah; Huttenlocher, Daniel P

2013-12-01

Recent work in structure from motion (SfM) has built 3D models from large collections of images downloaded from the Internet. Many approaches to this problem use incremental algorithms that solve progressively larger bundle adjustment problems. These incremental techniques scale poorly as the image collection grows, and can suffer from drift or local minima. We present an alternative framework for SfM based on finding a coarse initial solution using hybrid discrete-continuous optimization and then improving that solution using bundle adjustment. The initial optimization step uses a discrete Markov random field (MRF) formulation, coupled with a continuous Levenberg-Marquardt refinement. The formulation naturally incorporates various sources of information about both the cameras and points, including noisy geotags and vanishing point (VP) estimates. We test our method on several large-scale photo collections, including one with measured camera positions, and show that it produces models that are similar to or better than those produced by incremental bundle adjustment, but more robustly and in a fraction of the time.

Fast Appearance Modeling for Automatic Primary Video Object Segmentation.

PubMed

Yang, Jiong; Price, Brian; Shen, Xiaohui; Lin, Zhe; Yuan, Junsong

2016-02-01

Automatic segmentation of the primary object in a video clip is a challenging problem as there is no prior knowledge of the primary object. Most existing techniques thus adapt an iterative approach for foreground and background appearance modeling, i.e., fix the appearance model while optimizing the segmentation and fix the segmentation while optimizing the appearance model. However, these approaches may rely on good initialization and can be easily trapped in local optimal. In addition, they are usually time consuming for analyzing videos. To address these limitations, we propose a novel and efficient appearance modeling technique for automatic primary video object segmentation in the Markov random field (MRF) framework. It embeds the appearance constraint as auxiliary nodes and edges in the MRF structure, and can optimize both the segmentation and appearance model parameters simultaneously in one graph cut. The extensive experimental evaluations validate the superiority of the proposed approach over the state-of-the-art methods, in both efficiency and effectiveness.

Characterization of the rat exploratory behavior in the elevated plus-maze with Markov chains.

PubMed

Tejada, Julián; Bosco, Geraldine G; Morato, Silvio; Roque, Antonio C

2010-11-30

The elevated plus-maze is an animal model of anxiety used to study the effect of different drugs on the behavior of the animal. It consists of a plus-shaped maze with two open and two closed arms elevated 50cm from the floor. The standard measures used to characterize exploratory behavior in the elevated plus-maze are the time spent and the number of entries in the open arms. In this work, we use Markov chains to characterize the exploratory behavior of the rat in the elevated plus-maze under three different conditions: normal and under the effects of anxiogenic and anxiolytic drugs. The spatial structure of the elevated plus-maze is divided into squares, which are associated with states of a Markov chain. By counting the frequencies of transitions between states during 5-min sessions in the elevated plus-maze, we constructed stochastic matrices for the three conditions studied. The stochastic matrices show specific patterns, which correspond to the observed behaviors of the rat under the three different conditions. For the control group, the stochastic matrix shows a clear preference for places in the closed arms. This preference is enhanced for the anxiogenic group. For the anxiolytic group, the stochastic matrix shows a pattern similar to a random walk. Our results suggest that Markov chains can be used together with the standard measures to characterize the rat behavior in the elevated plus-maze. Copyright © 2010 Elsevier B.V. All rights reserved.

Stratification of the phase clouds and statistical effects of the non-Markovity in chaotic time series of human gait for healthy people and Parkinson patients

NASA Astrophysics Data System (ADS)

Yulmetyev, Renat; Demin, Sergey; Emelyanova, Natalya; Gafarov, Fail; Hänggi, Peter

2003-03-01

In this work we develop a new method of diagnosing the nervous system diseases and a new approach in studying human gait dynamics with the help of the theory of discrete non-Markov random processes (Phys. Rev. E 62 (5) (2000) 6178, Phys. Rev. E 64 (2001) 066132, Phys. Rev. E 65 (2002) 046107, Physica A 303 (2002) 427). The stratification of the phase clouds and the statistical non-Markov effects in the time series of the dynamics of human gait are considered. We carried out the comparative analysis of the data of four age groups of healthy people: children (from 3 to 10 year olds), teenagers (from 11 to 14 year olds), young people (from 21 up to 29 year olds), elderly persons (from 71 to 77 year olds) and Parkinson patients. The full data set are analyzed with the help of the phase portraits of the four dynamic variables, the power spectra of the initial time correlation function and the memory functions of junior orders, the three first points in the spectra of the statistical non-Markov parameter. The received results allow to define the predisposition of the probationers to deflections in the central nervous system caused by Parkinson's disease. We have found out distinct differences between the five submitted groups. On this basis we offer a new method of diagnostics and forecasting Parkinson's disease.

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

PubMed Central

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

2018-01-01

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

Application of Simulated Annealing and Related Algorithms to TWTA Design

NASA Technical Reports Server (NTRS)

Radke, Eric M.

2004-01-01

Simulated Annealing (SA) is a stochastic optimization algorithm used to search for global minima in complex design surfaces where exhaustive searches are not computationally feasible. The algorithm is derived by simulating the annealing process, whereby a solid is heated to a liquid state and then cooled slowly to reach thermodynamic equilibrium at each temperature. The idea is that atoms in the solid continually bond and re-bond at various quantum energy levels, and with sufficient cooling time they will rearrange at the minimum energy state to form a perfect crystal. The distribution of energy levels is given by the Boltzmann distribution: as temperature drops, the probability of the presence of high-energy bonds decreases. In searching for an optimal design, local minima and discontinuities are often present in a design surface. SA presents a distinct advantage over other optimization algorithms in its ability to escape from these local minima. Just as high-energy atomic configurations are visited in the actual annealing process in order to eventually reach the minimum energy state, in SA highly non-optimal configurations are visited in order to find otherwise inaccessible global minima. The SA algorithm produces a Markov chain of points in the design space at each temperature, with a monotonically decreasing temperature. A random point is started upon, and the objective function is evaluated at that point. A stochastic perturbation is then made to the parameters of the point to arrive at a proposed new point in the design space, at which the objection function is evaluated as well. If the change in objective function values (Delta)E is negative, the proposed new point is accepted. If (Delta)E is positive, the proposed new point is accepted according to the Metropolis criterion: rho((Delta)f) = exp((-Delta)E/T), where T is the temperature for the current Markov chain. The process then repeats for the remainder of the Markov chain, after which the temperature is decremented and the process repeats. Eventually (and hopefully), a near-globally optimal solution is attained as T approaches zero. Several exciting variants of SA have recently emerged, including Discrete-State Simulated Annealing (DSSA) and Simulated Tempering (ST). The DSSA algorithm takes the thermodynamic analogy one step further by categorizing objective function evaluations into discrete states. In doing so, many of the case-specific problems associated with fine-tuning the SA algorithm can be avoided; for example, theoretical approximations for the initial and final temperature can be derived independently of the case. In this manner, DSSA provides a scheme that is more robust with respect to widely differing design surfaces. ST differs from SA in that the temperature T becomes an additional random variable in the optimization. The system is also kept in equilibrium as the temperature changes, as opposed to the system being driven out of equilibrium as temperature changes in SA. ST is designed to overcome obstacles in design surfaces where numerous local minima are separated by high barriers. These algorithms are incorporated into the optimal design of the traveling-wave tube amplifier (TWTA). The area under scrutiny is the collector, in which it would be ideal to use negative potential to decelerate the spent electron beam to zero kinetic energy just as it reaches the collector surface. In reality this is not plausible due to a number of physical limitations, including repulsion and differing levels of kinetic energy among individual electrons. Instead, the collector is designed with multiple stages depressed below ground potential. The design of this multiple-stage collector is the optimization problem of interest. One remaining problem in SA and DSSA is the difficulty in determining when equilibrium has been reached so that the current Markov chain can be terminated. It has been suggested in recent literature that simulating the thermodynamic properties opecific heat, entropy, and internal energy from the Boltzmann distribution can provide good indicators of having reached equilibrium at a certain temperature. These properties are tested for their efficacy and implemented in SA and DSSA code with respect to TWTA collector optimization.

Improving Localization Accuracy: Successive Measurements Error Modeling

PubMed Central

Abu Ali, Najah; Abu-Elkheir, Mervat

2015-01-01

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

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

PubMed

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

2014-12-19

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

Multiframe video coding for improved performance over wireless channels.

PubMed

Budagavi, M; Gibson, J D

2001-01-01

We propose and evaluate a multi-frame extension to block motion compensation (BMC) coding of videoconferencing-type video signals for wireless channels. The multi-frame BMC (MF-BMC) coder makes use of the redundancy that exists across multiple frames in typical videoconferencing sequences to achieve additional compression over that obtained by using the single frame BMC (SF-BMC) approach, such as in the base-level H.263 codec. The MF-BMC approach also has an inherent ability of overcoming some transmission errors and is thus more robust when compared to the SF-BMC approach. We model the error propagation process in MF-BMC coding as a multiple Markov chain and use Markov chain analysis to infer that the use of multiple frames in motion compensation increases robustness. The Markov chain analysis is also used to devise a simple scheme which randomizes the selection of the frame (amongst the multiple previous frames) used in BMC to achieve additional robustness. The MF-BMC coders proposed are a multi-frame extension of the base level H.263 coder and are found to be more robust than the base level H.263 coder when subjected to simulated errors commonly encountered on wireless channels.

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

NASA Astrophysics Data System (ADS)

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

2014-12-01

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

Fracture overprinting history using Markov chain analysis: Windsor-Kennetcook subbasin, Maritimes Basin, Canada

NASA Astrophysics Data System (ADS)

Snyder, Morgan E.; Waldron, John W. F.

2018-03-01

The deformation history of the Upper Paleozoic Maritimes Basin, Atlantic Canada, can be partially unraveled by examining fractures (joints, veins, and faults) that are well exposed on the shorelines of the macrotidal Bay of Fundy, in subsurface core, and on image logs. Data were collected from coastal outcrops and well core across the Windsor-Kennetcook subbasin, a subbasin in the Maritimes Basin, using the circular scan-line and vertical scan-line methods in outcrop, and FMI Image log analysis of core. We use cross-cutting and abutting relationships between fractures to understand relative timing of fracturing, followed by a statistical test (Markov chain analysis) to separate groups of fractures. This analysis, previously used in sedimentology, was modified to statistically test the randomness of fracture timing relationships. The results of the Markov chain analysis suggest that fracture initiation can be attributed to movement along the Minas Fault Zone, an E-W fault system that bounds the Windsor-Kennetcook subbasin to the north. Four sets of fractures are related to dextral strike slip along the Minas Fault Zone in the late Paleozoic, and four sets are related to sinistral reactivation of the same boundary in the Mesozoic.

A stochastic approach to noise modeling for barometric altimeters.

PubMed

Sabatini, Angelo Maria; Genovese, Vincenzo

2013-11-18

The question whether barometric altimeters can be applied to accurately track human motions is still debated, since their measurement performance are rather poor due to either coarse resolution or drifting behavior problems. As a step toward accurate short-time tracking of changes in height (up to few minutes), we develop a stochastic model that attempts to capture some statistical properties of the barometric altimeter noise. The barometric altimeter noise is decomposed in three components with different physical origin and properties: a deterministic time-varying mean, mainly correlated with global environment changes, and a first-order Gauss-Markov (GM) random process, mainly accounting for short-term, local environment changes, the effects of which are prominent, respectively, for long-time and short-time motion tracking; an uncorrelated random process, mainly due to wideband electronic noise, including quantization noise. Autoregressive-moving average (ARMA) system identification techniques are used to capture the correlation structure of the piecewise stationary GM component, and to estimate its standard deviation, together with the standard deviation of the uncorrelated component. M-point moving average filters used alone or in combination with whitening filters learnt from ARMA model parameters are further tested in few dynamic motion experiments and discussed for their capability of short-time tracking small-amplitude, low-frequency motions.

Figure-Ground Segmentation Using Factor Graphs

PubMed Central

Shen, Huiying; Coughlan, James; Ivanchenko, Volodymyr

2009-01-01

Foreground-background segmentation has recently been applied [26,12] to the detection and segmentation of specific objects or structures of interest from the background as an efficient alternative to techniques such as deformable templates [27]. We introduce a graphical model (i.e. Markov random field)-based formulation of structure-specific figure-ground segmentation based on simple geometric features extracted from an image, such as local configurations of linear features, that are characteristic of the desired figure structure. Our formulation is novel in that it is based on factor graphs, which are graphical models that encode interactions among arbitrary numbers of random variables. The ability of factor graphs to express interactions higher than pairwise order (the highest order encountered in most graphical models used in computer vision) is useful for modeling a variety of pattern recognition problems. In particular, we show how this property makes factor graphs a natural framework for performing grouping and segmentation, and demonstrate that the factor graph framework emerges naturally from a simple maximum entropy model of figure-ground segmentation. We cast our approach in a learning framework, in which the contributions of multiple grouping cues are learned from training data, and apply our framework to the problem of finding printed text in natural scenes. Experimental results are described, including a performance analysis that demonstrates the feasibility of the approach. PMID:20160994

Detecting brain tumor in computed tomography images using Markov random fields and fuzzy C-means clustering techniques

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

Abdulbaqi, Hayder Saad; Department of Physics, College of Education, University of Al-Qadisiya, Al-Qadisiya; Jafri, Mohd Zubir Mat

Brain tumors, are an abnormal growth of tissues in the brain. They may arise in people of any age. They must be detected early, diagnosed accurately, monitored carefully, and treated effectively in order to optimize patient outcomes regarding both survival and quality of life. Manual segmentation of brain tumors from CT scan images is a challenging and time consuming task. Size and location accurate detection of brain tumor plays a vital role in the successful diagnosis and treatment of tumors. Brain tumor detection is considered a challenging mission in medical image processing. The aim of this paper is to introducemore » a scheme for tumor detection in CT scan images using two different techniques Hidden Markov Random Fields (HMRF) and Fuzzy C-means (FCM). The proposed method has been developed in this research in order to construct hybrid method between (HMRF) and threshold. These methods have been applied on 4 different patient data sets. The result of comparison among these methods shows that the proposed method gives good results for brain tissue detection, and is more robust and effective compared with (FCM) techniques.« less

Detection and inpainting of facial wrinkles using texture orientation fields and Markov random field modeling.

PubMed

Batool, Nazre; Chellappa, Rama

2014-09-01

Facial retouching is widely used in media and entertainment industry. Professional software usually require a minimum level of user expertise to achieve the desirable results. In this paper, we present an algorithm to detect facial wrinkles/imperfection. We believe that any such algorithm would be amenable to facial retouching applications. The detection of wrinkles/imperfections can allow these skin features to be processed differently than the surrounding skin without much user interaction. For detection, Gabor filter responses along with texture orientation field are used as image features. A bimodal Gaussian mixture model (GMM) represents distributions of Gabor features of normal skin versus skin imperfections. Then, a Markov random field model is used to incorporate the spatial relationships among neighboring pixels for their GMM distributions and texture orientations. An expectation-maximization algorithm then classifies skin versus skin wrinkles/imperfections. Once detected automatically, wrinkles/imperfections are removed completely instead of being blended or blurred. We propose an exemplar-based constrained texture synthesis algorithm to inpaint irregularly shaped gaps left by the removal of detected wrinkles/imperfections. We present results conducted on images downloaded from the Internet to show the efficacy of our algorithms.

Hidden Markov random field model and Broyden-Fletcher-Goldfarb-Shanno algorithm for brain image segmentation

NASA Astrophysics Data System (ADS)

Guerrout, EL-Hachemi; Ait-Aoudia, Samy; Michelucci, Dominique; Mahiou, Ramdane

2018-05-01

Many routine medical examinations produce images of patients suffering from various pathologies. With the huge number of medical images, the manual analysis and interpretation became a tedious task. Thus, automatic image segmentation became essential for diagnosis assistance. Segmentation consists in dividing the image into homogeneous and significant regions. We focus on hidden Markov random fields referred to as HMRF to model the problem of segmentation. This modelisation leads to a classical function minimisation problem. Broyden-Fletcher-Goldfarb-Shanno algorithm referred to as BFGS is one of the most powerful methods to solve unconstrained optimisation problem. In this paper, we investigate the combination of HMRF and BFGS algorithm to perform the segmentation operation. The proposed method shows very good segmentation results comparing with well-known approaches. The tests are conducted on brain magnetic resonance image databases (BrainWeb and IBSR) largely used to objectively confront the results obtained. The well-known Dice coefficient (DC) was used as similarity metric. The experimental results show that, in many cases, our proposed method approaches the perfect segmentation with a Dice Coefficient above .9. Moreover, it generally outperforms other methods in the tests conducted.

Unsupervised change detection of multispectral images based on spatial constraint chi-squared transform and Markov random field model

NASA Astrophysics Data System (ADS)

Shi, Aiye; Wang, Chao; Shen, Shaohong; Huang, Fengchen; Ma, Zhenli

2016-10-01

Chi-squared transform (CST), as a statistical method, can describe the difference degree between vectors. The CST-based methods operate directly on information stored in the difference image and are simple and effective methods for detecting changes in remotely sensed images that have been registered and aligned. However, the technique does not take spatial information into consideration, which leads to much noise in the result of change detection. An improved unsupervised change detection method is proposed based on spatial constraint CST (SCCST) in combination with a Markov random field (MRF) model. First, the mean and variance matrix of the difference image of bitemporal images are estimated by an iterative trimming method. In each iteration, spatial information is injected to reduce scattered changed points (also known as "salt and pepper" noise). To determine the key parameter confidence level in the SCCST method, a pseudotraining dataset is constructed to estimate the optimal value. Then, the result of SCCST, as an initial solution of change detection, is further improved by the MRF model. The experiments on simulated and real multitemporal and multispectral images indicate that the proposed method performs well in comprehensive indices compared with other methods.

Incorporating interaction networks into the determination of functionally related hit genes in genomic experiments with Markov random fields

PubMed Central

Robinson, Sean; Nevalainen, Jaakko; Pinna, Guillaume; Campalans, Anna; Radicella, J. Pablo; Guyon, Laurent

2017-01-01

Abstract Motivation: Incorporating gene interaction data into the identification of ‘hit’ genes in genomic experiments is a well-established approach leveraging the ‘guilt by association’ assumption to obtain a network based hit list of functionally related genes. We aim to develop a method to allow for multivariate gene scores and multiple hit labels in order to extend the analysis of genomic screening data within such an approach. Results: We propose a Markov random field-based method to achieve our aim and show that the particular advantages of our method compared with those currently used lead to new insights in previously analysed data as well as for our own motivating data. Our method additionally achieves the best performance in an independent simulation experiment. The real data applications we consider comprise of a survival analysis and differential expression experiment and a cell-based RNA interference functional screen. Availability and implementation: We provide all of the data and code related to the results in the paper. Contact: sean.j.robinson@utu.fi or laurent.guyon@cea.fr Supplementary information: Supplementary data are available at Bioinformatics online. PMID:28881978

Enhancing gene regulatory network inference through data integration with markov random fields

DOE PAGES

Banf, Michael; Rhee, Seung Y.

2017-02-01

Here, a gene regulatory network links transcription factors to their target genes and represents a map of transcriptional regulation. Much progress has been made in deciphering gene regulatory networks computationally. However, gene regulatory network inference for most eukaryotic organisms remain challenging. To improve the accuracy of gene regulatory network inference and facilitate candidate selection for experimentation, we developed an algorithm called GRACE (Gene Regulatory network inference ACcuracy Enhancement). GRACE exploits biological a priori and heterogeneous data integration to generate high- confidence network predictions for eukaryotic organisms using Markov Random Fields in a semi-supervised fashion. GRACE uses a novel optimization schememore » to integrate regulatory evidence and biological relevance. It is particularly suited for model learning with sparse regulatory gold standard data. We show GRACE’s potential to produce high confidence regulatory networks compared to state of the art approaches using Drosophila melanogaster and Arabidopsis thaliana data. In an A. thaliana developmental gene regulatory network, GRACE recovers cell cycle related regulatory mechanisms and further hypothesizes several novel regulatory links, including a putative control mechanism of vascular structure formation due to modifications in cell proliferation.« less

Enhancing gene regulatory network inference through data integration with markov random fields

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

Banf, Michael; Rhee, Seung Y.

Here, a gene regulatory network links transcription factors to their target genes and represents a map of transcriptional regulation. Much progress has been made in deciphering gene regulatory networks computationally. However, gene regulatory network inference for most eukaryotic organisms remain challenging. To improve the accuracy of gene regulatory network inference and facilitate candidate selection for experimentation, we developed an algorithm called GRACE (Gene Regulatory network inference ACcuracy Enhancement). GRACE exploits biological a priori and heterogeneous data integration to generate high- confidence network predictions for eukaryotic organisms using Markov Random Fields in a semi-supervised fashion. GRACE uses a novel optimization schememore » to integrate regulatory evidence and biological relevance. It is particularly suited for model learning with sparse regulatory gold standard data. We show GRACE’s potential to produce high confidence regulatory networks compared to state of the art approaches using Drosophila melanogaster and Arabidopsis thaliana data. In an A. thaliana developmental gene regulatory network, GRACE recovers cell cycle related regulatory mechanisms and further hypothesizes several novel regulatory links, including a putative control mechanism of vascular structure formation due to modifications in cell proliferation.« less

Distributed memory parallel Markov random fields using graph partitioning

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

Heinemann, C.; Perciano, T.; Ushizima, D.

Markov random fields (MRF) based algorithms have attracted a large amount of interest in image analysis due to their ability to exploit contextual information about data. Image data generated by experimental facilities, though, continues to grow larger and more complex, making it more difficult to analyze in a reasonable amount of time. Applying image processing algorithms to large datasets requires alternative approaches to circumvent performance problems. Aiming to provide scientists with a new tool to recover valuable information from such datasets, we developed a general purpose distributed memory parallel MRF-based image analysis framework (MPI-PMRF). MPI-PMRF overcomes performance and memory limitationsmore » by distributing data and computations across processors. The proposed approach was successfully tested with synthetic and experimental datasets. Additionally, the performance of the MPI-PMRF framework is analyzed through a detailed scalability study. We show that a performance increase is obtained while maintaining an accuracy of the segmentation results higher than 98%. The contributions of this paper are: (a) development of a distributed memory MRF framework; (b) measurement of the performance increase of the proposed approach; (c) verification of segmentation accuracy in both synthetic and experimental, real-world datasets« less

Interferometric synthetic aperture radar phase unwrapping based on sparse Markov random fields by graph cuts

NASA Astrophysics Data System (ADS)

Zhou, Lifan; Chai, Dengfeng; Xia, Yu; Ma, Peifeng; Lin, Hui

2018-01-01

Phase unwrapping (PU) is one of the key processes in reconstructing the digital elevation model of a scene from its interferometric synthetic aperture radar (InSAR) data. It is known that two-dimensional (2-D) PU problems can be formulated as maximum a posteriori estimation of Markov random fields (MRFs). However, considering that the traditional MRF algorithm is usually defined on a rectangular grid, it fails easily if large parts of the wrapped data are dominated by noise caused by large low-coherence area or rapid-topography variation. A PU solution based on sparse MRF is presented to extend the traditional MRF algorithm to deal with sparse data, which allows the unwrapping of InSAR data dominated by high phase noise. To speed up the graph cuts algorithm for sparse MRF, we designed dual elementary graphs and merged them to obtain the Delaunay triangle graph, which is used to minimize the energy function efficiently. The experiments on simulated and real data, compared with other existing algorithms, both confirm the effectiveness of the proposed MRF approach, which suffers less from decorrelation effects caused by large low-coherence area or rapid-topography variation.

SMURFLite: combining simplified Markov random fields with simulated evolution improves remote homology detection for beta-structural proteins into the twilight zone.

PubMed

Daniels, Noah M; Hosur, Raghavendra; Berger, Bonnie; Cowen, Lenore J

2012-05-01

One of the most successful methods to date for recognizing protein sequences that are evolutionarily related has been profile hidden Markov models (HMMs). However, these models do not capture pairwise statistical preferences of residues that are hydrogen bonded in beta sheets. These dependencies have been partially captured in the HMM setting by simulated evolution in the training phase and can be fully captured by Markov random fields (MRFs). However, the MRFs can be computationally prohibitive when beta strands are interleaved in complex topologies. We introduce SMURFLite, a method that combines both simplified MRFs and simulated evolution to substantially improve remote homology detection for beta structures. Unlike previous MRF-based methods, SMURFLite is computationally feasible on any beta-structural motif. We test SMURFLite on all propeller and barrel folds in the mainly-beta class of the SCOP hierarchy in stringent cross-validation experiments. We show a mean 26% (median 16%) improvement in area under curve (AUC) for beta-structural motif recognition as compared with HMMER (a well-known HMM method) and a mean 33% (median 19%) improvement as compared with RAPTOR (a well-known threading method) and even a mean 18% (median 10%) improvement in AUC over HHPred (a profile-profile HMM method), despite HHpred's use of extensive additional training data. We demonstrate SMURFLite's ability to scale to whole genomes by running a SMURFLite library of 207 beta-structural SCOP superfamilies against the entire genome of Thermotoga maritima, and make over a 100 new fold predictions. Availability and implementaion: A webserver that runs SMURFLite is available at: http://smurf.cs.tufts.edu/smurflite/

Neoadjuvant therapy versus upfront surgical strategies in resectable pancreatic cancer: A Markov decision analysis.

PubMed

de Geus, S W L; Evans, D B; Bliss, L A; Eskander, M F; Smith, J K; Wolff, R A; Miksad, R A; Weinstein, M C; Tseng, J F

2016-10-01

Neoadjuvant therapy is gaining acceptance as a valid treatment option for borderline resectable pancreatic cancer; however, its value for clearly resectable pancreatic cancer remains controversial. The aim of this study was to use a Markov decision analysis model, in the absence of adequately powered randomized trials, to compare the life expectancy (LE) and quality-adjusted life expectancy (QALE) of neoadjuvant therapy to conventional upfront surgical strategies in resectable pancreatic cancer patients. A Markov decision model was created to compare two strategies: attempted pancreatic resection followed by adjuvant chemoradiotherapy and neoadjuvant chemoradiotherapy followed by restaging with, if appropriate, attempted pancreatic resection. Data obtained through a comprehensive systematic search in PUBMED of the literature from 2000 to 2015 were used to estimate the probabilities used in the model. Deterministic and probabilistic sensitivity analyses were performed. Of the 786 potentially eligible studies identified, 22 studies met the inclusion criteria and were used to extract the probabilities used in the model. Base case analyses of the model showed a higher LE (32.2 vs. 26.7 months) and QALE (25.5 vs. 20.8 quality-adjusted life months) for patients in the neoadjuvant therapy arm compared to upfront surgery. Probabilistic sensitivity analyses for LE and QALE revealed that neoadjuvant therapy is favorable in 59% and 60% of the cases respectively. Although conceptual, these data suggest that neoadjuvant therapy offers substantial benefit in LE and QALE for resectable pancreatic cancer patients. These findings highlight the value of further prospective randomized trials comparing neoadjuvant therapy to conventional upfront surgical strategies. Copyright © 2016 Elsevier Ltd, BASO ~ The Association for Cancer Surgery, and the European Society of Surgical Oncology. All rights reserved.

Statistical significance approximation in local trend analysis of high-throughput time-series data using the theory of Markov chains.

PubMed

Xia, Li C; Ai, Dongmei; Cram, Jacob A; Liang, Xiaoyi; Fuhrman, Jed A; Sun, Fengzhu

2015-09-21

Local trend (i.e. shape) analysis of time series data reveals co-changing patterns in dynamics of biological systems. However, slow permutation procedures to evaluate the statistical significance of local trend scores have limited its applications to high-throughput time series data analysis, e.g., data from the next generation sequencing technology based studies. By extending the theories for the tail probability of the range of sum of Markovian random variables, we propose formulae for approximating the statistical significance of local trend scores. Using simulations and real data, we show that the approximate p-value is close to that obtained using a large number of permutations (starting at time points >20 with no delay and >30 with delay of at most three time steps) in that the non-zero decimals of the p-values obtained by the approximation and the permutations are mostly the same when the approximate p-value is less than 0.05. In addition, the approximate p-value is slightly larger than that based on permutations making hypothesis testing based on the approximate p-value conservative. The approximation enables efficient calculation of p-values for pairwise local trend analysis, making large scale all-versus-all comparisons possible. We also propose a hybrid approach by integrating the approximation and permutations to obtain accurate p-values for significantly associated pairs. We further demonstrate its use with the analysis of the Polymouth Marine Laboratory (PML) microbial community time series from high-throughput sequencing data and found interesting organism co-occurrence dynamic patterns. The software tool is integrated into the eLSA software package that now provides accelerated local trend and similarity analysis pipelines for time series data. The package is freely available from the eLSA website: http://bitbucket.org/charade/elsa.

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

PubMed

Namikawa, Jun

2005-08-01

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

Bayesian spatial transformation models with applications in neuroimaging data.

PubMed

Miranda, Michelle F; Zhu, Hongtu; Ibrahim, Joseph G

2013-12-01

The aim of this article is to develop a class of spatial transformation models (STM) to spatially model the varying association between imaging measures in a three-dimensional (3D) volume (or 2D surface) and a set of covariates. The proposed STM include a varying Box-Cox transformation model for dealing with the issue of non-Gaussian distributed imaging data and a Gaussian Markov random field model for incorporating spatial smoothness of the imaging data. Posterior computation proceeds via an efficient Markov chain Monte Carlo algorithm. Simulations and real data analysis demonstrate that the STM significantly outperforms the voxel-wise linear model with Gaussian noise in recovering meaningful geometric patterns. Our STM is able to reveal important brain regions with morphological changes in children with attention deficit hyperactivity disorder. © 2013, The International Biometric Society.

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

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

Cavazos-Cadena, Rolando; Hernandez-Hernandez, Daniel

2006-01-15

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

Markov chain aggregation and its applications to combinatorial reaction networks.

PubMed

Ganguly, Arnab; Petrov, Tatjana; Koeppl, Heinz

2014-09-01

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

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

PubMed

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

2018-06-01

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

Distance between configurations in Markov chain Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Fukuma, Masafumi; Matsumoto, Nobuyuki; Umeda, Naoya

2017-12-01

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

Detection and Classification of Network Intrusions Using Hidden Markov Models

DTIC Science & Technology

2002-01-01

31 2.2.3 High-level state machines for misuse detection . . . . . . . 32 2.2.4 EMERALD ...Solaris host audit data to detect Solaris R2L (Remote-to-Local) and U2R (User-to-Root) attacks. 7 login as a legitimate user on a local system and use a...as suspicious rather than the entire login session and it can detect some anomalies that are difficult to detect with traditional approaches. It’s

A Pumping Algorithm for Ergodic Stochastic Mean Payoff Games with Perfect Information

NASA Astrophysics Data System (ADS)

Boros, Endre; Elbassioni, Khaled; Gurvich, Vladimir; Makino, Kazuhisa

In this paper, we consider two-person zero-sum stochastic mean payoff games with perfect information, or BWR-games, given by a digraph G = (V = V B ∪ V W ∪ V R , E), with local rewards r: E to { R}, and three types of vertices: black V B , white V W , and random V R . The game is played by two players, White and Black: When the play is at a white (black) vertex v, White (Black) selects an outgoing arc (v,u). When the play is at a random vertex v, a vertex u is picked with the given probability p(v,u). In all cases, Black pays White the value r(v,u). The play continues forever, and White aims to maximize (Black aims to minimize) the limiting mean (that is, average) payoff. It was recently shown in [7] that BWR-games are polynomially equivalent with the classical Gillette games, which include many well-known subclasses, such as cyclic games, simple stochastic games (SSG's), stochastic parity games, and Markov decision processes. In this paper, we give a new algorithm for solving BWR-games in the ergodic case, that is when the optimal values do not depend on the initial position. Our algorithm solves a BWR-game by reducing it, using a potential transformation, to a canonical form in which the optimal strategies of both players and the value for every initial position are obvious, since a locally optimal move in it is optimal in the whole game. We show that this algorithm is pseudo-polynomial when the number of random nodes is constant. We also provide an almost matching lower bound on its running time, and show that this bound holds for a wider class of algorithms. Let us add that the general (non-ergodic) case is at least as hard as SSG's, for which no pseudo-polynomial algorithm is known.

Multi-Observation Continuous Density Hidden Markov Models for Anomaly Detection in Full Motion Video

DTIC Science & Technology

2012-06-01

response profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.5 Method for measuring angular movement versus average direction...of movement 49 3.6 Method for calculating Angular Deviation, Θ . . . . . . . . . . . . . . . . . . 50 4.1 HMM produced by K Means Learning for agent H... Angular Deviation. A random variable, the difference in heading (in degrees) from the overall direction of movement over the sequence • S : Speed. A

Sparse Representation for Color Image Restoration (PREPRINT)

DTIC Science & Technology

2006-10-01

as a universal denoiser of images, which learns the posterior from the given image in a way inspired by the Lempel - Ziv universal compression ...such as images, admit a sparse decomposition over a redundant dictionary leads to efficient algorithms for handling such sources of data . In...describe the data source. Such a model becomes paramount when developing algorithms for processing these signals. In this context, Markov-Random-Field

Detection of Gauss-Markov Random Fields with Nearest-Neighbor Dependency

DTIC Science & Technology

2010-01-01

sgn(Y )C log n, o.w, (45b) where sgn is the sign function and C > 0 is a constant. Consider the functionals H ′2, φ ′ 2 by replacing Yn with Zn in H2...Gaussian signal processing, and has held visiting faculty positions at INP , Toulouse. He is currently with the US Army Research Laboratory where his work

Randomizing Genome-Scale Metabolic Networks

PubMed Central

Samal, Areejit; Martin, Olivier C.

2011-01-01

Networks coming from protein-protein interactions, transcriptional regulation, signaling, or metabolism may appear to have “unusual” properties. To quantify this, it is appropriate to randomize the network and test the hypothesis that the network is not statistically different from expected in a motivated ensemble. However, when dealing with metabolic networks, the randomization of the network using edge exchange generates fictitious reactions that are biochemically meaningless. Here we provide several natural ensembles of randomized metabolic networks. A first constraint is to use valid biochemical reactions. Further constraints correspond to imposing appropriate functional constraints. We explain how to perform these randomizations with the help of Markov Chain Monte Carlo (MCMC) and show that they allow one to approach the properties of biological metabolic networks. The implication of the present work is that the observed global structural properties of real metabolic networks are likely to be the consequence of simple biochemical and functional constraints. PMID:21779409

Statistical analysis of loopy belief propagation in random fields

NASA Astrophysics Data System (ADS)

Yasuda, Muneki; Kataoka, Shun; Tanaka, Kazuyuki

2015-10-01

Loopy belief propagation (LBP), which is equivalent to the Bethe approximation in statistical mechanics, is a message-passing-type inference method that is widely used to analyze systems based on Markov random fields (MRFs). In this paper, we propose a message-passing-type method to analytically evaluate the quenched average of LBP in random fields by using the replica cluster variation method. The proposed analytical method is applicable to general pairwise MRFs with random fields whose distributions differ from each other and can give the quenched averages of the Bethe free energies over random fields, which are consistent with numerical results. The order of its computational cost is equivalent to that of standard LBP. In the latter part of this paper, we describe the application of the proposed method to Bayesian image restoration, in which we observed that our theoretical results are in good agreement with the numerical results for natural images.

Bayesian analysis of zero inflated spatiotemporal HIV/TB child mortality data through the INLA and SPDE approaches: Applied to data observed between 1992 and 2010 in rural North East South Africa

NASA Astrophysics Data System (ADS)

Musenge, Eustasius; Chirwa, Tobias Freeman; Kahn, Kathleen; Vounatsou, Penelope

2013-06-01

Longitudinal mortality data with few deaths usually have problems of zero-inflation. This paper presents and applies two Bayesian models which cater for zero-inflation, spatial and temporal random effects. To reduce the computational burden experienced when a large number of geo-locations are treated as a Gaussian field (GF) we transformed the field to a Gaussian Markov Random Fields (GMRF) by triangulation. We then modelled the spatial random effects using the Stochastic Partial Differential Equations (SPDEs). Inference was done using a computationally efficient alternative to Markov chain Monte Carlo (MCMC) called Integrated Nested Laplace Approximation (INLA) suited for GMRF. The models were applied to data from 71,057 children aged 0 to under 10 years from rural north-east South Africa living in 15,703 households over the years 1992-2010. We found protective effects on HIV/TB mortality due to greater birth weight, older age and more antenatal clinic visits during pregnancy (adjusted RR (95% CI)): 0.73(0.53;0.99), 0.18(0.14;0.22) and 0.96(0.94;0.97) respectively. Therefore childhood HIV/TB mortality could be reduced if mothers are better catered for during pregnancy as this can reduce mother-to-child transmissions and contribute to improved birth weights. The INLA and SPDE approaches are computationally good alternatives in modelling large multilevel spatiotemporal GMRF data structures.

Markovian robots: Minimal navigation strategies for active particles

NASA Astrophysics Data System (ADS)

Nava, Luis Gómez; Großmann, Robert; Peruani, Fernando

2018-04-01

We explore minimal navigation strategies for active particles in complex, dynamical, external fields, introducing a class of autonomous, self-propelled particles which we call Markovian robots (MR). These machines are equipped with a navigation control system (NCS) that triggers random changes in the direction of self-propulsion of the robots. The internal state of the NCS is described by a Boolean variable that adopts two values. The temporal dynamics of this Boolean variable is dictated by a closed Markov chain—ensuring the absence of fixed points in the dynamics—with transition rates that may depend exclusively on the instantaneous, local value of the external field. Importantly, the NCS does not store past measurements of this value in continuous, internal variables. We show that despite the strong constraints, it is possible to conceive closed Markov chain motifs that lead to nontrivial motility behaviors of the MR in one, two, and three dimensions. By analytically reducing the complexity of the NCS dynamics, we obtain an effective description of the long-time motility behavior of the MR that allows us to identify the minimum requirements in the design of NCS motifs and transition rates to perform complex navigation tasks such as adaptive gradient following, detection of minima or maxima, or selection of a desired value in a dynamical, external field. We put these ideas in practice by assembling a robot that operates by the proposed minimalistic NCS to evaluate the robustness of MR, providing a proof of concept that is possible to navigate through complex information landscapes with such a simple NCS whose internal state can be stored in one bit. These ideas may prove useful for the engineering of miniaturized robots.

A protein-dependent side-chain rotamer library.

PubMed

Bhuyan, Md Shariful Islam; Gao, Xin

2011-12-14

Protein side-chain packing problem has remained one of the key open problems in bioinformatics. The three main components of protein side-chain prediction methods are a rotamer library, an energy function and a search algorithm. Rotamer libraries summarize the existing knowledge of the experimentally determined structures quantitatively. Depending on how much contextual information is encoded, there are backbone-independent rotamer libraries and backbone-dependent rotamer libraries. Backbone-independent libraries only encode sequential information, whereas backbone-dependent libraries encode both sequential and locally structural information. However, side-chain conformations are determined by spatially local information, rather than sequentially local information. Since in the side-chain prediction problem, the backbone structure is given, spatially local information should ideally be encoded into the rotamer libraries. In this paper, we propose a new type of backbone-dependent rotamer library, which encodes structural information of all the spatially neighboring residues. We call it protein-dependent rotamer libraries. Given any rotamer library and a protein backbone structure, we first model the protein structure as a Markov random field. Then the marginal distributions are estimated by the inference algorithms, without doing global optimization or search. The rotamers from the given library are then re-ranked and associated with the updated probabilities. Experimental results demonstrate that the proposed protein-dependent libraries significantly outperform the widely used backbone-dependent libraries in terms of the side-chain prediction accuracy and the rotamer ranking ability. Furthermore, without global optimization/search, the side-chain prediction power of the protein-dependent library is still comparable to the global-search-based side-chain prediction methods.

LocalMove: computing on-lattice fits for biopolymers

PubMed Central

Ponty, Y.; Istrate, R.; Porcelli, E.; Clote, P.

2008-01-01

Given an input Protein Data Bank file (PDB) for a protein or RNA molecule, LocalMove is a web server that determines an on-lattice representation for the input biomolecule. The web server implements a Markov Chain Monte-Carlo algorithm with simulated annealing to compute an approximate fit for either the coarse-grain model or backbone model on either the cubic or face-centered cubic lattice. LocalMove returns a PDB file as output, as well as dynamic movie of 3D images of intermediate conformations during the computation. The LocalMove server is publicly available at http://bioinformatics.bc.edu/clotelab/localmove/. PMID:18556754

Decay of random correlation functions for unimodal maps

NASA Astrophysics Data System (ADS)

Baladi, Viviane; Benedicks, Michael; Maume-Deschamps, Véronique

2000-10-01

Since the pioneering results of Jakobson and subsequent work by Benedicks-Carleson and others, it is known that quadratic maps tfa( χ) = a - χ2 admit a unique absolutely continuous invariant measure for a positive measure set of parameters a. For topologically mixing tfa, Young and Keller-Nowicki independently proved exponential decay of correlation functions for this a.c.i.m. and smooth observables. We consider random compositions of small perturbations tf + ωt, with tf = tfa or another unimodal map satisfying certain nonuniform hyperbolicity axioms, and ωt chosen independently and identically in [-ɛ, ɛ]. Baladi-Viana showed exponential mixing of the associated Markov chain, i.e., averaging over all random itineraries. We obtain stretched exponential bounds for the random correlation functions of Lipschitz observables for the sample measure μωof almost every itinerary.

Sorting processes with energy-constrained comparisons*

NASA Astrophysics Data System (ADS)

Geissmann, Barbara; Penna, Paolo

2018-05-01

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

An information hidden model holding cover distributions

NASA Astrophysics Data System (ADS)

Fu, Min; Cai, Chao; Dai, Zuxu

2018-03-01

The goal of steganography is to embed secret data into a cover so no one apart from the sender and intended recipients can find the secret data. Usually, the way the cover changing was decided by a hidden function. There were no existing model could be used to find an optimal function which can greatly reduce the distortion the cover suffered. This paper considers the cover carrying secret message as a random Markov chain, taking the advantages of a deterministic relation between initial distributions and transferring matrix of the Markov chain, and takes the transferring matrix as a constriction to decrease statistical distortion the cover suffered in the process of information hiding. Furthermore, a hidden function is designed and the transferring matrix is also presented to be a matrix from the original cover to the stego cover. Experiment results show that the new model preserves a consistent statistical characterizations of original and stego cover.

Optimized nested Markov chain Monte Carlo sampling: theory

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

Coe, Joshua D; Shaw, M Sam; Sewell, Thomas D

2009-01-01

Metropolis Monte Carlo sampling of a reference potential is used to build a Markov chain in the isothermal-isobaric ensemble. At the endpoints of the chain, the energy is reevaluated at a different level of approximation (the 'full' energy) and a composite move encompassing all of the intervening steps is accepted on the basis of a modified Metropolis criterion. By manipulating the thermodynamic variables characterizing the reference system we maximize the average acceptance probability of composite moves, lengthening significantly the random walk made between consecutive evaluations of the full energy at a fixed acceptance probability. This provides maximally decorrelated samples ofmore » the full potential, thereby lowering the total number required to build ensemble averages of a given variance. The efficiency of the method is illustrated using model potentials appropriate to molecular fluids at high pressure. Implications for ab initio or density functional theory (DFT) treatment are discussed.« less

Traces of business cycles in credit-rating migrations

PubMed Central

Boreiko, Dmitri; Kaniovski, Serguei; Pflug, Georg

2017-01-01

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

Traces of business cycles in credit-rating migrations.

PubMed

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

2017-01-01

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

Motion of kinesin in a viscoelastic medium

NASA Astrophysics Data System (ADS)

Knoops, Gert; Vanderzande, Carlo

2018-05-01

Kinesin is a molecular motor that transports cargo along microtubules. The results of many in vitro experiments on kinesin-1 are described by kinetic models in which one transition corresponds to the forward motion and subsequent binding of the tethered motor head. We argue that in a viscoelastic medium like the cytosol of a cell this step is not Markov and has to be described by a nonexponential waiting time distribution. We introduce a semi-Markov kinetic model for kinesin that takes this effect into account. We calculate, for arbitrary waiting time distributions, the moment generating function of the number of steps made, and determine from this the average velocity and the diffusion constant of the motor. We illustrate our results for the case of a waiting time distribution that is Weibull. We find that for realistic parameter values, viscoelasticity decreases the velocity and the diffusion constant, but increases the randomness (or Fano factor).

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

PubMed Central

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

2014-01-01

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

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

PubMed

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

2016-12-28

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

Colonoscopy video quality assessment using hidden Markov random fields

NASA Astrophysics Data System (ADS)

Park, Sun Young; Sargent, Dusty; Spofford, Inbar; Vosburgh, Kirby

2011-03-01

With colonoscopy becoming a common procedure for individuals aged 50 or more who are at risk of developing colorectal cancer (CRC), colon video data is being accumulated at an ever increasing rate. However, the clinically valuable information contained in these videos is not being maximally exploited to improve patient care and accelerate the development of new screening methods. One of the well-known difficulties in colonoscopy video analysis is the abundance of frames with no diagnostic information. Approximately 40% - 50% of the frames in a colonoscopy video are contaminated by noise, acquisition errors, glare, blur, and uneven illumination. Therefore, filtering out low quality frames containing no diagnostic information can significantly improve the efficiency of colonoscopy video analysis. To address this challenge, we present a quality assessment algorithm to detect and remove low quality, uninformative frames. The goal of our algorithm is to discard low quality frames while retaining all diagnostically relevant information. Our algorithm is based on a hidden Markov model (HMM) in combination with two measures of data quality to filter out uninformative frames. Furthermore, we present a two-level framework based on an embedded hidden Markov model (EHHM) to incorporate the proposed quality assessment algorithm into a complete, automated diagnostic image analysis system for colonoscopy video.

Hierarchical probabilistic Gabor and MRF segmentation of brain tumours in MRI volumes.

PubMed

Subbanna, Nagesh K; Precup, Doina; Collins, D Louis; Arbel, Tal

2013-01-01

In this paper, we present a fully automated hierarchical probabilistic framework for segmenting brain tumours from multispectral human brain magnetic resonance images (MRIs) using multiwindow Gabor filters and an adapted Markov Random Field (MRF) framework. In the first stage, a customised Gabor decomposition is developed, based on the combined-space characteristics of the two classes (tumour and non-tumour) in multispectral brain MRIs in order to optimally separate tumour (including edema) from healthy brain tissues. A Bayesian framework then provides a coarse probabilistic texture-based segmentation of tumours (including edema) whose boundaries are then refined at the voxel level through a modified MRF framework that carefully separates the edema from the main tumour. This customised MRF is not only built on the voxel intensities and class labels as in traditional MRFs, but also models the intensity differences between neighbouring voxels in the likelihood model, along with employing a prior based on local tissue class transition probabilities. The second inference stage is shown to resolve local inhomogeneities and impose a smoothing constraint, while also maintaining the appropriate boundaries as supported by the local intensity difference observations. The method was trained and tested on the publicly available MICCAI 2012 Brain Tumour Segmentation Challenge (BRATS) Database [1] on both synthetic and clinical volumes (low grade and high grade tumours). Our method performs well compared to state-of-the-art techniques, outperforming the results of the top methods in cases of clinical high grade and low grade tumour core segmentation by 40% and 45% respectively.

Markov models for fMRI correlation structure: Is brain functional connectivity small world, or decomposable into networks?

PubMed

Varoquaux, G; Gramfort, A; Poline, J B; Thirion, B

2012-01-01

Correlations in the signal observed via functional Magnetic Resonance Imaging (fMRI), are expected to reveal the interactions in the underlying neural populations through hemodynamic response. In particular, they highlight distributed set of mutually correlated regions that correspond to brain networks related to different cognitive functions. Yet graph-theoretical studies of neural connections give a different picture: that of a highly integrated system with small-world properties: local clustering but with short pathways across the complete structure. We examine the conditional independence properties of the fMRI signal, i.e. its Markov structure, to find realistic assumptions on the connectivity structure that are required to explain the observed functional connectivity. In particular we seek a decomposition of the Markov structure into segregated functional networks using decomposable graphs: a set of strongly-connected and partially overlapping cliques. We introduce a new method to efficiently extract such cliques on a large, strongly-connected graph. We compare methods learning different graph structures from functional connectivity by testing the goodness of fit of the model they learn on new data. We find that summarizing the structure as strongly-connected networks can give a good description only for very large and overlapping networks. These results highlight that Markov models are good tools to identify the structure of brain connectivity from fMRI signals, but for this purpose they must reflect the small-world properties of the underlying neural systems. Copyright © 2012 Elsevier Ltd. All rights reserved.

Service-Oriented Node Scheduling Scheme for Wireless Sensor Networks Using Markov Random Field Model

PubMed Central

Cheng, Hongju; Su, Zhihuang; Lloret, Jaime; Chen, Guolong

2014-01-01

Future wireless sensor networks are expected to provide various sensing services and energy efficiency is one of the most important criterions. The node scheduling strategy aims to increase network lifetime by selecting a set of sensor nodes to provide the required sensing services in a periodic manner. In this paper, we are concerned with the service-oriented node scheduling problem to provide multiple sensing services while maximizing the network lifetime. We firstly introduce how to model the data correlation for different services by using Markov Random Field (MRF) model. Secondly, we formulate the service-oriented node scheduling issue into three different problems, namely, the multi-service data denoising problem which aims at minimizing the noise level of sensed data, the representative node selection problem concerning with selecting a number of active nodes while determining the services they provide, and the multi-service node scheduling problem which aims at maximizing the network lifetime. Thirdly, we propose a Multi-service Data Denoising (MDD) algorithm, a novel multi-service Representative node Selection and service Determination (RSD) algorithm, and a novel MRF-based Multi-service Node Scheduling (MMNS) scheme to solve the above three problems respectively. Finally, extensive experiments demonstrate that the proposed scheme efficiently extends the network lifetime. PMID:25384005

Influence of Averaging Preprocessing on Image Analysis with a Markov Random Field Model

NASA Astrophysics Data System (ADS)

Sakamoto, Hirotaka; Nakanishi-Ohno, Yoshinori; Okada, Masato

2018-02-01

This paper describes our investigations into the influence of averaging preprocessing on the performance of image analysis. Averaging preprocessing involves a trade-off: image averaging is often undertaken to reduce noise while the number of image data available for image analysis is decreased. We formulated a process of generating image data by using a Markov random field (MRF) model to achieve image analysis tasks such as image restoration and hyper-parameter estimation by a Bayesian approach. According to the notions of Bayesian inference, posterior distributions were analyzed to evaluate the influence of averaging. There are three main results. First, we found that the performance of image restoration with a predetermined value for hyper-parameters is invariant regardless of whether averaging is conducted. We then found that the performance of hyper-parameter estimation deteriorates due to averaging. Our analysis of the negative logarithm of the posterior probability, which is called the free energy based on an analogy with statistical mechanics, indicated that the confidence of hyper-parameter estimation remains higher without averaging. Finally, we found that when the hyper-parameters are estimated from the data, the performance of image restoration worsens as averaging is undertaken. We conclude that averaging adversely influences the performance of image analysis through hyper-parameter estimation.

Automatic lung tumor segmentation on PET/CT images using fuzzy Markov random field model.

PubMed

Guo, Yu; Feng, Yuanming; Sun, Jian; Zhang, Ning; Lin, Wang; Sa, Yu; Wang, Ping

2014-01-01

The combination of positron emission tomography (PET) and CT images provides complementary functional and anatomical information of human tissues and it has been used for better tumor volume definition of lung cancer. This paper proposed a robust method for automatic lung tumor segmentation on PET/CT images. The new method is based on fuzzy Markov random field (MRF) model. The combination of PET and CT image information is achieved by using a proper joint posterior probability distribution of observed features in the fuzzy MRF model which performs better than the commonly used Gaussian joint distribution. In this study, the PET and CT simulation images of 7 non-small cell lung cancer (NSCLC) patients were used to evaluate the proposed method. Tumor segmentations with the proposed method and manual method by an experienced radiation oncologist on the fused images were performed, respectively. Segmentation results obtained with the two methods were similar and Dice's similarity coefficient (DSC) was 0.85 ± 0.013. It has been shown that effective and automatic segmentations can be achieved with this method for lung tumors which locate near other organs with similar intensities in PET and CT images, such as when the tumors extend into chest wall or mediastinum.

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

PubMed

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

2014-01-01

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

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

PubMed Central

Lu, Yisu; Jiang, Jun; Chen, Wufan

2014-01-01

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

Measuring the volume of brain tumour and determining its location in T2-weighted MRI images using hidden Markov random field: expectation maximization algorithm

NASA Astrophysics Data System (ADS)

Mat Jafri, Mohd. Zubir; Abdulbaqi, Hayder Saad; Mutter, Kussay N.; Mustapha, Iskandar Shahrim; Omar, Ahmad Fairuz

2017-06-01

A brain tumour is an abnormal growth of tissue in the brain. Most tumour volume measurement processes are carried out manually by the radiographer and radiologist without relying on any auto program. This manual method is a timeconsuming task and may give inaccurate results. Treatment, diagnosis, signs and symptoms of the brain tumours mainly depend on the tumour volume and its location. In this paper, an approach is proposed to improve volume measurement of brain tumors as well as using a new method to determine the brain tumour location. The current study presents a hybrid method that includes two methods. One method is hidden Markov random field - expectation maximization (HMRFEM), which employs a positive initial classification of the image. The other method employs the threshold, which enables the final segmentation. In this method, the tumour volume is calculated using voxel dimension measurements. The brain tumour location was determined accurately in T2- weighted MRI image using a new algorithm. According to the results, this process was proven to be more useful compared to the manual method. Thus, it provides the possibility of calculating the volume and determining location of a brain tumour.

Recursive recovery of Markov transition probabilities from boundary value data

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

Patch, Sarah Kathyrn

1994-04-01

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

Phylogenetic mixtures and linear invariants for equal input models.

PubMed

Casanellas, Marta; Steel, Mike

2017-04-01

The reconstruction of phylogenetic trees from molecular sequence data relies on modelling site substitutions by a Markov process, or a mixture of such processes. In general, allowing mixed processes can result in different tree topologies becoming indistinguishable from the data, even for infinitely long sequences. However, when the underlying Markov process supports linear phylogenetic invariants, then provided these are sufficiently informative, the identifiability of the tree topology can be restored. In this paper, we investigate a class of processes that support linear invariants once the stationary distribution is fixed, the 'equal input model'. This model generalizes the 'Felsenstein 1981' model (and thereby the Jukes-Cantor model) from four states to an arbitrary number of states (finite or infinite), and it can also be described by a 'random cluster' process. We describe the structure and dimension of the vector spaces of phylogenetic mixtures and of linear invariants for any fixed phylogenetic tree (and for all trees-the so called 'model invariants'), on any number n of leaves. We also provide a precise description of the space of mixtures and linear invariants for the special case of [Formula: see text] leaves. By combining techniques from discrete random processes and (multi-) linear algebra, our results build on a classic result that was first established by James Lake (Mol Biol Evol 4:167-191, 1987).

Exact distribution of a pattern in a set of random sequences generated by a Markov source: applications to biological data

PubMed Central

2010-01-01

Background In bioinformatics it is common to search for a pattern of interest in a potentially large set of rather short sequences (upstream gene regions, proteins, exons, etc.). Although many methodological approaches allow practitioners to compute the distribution of a pattern count in a random sequence generated by a Markov source, no specific developments have taken into account the counting of occurrences in a set of independent sequences. We aim to address this problem by deriving efficient approaches and algorithms to perform these computations both for low and high complexity patterns in the framework of homogeneous or heterogeneous Markov models. Results The latest advances in the field allowed us to use a technique of optimal Markov chain embedding based on deterministic finite automata to introduce three innovative algorithms. Algorithm 1 is the only one able to deal with heterogeneous models. It also permits to avoid any product of convolution of the pattern distribution in individual sequences. When working with homogeneous models, Algorithm 2 yields a dramatic reduction in the complexity by taking advantage of previous computations to obtain moment generating functions efficiently. In the particular case of low or moderate complexity patterns, Algorithm 3 exploits power computation and binary decomposition to further reduce the time complexity to a logarithmic scale. All these algorithms and their relative interest in comparison with existing ones were then tested and discussed on a toy-example and three biological data sets: structural patterns in protein loop structures, PROSITE signatures in a bacterial proteome, and transcription factors in upstream gene regions. On these data sets, we also compared our exact approaches to the tempting approximation that consists in concatenating the sequences in the data set into a single sequence. Conclusions Our algorithms prove to be effective and able to handle real data sets with multiple sequences, as well as biological patterns of interest, even when the latter display a high complexity (PROSITE signatures for example). In addition, these exact algorithms allow us to avoid the edge effect observed under the single sequence approximation, which leads to erroneous results, especially when the marginal distribution of the model displays a slow convergence toward the stationary distribution. We end up with a discussion on our method and on its potential improvements. PMID:20205909

Exact distribution of a pattern in a set of random sequences generated by a Markov source: applications to biological data.

PubMed

Nuel, Gregory; Regad, Leslie; Martin, Juliette; Camproux, Anne-Claude

2010-01-26

In bioinformatics it is common to search for a pattern of interest in a potentially large set of rather short sequences (upstream gene regions, proteins, exons, etc.). Although many methodological approaches allow practitioners to compute the distribution of a pattern count in a random sequence generated by a Markov source, no specific developments have taken into account the counting of occurrences in a set of independent sequences. We aim to address this problem by deriving efficient approaches and algorithms to perform these computations both for low and high complexity patterns in the framework of homogeneous or heterogeneous Markov models. The latest advances in the field allowed us to use a technique of optimal Markov chain embedding based on deterministic finite automata to introduce three innovative algorithms. Algorithm 1 is the only one able to deal with heterogeneous models. It also permits to avoid any product of convolution of the pattern distribution in individual sequences. When working with homogeneous models, Algorithm 2 yields a dramatic reduction in the complexity by taking advantage of previous computations to obtain moment generating functions efficiently. In the particular case of low or moderate complexity patterns, Algorithm 3 exploits power computation and binary decomposition to further reduce the time complexity to a logarithmic scale. All these algorithms and their relative interest in comparison with existing ones were then tested and discussed on a toy-example and three biological data sets: structural patterns in protein loop structures, PROSITE signatures in a bacterial proteome, and transcription factors in upstream gene regions. On these data sets, we also compared our exact approaches to the tempting approximation that consists in concatenating the sequences in the data set into a single sequence. Our algorithms prove to be effective and able to handle real data sets with multiple sequences, as well as biological patterns of interest, even when the latter display a high complexity (PROSITE signatures for example). In addition, these exact algorithms allow us to avoid the edge effect observed under the single sequence approximation, which leads to erroneous results, especially when the marginal distribution of the model displays a slow convergence toward the stationary distribution. We end up with a discussion on our method and on its potential improvements.

A Hidden Markov Model Approach for Simultaneously Estimating Local Ancestry and Admixture Time Using Next Generation Sequence Data in Samples of Arbitrary Ploidy

PubMed Central

Nielsen, Rasmus

2017-01-01

Admixture—the mixing of genomes from divergent populations—is increasingly appreciated as a central process in evolution. To characterize and quantify patterns of admixture across the genome, a number of methods have been developed for local ancestry inference. However, existing approaches have a number of shortcomings. First, all local ancestry inference methods require some prior assumption about the expected ancestry tract lengths. Second, existing methods generally require genotypes, which is not feasible to obtain for many next-generation sequencing projects. Third, many methods assume samples are diploid, however a wide variety of sequencing applications will fail to meet this assumption. To address these issues, we introduce a novel hidden Markov model for estimating local ancestry that models the read pileup data, rather than genotypes, is generalized to arbitrary ploidy, and can estimate the time since admixture during local ancestry inference. We demonstrate that our method can simultaneously estimate the time since admixture and local ancestry with good accuracy, and that it performs well on samples of high ploidy—i.e. 100 or more chromosomes. As this method is very general, we expect it will be useful for local ancestry inference in a wider variety of populations than what previously has been possible. We then applied our method to pooled sequencing data derived from populations of Drosophila melanogaster on an ancestry cline on the east coast of North America. We find that regions of local recombination rates are negatively correlated with the proportion of African ancestry, suggesting that selection against foreign ancestry is the least efficient in low recombination regions. Finally we show that clinal outlier loci are enriched for genes associated with gene regulatory functions, consistent with a role of regulatory evolution in ecological adaptation of admixed D. melanogaster populations. Our results illustrate the potential of local ancestry inference for elucidating fundamental evolutionary processes. PMID:28045893

Cost-effectiveness of Stereotactic Body Radiation Therapy versus Radiofrequency Ablation for Hepatocellular Carcinoma: A Markov Modeling Study.

PubMed

Pollom, Erqi L; Lee, Kyueun; Durkee, Ben Y; Grade, Madeline; Mokhtari, Daniel A; Wahl, Daniel R; Feng, Mary; Kothary, Nishita; Koong, Albert C; Owens, Douglas K; Goldhaber-Fiebert, Jeremy; Chang, Daniel T

2017-05-01

Purpose To assess the cost-effectiveness of stereotactic body radiation therapy (SBRT) versus radiofrequency ablation (RFA) for patients with inoperable localized hepatocellular carcinoma (HCC) who are eligible for both SBRT and RFA. Materials and Methods A decision-analytic Markov model was developed for patients with inoperable, localized HCC who were eligible for both RFA and SBRT to evaluate the cost-effectiveness of the following treatment strategies: (a) SBRT as initial treatment followed by SBRT for local progression (SBRT-SBRT), (b) RFA followed by RFA for local progression (RFA-RFA), (c) SBRT followed by RFA for local progression (SBRT-RFA), and (d) RFA followed by SBRT for local progression (RFA-SBRT). Probabilities of disease progression, treatment characteristics, and mortality were derived from published studies. Outcomes included health benefits expressed as discounted quality-adjusted life years (QALYs), costs in U.S. dollars, and cost-effectiveness expressed as an incremental cost-effectiveness ratio. Deterministic and probabilistic sensitivity analysis was performed to assess the robustness of the findings. Results In the base case, SBRT-SBRT yielded the most QALYs (1.565) and cost $197 557. RFA-SBRT yielded 1.558 QALYs and cost $193 288. SBRT-SBRT was not cost-effective, at $558 679 per QALY gained relative to RFA-SBRT. RFA-SBRT was the preferred strategy, because RFA-RFA and SBRT-RFA were less effective and more costly. In all evaluated scenarios, SBRT was preferred as salvage therapy for local progression after RFA. Probabilistic sensitivity analysis showed that at a willingness-to-pay threshold of $100 000 per QALY gained, RFA-SBRT was preferred in 65.8% of simulations. Conclusion SBRT for initial treatment of localized, inoperable HCC is not cost-effective. However, SBRT is the preferred salvage therapy for local progression after RFA. © RSNA, 2017 Online supplemental material is available for this article.

Cost-effectiveness of Stereotactic Body Radiation Therapy versus Radiofrequency Ablation for Hepatocellular Carcinoma: A Markov Modeling Study

PubMed Central

Lee, Kyueun; Durkee, Ben Y.; Grade, Madeline; Mokhtari, Daniel A.; Wahl, Daniel R.; Feng, Mary; Kothary, Nishita; Koong, Albert C.; Owens, Douglas K.; Goldhaber-Fiebert, Jeremy; Chang, Daniel T.

2017-01-01

Purpose To assess the cost-effectiveness of stereotactic body radiation therapy (SBRT) versus radiofrequency ablation (RFA) for patients with inoperable localized hepatocellular carcinoma (HCC) who are eligible for both SBRT and RFA. Materials and Methods A decision-analytic Markov model was developed for patients with inoperable, localized HCC who were eligible for both RFA and SBRT to evaluate the cost-effectiveness of the following treatment strategies: (a) SBRT as initial treatment followed by SBRT for local progression (SBRT-SBRT), (b) RFA followed by RFA for local progression (RFA-RFA), (c) SBRT followed by RFA for local progression (SBRT-RFA), and (d) RFA followed by SBRT for local progression (RFA-SBRT). Probabilities of disease progression, treatment characteristics, and mortality were derived from published studies. Outcomes included health benefits expressed as discounted quality-adjusted life years (QALYs), costs in U.S. dollars, and cost-effectiveness expressed as an incremental cost-effectiveness ratio. Deterministic and probabilistic sensitivity analysis was performed to assess the robustness of the findings. Results In the base case, SBRT-SBRT yielded the most QALYs (1.565) and cost $197 557. RFA-SBRT yielded 1.558 QALYs and cost $193 288. SBRT-SBRT was not cost-effective, at $558 679 per QALY gained relative to RFA-SBRT. RFA-SBRT was the preferred strategy, because RFA-RFA and SBRT-RFA were less effective and more costly. In all evaluated scenarios, SBRT was preferred as salvage therapy for local progression after RFA. Probabilistic sensitivity analysis showed that at a willingness-to-pay threshold of $100 000 per QALY gained, RFA-SBRT was preferred in 65.8% of simulations. Conclusion SBRT for initial treatment of localized, inoperable HCC is not cost-effective. However, SBRT is the preferred salvage therapy for local progression after RFA. © RSNA, 2017 Online supplemental material is available for this article. PMID:28045603

PTBS segmentation scheme for synthetic aperture radar

NASA Astrophysics Data System (ADS)

Friedland, Noah S.; Rothwell, Brian J.

1995-07-01

The Image Understanding Group at Martin Marietta Technologies in Denver, Colorado has developed a model-based synthetic aperture radar (SAR) automatic target recognition (ATR) system using an integrated resource architecture (IRA). IRA, an adaptive Markov random field (MRF) environment, utilizes information from image, model, and neighborhood resources to create a discrete, 2D feature-based world description (FBWD). The IRA FBWD features are peak, target, background and shadow (PTBS). These features have been shown to be very useful for target discrimination. The FBWD is used to accrue evidence over a model hypothesis set. This paper presents the PTBS segmentation process utilizing two IRA resources. The image resource (IR) provides generic (the physics of image formation) and specific (the given image input) information. The neighborhood resource (NR) provides domain knowledge of localized FBWD site behaviors. A simulated annealing optimization algorithm is used to construct a `most likely' PTBS state. Results on simulated imagery illustrate the power of this technique to correctly segment PTBS features, even when vehicle signatures are immersed in heavy background clutter. These segmentations also suppress sidelobe effects and delineate shadows.

Bayesian spatiotemporal model of fMRI data using transfer functions.

PubMed

Quirós, Alicia; Diez, Raquel Montes; Wilson, Simon P

2010-09-01

This research describes a new Bayesian spatiotemporal model to analyse BOLD fMRI studies. In the temporal dimension, we describe the shape of the hemodynamic response function (HRF) with a transfer function model. The spatial continuity and local homogeneity of the evoked responses are modelled by a Gaussian Markov random field prior on the parameter indicating activations. The proposal constitutes an extension of the spatiotemporal model presented in a previous approach [Quirós, A., Montes Diez, R. and Gamerman, D., 2010. Bayesian spatiotemporal model of fMRI data, Neuroimage, 49: 442-456], offering more flexibility in the estimation of the HRF and computational advantages in the resulting MCMC algorithm. Simulations from the model are performed in order to ascertain the performance of the sampling scheme and the ability of the posterior to estimate model parameters, as well as to check the model sensitivity to signal to noise ratio. Results are shown on synthetic data and on a real data set from a block-design fMRI experiment. Copyright (c) 2010 Elsevier Inc. All rights reserved.

Concurrent Tumor Segmentation and Registration with Uncertainty-based Sparse non-Uniform Graphs

PubMed Central

Parisot, Sarah; Wells, William; Chemouny, Stéphane; Duffau, Hugues; Paragios, Nikos

2014-01-01

In this paper, we present a graph-based concurrent brain tumor segmentation and atlas to diseased patient registration framework. Both segmentation and registration problems are modeled using a unified pairwise discrete Markov Random Field model on a sparse grid superimposed to the image domain. Segmentation is addressed based on pattern classification techniques, while registration is performed by maximizing the similarity between volumes and is modular with respect to the matching criterion. The two problems are coupled by relaxing the registration term in the tumor area, corresponding to areas of high classification score and high dissimilarity between volumes. In order to overcome the main shortcomings of discrete approaches regarding appropriate sampling of the solution space as well as important memory requirements, content driven samplings of the discrete displacement set and the sparse grid are considered, based on the local segmentation and registration uncertainties recovered by the min marginal energies. State of the art results on a substantial low-grade glioma database demonstrate the potential of our method, while our proposed approach shows maintained performance and strongly reduced complexity of the model. PMID:24717540

Active contour-based visual tracking by integrating colors, shapes, and motions.

PubMed

Hu, Weiming; Zhou, Xue; Li, Wei; Luo, Wenhan; Zhang, Xiaoqin; Maybank, Stephen

2013-05-01

In this paper, we present a framework for active contour-based visual tracking using level sets. The main components of our framework include contour-based tracking initialization, color-based contour evolution, adaptive shape-based contour evolution for non-periodic motions, dynamic shape-based contour evolution for periodic motions, and the handling of abrupt motions. For the initialization of contour-based tracking, we develop an optical flow-based algorithm for automatically initializing contours at the first frame. For the color-based contour evolution, Markov random field theory is used to measure correlations between values of neighboring pixels for posterior probability estimation. For adaptive shape-based contour evolution, the global shape information and the local color information are combined to hierarchically evolve the contour, and a flexible shape updating model is constructed. For the dynamic shape-based contour evolution, a shape mode transition matrix is learnt to characterize the temporal correlations of object shapes. For the handling of abrupt motions, particle swarm optimization is adopted to capture the global motion which is applied to the contour in the current frame to produce an initial contour in the next frame.

Probabilistic Cellular Automata

PubMed Central

Agapie, Alexandru; Giuclea, Marius

2014-01-01

Abstract Cellular automata are binary lattices used for modeling complex dynamical systems. The automaton evolves iteratively from one configuration to another, using some local transition rule based on the number of ones in the neighborhood of each cell. With respect to the number of cells allowed to change per iteration, we speak of either synchronous or asynchronous automata. If randomness is involved to some degree in the transition rule, we speak of probabilistic automata, otherwise they are called deterministic. With either type of cellular automaton we are dealing with, the main theoretical challenge stays the same: starting from an arbitrary initial configuration, predict (with highest accuracy) the end configuration. If the automaton is deterministic, the outcome simplifies to one of two configurations, all zeros or all ones. If the automaton is probabilistic, the whole process is modeled by a finite homogeneous Markov chain, and the outcome is the corresponding stationary distribution. Based on our previous results for the asynchronous case—connecting the probability of a configuration in the stationary distribution to its number of zero-one borders—the article offers both numerical and theoretical insight into the long-term behavior of synchronous cellular automata. PMID:24999557

Probabilistic cellular automata.

PubMed

Agapie, Alexandru; Andreica, Anca; Giuclea, Marius

2014-09-01

Cellular automata are binary lattices used for modeling complex dynamical systems. The automaton evolves iteratively from one configuration to another, using some local transition rule based on the number of ones in the neighborhood of each cell. With respect to the number of cells allowed to change per iteration, we speak of either synchronous or asynchronous automata. If randomness is involved to some degree in the transition rule, we speak of probabilistic automata, otherwise they are called deterministic. With either type of cellular automaton we are dealing with, the main theoretical challenge stays the same: starting from an arbitrary initial configuration, predict (with highest accuracy) the end configuration. If the automaton is deterministic, the outcome simplifies to one of two configurations, all zeros or all ones. If the automaton is probabilistic, the whole process is modeled by a finite homogeneous Markov chain, and the outcome is the corresponding stationary distribution. Based on our previous results for the asynchronous case-connecting the probability of a configuration in the stationary distribution to its number of zero-one borders-the article offers both numerical and theoretical insight into the long-term behavior of synchronous cellular automata.

IoT/M2M wearable-based activity-calorie monitoring and analysis for elders.

PubMed

Soraya, Sabrina I; Ting-Hui Chiang; Guo-Jing Chan; Yi-Juan Su; Chih-Wei Yi; Yu-Chee Tseng; Yu-Tai Ching

2017-07-01

With the growth of aging population, elder care service has become an important part of the service industry of Internet of Things. Activity monitoring is one of the most important services in the field of the elderly care service. In this paper, we proposed a wearable solution to provide an activity monitoring service on elders for caregivers. The system uses wireless signals to estimate calorie burned by the walking and localization. In addition, it also uses wireless motion sensors to recognize physical activity, such as drinking and restroom activity. Overall, the system can be divided into four parts: wearable device, gateway, cloud server, and caregiver's android application. The algorithms we proposed for drinking activity are Decision Tree (J48) and Random Forest (RF). While for restroom activity, we proposed supervised Reduced Error Pruning (REP) Tree and Variable Order Hidden Markov Model (VOHMM). We developed a prototype service Android app to provide a life log for the recording of the activity sequence which would be useful for the caregiver to monitor elder activity and its calorie consumption.

Design of robust reliable control for T-S fuzzy Markovian jumping delayed neutral type neural networks with probabilistic actuator faults and leakage delays: An event-triggered communication scheme.

PubMed

Syed Ali, M; Vadivel, R; Saravanakumar, R

2018-06-01

This study examines the problem of robust reliable control for Takagi-Sugeno (T-S) fuzzy Markovian jumping delayed neural networks with probabilistic actuator faults and leakage terms. An event-triggered communication scheme. First, the randomly occurring actuator faults and their failures rates are governed by two sets of unrelated random variables satisfying certain probabilistic failures of every actuator, new type of distribution based event triggered fault model is proposed, which utilize the effect of transmission delay. Second, Takagi-Sugeno (T-S) fuzzy model is adopted for the neural networks and the randomness of actuators failures is modeled in a Markov jump model framework. Third, to guarantee the considered closed-loop system is exponential mean square stable with a prescribed reliable control performance, a Markov jump event-triggered scheme is designed in this paper, which is the main purpose of our study. Fourth, by constructing appropriate Lyapunov-Krasovskii functional, employing Newton-Leibniz formulation and integral inequalities, several delay-dependent criteria for the solvability of the addressed problem are derived. The obtained stability criteria are stated in terms of linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. Finally, numerical examples are given to illustrate the effectiveness and reduced conservatism of the proposed results over the existing ones, among them one example was supported by real-life application of the benchmark problem. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

UAV Swarm Tactics: An Agent-Based Simulation and Markov Process Analysis

DTIC Science & Technology

2013-06-01

CRN Common Random Numbers CSV Comma Separated Values DoE Design of Experiment GLM Generalized Linear Model HVT High Value Target JAR Java ARchive JMF... Java Media Framework JRE Java runtime environment Mason Multi-Agent Simulator Of Networks MOE Measure Of Effectiveness MOP Measures Of Performance...with every set several times, and to write a CSV file with the results. Rather than scripting the agent behavior deterministically, the agents should

A Multidisciplinary Approach to Health Monitoring and Materials Damage Prognosis for Metallic Aerospace Systems

DTIC Science & Technology

2013-03-01

framework of orientation distribution functions and crack-induced texture o Quantify effects of temperature on damage behavior and damage monitoring...measurement model was obtained from hidden Markov modeling (HMM) of joint time-frequency (TF) features extracted from the PZT sensor signals using the...considered PZT sensor signals recorded from a bolted aluminum plate. About only 20% of the samples of a signal were first randomly selected as

Statistical Inference on Memory Structure of Processes and Its Applications to Information Theory

DTIC Science & Technology

2016-05-12

valued times series from a sample. (A practical algorithm to compute the estimator is a work in progress.) Third, finitely-valued spatial processes...ES) U.S. Army Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 mathematical statistics; time series ; Markov chains; random...proved. Second, a statistical method is developed to estimate the memory depth of discrete- time and continuously-valued times series from a sample. (A

Combinatorial Markov Random Fields and Their Applications to Information Organization

DTIC Science & Technology

2008-02-01

titles, part-of- speech tags; • Image processing: images, colors, texture, blobs, interest points, caption words; • Video processing: video signal, audio...McGurk and MacDonald published their pioneering work [80] that revealed the multi-modal nature of speech perception: sound and moving lips compose one... Speech (POS) n-grams (that correspond to the syntactic structure of text). POS n-grams are extracted from sentences in an incremental manner: the first n

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.

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

PubMed Central

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

2016-01-01

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

DM-BLD: differential methylation detection using a hierarchical Bayesian model exploiting local dependency.

PubMed

Wang, Xiao; Gu, Jinghua; Hilakivi-Clarke, Leena; Clarke, Robert; Xuan, Jianhua

2017-01-15

The advent of high-throughput DNA methylation profiling techniques has enabled the possibility of accurate identification of differentially methylated genes for cancer research. The large number of measured loci facilitates whole genome methylation study, yet posing great challenges for differential methylation detection due to the high variability in tumor samples. We have developed a novel probabilistic approach, D: ifferential M: ethylation detection using a hierarchical B: ayesian model exploiting L: ocal D: ependency (DM-BLD), to detect differentially methylated genes based on a Bayesian framework. The DM-BLD approach features a joint model to capture both the local dependency of measured loci and the dependency of methylation change in samples. Specifically, the local dependency is modeled by Leroux conditional autoregressive structure; the dependency of methylation changes is modeled by a discrete Markov random field. A hierarchical Bayesian model is developed to fully take into account the local dependency for differential analysis, in which differential states are embedded as hidden variables. Simulation studies demonstrate that DM-BLD outperforms existing methods for differential methylation detection, particularly when the methylation change is moderate and the variability of methylation in samples is high. DM-BLD has been applied to breast cancer data to identify important methylated genes (such as polycomb target genes and genes involved in transcription factor activity) associated with breast cancer recurrence. A Matlab package of DM-BLD is available at http://www.cbil.ece.vt.edu/software.htm CONTACT: Xuan@vt.eduSupplementary information: Supplementary data are available at Bioinformatics online. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Energy-aware scheduling of surveillance in wireless multimedia sensor networks.

PubMed

Wang, Xue; Wang, Sheng; Ma, Junjie; Sun, Xinyao

2010-01-01

Wireless sensor networks involve a large number of sensor nodes with limited energy supply, which impacts the behavior of their application. In wireless multimedia sensor networks, sensor nodes are equipped with audio and visual information collection modules. Multimedia contents are ubiquitously retrieved in surveillance applications. To solve the energy problems during target surveillance with wireless multimedia sensor networks, an energy-aware sensor scheduling method is proposed in this paper. Sensor nodes which acquire acoustic signals are deployed randomly in the sensing fields. Target localization is based on the signal energy feature provided by multiple sensor nodes, employing particle swarm optimization (PSO). During the target surveillance procedure, sensor nodes are adaptively grouped in a totally distributed manner. Specially, the target motion information is extracted by a forecasting algorithm, which is based on the hidden Markov model (HMM). The forecasting results are utilized to awaken sensor node in the vicinity of future target position. According to the two properties, signal energy feature and residual energy, the sensor nodes decide whether to participate in target detection separately with a fuzzy control approach. Meanwhile, the local routing scheme of data transmission towards the observer is discussed. Experimental results demonstrate the efficiency of energy-aware scheduling of surveillance in wireless multimedia sensor network, where significant energy saving is achieved by the sensor awakening approach and data transmission paths are calculated with low computational complexity.

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

PubMed

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

2016-01-01

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

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

PubMed Central

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

2016-01-01

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

Nonlinear Markov Control Processes and Games

DTIC Science & Technology

2012-11-15

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

Zipf exponent of trajectory distribution in the hidden Markov model

NASA Astrophysics Data System (ADS)

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

2014-03-01

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

Markov blanket-based approach for learning multi-dimensional Bayesian network classifiers: an application to predict the European Quality of Life-5 Dimensions (EQ-5D) from the 39-item Parkinson's Disease Questionnaire (PDQ-39).

PubMed

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. Copyright © 2012 Elsevier Inc. All rights reserved.

Monte Carlo chord length sampling for d-dimensional Markov binary mixtures

NASA Astrophysics Data System (ADS)

Larmier, Coline; Lam, Adam; Brantley, Patrick; Malvagi, Fausto; Palmer, Todd; Zoia, Andrea

2018-01-01

The Chord Length Sampling (CLS) algorithm is a powerful Monte Carlo method that models the effects of stochastic media on particle transport by generating on-the-fly the material interfaces seen by the random walkers during their trajectories. This annealed disorder approach, which formally consists of solving the approximate Levermore-Pomraning equations for linear particle transport, enables a considerable speed-up with respect to transport in quenched disorder, where ensemble-averaging of the Boltzmann equation with respect to all possible realizations is needed. However, CLS intrinsically neglects the correlations induced by the spatial disorder, so that the accuracy of the solutions obtained by using this algorithm must be carefully verified with respect to reference solutions based on quenched disorder realizations. When the disorder is described by Markov mixing statistics, such comparisons have been attempted so far only for one-dimensional geometries, of the rod or slab type. In this work we extend these results to Markov media in two-dimensional (extruded) and three-dimensional geometries, by revisiting the classical set of benchmark configurations originally proposed by Adams, Larsen and Pomraning [1] and extended by Brantley [2]. In particular, we examine the discrepancies between CLS and reference solutions for scalar particle flux and transmission/reflection coefficients as a function of the material properties of the benchmark specifications and of the system dimensionality.

Monte Carlo chord length sampling for d-dimensional Markov binary mixtures

DOE PAGES

Larmier, Coline; Lam, Adam; Brantley, Patrick; ...

2017-09-27

The Chord Length Sampling (CLS) algorithm is a powerful Monte Carlo method that models the effects of stochastic media on particle transport by generating on-the-fly the material interfaces seen by the random walkers during their trajectories. This annealed disorder approach, which formally consists of solving the approximate Levermore–Pomraning equations for linear particle transport, enables a considerable speed-up with respect to transport in quenched disorder, where ensemble-averaging of the Boltzmann equation with respect to all possible realizations is needed. However, CLS intrinsically neglects the correlations induced by the spatial disorder, so that the accuracy of the solutions obtained by using thismore » algorithm must be carefully verified with respect to reference solutions based on quenched disorder realizations. When the disorder is described by Markov mixing statistics, such comparisons have been attempted so far only for one-dimensional geometries, of the rod or slab type. In this work we extend these results to Markov media in two-dimensional (extruded) and three-dimensional geometries, by revisiting the classical set of benchmark configurations originally proposed by Adams, Larsen and Pomraning and extended by Brantley. In particular, we examine the discrepancies between CLS and reference solutions for scalar particle flux and transmission/reflection coefficients as a function of the material properties of the benchmark specifications and of the system dimensionality.« less

Monte Carlo chord length sampling for d-dimensional Markov binary mixtures

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

Larmier, Coline; Lam, Adam; Brantley, Patrick

The Chord Length Sampling (CLS) algorithm is a powerful Monte Carlo method that models the effects of stochastic media on particle transport by generating on-the-fly the material interfaces seen by the random walkers during their trajectories. This annealed disorder approach, which formally consists of solving the approximate Levermore–Pomraning equations for linear particle transport, enables a considerable speed-up with respect to transport in quenched disorder, where ensemble-averaging of the Boltzmann equation with respect to all possible realizations is needed. However, CLS intrinsically neglects the correlations induced by the spatial disorder, so that the accuracy of the solutions obtained by using thismore » algorithm must be carefully verified with respect to reference solutions based on quenched disorder realizations. When the disorder is described by Markov mixing statistics, such comparisons have been attempted so far only for one-dimensional geometries, of the rod or slab type. In this work we extend these results to Markov media in two-dimensional (extruded) and three-dimensional geometries, by revisiting the classical set of benchmark configurations originally proposed by Adams, Larsen and Pomraning and extended by Brantley. In particular, we examine the discrepancies between CLS and reference solutions for scalar particle flux and transmission/reflection coefficients as a function of the material properties of the benchmark specifications and of the system dimensionality.« less

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

NASA Astrophysics Data System (ADS)

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

2005-12-01

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

Nonpoint source solute transport normal to aquifer bedding in heterogeneous, Markov chain random fields

NASA Astrophysics Data System (ADS)

Zhang, Hua; Harter, Thomas; Sivakumar, Bellie

2006-06-01

Facies-based geostatistical models have become important tools for analyzing flow and mass transport processes in heterogeneous aquifers. Yet little is known about the relationship between these latter processes and the parameters of facies-based geostatistical models. In this study, we examine the transport of a nonpoint source solute normal (perpendicular) to the major bedding plane of an alluvial aquifer medium that contains multiple geologic facies, including interconnected, high-conductivity (coarse textured) facies. We also evaluate the dependence of the transport behavior on the parameters of the constitutive facies model. A facies-based Markov chain geostatistical model is used to quantify the spatial variability of the aquifer system's hydrostratigraphy. It is integrated with a groundwater flow model and a random walk particle transport model to estimate the solute traveltime probability density function (pdf) for solute flux from the water table to the bottom boundary (the production horizon) of the aquifer. The cases examined include two-, three-, and four-facies models, with mean length anisotropy ratios for horizontal to vertical facies, ek, from 25:1 to 300:1 and with a wide range of facies volume proportions (e.g., from 5 to 95% coarse-textured facies). Predictions of traveltime pdfs are found to be significantly affected by the number of hydrostratigraphic facies identified in the aquifer. Those predictions of traveltime pdfs also are affected by the proportions of coarse-textured sediments, the mean length of the facies (particularly the ratio of length to thickness of coarse materials), and, to a lesser degree, the juxtapositional preference among the hydrostratigraphic facies. In transport normal to the sedimentary bedding plane, traveltime is not lognormally distributed as is often assumed. Also, macrodispersive behavior (variance of the traveltime) is found not to be a unique function of the conductivity variance. For the parameter range examined, the third moment of the traveltime pdf varies from negatively skewed to strongly positively skewed. We also show that the Markov chain approach may give significantly different traveltime distributions when compared to the more commonly used Gaussian random field approach, even when the first- and second-order moments in the geostatistical distribution of the lnK field are identical. The choice of the appropriate geostatistical model is therefore critical in the assessment of nonpoint source transport, and uncertainty about that choice must be considered in evaluating the results.

Supercomputer optimizations for stochastic optimal control applications

NASA Technical Reports Server (NTRS)

Chung, Siu-Leung; Hanson, Floyd B.; Xu, Huihuang

1991-01-01

Supercomputer optimizations for a computational method of solving stochastic, multibody, dynamic programming problems are presented. The computational method is valid for a general class of optimal control problems that are nonlinear, multibody dynamical systems, perturbed by general Markov noise in continuous time, i.e., nonsmooth Gaussian as well as jump Poisson random white noise. Optimization techniques for vector multiprocessors or vectorizing supercomputers include advanced data structures, loop restructuring, loop collapsing, blocking, and compiler directives. These advanced computing techniques and superconducting hardware help alleviate Bellman's curse of dimensionality in dynamic programming computations, by permitting the solution of large multibody problems. Possible applications include lumped flight dynamics models for uncertain environments, such as large scale and background random aerospace fluctuations.

Accuracy of Reaction Cross Section for Exotic Nuclei in Glauber Model Based on MCMC Diagnostics

NASA Astrophysics Data System (ADS)

Rueter, Keiti; Novikov, Ivan

2017-01-01

Parameters of a nuclear density distribution for an exotic nuclei with halo or skin structures can be determined from the experimentally measured reaction cross-section. In the presented work, to extract parameters such as nuclear size information for a halo and core, we compare experimental data on reaction cross-sections with values obtained using expressions of the Glauber Model. These calculations are performed using a Markov Chain Monte Carlo algorithm. We discuss the accuracy of the Monte Carlo approach and its dependence on k*, the power law turnover point in the discreet power spectrum of the random number sequence and on the lag-1 autocorrelation time of the random number sequence.

Hierarchical Regularization of Polygons for Photogrammetric Point Clouds of Oblique Images

NASA Astrophysics Data System (ADS)

Xie, L.; Hu, H.; Zhu, Q.; Wu, B.; Zhang, Y.

2017-05-01

Despite the success of multi-view stereo (MVS) reconstruction from massive oblique images in city scale, only point clouds and triangulated meshes are available from existing MVS pipelines, which are topologically defect laden, free of semantical information and hard to edit and manipulate interactively in further applications. On the other hand, 2D polygons and polygonal models are still the industrial standard. However, extraction of the 2D polygons from MVS point clouds is still a non-trivial task, given the fact that the boundaries of the detected planes are zigzagged and regularities, such as parallel and orthogonal, cannot preserve. Aiming to solve these issues, this paper proposes a hierarchical polygon regularization method for the photogrammetric point clouds from existing MVS pipelines, which comprises of local and global levels. After boundary points extraction, e.g. using alpha shapes, the local level is used to consolidate the original points, by refining the orientation and position of the points using linear priors. The points are then grouped into local segments by forward searching. In the global level, regularities are enforced through a labeling process, which encourage the segments share the same label and the same label represents segments are parallel or orthogonal. This is formulated as Markov Random Field and solved efficiently. Preliminary results are made with point clouds from aerial oblique images and compared with two classical regularization methods, which have revealed that the proposed method are more powerful in abstracting a single building and is promising for further 3D polygonal model reconstruction and GIS applications.

Exact Markov chain and approximate diffusion solution for haploid genetic drift with one-way mutation.

PubMed

Hössjer, Ola; Tyvand, Peder A; Miloh, Touvia

2016-02-01

The classical Kimura solution of the diffusion equation is investigated for a haploid random mating (Wright-Fisher) model, with one-way mutations and initial-value specified by the founder population. The validity of the transient diffusion solution is checked by exact Markov chain computations, using a Jordan decomposition of the transition matrix. The conclusion is that the one-way diffusion model mostly works well, although the rate of convergence depends on the initial allele frequency and the mutation rate. The diffusion approximation is poor for mutation rates so low that the non-fixation boundary is regular. When this happens we perturb the diffusion solution around the non-fixation boundary and obtain a more accurate approximation that takes quasi-fixation of the mutant allele into account. The main application is to quantify how fast a specific genetic variant of the infinite alleles model is lost. We also discuss extensions of the quasi-fixation approach to other models with small mutation rates. Copyright © 2015 Elsevier Inc. All rights reserved.

Equivalence of Szegedy's and coined quantum walks

NASA Astrophysics Data System (ADS)

Wong, Thomas G.

2017-09-01

Szegedy's quantum walk is a quantization of a classical random walk or Markov chain, where the walk occurs on the edges of the bipartite double cover of the original graph. To search, one can simply quantize a Markov chain with absorbing vertices. Recently, Santos proposed two alternative search algorithms that instead utilize the sign-flip oracle in Grover's algorithm rather than absorbing vertices. In this paper, we show that these two algorithms are exactly equivalent to two algorithms involving coined quantum walks, which are walks on the vertices of the original graph with an internal degree of freedom. The first scheme is equivalent to a coined quantum walk with one walk step per query of Grover's oracle, and the second is equivalent to a coined quantum walk with two walk steps per query of Grover's oracle. These equivalences lie outside the previously known equivalence of Szegedy's quantum walk with absorbing vertices and the coined quantum walk with the negative identity operator as the coin for marked vertices, whose precise relationships we also investigate.

A TWO-STATE MIXED HIDDEN MARKOV MODEL FOR RISKY TEENAGE DRIVING BEHAVIOR

PubMed Central

Jackson, John C.; Albert, Paul S.; Zhang, Zhiwei

2016-01-01

This paper proposes a joint model for longitudinal binary and count outcomes. We apply the model to a unique longitudinal study of teen driving where risky driving behavior and the occurrence of crashes or near crashes are measured prospectively over the first 18 months of licensure. Of scientific interest is relating the two processes and predicting crash and near crash outcomes. We propose a two-state mixed hidden Markov model whereby the hidden state characterizes the mean for the joint longitudinal crash/near crash outcomes and elevated g-force events which are a proxy for risky driving. Heterogeneity is introduced in both the conditional model for the count outcomes and the hidden process using a shared random effect. An estimation procedure is presented using the forward–backward algorithm along with adaptive Gaussian quadrature to perform numerical integration. The estimation procedure readily yields hidden state probabilities as well as providing for a broad class of predictors. PMID:27766124

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

NASA Astrophysics Data System (ADS)

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

2017-05-01

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

Generalized species sampling priors with latent Beta reinforcements

PubMed Central

Airoldi, Edoardo M.; Costa, Thiago; Bassetti, Federico; Leisen, Fabrizio; Guindani, Michele

2014-01-01

Many popular Bayesian nonparametric priors can be characterized in terms of exchangeable species sampling sequences. However, in some applications, exchangeability may not be appropriate. We introduce a novel and probabilistically coherent family of non-exchangeable species sampling sequences characterized by a tractable predictive probability function with weights driven by a sequence of independent Beta random variables. We compare their theoretical clustering properties with those of the Dirichlet Process and the two parameters Poisson-Dirichlet process. The proposed construction provides a complete characterization of the joint process, differently from existing work. We then propose the use of such process as prior distribution in a hierarchical Bayes modeling framework, and we describe a Markov Chain Monte Carlo sampler for posterior inference. We evaluate the performance of the prior and the robustness of the resulting inference in a simulation study, providing a comparison with popular Dirichlet Processes mixtures and Hidden Markov Models. Finally, we develop an application to the detection of chromosomal aberrations in breast cancer by leveraging array CGH data. PMID:25870462

Enhancing speech recognition using improved particle swarm optimization based hidden Markov model.

PubMed

Selvaraj, Lokesh; Ganesan, Balakrishnan

2014-01-01

Enhancing speech recognition is the primary intention of this work. In this paper a novel speech recognition method based on vector quantization and improved particle swarm optimization (IPSO) is suggested. The suggested methodology contains four stages, namely, (i) denoising, (ii) feature mining (iii), vector quantization, and (iv) IPSO based hidden Markov model (HMM) technique (IP-HMM). At first, the speech signals are denoised using median filter. Next, characteristics such as peak, pitch spectrum, Mel frequency Cepstral coefficients (MFCC), mean, standard deviation, and minimum and maximum of the signal are extorted from the denoised signal. Following that, to accomplish the training process, the extracted characteristics are given to genetic algorithm based codebook generation in vector quantization. The initial populations are created by selecting random code vectors from the training set for the codebooks for the genetic algorithm process and IP-HMM helps in doing the recognition. At this point the creativeness will be done in terms of one of the genetic operation crossovers. The proposed speech recognition technique offers 97.14% accuracy.

Track-before-detect labeled multi-bernoulli particle filter with label switching

NASA Astrophysics Data System (ADS)

Garcia-Fernandez, Angel F.

2016-10-01

This paper presents a multitarget tracking particle filter (PF) for general track-before-detect measurement models. The PF is presented in the random finite set framework and uses a labelled multi-Bernoulli approximation. We also present a label switching improvement algorithm based on Markov chain Monte Carlo that is expected to increase filter performance if targets get in close proximity for a sufficiently long time. The PF is tested in two challenging numerical examples.

Application of the quantum spin glass theory to image restoration.

PubMed

Inoue, J I

2001-04-01

Quantum fluctuation is introduced into the Markov random-field model for image restoration in the context of a Bayesian approach. We investigate the dependence of the quantum fluctuation on the quality of a black and white image restoration by making use of statistical mechanics. We find that the maximum posterior marginal (MPM) estimate based on the quantum fluctuation gives a fine restoration in comparison with the maximum a posteriori estimate or the thermal fluctuation based MPM estimate.

Monocular Depth Perception and Robotic Grasping of Novel Objects

DTIC Science & Technology

2009-06-01

resulting algorithm is able to learn monocular vision cues that accurately estimate the relative depths of obstacles in a scene. Reinforcement learning ... learning still make sense in these settings? Since many of the cues that are useful for estimating depth can be re-created in synthetic images, we...supervised learning approach to this problem, and use a Markov Random Field (MRF) to model the scene depth as a function of the image features. We show

Exact Solution of the Markov Propagator for the Voter Model on the Complete Graph

DTIC Science & Technology

2014-07-01

distribution of the random walk. This process can also be applied to other models, incomplete graphs, or to multiple dimensions. An advantage of this...since any multiple of an eigenvector remains an eigenvector. Without any loss, let bk = 1. Now we can ascertain the explicit solution for bj when k < j...this bound is valid for all initial probability distributions. However, without detailed information about the eigenvectors, we cannot extract more

Segmentation of Image Data from Complex Organotypic 3D Models of Cancer Tissues with Markov Random Fields

PubMed Central

Robinson, Sean; Guyon, Laurent; Nevalainen, Jaakko; Toriseva, Mervi

2015-01-01

Organotypic, three dimensional (3D) cell culture models of epithelial tumour types such as prostate cancer recapitulate key aspects of the architecture and histology of solid cancers. Morphometric analysis of multicellular 3D organoids is particularly important when additional components such as the extracellular matrix and tumour microenvironment are included in the model. The complexity of such models has so far limited their successful implementation. There is a great need for automatic, accurate and robust image segmentation tools to facilitate the analysis of such biologically relevant 3D cell culture models. We present a segmentation method based on Markov random fields (MRFs) and illustrate our method using 3D stack image data from an organotypic 3D model of prostate cancer cells co-cultured with cancer-associated fibroblasts (CAFs). The 3D segmentation output suggests that these cell types are in physical contact with each other within the model, which has important implications for tumour biology. Segmentation performance is quantified using ground truth labels and we show how each step of our method increases segmentation accuracy. We provide the ground truth labels along with the image data and code. Using independent image data we show that our segmentation method is also more generally applicable to other types of cellular microscopy and not only limited to fluorescence microscopy. PMID:26630674

Markov random field based automatic image alignment for electron tomography.

PubMed

Amat, Fernando; Moussavi, Farshid; Comolli, Luis R; Elidan, Gal; Downing, Kenneth H; Horowitz, Mark

2008-03-01

We present a method for automatic full-precision alignment of the images in a tomographic tilt series. Full-precision automatic alignment of cryo electron microscopy images has remained a difficult challenge to date, due to the limited electron dose and low image contrast. These facts lead to poor signal to noise ratio (SNR) in the images, which causes automatic feature trackers to generate errors, even with high contrast gold particles as fiducial features. To enable fully automatic alignment for full-precision reconstructions, we frame the problem probabilistically as finding the most likely particle tracks given a set of noisy images, using contextual information to make the solution more robust to the noise in each image. To solve this maximum likelihood problem, we use Markov Random Fields (MRF) to establish the correspondence of features in alignment and robust optimization for projection model estimation. The resulting algorithm, called Robust Alignment and Projection Estimation for Tomographic Reconstruction, or RAPTOR, has not needed any manual intervention for the difficult datasets we have tried, and has provided sub-pixel alignment that is as good as the manual approach by an expert user. We are able to automatically map complete and partial marker trajectories and thus obtain highly accurate image alignment. Our method has been applied to challenging cryo electron tomographic datasets with low SNR from intact bacterial cells, as well as several plastic section and X-ray datasets.

Tropical land use land cover mapping in Pará (Brazil) using discriminative Markov random fields and multi-temporal TerraSAR-X data

NASA Astrophysics Data System (ADS)

Hagensieker, Ron; Roscher, Ribana; Rosentreter, Johannes; Jakimow, Benjamin; Waske, Björn

2017-12-01

Remote sensing satellite data offer the unique possibility to map land use land cover transformations by providing spatially explicit information. However, detection of short-term processes and land use patterns of high spatial-temporal variability is a challenging task. We present a novel framework using multi-temporal TerraSAR-X data and machine learning techniques, namely discriminative Markov random fields with spatio-temporal priors, and import vector machines, in order to advance the mapping of land cover characterized by short-term changes. Our study region covers a current deforestation frontier in the Brazilian state Pará with land cover dominated by primary forests, different types of pasture land and secondary vegetation, and land use dominated by short-term processes such as slash-and-burn activities. The data set comprises multi-temporal TerraSAR-X imagery acquired over the course of the 2014 dry season, as well as optical data (RapidEye, Landsat) for reference. Results show that land use land cover is reliably mapped, resulting in spatially adjusted overall accuracies of up to 79% in a five class setting, yet limitations for the differentiation of different pasture types remain. The proposed method is applicable on multi-temporal data sets, and constitutes a feasible approach to map land use land cover in regions that are affected by high-frequent temporal changes.

Structure-based Markov random field model for representing evolutionary constraints on functional sites.

PubMed

Jeong, Chan-Seok; Kim, Dongsup

2016-02-24

Elucidating the cooperative mechanism of interconnected residues is an important component toward understanding the biological function of a protein. Coevolution analysis has been developed to model the coevolutionary information reflecting structural and functional constraints. Recently, several methods have been developed based on a probabilistic graphical model called the Markov random field (MRF), which have led to significant improvements for coevolution analysis; however, thus far, the performance of these models has mainly been assessed by focusing on the aspect of protein structure. In this study, we built an MRF model whose graphical topology is determined by the residue proximity in the protein structure, and derived a novel positional coevolution estimate utilizing the node weight of the MRF model. This structure-based MRF method was evaluated for three data sets, each of which annotates catalytic site, allosteric site, and comprehensively determined functional site information. We demonstrate that the structure-based MRF architecture can encode the evolutionary information associated with biological function. Furthermore, we show that the node weight can more accurately represent positional coevolution information compared to the edge weight. Lastly, we demonstrate that the structure-based MRF model can be reliably built with only a few aligned sequences in linear time. The results show that adoption of a structure-based architecture could be an acceptable approximation for coevolution modeling with efficient computation complexity.

Segmentation of Image Data from Complex Organotypic 3D Models of Cancer Tissues with Markov Random Fields.

PubMed

Robinson, Sean; Guyon, Laurent; Nevalainen, Jaakko; Toriseva, Mervi; Åkerfelt, Malin; Nees, Matthias

2015-01-01

Organotypic, three dimensional (3D) cell culture models of epithelial tumour types such as prostate cancer recapitulate key aspects of the architecture and histology of solid cancers. Morphometric analysis of multicellular 3D organoids is particularly important when additional components such as the extracellular matrix and tumour microenvironment are included in the model. The complexity of such models has so far limited their successful implementation. There is a great need for automatic, accurate and robust image segmentation tools to facilitate the analysis of such biologically relevant 3D cell culture models. We present a segmentation method based on Markov random fields (MRFs) and illustrate our method using 3D stack image data from an organotypic 3D model of prostate cancer cells co-cultured with cancer-associated fibroblasts (CAFs). The 3D segmentation output suggests that these cell types are in physical contact with each other within the model, which has important implications for tumour biology. Segmentation performance is quantified using ground truth labels and we show how each step of our method increases segmentation accuracy. We provide the ground truth labels along with the image data and code. Using independent image data we show that our segmentation method is also more generally applicable to other types of cellular microscopy and not only limited to fluorescence microscopy.

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.…

Markov chains at the interface of combinatorics, computing, and statistical physics

NASA Astrophysics Data System (ADS)

Streib, Amanda Pascoe

The fields of statistical physics, discrete probability, combinatorics, and theoretical computer science have converged around efforts to understand random structures and algorithms. Recent activity in the interface of these fields has enabled tremendous breakthroughs in each domain and has supplied a new set of techniques for researchers approaching related problems. This thesis makes progress on several problems in this interface whose solutions all build on insights from multiple disciplinary perspectives. First, we consider a dynamic growth process arising in the context of DNA-based self-assembly. The assembly process can be modeled as a simple Markov chain. We prove that the chain is rapidly mixing for large enough bias in regions of Zd. The proof uses a geometric distance function and a variant of path coupling in order to handle distances that can be exponentially large. We also provide the first results in the case of fluctuating bias, where the bias can vary depending on the location of the tile, which arises in the nanotechnology application. Moreover, we use intuition from statistical physics to construct a choice of the biases for which the Markov chain Mmon requires exponential time to converge. Second, we consider a related problem regarding the convergence rate of biased permutations that arises in the context of self-organizing lists. The Markov chain Mnn in this case is a nearest-neighbor chain that allows adjacent transpositions, and the rate of these exchanges is governed by various input parameters. It was conjectured that the chain is always rapidly mixing when the inversion probabilities are positively biased, i.e., we put nearest neighbor pair x < y in order with bias 1/2 ≤ pxy ≤ 1 and out of order with bias 1 - pxy. The Markov chain Mmon was known to have connections to a simplified version of this biased card-shuffling. We provide new connections between Mnn and Mmon by using simple combinatorial bijections, and we prove that Mnn is always rapidly mixing for two general classes of positively biased { pxy}. More significantly, we also prove that the general conjecture is false by exhibiting values for the pxy, with 1/2 ≤ pxy ≤ 1 for all x < y, but for which the transposition chain will require exponential time to converge. Finally, we consider a model of colloids, which are binary mixtures of molecules with one type of molecule suspended in another. It is believed that at low density typical configurations will be well-mixed throughout, while at high density they will separate into clusters. This clustering has proved elusive to verify, since all local sampling algorithms are known to be inefficient at high density, and in fact a new nonlocal algorithm was recently shown to require exponential time in some cases. We characterize the high and low density phases for a general family of discrete interfering binary mixtures by showing that they exhibit a "clustering property" at high density and not at low density. The clustering property states that there will be a region that has very high area, very small perimeter, and high density of one type of molecule. Special cases of interfering binary mixtures include the Ising model at fixed magnetization and independent sets.

Asymptotic inference in system identification for the atom maser.

PubMed

Catana, Catalin; van Horssen, Merlijn; Guta, Madalin

2012-11-28

System identification is closely related to control theory and plays an increasing role in quantum engineering. In the quantum set-up, system identification is usually equated to process tomography, i.e. estimating a channel by probing it repeatedly with different input states. However, for quantum dynamical systems such as quantum Markov processes, it is more natural to consider the estimation based on continuous measurements of the output, with a given input that may be stationary. We address this problem using asymptotic statistics tools, for the specific example of estimating the Rabi frequency of an atom maser. We compute the Fisher information of different measurement processes as well as the quantum Fisher information of the atom maser, and establish the local asymptotic normality of these statistical models. The statistical notions can be expressed in terms of spectral properties of certain deformed Markov generators, and the connection to large deviations is briefly discussed.

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

PubMed Central

Takayasu, Hideki; Takayasu, Misako

2017-01-01

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

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.

Discrete-time Markovian-jump linear quadratic optimal control

NASA Technical Reports Server (NTRS)

Chizeck, H. J.; Willsky, A. S.; Castanon, D.

1986-01-01

This paper is concerned with the optimal control of discrete-time linear systems that possess randomly jumping parameters described by finite-state Markov processes. For problems having quadratic costs and perfect observations, the optimal control laws and expected costs-to-go can be precomputed from a set of coupled Riccati-like matrix difference equations. Necessary and sufficient conditions are derived for the existence of optimal constant control laws which stabilize the controlled system as the time horizon becomes infinite, with finite optimal expected cost.

Effects of Non-Normal Outlier-Prone Error Distribution on Kalman Filter Track

DTIC Science & Technology

1991-09-01

other possibilities exist. For example the GST (Generic Statistical Tracker) uses four motion models [Ref. 41. The GST keeps track of both the target...1.011 + + + 3.113 1.291 4 Although this procedure is not easily statistically interpretable, it was used for the sake of comparison with the other... TRANSITOR TARGET’ WRITE(6,*)’ 3 SECOND ORDER GAUSS MARKOV TARGET’ WRITE(6,*)’ 4 RANDOM TOUR TARGET’ READ(6,*) CHOICE IF((CHOICE.LT.1).OR.(CHOICE.GT.4

A fast Karhunen-Loeve transform for a class of random processes

NASA Technical Reports Server (NTRS)

Jain, A. K.

1976-01-01

It is shown that for a class of finite first-order Markov signals, the Karhunen-Loeve (KL) transform for data compression is a set of periodic sine functions if the boundary values of the signal are fixed or known. These sine functions are shown to be related to the Fourier transform so that a fast Fourier transform algorithm can be used to implement the KL transform. Extension to two dimensions with reference to images with separable contravariance function is shown.

Local neighborhood transition probability estimation and its use in contextual classification

NASA Technical Reports Server (NTRS)

Chittineni, C. B.

1979-01-01

The problem of incorporating spatial or contextual information into classifications is considered. A simple model that describes the spatial dependencies between the neighboring pixels with a single parameter, Theta, is presented. Expressions are derived for updating the posteriori probabilities of the states of nature of the pattern under consideration using information from the neighboring patterns, both for spatially uniform context and for Markov dependencies in terms of Theta. Techniques for obtaining the optimal value of the parameter Theta as a maximum likelihood estimate from the local neighborhood of the pattern under consideration are developed.

The effect of dissipative inhomogeneous medium on the statistics of the wave intensity

NASA Technical Reports Server (NTRS)

Saatchi, Sasan S.

1993-01-01

One of the main theoretical points in the theory of wave propagation in random medium is the derivation of closed form equations to describe the statistics of the propagating waves. In particular, in one dimensional problems, the closed form representation of the multiple scattering effects is important since it contributes in understanding such problems like wave localization, backscattering enhancement, and intensity fluctuations. In this the propagation of plane waves in a layer of one-dimensional dissipative random medium is considered. The medium is modeled by a complex permittivity whose real part is a constant representing the absorption. The one dimensional problem is mathematically equivalent to the analysis of a transmission line with randomly perturbed distributed parameters and a single mode lossy waveguide and the results can be used to study the propagation of radio waves through atmosphere and the remote sensing of geophysical media. It is assumed the scattering medium consists of an ensemble of one-dimensional point scatterers randomly positioned in a layer of thickness L with diffuse boundaries. A Poisson impulse process with density lambda is used to model the position of scatterers in the medium. By employing the Markov properties of this process an exact closed form equation of Kolmogorov-Feller type was obtained for the probability density of the reflection coefficient. This equation was solved by combining two limiting cases: (1) when the density of scatterers is small; and (2) when the medium is weakly dissipative. A two variable perturbation method for small lambda was used to obtain solutions valid for thick layers. These solutions are then asymptotically evaluated for small dissipation. To show the effect of dissipation, the mean and fluctuations of the reflected power are obtained. The results were compared with a lossy homogeneous medium and with a lossless inhomogeneous medium and the regions where the effect of absorption is not essential were discussed.

Markov Dynamics as a Zooming Lens for Multiscale Community Detection: Non Clique-Like Communities and the Field-of-View Limit

PubMed Central

Schaub, Michael T.; Delvenne, Jean-Charles; Yaliraki, Sophia N.; Barahona, Mauricio

2012-01-01

In recent years, there has been a surge of interest in community detection algorithms for complex networks. A variety of computational heuristics, some with a long history, have been proposed for the identification of communities or, alternatively, of good graph partitions. In most cases, the algorithms maximize a particular objective function, thereby finding the ‘right’ split into communities. Although a thorough comparison of algorithms is still lacking, there has been an effort to design benchmarks, i.e., random graph models with known community structure against which algorithms can be evaluated. However, popular community detection methods and benchmarks normally assume an implicit notion of community based on clique-like subgraphs, a form of community structure that is not always characteristic of real networks. Specifically, networks that emerge from geometric constraints can have natural non clique-like substructures with large effective diameters, which can be interpreted as long-range communities. In this work, we show that long-range communities escape detection by popular methods, which are blinded by a restricted ‘field-of-view’ limit, an intrinsic upper scale on the communities they can detect. The field-of-view limit means that long-range communities tend to be overpartitioned. We show how by adopting a dynamical perspective towards community detection [1], [2], in which the evolution of a Markov process on the graph is used as a zooming lens over the structure of the network at all scales, one can detect both clique- or non clique-like communities without imposing an upper scale to the detection. Consequently, the performance of algorithms on inherently low-diameter, clique-like benchmarks may not always be indicative of equally good results in real networks with local, sparser connectivity. We illustrate our ideas with constructive examples and through the analysis of real-world networks from imaging, protein structures and the power grid, where a multiscale structure of non clique-like communities is revealed. PMID:22384178

Uncertainty Quantification of Hypothesis Testing for the Integrated Knowledge Engine

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

Cuellar, Leticia

2012-05-31

The Integrated Knowledge Engine (IKE) is a tool of Bayesian analysis, based on Bayesian Belief Networks or Bayesian networks for short. A Bayesian network is a graphical model (directed acyclic graph) that allows representing the probabilistic structure of many variables assuming a localized type of dependency called the Markov property. The Markov property in this instance makes any node or random variable to be independent of any non-descendant node given information about its parent. A direct consequence of this property is that it is relatively easy to incorporate new evidence and derive the appropriate consequences, which in general is notmore » an easy or feasible task. Typically we use Bayesian networks as predictive models for a small subset of the variables, either the leave nodes or the root nodes. In IKE, since most applications deal with diagnostics, we are interested in predicting the likelihood of the root nodes given new observations on any of the children nodes. The root nodes represent the various possible outcomes of the analysis, and an important problem is to determine when we have gathered enough evidence to lean toward one of these particular outcomes. This document presents criteria to decide when the evidence gathered is sufficient to draw a particular conclusion or decide in favor of a particular outcome by quantifying the uncertainty in the conclusions that are drawn from the data. The material in this document is organized as follows: Section 2 presents briefly a forensics Bayesian network, and we explore evaluating the information provided by new evidence by looking first at the posterior distribution of the nodes of interest, and then at the corresponding posterior odds ratios. Section 3 presents a third alternative: Bayes Factors. In section 4 we finalize by showing the relation between the posterior odds ratios and Bayes factors and showing examples these cases, and in section 5 we conclude by providing clear guidelines of how to use these for the type of Bayesian networks used in IKE.« less

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

NASA Technical Reports Server (NTRS)

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

1988-01-01

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

Concurrent tumor segmentation and registration with uncertainty-based sparse non-uniform graphs.

PubMed

Parisot, Sarah; Wells, William; Chemouny, Stéphane; Duffau, Hugues; Paragios, Nikos

2014-05-01

In this paper, we present a graph-based concurrent brain tumor segmentation and atlas to diseased patient registration framework. Both segmentation and registration problems are modeled using a unified pairwise discrete Markov Random Field model on a sparse grid superimposed to the image domain. Segmentation is addressed based on pattern classification techniques, while registration is performed by maximizing the similarity between volumes and is modular with respect to the matching criterion. The two problems are coupled by relaxing the registration term in the tumor area, corresponding to areas of high classification score and high dissimilarity between volumes. In order to overcome the main shortcomings of discrete approaches regarding appropriate sampling of the solution space as well as important memory requirements, content driven samplings of the discrete displacement set and the sparse grid are considered, based on the local segmentation and registration uncertainties recovered by the min marginal energies. State of the art results on a substantial low-grade glioma database demonstrate the potential of our method, while our proposed approach shows maintained performance and strongly reduced complexity of the model. Copyright © 2014 Elsevier B.V. All rights reserved.

Open Markov Processes and Reaction Networks

ERIC Educational Resources Information Center

Swistock Pollard, Blake Stephen

2017-01-01

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

Stochastic mechanics of reciprocal diffusions

NASA Astrophysics Data System (ADS)

Levy, Bernard C.; Krener, Arthur J.

1996-02-01

The dynamics and kinematics of reciprocal diffusions were examined in a previous paper [J. Math. Phys. 34, 1846 (1993)], where it was shown that reciprocal diffusions admit a chain of conservation laws, which close after the first two laws for two disjoint subclasses of reciprocal diffusions, the Markov and quantum diffusions. For the case of quantum diffusions, the conservation laws are equivalent to Schrödinger's equation. The Markov diffusions were employed by Schrödinger [Sitzungsber. Preuss. Akad. Wiss. Phys. Math Kl. 144 (1931); Ann. Inst. H. Poincaré 2, 269 (1932)], Nelson [Dynamical Theories of Brownian Motion (Princeton University, Princeton, NJ, 1967); Quantum Fluctuations (Princeton University, Princeton, NJ, 1985)], and other researchers to develop stochastic formulations of quantum mechanics, called stochastic mechanics. We propose here an alternative version of stochastic mechanics based on quantum diffusions. A procedure is presented for constructing the quantum diffusion associated to a given wave function. It is shown that quantum diffusions satisfy the uncertainty principle, and have a locality property, whereby given two dynamically uncoupled but statistically correlated particles, the marginal statistics of each particle depend only on the local fields to which the particle is subjected. However, like Wigner's joint probability distribution for the position and momentum of a particle, the finite joint probability densities of quantum diffusions may take negative values.

Stochastic Averaging Principle for Spatial Birth-and-Death Evolutions in the Continuum

NASA Astrophysics Data System (ADS)

Friesen, Martin; Kondratiev, Yuri

2018-06-01

We study a spatial birth-and-death process on the phase space of locally finite configurations Γ^+ × Γ^- over R}^d. Dynamics is described by an non-equilibrium evolution of states obtained from the Fokker-Planck equation and associated with the Markov operator L^+(γ ^-) + 1/ɛ L^-, ɛ > 0. Here L^- describes the environment process on Γ^- and L^+(γ ^-) describes the system process on Γ^+, where γ ^- indicates that the corresponding birth-and-death rates depend on another locally finite configuration γ ^- \\in Γ^-. We prove that, for a certain class of birth-and-death rates, the corresponding Fokker-Planck equation is well-posed, i.e. there exists a unique evolution of states μ _t^{ɛ } on Γ^+ × Γ^-. Moreover, we give a sufficient condition such that the environment is ergodic with exponential rate. Let μ _{inv} be the invariant measure for the environment process on Γ^-. In the main part of this work we establish the stochastic averaging principle, i.e. we prove that the marginal of μ _t^{ɛ } onto Γ^+ converges weakly to an evolution of states on {Γ}^+ associated with the averaged Markov birth-and-death operator {\\overline{L}} = \\int _{Γ}^- L^+(γ ^-)d μ _{inv}(γ ^-).

Stochastic Averaging Principle for Spatial Birth-and-Death Evolutions in the Continuum

NASA Astrophysics Data System (ADS)

Friesen, Martin; Kondratiev, Yuri

2018-04-01

We study a spatial birth-and-death process on the phase space of locally finite configurations Γ^+ × Γ^- over R^d . Dynamics is described by an non-equilibrium evolution of states obtained from the Fokker-Planck equation and associated with the Markov operator L^+(γ ^-) + 1/ɛ L^- , ɛ > 0 . Here L^- describes the environment process on Γ^- and L^+(γ ^-) describes the system process on Γ^+ , where γ ^- indicates that the corresponding birth-and-death rates depend on another locally finite configuration γ ^- \\in Γ^- . We prove that, for a certain class of birth-and-death rates, the corresponding Fokker-Planck equation is well-posed, i.e. there exists a unique evolution of states μ _t^{ɛ } on Γ^+ × Γ^- . Moreover, we give a sufficient condition such that the environment is ergodic with exponential rate. Let μ _{inv} be the invariant measure for the environment process on Γ^- . In the main part of this work we establish the stochastic averaging principle, i.e. we prove that the marginal of μ _t^{ɛ } onto Γ^+ converges weakly to an evolution of states on Γ^+ associated with the averaged Markov birth-and-death operator \\overline{L} = \\int _{Γ}^-}L^+(γ ^-)d μ _{inv}(γ ^-).

Harnessing graphical structure in Markov chain Monte Carlo learning

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

Stolorz, P.E.; Chew P.C.

1996-12-31

The Monte Carlo method is recognized as a useful tool in learning and probabilistic inference methods common to many datamining problems. Generalized Hidden Markov Models and Bayes nets are especially popular applications. However, the presence of multiple modes in many relevant integrands and summands often renders the method slow and cumbersome. Recent mean field alternatives designed to speed things up have been inspired by experience gleaned from physics. The current work adopts an approach very similar to this in spirit, but focusses instead upon dynamic programming notions as a basis for producing systematic Monte Carlo improvements. The idea is tomore » approximate a given model by a dynamic programming-style decomposition, which then forms a scaffold upon which to build successively more accurate Monte Carlo approximations. Dynamic programming ideas alone fail to account for non-local structure, while standard Monte Carlo methods essentially ignore all structure. However, suitably-crafted hybrids can successfully exploit the strengths of each method, resulting in algorithms that combine speed with accuracy. The approach relies on the presence of significant {open_quotes}local{close_quotes} information in the problem at hand. This turns out to be a plausible assumption for many important applications. Example calculations are presented, and the overall strengths and weaknesses of the approach are discussed.« less

Metric Ranking of Invariant Networks with Belief Propagation

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

Tao, Changxia; Ge, Yong; Song, Qinbao

The management of large-scale distributed information systems relies on the effective use and modeling of monitoring data collected at various points in the distributed information systems. A promising approach is to discover invariant relationships among the monitoring data and generate invariant networks, where a node is a monitoring data source (metric) and a link indicates an invariant relationship between two monitoring data. Such an invariant network representation can help system experts to localize and diagnose the system faults by examining those broken invariant relationships and their related metrics, because system faults usually propagate among the monitoring data and eventually leadmore » to some broken invariant relationships. However, at one time, there are usually a lot of broken links (invariant relationships) within an invariant network. Without proper guidance, it is difficult for system experts to manually inspect this large number of broken links. Thus, a critical challenge is how to effectively and efficiently rank metrics (nodes) of invariant networks according to the anomaly levels of metrics. The ranked list of metrics will provide system experts with useful guidance for them to localize and diagnose the system faults. To this end, we propose to model the nodes and the broken links as a Markov Random Field (MRF), and develop an iteration algorithm to infer the anomaly of each node based on belief propagation (BP). Finally, we validate the proposed algorithm on both realworld and synthetic data sets to illustrate its effectiveness.« less

Template-based automatic extraction of the joint space of foot bones from CT scan

NASA Astrophysics Data System (ADS)

Park, Eunbi; Kim, Taeho; Park, Jinah

2016-03-01

Clean bone segmentation is critical in studying the joint anatomy for measuring the spacing between the bones. However, separation of the coupled bones in CT images is sometimes difficult due to ambiguous gray values coming from the noise and the heterogeneity of bone materials as well as narrowing of the joint space. For fine reconstruction of the individual local boundaries, manual operation is a common practice where the segmentation remains to be a bottleneck. In this paper, we present an automatic method for extracting the joint space by applying graph cut on Markov random field model to the region of interest (ROI) which is identified by a template of 3D bone structures. The template includes encoded articular surface which identifies the tight region of the high-intensity bone boundaries together with the fuzzy joint area of interest. The localized shape information from the template model within the ROI effectively separates the bones nearby. By narrowing the ROI down to the region including two types of tissue, the object extraction problem was reduced to binary segmentation and solved via graph cut. Based on the shape of a joint space marked by the template, the hard constraint was set by the initial seeds which were automatically generated from thresholding and morphological operations. The performance and the robustness of the proposed method are evaluated on 12 volumes of ankle CT data, where each volume includes a set of 4 tarsal bones (calcaneus, talus, navicular and cuboid).

Communication: Introducing prescribed biases in out-of-equilibrium Markov models

NASA Astrophysics Data System (ADS)

Dixit, Purushottam D.

2018-03-01

Markov models are often used in modeling complex out-of-equilibrium chemical and biochemical systems. However, many times their predictions do not agree with experiments. We need a systematic framework to update existing Markov models to make them consistent with constraints that are derived from experiments. Here, we present a framework based on the principle of maximum relative path entropy (minimum Kullback-Leibler divergence) to update Markov models using stationary state and dynamical trajectory-based constraints. We illustrate the framework using a biochemical model network of growth factor-based signaling. We also show how to find the closest detailed balanced Markov model to a given Markov model. Further applications and generalizations are discussed.

Landslide Inventory Mapping from Bitemporal 10 m SENTINEL-2 Images Using Change Detection Based Markov Random Field

NASA Astrophysics Data System (ADS)

Qin, Y.; Lu, P.; Li, Z.

2018-04-01

Landslide inventory mapping is essential for hazard assessment and mitigation. In most previous studies, landslide mapping was achieved by visual interpretation of aerial photos and remote sensing images. However, such method is labor-intensive and time-consuming, especially over large areas. Although a number of semi-automatic landslide mapping methods have been proposed over the past few years, limitations remain in terms of their applicability over different study areas and data, and there is large room for improvement in terms of the accuracy and automation degree. For these reasons, we developed a change detection-based Markov Random Field (CDMRF) method for landslide inventory mapping. The proposed method mainly includes two steps: 1) change detection-based multi-threshold for training samples generation and 2) MRF for landslide inventory mapping. Compared with the previous methods, the proposed method in this study has three advantages: 1) it combines multiple image difference techniques with multi-threshold method to generate reliable training samples; 2) it takes the spectral characteristics of landslides into account; and 3) it is highly automatic with little parameter tuning. The proposed method was applied for regional landslides mapping from 10 m Sentinel-2 images in Western China. Results corroborated the effectiveness and applicability of the proposed method especially the capability of rapid landslide mapping. Some directions for future research are offered. This study to our knowledge is the first attempt to map landslides from free and medium resolution satellite (i.e., Sentinel-2) images in China.

Cost-effectiveness of surgical decompression for space-occupying hemispheric infarction.

PubMed

Hofmeijer, Jeannette; van der Worp, H Bart; Kappelle, L Jaap; Eshuis, Sara; Algra, Ale; Greving, Jacoba P

2013-10-01

Surgical decompression reduces mortality and increases the probability of a favorable functional outcome after space-occupying hemispheric infarction. Its cost-effectiveness is uncertain. We assessed clinical outcomes, costs, and cost-effectiveness for the first 3 years in patients who were randomized to surgical decompression or best medical treatment within 48 hours after symptom onset in the Hemicraniectomy After Middle Cerebral Artery Infarction With Life-Threatening Edema Trial (HAMLET). Data on medical consumption were derived from case record files, hospital charts, and general practitioners. We calculated costs per quality-adjusted life year (QALY). Uncertainty was assessed with bootstrapping. A Markov model was constructed to estimate costs and health outcomes after 3 years. Of 39 patients enrolled within 48 hours, 21 were randomized to surgical decompression. After 3 years, 5 surgical (24%) and 14 medical patients (78%) had died. In the first 3 years after enrollment, operated patients had more QALYs than medically treated patients (mean difference, 1.0 QALY [95% confidence interval, 0.6-1.4]), but at higher costs (mean difference, €127,000 [95% confidence interval, 73,100-181,000]), indicating incremental costs of €127,000 per QALY gained. Ninety-eight percent of incremental cost-effectiveness ratios replicated by bootstrapping were >€80,000 per QALY gained. Markov modeling suggested costs of ≈€60,000 per QALY gained for a patient's lifetime. Surgical decompression for space-occupying infarction results in an increase in QALYs, but at very high costs. http://www.controlled-trials.com. Unique identifier: ISRCTN94237756.

Gene expression based mouse brain parcellation using Markov random field regularized non-negative matrix factorization

NASA Astrophysics Data System (ADS)

Pathak, Sayan D.; Haynor, David R.; Thompson, Carol L.; Lein, Ed; Hawrylycz, Michael

2009-02-01

Understanding the geography of genetic expression in the mouse brain has opened previously unexplored avenues in neuroinformatics. The Allen Brain Atlas (www.brain-map.org) (ABA) provides genome-wide colorimetric in situ hybridization (ISH) gene expression images at high spatial resolution, all mapped to a common three-dimensional 200μm3 spatial framework defined by the Allen Reference Atlas (ARA) and is a unique data set for studying expression based structural and functional organization of the brain. The goal of this study was to facilitate an unbiased data-driven structural partitioning of the major structures in the mouse brain. We have developed an algorithm that uses nonnegative matrix factorization (NMF) to perform parts based analysis of ISH gene expression images. The standard NMF approach and its variants are limited in their ability to flexibly integrate prior knowledge, in the context of spatial data. In this paper, we introduce spatial connectivity as an additional regularization in NMF decomposition via the use of Markov Random Fields (mNMF). The mNMF algorithm alternates neighborhood updates with iterations of the standard NMF algorithm to exploit spatial correlations in the data. We present the algorithm and show the sub-divisions of hippocampus and somatosensory-cortex obtained via this approach. The results are compared with established neuroanatomic knowledge. We also highlight novel gene expression based sub divisions of the hippocampus identified by using the mNMF algorithm.

Oriented Markov random field based dendritic spine segmentation for fluorescence microscopy images.

PubMed

Cheng, Jie; Zhou, Xiaobo; Miller, Eric L; Alvarez, Veronica A; Sabatini, Bernardo L; Wong, Stephen T C

2010-10-01

Dendritic spines have been shown to be closely related to various functional properties of the neuron. Usually dendritic spines are manually labeled to analyze their morphological changes, which is very time-consuming and susceptible to operator bias, even with the assistance of computers. To deal with these issues, several methods have been recently proposed to automatically detect and measure the dendritic spines with little human interaction. However, problems such as degraded detection performance for images with larger pixel size (e.g. 0.125 μm/pixel instead of 0.08 μm/pixel) still exist in these methods. Moreover, the shapes of detected spines are also distorted. For example, the "necks" of some spines are missed. Here we present an oriented Markov random field (OMRF) based algorithm which improves spine detection as well as their geometric characterization. We begin with the identification of a region of interest (ROI) containing all the dendrites and spines to be analyzed. For this purpose, we introduce an adaptive procedure for identifying the image background. Next, the OMRF model is discussed within a statistical framework and the segmentation is solved as a maximum a posteriori estimation (MAP) problem, whose optimal solution is found by a knowledge-guided iterative conditional mode (KICM) algorithm. Compared with the existing algorithms, the proposed algorithm not only provides a more accurate representation of the spine shape, but also improves the detection performance by more than 50% with regard to reducing both the misses and false detection.

EMR-based medical knowledge representation and inference via Markov random fields and distributed representation learning.

PubMed

Zhao, Chao; Jiang, Jingchi; Guan, Yi; Guo, Xitong; He, Bin

2018-05-01

Electronic medical records (EMRs) contain medical knowledge that can be used for clinical decision support (CDS). Our objective is to develop a general system that can extract and represent knowledge contained in EMRs to support three CDS tasks-test recommendation, initial diagnosis, and treatment plan recommendation-given the condition of a patient. We extracted four kinds of medical entities from records and constructed an EMR-based medical knowledge network (EMKN), in which nodes are entities and edges reflect their co-occurrence in a record. Three bipartite subgraphs (bigraphs) were extracted from the EMKN, one to support each task. One part of the bigraph was the given condition (e.g., symptoms), and the other was the condition to be inferred (e.g., diseases). Each bigraph was regarded as a Markov random field (MRF) to support the inference. We proposed three graph-based energy functions and three likelihood-based energy functions. Two of these functions are based on knowledge representation learning and can provide distributed representations of medical entities. Two EMR datasets and three metrics were utilized to evaluate the performance. As a whole, the evaluation results indicate that the proposed system outperformed the baseline methods. The distributed representation of medical entities does reflect similarity relationships with respect to knowledge level. Combining EMKN and MRF is an effective approach for general medical knowledge representation and inference. Different tasks, however, require individually designed energy functions. Copyright © 2018 Elsevier B.V. All rights reserved.

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…

Markovian Analysis of the Sequential Behavior of the Spontaneous Spinal Cord Dorsum Potentials Induced by Acute Nociceptive Stimulation in the Anesthetized Cat.

PubMed

Martin, Mario; Béjar, Javier; Esposito, Gennaro; Chávez, Diógenes; Contreras-Hernández, Enrique; Glusman, Silvio; Cortés, Ulises; Rudomín, Pablo

2017-01-01

In a previous study we developed a Machine Learning procedure for the automatic identification and classification of spontaneous cord dorsum potentials ( CDPs ). This study further supported the proposal that in the anesthetized cat, the spontaneous CDPs recorded from different lumbar spinal segments are generated by a distributed network of dorsal horn neurons with structured (non-random) patterns of functional connectivity and that these configurations can be changed to other non-random and stable configurations after the noceptive stimulation produced by the intradermic injection of capsaicin in the anesthetized cat. Here we present a study showing that the sequence of identified forms of the spontaneous CDPs follows a Markov chain of at least order one. That is, the system has memory in the sense that the spontaneous activation of dorsal horn neuronal ensembles producing the CDPs is not independent of the most recent activity. We used this markovian property to build a procedure to identify portions of signals as belonging to a specific functional state of connectivity among the neuronal networks involved in the generation of the CDPs . We have tested this procedure during acute nociceptive stimulation produced by the intradermic injection of capsaicin in intact as well as spinalized preparations. Altogether, our results indicate that CDP sequences cannot be generated by a renewal stochastic process. Moreover, it is possible to describe some functional features of activity in the cord dorsum by modeling the CDP sequences as generated by a Markov order one stochastic process. Finally, these Markov models make possible to determine the functional state which produced a CDP sequence. The proposed identification procedures appear to be useful for the analysis of the sequential behavior of the ongoing CDPs recorded from different spinal segments in response to a variety of experimental procedures including the changes produced by acute nociceptive stimulation. They are envisaged as a useful tool to examine alterations of the patterns of functional connectivity between dorsal horn neurons under normal and different pathological conditions, an issue of potential clinical concern.

Clinical and economic benefit of enzymatic debridement of pressure ulcers compared to autolytic debridement with a hydrogel dressing.

PubMed

Waycaster, Curtis; Milne, Catherine T

2013-07-01

The purpose of this study was to determine the cost-effectiveness of enzymatic debridement using collagenase relative to autolytic debridement with a hydrogel dressing for the treatment of pressure ulcers. A 3-stage Markov model was used to determine the expected costs and outcomes of wound care for collagenase and hydrogel dressings. Outcome data used in the analysis were taken from a randomized clinical trial that directly compared collagenase and hydrogel dressings. The primary outcome in the clinical trial was the proportion of patients achieving a closed epithelialized wound. Transition probabilities for the Markov states were estimated from the clinical trial. A 1-year time horizon was used to determine the expected number of closed wound days and the expected costs for the two alternative debridement therapies. Resource utilization was based on the wound care treatment regimen used in the clinical trial. Resource costs were derived from standard cost references and medical supply wholesalers. The economic perspective taken was that of the long-term care facility. No cost discounting was performed due to the short time horizon of the analysis. A deterministic sensitivity analysis was conducted to analyze economic uncertainty. The number of expected wound days for the collagenase and hydrogel cohorts are estimated at 48 and 147, respectively. The expected direct cost per patient for pressure ulcer care was $2003 for collagenase and $5480 for hydrogel debridement. The number of closed wound days was 1.5-times higher for collagenase (317 vs 218 days) than with the hydrogel. The estimated cost/closed wound day was 4-times higher for the hydrogel ($25) vs collagenase ($6). In this Markov model based on a randomized trial of pressure ulcer care in a long-term care setting collagenase debridement was economically dominant over autolytic debridement, yielding better outcomes at a lower total cost. Since it was a single institution study with a small sample size, the results should be interpreted with caution. Specifically, the findings may not necessarily be generalized to other hydrogel dressings, healthcare settings, age groups, or to wounds of other etiologies.

Continuous-Time Semi-Markov Models in Health Economic Decision Making: An Illustrative Example in Heart Failure Disease Management.

PubMed

Cao, Qi; Buskens, Erik; Feenstra, Talitha; Jaarsma, Tiny; Hillege, Hans; Postmus, Douwe

2016-01-01

Continuous-time state transition models may end up having large unwieldy structures when trying to represent all relevant stages of clinical disease processes by means of a standard Markov model. In such situations, a more parsimonious, and therefore easier-to-grasp, model of a patient's disease progression can often be obtained by assuming that the future state transitions do not depend only on the present state (Markov assumption) but also on the past through time since entry in the present state. Despite that these so-called semi-Markov models are still relatively straightforward to specify and implement, they are not yet routinely applied in health economic evaluation to assess the cost-effectiveness of alternative interventions. To facilitate a better understanding of this type of model among applied health economic analysts, the first part of this article provides a detailed discussion of what the semi-Markov model entails and how such models can be specified in an intuitive way by adopting an approach called vertical modeling. In the second part of the article, we use this approach to construct a semi-Markov model for assessing the long-term cost-effectiveness of 3 disease management programs for heart failure. Compared with a standard Markov model with the same disease states, our proposed semi-Markov model fitted the observed data much better. When subsequently extrapolating beyond the clinical trial period, these relatively large differences in goodness-of-fit translated into almost a doubling in mean total cost and a 60-d decrease in mean survival time when using the Markov model instead of the semi-Markov model. For the disease process considered in our case study, the semi-Markov model thus provided a sensible balance between model parsimoniousness and computational complexity. © The Author(s) 2015.

Finding and testing network communities by lumped Markov chains.

PubMed

Piccardi, Carlo

2011-01-01

Identifying communities (or clusters), namely groups of nodes with comparatively strong internal connectivity, is a fundamental task for deeply understanding the structure and function of a network. Yet, there is a lack of formal criteria for defining communities and for testing their significance. We propose a sharp definition that is based on a quality threshold. By means of a lumped Markov chain model of a random walker, a quality measure called "persistence probability" is associated to a cluster, which is then defined as an "α-community" if such a probability is not smaller than α. Consistently, a partition composed of α-communities is an "α-partition." These definitions turn out to be very effective for finding and testing communities. If a set of candidate partitions is available, setting the desired α-level allows one to immediately select the α-partition with the finest decomposition. Simultaneously, the persistence probabilities quantify the quality of each single community. Given its ability in individually assessing each single cluster, this approach can also disclose single well-defined communities even in networks that overall do not possess a definite clusterized structure.

Hierarchical Bayesian modeling of ionospheric TEC disturbances as non-stationary processes

NASA Astrophysics Data System (ADS)

Seid, Abdu Mohammed; Berhane, Tesfahun; Roininen, Lassi; Nigussie, Melessew

2018-03-01

We model regular and irregular variation of ionospheric total electron content as stationary and non-stationary processes, respectively. We apply the method developed to SCINDA GPS data set observed at Bahir Dar, Ethiopia (11.6 °N, 37.4 °E) . We use hierarchical Bayesian inversion with Gaussian Markov random process priors, and we model the prior parameters in the hyperprior. We use Matérn priors via stochastic partial differential equations, and use scaled Inv -χ2 hyperpriors for the hyperparameters. For drawing posterior estimates, we use Markov Chain Monte Carlo methods: Gibbs sampling and Metropolis-within-Gibbs for parameter and hyperparameter estimations, respectively. This allows us to quantify model parameter estimation uncertainties as well. We demonstrate the applicability of the method proposed using a synthetic test case. Finally, we apply the method to real GPS data set, which we decompose to regular and irregular variation components. The result shows that the approach can be used as an accurate ionospheric disturbance characterization technique that quantifies the total electron content variability with corresponding error uncertainties.

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

NASA Technical Reports Server (NTRS)

Bole, Brian; Goebel, Kai; Vachtsevanos, George

2012-01-01

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

Comparison of RF spectrum prediction methods for dynamic spectrum access

NASA Astrophysics Data System (ADS)

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

2017-05-01

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

Lieb-Robinson bound and locality for general markovian quantum dynamics.

PubMed

Poulin, David

2010-05-14

The Lieb-Robinson bound shows the existence of a maximum speed of signal propagation in discrete quantum mechanical systems with local interactions. This generalizes the concept of relativistic causality beyond field theory, and provides a powerful tool in theoretical condensed matter physics and quantum information science. Here, we extend the scope of this seminal result by considering general markovian quantum evolution, where we prove that an equivalent bound holds. In addition, we use the generalized bound to demonstrate that correlations in the stationary state of a Markov process decay on a length scale set by the Lieb-Robinson velocity and the system's relaxation time.

Random telegraph noise in 2D hexagonal boron nitride dielectric films

NASA Astrophysics Data System (ADS)

Ranjan, A.; Puglisi, F. M.; Raghavan, N.; O'Shea, S. J.; Shubhakar, K.; Pavan, P.; Padovani, A.; Larcher, L.; Pey, K. L.

2018-03-01

This study reports the observation of low frequency random telegraph noise (RTN) in a 2D layered hexagonal boron nitride dielectric film in the pre- and post-soft breakdown phases using conductive atomic force microscopy as a nanoscale spectroscopy tool. The RTN traces of the virgin and electrically stressed dielectric (after percolation breakdown) were compared, and the signal features were statistically analyzed using the Factorial Hidden Markov Model technique. We observe a combination of both two-level and multi-level RTN signals in h-BN, akin to the trends commonly observed for bulk oxides such as SiO2 and HfO2. Experimental evidence suggests frequent occurrence of unstable and anomalous RTN traces in 2D dielectrics which makes extraction of defect energetics challenging.

Derivation of Markov processes that violate detailed balance

NASA Astrophysics Data System (ADS)

Lee, Julian

2018-03-01

Time-reversal symmetry of the microscopic laws dictates that the equilibrium distribution of a stochastic process must obey the condition of detailed balance. However, cyclic Markov processes that do not admit equilibrium distributions with detailed balance are often used to model systems driven out of equilibrium by external agents. I show that for a Markov model without detailed balance, an extended Markov model can be constructed, which explicitly includes the degrees of freedom for the driving agent and satisfies the detailed balance condition. The original cyclic Markov model for the driven system is then recovered as an approximation at early times by summing over the degrees of freedom for the driving agent. I also show that the widely accepted expression for the entropy production in a cyclic Markov model is actually a time derivative of an entropy component in the extended model. Further, I present an analytic expression for the entropy component that is hidden in the cyclic Markov model.

Performance analysis of replication ALOHA for fading mobile communications channels

NASA Technical Reports Server (NTRS)

Yan, Tsun-Yee; Clare, Loren P.

1986-01-01

This paper describes an ALOHA random access protocol for fading communications channels. A two-state Markov model is used for the channel error process to account for the channel fading memory. The ALOHA protocol is modified to send multiple contiguous copies of a message at each transmission attempt. Both pure and slotted ALOHA channels are considered. The analysis is applicable to fading environments where the channel memory is short compared to the propagation delay. It is shown that smaller delay may be achieved using replications and, in noisy conditions, can also improve throughput.

Identifying and correcting non-Markov states in peptide conformational dynamics

NASA Astrophysics Data System (ADS)

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

2010-02-01

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

Fisher information and asymptotic normality in system identification for quantum Markov chains

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

Guta, Madalin

2011-06-15

This paper deals with the problem of estimating the coupling constant {theta} of a mixing quantum Markov chain. For a repeated measurement on the chain's output we show that the outcomes' time average has an asymptotically normal (Gaussian) distribution, and we give the explicit expressions of its mean and variance. In particular, we obtain a simple estimator of {theta} whose classical Fisher information can be optimized over different choices of measured observables. We then show that the quantum state of the output together with the system is itself asymptotically Gaussian and compute its quantum Fisher information, which sets an absolutemore » bound to the estimation error. The classical and quantum Fisher information are compared in a simple example. In the vicinity of {theta}=0 we find that the quantum Fisher information has a quadratic rather than linear scaling in output size, and asymptotically the Fisher information is localized in the system, while the output is independent of the parameter.« less

Monthly streamflow forecasting based on hidden Markov model and Gaussian Mixture Regression

NASA Astrophysics Data System (ADS)

Liu, Yongqi; Ye, Lei; Qin, Hui; Hong, Xiaofeng; Ye, Jiajun; Yin, Xingli

2018-06-01

Reliable streamflow forecasts can be highly valuable for water resources planning and management. In this study, we combined a hidden Markov model (HMM) and Gaussian Mixture Regression (GMR) for probabilistic monthly streamflow forecasting. The HMM is initialized using a kernelized K-medoids clustering method, and the Baum-Welch algorithm is then executed to learn the model parameters. GMR derives a conditional probability distribution for the predictand given covariate information, including the antecedent flow at a local station and two surrounding stations. The performance of HMM-GMR was verified based on the mean square error and continuous ranked probability score skill scores. The reliability of the forecasts was assessed by examining the uniformity of the probability integral transform values. The results show that HMM-GMR obtained reasonably high skill scores and the uncertainty spread was appropriate. Different HMM states were assumed to be different climate conditions, which would lead to different types of observed values. We demonstrated that the HMM-GMR approach can handle multimodal and heteroscedastic data.

Irreversible Markov chains in spin models: Topological excitations

NASA Astrophysics Data System (ADS)

Lei, Ze; Krauth, Werner

2018-01-01

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

Invariant graphs of a family of non-uniformly expanding skew products over Markov maps

NASA Astrophysics Data System (ADS)

Walkden, C. P.; Withers, T.

2018-06-01

We consider a family of skew-products of the form where T is a continuous, expanding, locally eventually onto Markov map and is a family of homeomorphisms of . A function is said to be an invariant graph if is an invariant set for the skew-product; equivalently, u(T(x))  =  g x (u(x)). A well-studied problem is to consider the existence, regularity and dimension-theoretic properties of such functions, usually under strong contraction or expansion conditions (in terms of Lyapunov exponents or partial hyperbolicity) in the fibre direction. Here we consider such problems in a setting where the Lyapunov exponent in the fibre direction is zero on a set of periodic orbits but expands except on a neighbourhood of these periodic orbits. We prove that u either has the structure of a ‘quasi-graph’ (or ‘bony graph’) or is as smooth as the dynamics, and we give a criteria for this to happen.

Modeling carbachol-induced hippocampal network synchronization using hidden Markov models

NASA Astrophysics Data System (ADS)

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

2010-10-01

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

Representing Lumped Markov Chains by Minimal Polynomials over Field GF(q)

NASA Astrophysics Data System (ADS)

Zakharov, V. M.; Shalagin, S. V.; Eminov, B. F.

2018-05-01

A method has been proposed to represent lumped Markov chains by minimal polynomials over a finite field. The accuracy of representing lumped stochastic matrices, the law of lumped Markov chains depends linearly on the minimum degree of polynomials over field GF(q). The method allows constructing the realizations of lumped Markov chains on linear shift registers with a pre-defined “linear complexity”.

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

PubMed

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

2012-01-01

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

Robotic Versus Open Renal Transplantation in Obese Patients: Protocol for a Cost-Benefit Markov Model Analysis

PubMed Central

Puttarajappa, Chethan; Wijkstrom, Martin; Ganoza, Armando; Lopez, Roberto; Tevar, Amit

2018-01-01

Background Recent studies have reported a significant decrease in wound problems and hospital stay in obese patients undergoing renal transplantation by robotic-assisted minimally invasive techniques with no difference in graft function. Objective Due to the lack of cost-benefit studies on the use of robotic-assisted renal transplantation versus open surgical procedure, the primary aim of our study is to develop a Markov model to analyze the cost-benefit of robotic surgery versus open traditional surgery in obese patients in need of a renal transplant. Methods Electronic searches will be conducted to identify studies comparing open renal transplantation versus robotic-assisted renal transplantation. Costs associated with the two surgical techniques will incorporate the expenses of the resources used for the operations. A decision analysis model will be developed to simulate a randomized controlled trial comparing three interventional arms: (1) continuation of renal replacement therapy for patients who are considered non-suitable candidates for renal transplantation due to obesity, (2) transplant recipients undergoing open transplant surgery, and (3) transplant patients undergoing robotic-assisted renal transplantation. TreeAge Pro 2017 R1 TreeAge Software, Williamstown, MA, USA) will be used to create a Markov model and microsimulation will be used to compare costs and benefits for the two competing surgical interventions. Results The model will simulate a randomized controlled trial of adult obese patients affected by end-stage renal disease undergoing renal transplantation. The absorbing state of the model will be patients' death from any cause. By choosing death as the absorbing state, we will be able simulate the population of renal transplant recipients from the day of their randomization to transplant surgery or continuation on renal replacement therapy to their death and perform sensitivity analysis around patients' age at the time of randomization to determine if age is a critical variable for cost-benefit analysis or cost-effectiveness analysis comparing renal replacement therapy, robotic-assisted surgery or open renal transplant surgery. After running the model, one of the three competing strategies will result as the most cost-beneficial or cost-effective under common circumstances. To assess the robustness of the results of the model, a multivariable probabilistic sensitivity analysis will be performed by modifying the mean values and confidence intervals of key parameters with the main intent of assessing if the winning strategy is sensitive to rigorous and plausible variations of those values. Conclusions After running the model, one of the three competing strategies will result as the most cost-beneficial or cost-effective under common circumstances. To assess the robustness of the results of the model, a multivariable probabilistic sensitivity analysis will be performed by modifying the mean values and confidence intervals of key parameters with the main intent of assessing if the winning strategy is sensitive to rigorous and plausible variations of those values. PMID:29519780

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

PubMed

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

2018-01-01

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

Multiple Scattering in Random Mechanical Systems and Diffusion Approximation

NASA Astrophysics Data System (ADS)

Feres, Renato; Ng, Jasmine; Zhang, Hong-Kun

2013-10-01

This paper is concerned with stochastic processes that model multiple (or iterated) scattering in classical mechanical systems of billiard type, defined below. From a given (deterministic) system of billiard type, a random process with transition probabilities operator P is introduced by assuming that some of the dynamical variables are random with prescribed probability distributions. Of particular interest are systems with weak scattering, which are associated to parametric families of operators P h , depending on a geometric or mechanical parameter h, that approaches the identity as h goes to 0. It is shown that ( P h - I)/ h converges for small h to a second order elliptic differential operator on compactly supported functions and that the Markov chain process associated to P h converges to a diffusion with infinitesimal generator . Both P h and are self-adjoint (densely) defined on the space of square-integrable functions over the (lower) half-space in , where η is a stationary measure. This measure's density is either (post-collision) Maxwell-Boltzmann distribution or Knudsen cosine law, and the random processes with infinitesimal generator respectively correspond to what we call MB diffusion and (generalized) Legendre diffusion. Concrete examples of simple mechanical systems are given and illustrated by numerically simulating the random processes.

Cure fraction model with random effects for regional variation in cancer survival.

PubMed

Seppä, Karri; Hakulinen, Timo; Kim, Hyon-Jung; Läärä, Esa

2010-11-30

Assessing regional differences in the survival of cancer patients is important but difficult when separate regions are small or sparsely populated. In this paper, we apply a mixture cure fraction model with random effects to cause-specific survival data of female breast cancer patients collected by the population-based Finnish Cancer Registry. Two sets of random effects were used to capture the regional variation in the cure fraction and in the survival of the non-cured patients, respectively. This hierarchical model was implemented in a Bayesian framework using a Metropolis-within-Gibbs algorithm. To avoid poor mixing of the Markov chain, when the variance of either set of random effects was close to zero, posterior simulations were based on a parameter-expanded model with tailor-made proposal distributions in Metropolis steps. The random effects allowed the fitting of the cure fraction model to the sparse regional data and the estimation of the regional variation in 10-year cause-specific breast cancer survival with a parsimonious number of parameters. Before 1986, the capital of Finland clearly stood out from the rest, but since then all the 21 hospital districts have achieved approximately the same level of survival. Copyright © 2010 John Wiley & Sons, Ltd.

Stochastic dynamics of time correlation in complex systems with discrete time

NASA Astrophysics Data System (ADS)

Yulmetyev, Renat; Hänggi, Peter; Gafarov, Fail

2000-11-01

In this paper we present the concept of description of random processes in complex systems with discrete time. It involves the description of kinetics of discrete processes by means of the chain of finite-difference non-Markov equations for time correlation functions (TCFs). We have introduced the dynamic (time dependent) information Shannon entropy Si(t) where i=0,1,2,3,..., as an information measure of stochastic dynamics of time correlation (i=0) and time memory (i=1,2,3,...). The set of functions Si(t) constitute the quantitative measure of time correlation disorder (i=0) and time memory disorder (i=1,2,3,...) in complex system. The theory developed started from the careful analysis of time correlation involving dynamics of vectors set of various chaotic states. We examine two stochastic processes involving the creation and annihilation of time correlation (or time memory) in details. We carry out the analysis of vectors' dynamics employing finite-difference equations for random variables and the evolution operator describing their natural motion. The existence of TCF results in the construction of the set of projection operators by the usage of scalar product operation. Harnessing the infinite set of orthogonal dynamic random variables on a basis of Gram-Shmidt orthogonalization procedure tends to creation of infinite chain of finite-difference non-Markov kinetic equations for discrete TCFs and memory functions (MFs). The solution of the equations above thereof brings to the recurrence relations between the TCF and MF of senior and junior orders. This offers new opportunities for detecting the frequency spectra of power of entropy function Si(t) for time correlation (i=0) and time memory (i=1,2,3,...). The results obtained offer considerable scope for attack on stochastic dynamics of discrete random processes in a complex systems. Application of this technique on the analysis of stochastic dynamics of RR intervals from human ECG's shows convincing evidence for a non-Markovian phenomemena associated with a peculiarities in short- and long-range scaling. This method may be of use in distinguishing healthy from pathologic data sets based in differences in these non-Markovian properties.

Modeling of dialogue regimes of distance robot control

NASA Astrophysics Data System (ADS)

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

2017-02-01

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

Statistical Analysis of Notational AFL Data Using Continuous Time Markov Chains

PubMed Central

Meyer, Denny; Forbes, Don; Clarke, Stephen R.

2006-01-01

Animal biologists commonly use continuous time Markov chain models to describe patterns of animal behaviour. In this paper we consider the use of these models for describing AFL football. In particular we test the assumptions for continuous time Markov chain models (CTMCs), with time, distance and speed values associated with each transition. Using a simple event categorisation it is found that a semi-Markov chain model is appropriate for this data. This validates the use of Markov Chains for future studies in which the outcomes of AFL matches are simulated. Key Points A comparison of four AFL matches suggests similarity in terms of transition probabilities for events and the mean times, distances and speeds associated with each transition. The Markov assumption appears to be valid. However, the speed, time and distance distributions associated with each transition are not exponential suggesting that semi-Markov model can be used to model and simulate play. Team identified events and directions associated with transitions are required to develop the model into a tool for the prediction of match outcomes. PMID:24357946

Statistical Analysis of Notational AFL Data Using Continuous Time Markov Chains.

PubMed

Meyer, Denny; Forbes, Don; Clarke, Stephen R

2006-01-01

Animal biologists commonly use continuous time Markov chain models to describe patterns of animal behaviour. In this paper we consider the use of these models for describing AFL football. In particular we test the assumptions for continuous time Markov chain models (CTMCs), with time, distance and speed values associated with each transition. Using a simple event categorisation it is found that a semi-Markov chain model is appropriate for this data. This validates the use of Markov Chains for future studies in which the outcomes of AFL matches are simulated. Key PointsA comparison of four AFL matches suggests similarity in terms of transition probabilities for events and the mean times, distances and speeds associated with each transition.The Markov assumption appears to be valid.However, the speed, time and distance distributions associated with each transition are not exponential suggesting that semi-Markov model can be used to model and simulate play.Team identified events and directions associated with transitions are required to develop the model into a tool for the prediction of match outcomes.

Comparative verification between GEM model and official aviation terminal forecasts

NASA Technical Reports Server (NTRS)

Miller, Robert G.

1988-01-01

The Generalized Exponential Markov (GEM) model uses the local standard airways observation (SAO) to predict hour-by-hour the following elements: temperature, pressure, dew point depression, first and second cloud-layer height and amount, ceiling, total cloud amount, visibility, wind, and present weather conditions. GEM is superior to persistence at all projections for all elements in a large independent sample. A minute-by-minute GEM forecasting system utilizing the Automated Weather Observation System (AWOS) is under development.

Improving the Fitness of High-Dimensional Biomechanical Models via Data-Driven Stochastic Exploration

PubMed Central

Bustamante, Carlos D.; Valero-Cuevas, Francisco J.

2010-01-01

The field of complex biomechanical modeling has begun to rely on Monte Carlo techniques to investigate the effects of parameter variability and measurement uncertainty on model outputs, search for optimal parameter combinations, and define model limitations. However, advanced stochastic methods to perform data-driven explorations, such as Markov chain Monte Carlo (MCMC), become necessary as the number of model parameters increases. Here, we demonstrate the feasibility and, what to our knowledge is, the first use of an MCMC approach to improve the fitness of realistically large biomechanical models. We used a Metropolis–Hastings algorithm to search increasingly complex parameter landscapes (3, 8, 24, and 36 dimensions) to uncover underlying distributions of anatomical parameters of a “truth model” of the human thumb on the basis of simulated kinematic data (thumbnail location, orientation, and linear and angular velocities) polluted by zero-mean, uncorrelated multivariate Gaussian “measurement noise.” Driven by these data, ten Markov chains searched each model parameter space for the subspace that best fit the data (posterior distribution). As expected, the convergence time increased, more local minima were found, and marginal distributions broadened as the parameter space complexity increased. In the 36-D scenario, some chains found local minima but the majority of chains converged to the true posterior distribution (confirmed using a cross-validation dataset), thus demonstrating the feasibility and utility of these methods for realistically large biomechanical problems. PMID:19272906

Entanglement dynamics in random media

NASA Astrophysics Data System (ADS)

Menezes, G.; Svaiter, N. F.; Zarro, C. A. D.

2017-12-01

We study how the entanglement dynamics between two-level atoms is impacted by random fluctuations of the light cone. In our model the two-atom system is envisaged as an open system coupled with an electromagnetic field in the vacuum state. We employ the quantum master equation in the Born-Markov approximation in order to describe the completely positive time evolution of the atomic system. We restrict our investigations to the situation in which the atoms are coupled individually to two spatially separated cavities, one of which displays the emergence of light-cone fluctuations. In such a disordered cavity, we assume that the coefficients of the Klein-Gordon equation are random functions of the spatial coordinates. The disordered medium is modeled by a centered, stationary, and Gaussian process. We demonstrate that disorder has the effect of slowing down the entanglement decay. We conjecture that in a strong-disorder environment the mean life of entangled states can be enhanced in such a way as to almost completely suppress quantum nonlocal decoherence.

Optimum random and age replacement policies for customer-demand multi-state system reliability under imperfect maintenance

NASA Astrophysics Data System (ADS)

Chen, Yen-Luan; Chang, Chin-Chih; Sheu, Dwan-Fang

2016-04-01

This paper proposes the generalised random and age replacement policies for a multi-state system composed of multi-state elements. The degradation of the multi-state element is assumed to follow the non-homogeneous continuous time Markov process which is a continuous time and discrete state process. A recursive approach is presented to efficiently compute the time-dependent state probability distribution of the multi-state element. The state and performance distribution of the entire multi-state system is evaluated via the combination of the stochastic process and the Lz-transform method. The concept of customer-centred reliability measure is developed based on the system performance and the customer demand. We develop the random and age replacement policies for an aging multi-state system subject to imperfect maintenance in a failure (or unacceptable) state. For each policy, the optimum replacement schedule which minimises the mean cost rate is derived analytically and discussed numerically.

Two approximations of the present value distribution of a disability annuity

NASA Astrophysics Data System (ADS)

Spreeuw, Jaap

2006-02-01

The distribution function of the present value of a cash flow can be approximated by means of a distribution function of a random variable, which is also the present value of a sequence of payments, but with a simpler structure. The corresponding random variable has the same expectation as the random variable corresponding to the original distribution function and is a stochastic upper bound of convex order. A sharper upper bound can be obtained if more information about the risk is available. In this paper, it will be shown that such an approach can be adopted for disability annuities (also known as income protection policies) in a three state model under Markov assumptions. Benefits are payable during any spell of disability whilst premiums are only due whenever the insured is healthy. The quality of the two approximations is investigated by comparing the distributions obtained with the one derived from the algorithm presented in the paper by Hesselager and Norberg [Insurance Math. Econom. 18 (1996) 35-42].

Regenerative Simulation of Harris Recurrent Markov Chains.

DTIC Science & Technology

1982-07-01

Sutijle) S. TYPE OF REPORT A PERIOD COVERED REGENERATIVE SIMULATION OF HARRIS RECURRENT Technical Report MARKOV CHAINS 14. PERFORMING ORG. REPORT NUMBER...7 AD-Ag 251 STANFORD UNIV CA DEPT OF OPERATIONS RESEARCH /s i2/ REGENERATIVE SIMULATION OF HARRIS RECURRENT MARKOV CHAINS,(U) JUL 82 P W GLYNN N0001...76-C-0578 UNtLASSIFIED TR-62 NL EhhhIhEEEEEEI EEEEEIIIIIII REGENERATIVE SIMULATION OF HARRIS RECURRENT MARKOV CHAINS by Peter W. Glynn TECHNICAL

Generalized expectation-maximization segmentation of brain MR images

NASA Astrophysics Data System (ADS)

Devalkeneer, Arnaud A.; Robe, Pierre A.; Verly, Jacques G.; Phillips, Christophe L. M.

2006-03-01

Manual segmentation of medical images is unpractical because it is time consuming, not reproducible, and prone to human error. It is also very difficult to take into account the 3D nature of the images. Thus, semi- or fully-automatic methods are of great interest. Current segmentation algorithms based on an Expectation- Maximization (EM) procedure present some limitations. The algorithm by Ashburner et al., 2005, does not allow multichannel inputs, e.g. two MR images of different contrast, and does not use spatial constraints between adjacent voxels, e.g. Markov random field (MRF) constraints. The solution of Van Leemput et al., 1999, employs a simplified model (mixture coefficients are not estimated and only one Gaussian is used by tissue class, with three for the image background). We have thus implemented an algorithm that combines the features of these two approaches: multichannel inputs, intensity bias correction, multi-Gaussian histogram model, and Markov random field (MRF) constraints. Our proposed method classifies tissues in three iterative main stages by way of a Generalized-EM (GEM) algorithm: (1) estimation of the Gaussian parameters modeling the histogram of the images, (2) correction of image intensity non-uniformity, and (3) modification of prior classification knowledge by MRF techniques. The goal of the GEM algorithm is to maximize the log-likelihood across the classes and voxels. Our segmentation algorithm was validated on synthetic data (with the Dice metric criterion) and real data (by a neurosurgeon) and compared to the original algorithms by Ashburner et al. and Van Leemput et al. Our combined approach leads to more robust and accurate segmentation.

A Markov random field based approach to the identification of meat and bone meal in feed by near-infrared spectroscopic imaging.

PubMed

Jiang, Xunpeng; Yang, Zengling; Han, Lujia

2014-07-01

Contaminated meat and bone meal (MBM) in animal feedstuff has been the source of bovine spongiform encephalopathy (BSE) disease in cattle, leading to a ban in its use, so methods for its detection are essential. In this study, five pure feed and five pure MBM samples were used to prepare two sets of sample arrangements: set A for investigating the discrimination of individual feed/MBM particles and set B for larger numbers of overlapping particles. The two sets were used to test a Markov random field (MRF)-based approach. A Fourier transform infrared (FT-IR) imaging system was used for data acquisition. The spatial resolution of the near-infrared (NIR) spectroscopic image was 25 μm × 25 μm. Each spectrum was the average of 16 scans across the wavenumber range 7,000-4,000 cm(-1), at intervals of 8 cm(-1). This study introduces an innovative approach to analyzing NIR spectroscopic images: an MRF-based approach has been developed using the iterated conditional mode (ICM) algorithm, integrating initial labeling-derived results from support vector machine discriminant analysis (SVMDA) and observation data derived from the results of principal component analysis (PCA). The results showed that MBM covered by feed could be successfully recognized with an overall accuracy of 86.59% and a Kappa coefficient of 0.68. Compared with conventional methods, the MRF-based approach is capable of extracting spectral information combined with spatial information from NIR spectroscopic images. This new approach enhances the identification of MBM using NIR spectroscopic imaging.

A Hybrid Seismic Inversion Method for V P/V S Ratio and Its Application to Gas Identification

NASA Astrophysics Data System (ADS)

Guo, Qiang; Zhang, Hongbing; Han, Feilong; Xiao, Wei; Shang, Zuoping

2018-03-01

The ratio of compressional wave velocity to shear wave velocity (V P/V S ratio) has established itself as one of the most important parameters in identifying gas reservoirs. However, considering that seismic inversion process is highly non-linear and geological conditions encountered may be complex, a direct estimation of V P/V S ratio from pre-stack seismic data remains a challenging task. In this paper, we propose a hybrid seismic inversion method to estimate V P/V S ratio directly. In this method, post- and pre-stack inversions are combined in which the pre-stack inversion for V P/V S ratio is driven by the post-stack inversion results (i.e., V P and density). In particular, the V P/V S ratio is considered as a model parameter and is directly inverted from the pre-stack inversion based on the exact Zoeppritz equation. Moreover, anisotropic Markov random field is employed in order to regularise the inversion process as well as taking care of geological structures (boundaries) information. Aided by the proposed hybrid inversion strategy, the directional weighting coefficients incorporated in the anisotropic Markov random field neighbourhoods are quantitatively calculated by the anisotropic diffusion method. The synthetic test demonstrates the effectiveness of the proposed inversion method. In particular, given low quality of the pre-stack data and high heterogeneity of the target layers in the field data, the proposed inversion method reveals the detailed model of V P/V S ratio that can successfully identify the gas-bearing zones.

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

NASA Astrophysics Data System (ADS)

Yan, Jihong; Guo, Chaozhong; Wang, Xing

2011-05-01

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

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

PubMed

Lee, Kyung-Eun; Park, Hyun-Seok

2015-01-01

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

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

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

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

2008-10-14

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

Hierarchical Markov blankets and adaptive active inference. Comment on "Answering Schrödinger's question: A free-energy formulation" by Maxwell James Désormeau Ramstead et al.

NASA Astrophysics Data System (ADS)

Kirchhoff, Michael

2018-03-01

Ramstead MJD, Badcock PB, Friston KJ. Answering Schrödinger's question: A free-energy formulation. Phys Life Rev 2018. https://doi.org/10.1016/j.plrev.2017.09.001 [this issue] motivate a multiscale characterisation of living systems in terms of hierarchically structured Markov blankets - a view of living systems as comprised of Markov blankets of Markov blankets [1-4]. It is effectively a treatment of what life is and how it is realised, cast in terms of how Markov blankets of living systems self-organise via active inference - a corollary of the free energy principle [5-7].

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

NASA Technical Reports Server (NTRS)

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

1992-01-01

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

A Perron-Frobenius type of theorem for quantum operations

NASA Astrophysics Data System (ADS)

Lagro, Matthew

Quantum random walks are a generalization of classical Markovian random walks to a quantum mechanical or quantum computing setting. Quantum walks have promising applications but are complicated by quantum decoherence. We prove that the long-time limiting behavior of the class of quantum operations which are the convex combination of norm one operators is governed by the eigenvectors with norm one eigenvalues which are shared by the operators. This class includes all operations formed by a coherent operation with positive probability of orthogonal measurement at each step. We also prove that any operation that has range contained in a low enough dimension subspace of the space of density operators has limiting behavior isomorphic to an associated Markov chain. A particular class of such operations are coherent operations followed by an orthogonal measurement. Applications of the convergence theorems to quantum walks are given.

Gibbs sampling on large lattice with GMRF

NASA Astrophysics Data System (ADS)

Marcotte, Denis; Allard, Denis

2018-02-01

Gibbs sampling is routinely used to sample truncated Gaussian distributions. These distributions naturally occur when associating latent Gaussian fields to category fields obtained by discrete simulation methods like multipoint, sequential indicator simulation and object-based simulation. The latent Gaussians are often used in data assimilation and history matching algorithms. When the Gibbs sampling is applied on a large lattice, the computing cost can become prohibitive. The usual practice of using local neighborhoods is unsatisfying as it can diverge and it does not reproduce exactly the desired covariance. A better approach is to use Gaussian Markov Random Fields (GMRF) which enables to compute the conditional distributions at any point without having to compute and invert the full covariance matrix. As the GMRF is locally defined, it allows simultaneous updating of all points that do not share neighbors (coding sets). We propose a new simultaneous Gibbs updating strategy on coding sets that can be efficiently computed by convolution and applied with an acceptance/rejection method in the truncated case. We study empirically the speed of convergence, the effect of choice of boundary conditions, of the correlation range and of GMRF smoothness. We show that the convergence is slower in the Gaussian case on the torus than for the finite case studied in the literature. However, in the truncated Gaussian case, we show that short scale correlation is quickly restored and the conditioning categories at each lattice point imprint the long scale correlation. Hence our approach enables to realistically apply Gibbs sampling on large 2D or 3D lattice with the desired GMRF covariance.

Conditional adaptive Bayesian spectral analysis of nonstationary biomedical time series.

PubMed

Bruce, Scott A; Hall, Martica H; Buysse, Daniel J; Krafty, Robert T

2018-03-01

Many studies of biomedical time series signals aim to measure the association between frequency-domain properties of time series and clinical and behavioral covariates. However, the time-varying dynamics of these associations are largely ignored due to a lack of methods that can assess the changing nature of the relationship through time. This article introduces a method for the simultaneous and automatic analysis of the association between the time-varying power spectrum and covariates, which we refer to as conditional adaptive Bayesian spectrum analysis (CABS). The procedure adaptively partitions the grid of time and covariate values into an unknown number of approximately stationary blocks and nonparametrically estimates local spectra within blocks through penalized splines. CABS is formulated in a fully Bayesian framework, in which the number and locations of partition points are random, and fit using reversible jump Markov chain Monte Carlo techniques. Estimation and inference averaged over the distribution of partitions allows for the accurate analysis of spectra with both smooth and abrupt changes. The proposed methodology is used to analyze the association between the time-varying spectrum of heart rate variability and self-reported sleep quality in a study of older adults serving as the primary caregiver for their ill spouse. © 2017, The International Biometric Society.

Stochastic control of smart home energy management with plug-in electric vehicle battery energy storage and photovoltaic array

NASA Astrophysics Data System (ADS)

Wu, Xiaohua; Hu, Xiaosong; Moura, Scott; Yin, Xiaofeng; Pickert, Volker

2016-11-01

Energy management strategies are instrumental in the performance and economy of smart homes integrating renewable energy and energy storage. This article focuses on stochastic energy management of a smart home with PEV (plug-in electric vehicle) energy storage and photovoltaic (PV) array. It is motivated by the challenges associated with sustainable energy supplies and the local energy storage opportunity provided by vehicle electrification. This paper seeks to minimize a consumer's energy charges under a time-of-use tariff, while satisfying home power demand and PEV charging requirements, and accommodating the variability of solar power. First, the random-variable models are developed, including Markov Chain model of PEV mobility, as well as predictive models of home power demand and PV power supply. Second, a stochastic optimal control problem is mathematically formulated for managing the power flow among energy sources in the smart home. Finally, based on time-varying electricity price, we systematically examine the performance of the proposed control strategy. As a result, the electric cost is 493.6% less for a Tesla Model S with optimal stochastic dynamic programming (SDP) control relative to the no optimal control case, and it is by 175.89% for a Nissan Leaf.

Weakly supervised visual dictionary learning by harnessing image attributes.

PubMed

Gao, Yue; Ji, Rongrong; Liu, Wei; Dai, Qionghai; Hua, Gang

2014-12-01

Bag-of-features (BoFs) representation has been extensively applied to deal with various computer vision applications. To extract discriminative and descriptive BoF, one important step is to learn a good dictionary to minimize the quantization loss between local features and codewords. While most existing visual dictionary learning approaches are engaged with unsupervised feature quantization, the latest trend has turned to supervised learning by harnessing the semantic labels of images or regions. However, such labels are typically too expensive to acquire, which restricts the scalability of supervised dictionary learning approaches. In this paper, we propose to leverage image attributes to weakly supervise the dictionary learning procedure without requiring any actual labels. As a key contribution, our approach establishes a generative hidden Markov random field (HMRF), which models the quantized codewords as the observed states and the image attributes as the hidden states, respectively. Dictionary learning is then performed by supervised grouping the observed states, where the supervised information is stemmed from the hidden states of the HMRF. In such a way, the proposed dictionary learning approach incorporates the image attributes to learn a semantic-preserving BoF representation without any genuine supervision. Experiments in large-scale image retrieval and classification tasks corroborate that our approach significantly outperforms the state-of-the-art unsupervised dictionary learning approaches.

Mind wandering at the fingertips: automatic parsing of subjective states based on response time variability

PubMed Central

Bastian, Mikaël; Sackur, Jérôme

2013-01-01

Research from the last decade has successfully used two kinds of thought reports in order to assess whether the mind is wandering: random thought-probes and spontaneous reports. However, none of these two methods allows any assessment of the subjective state of the participant between two reports. In this paper, we present a step by step elaboration and testing of a continuous index, based on response time variability within Sustained Attention to Response Tasks (N = 106, for a total of 10 conditions). We first show that increased response time variability predicts mind wandering. We then compute a continuous index of response time variability throughout full experiments and show that the temporal position of a probe relative to the nearest local peak of the continuous index is predictive of mind wandering. This suggests that our index carries information about the subjective state of the subject even when he or she is not probed, and opens the way for on-line tracking of mind wandering. Finally we proceed a step further and infer the internal attentional states on the basis of the variability of response times. To this end we use the Hidden Markov Model framework, which allows us to estimate the durations of on-task and off-task episodes. PMID:24046753

Dense image registration through MRFs and efficient linear programming.

PubMed

Glocker, Ben; Komodakis, Nikos; Tziritas, Georgios; Navab, Nassir; Paragios, Nikos

2008-12-01

In this paper, we introduce a novel and efficient approach to dense image registration, which does not require a derivative of the employed cost function. In such a context, the registration problem is formulated using a discrete Markov random field objective function. First, towards dimensionality reduction on the variables we assume that the dense deformation field can be expressed using a small number of control points (registration grid) and an interpolation strategy. Then, the registration cost is expressed using a discrete sum over image costs (using an arbitrary similarity measure) projected on the control points, and a smoothness term that penalizes local deviations on the deformation field according to a neighborhood system on the grid. Towards a discrete approach, the search space is quantized resulting in a fully discrete model. In order to account for large deformations and produce results on a high resolution level, a multi-scale incremental approach is considered where the optimal solution is iteratively updated. This is done through successive morphings of the source towards the target image. Efficient linear programming using the primal dual principles is considered to recover the lowest potential of the cost function. Very promising results using synthetic data with known deformations and real data demonstrate the potentials of our approach.

LECTURES ON GAME THEORY, MARKOV CHAINS, AND RELATED TOPICS

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

Thompson, G L

1958-03-01

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

Markov chains: computing limit existence and approximations with DNA.

PubMed

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

2005-09-01

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

Machine learning in sentiment reconstruction of the simulated stock market

NASA Astrophysics Data System (ADS)

Goykhman, Mikhail; Teimouri, Ali

2018-02-01

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

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

PubMed

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

2012-10-01

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

On the distribution of interspecies correlation for Markov models of character evolution on Yule trees.

PubMed

Mulder, Willem H; Crawford, Forrest W

2015-01-07

Efforts to reconstruct phylogenetic trees and understand evolutionary processes depend fundamentally on stochastic models of speciation and mutation. The simplest continuous-time model for speciation in phylogenetic trees is the Yule process, in which new species are "born" from existing lineages at a constant rate. Recent work has illuminated some of the structural properties of Yule trees, but it remains mostly unknown how these properties affect sequence and trait patterns observed at the tips of the phylogenetic tree. Understanding the interplay between speciation and mutation under simple models of evolution is essential for deriving valid phylogenetic inference methods and gives insight into the optimal design of phylogenetic studies. In this work, we derive the probability distribution of interspecies covariance under Brownian motion and Ornstein-Uhlenbeck models of phenotypic change on a Yule tree. We compute the probability distribution of the number of mutations shared between two randomly chosen taxa in a Yule tree under discrete Markov mutation models. Our results suggest summary measures of phylogenetic information content, illuminate the correlation between site patterns in sequences or traits of related organisms, and provide heuristics for experimental design and reconstruction of phylogenetic trees. Copyright © 2014 Elsevier Ltd. All rights reserved.

Robust Spectral Unmixing of Sparse Multispectral Lidar Waveforms using Gamma Markov Random Fields

DOE PAGES

Altmann, Yoann; Maccarone, Aurora; McCarthy, Aongus; ...

2017-05-10

Here, this paper presents a new Bayesian spectral un-mixing algorithm to analyse remote scenes sensed via sparse multispectral Lidar measurements. To a first approximation, in the presence of a target, each Lidar waveform consists of a main peak, whose position depends on the target distance and whose amplitude depends on the wavelength of the laser source considered (i.e, on the target reflectivity). Besides, these temporal responses are usually assumed to be corrupted by Poisson noise in the low photon count regime. When considering multiple wavelengths, it becomes possible to use spectral information in order to identify and quantify the mainmore » materials in the scene, in addition to estimation of the Lidar-based range profiles. Due to its anomaly detection capability, the proposed hierarchical Bayesian model, coupled with an efficient Markov chain Monte Carlo algorithm, allows robust estimation of depth images together with abundance and outlier maps associated with the observed 3D scene. The proposed methodology is illustrated via experiments conducted with real multispectral Lidar data acquired in a controlled environment. The results demonstrate the possibility to unmix spectral responses constructed from extremely sparse photon counts (less than 10 photons per pixel and band).« less

Bayesian structural inference for hidden processes.

PubMed

Strelioff, Christopher C; Crutchfield, James P

2014-04-01

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

Bayesian structural inference for hidden processes

NASA Astrophysics Data System (ADS)

Strelioff, Christopher C.; Crutchfield, James P.

2014-04-01

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

Distribution majorization of corner points by reinforcement learning for moving object detection

NASA Astrophysics Data System (ADS)

Wu, Hao; Yu, Hao; Zhou, Dongxiang; Cheng, Yongqiang

2018-04-01

Corner points play an important role in moving object detection, especially in the case of free-moving camera. Corner points provide more accurate information than other pixels and reduce the computation which is unnecessary. Previous works only use intensity information to locate the corner points, however, the information that former and the last frames provided also can be used. We utilize the information to focus on more valuable area and ignore the invaluable area. The proposed algorithm is based on reinforcement learning, which regards the detection of corner points as a Markov process. In the Markov model, the video to be detected is regarded as environment, the selections of blocks for one corner point are regarded as actions and the performance of detection is regarded as state. Corner points are assigned to be the blocks which are seperated from original whole image. Experimentally, we select a conventional method which uses marching and Random Sample Consensus algorithm to obtain objects as the main framework and utilize our algorithm to improve the result. The comparison between the conventional method and the same one with our algorithm show that our algorithm reduce 70% of the false detection.

Performance evaluation of an automatic MGRF-based lung segmentation approach

NASA Astrophysics Data System (ADS)

Soliman, Ahmed; Khalifa, Fahmi; Alansary, Amir; Gimel'farb, Georgy; El-Baz, Ayman

2013-10-01

The segmentation of the lung tissues in chest Computed Tomography (CT) images is an important step for developing any Computer-Aided Diagnostic (CAD) system for lung cancer and other pulmonary diseases. In this paper, we introduce a new framework for validating the accuracy of our developed Joint Markov-Gibbs based lung segmentation approach using 3D realistic synthetic phantoms. These phantoms are created using a 3D Generalized Gauss-Markov Random Field (GGMRF) model of voxel intensities with pairwise interaction to model the 3D appearance of the lung tissues. Then, the appearance of the generated 3D phantoms is simulated based on iterative minimization of an energy function that is based on the learned 3D-GGMRF image model. These 3D realistic phantoms can be used to evaluate the performance of any lung segmentation approach. The performance of our segmentation approach is evaluated using three metrics, namely, the Dice Similarity Coefficient (DSC), the modified Hausdorff distance, and the Average Volume Difference (AVD) between our segmentation and the ground truth. Our approach achieves mean values of 0.994±0.003, 8.844±2.495 mm, and 0.784±0.912 mm3, for the DSC, Hausdorff distance, and the AVD, respectively.

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

PubMed

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

2014-12-01

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

Markov Transition Model to Dementia with Death as a Competing Event

PubMed Central

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

2014-01-01

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

No Magic Bullet: A Theory-Based Meta-Analysis of Markov Transition Probabilities in Studies of Service Systems for Persons With Mental Disabilities.

PubMed

Leff, Hugh Stephen; Chow, Clifton M; Graves, Stephen C

2017-03-01

A random-effects meta-analysis of studies that used Markov transition probabilities (TPs) to describe outcomes for mental health service systems of differing quality for persons with serious mental illness was implemented to improve the scientific understanding of systems performance, to use in planning simulations to project service system costs and outcomes over time, and to test a theory of how outcomes for systems varying in quality differ. Nineteen systems described in 12 studies were coded as basic (B), maintenance (M), and recovery oriented (R) on the basis of descriptions of services provided. TPs for studies were aligned with a common functional-level framework, converted to a one-month time period, synthesized, and compared with theory-based expectations. Meta-regression was employed to explore associations between TPs and characteristics of service recipients and studies. R systems performed better than M and B systems. However, M systems did not perform better than B systems. All systems showed negative as well as positive TPs. For approximately one-third of synthesized TPs, substantial interstudy heterogeneity was noted. Associations were found between TPs and service recipient and study variables Conclusions: Conceptualizing systems as B, M, and R has potential for improving scientific understanding and systems planning. R systems appear more effective than B and M systems, although there is no "magic bullet" system for all service recipients. Interstudy heterogeneity indicates need for common approaches to reporting service recipient states, time periods for TPs, service recipient attributes, and service system characteristics. TPs found should be used in Markov simulations to project system effectiveness and costs of over time.

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

PubMed

Djordjevic, Ivan B

2015-08-24

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

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

PubMed Central

Djordjevic, Ivan B.

2015-01-01

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

Equations for normal-mode statistics of sound scattering by a rough elastic boundary in an underwater waveguide, including backscattering.

PubMed

Morozov, Andrey K; Colosi, John A

2017-09-01

Underwater sound scattering by a rough sea surface, ice, or a rough elastic bottom is studied. The study includes both the scattering from the rough boundary and the elastic effects in the solid layer. A coupled mode matrix is approximated by a linear function of one random perturbation parameter such as the ice-thickness or a perturbation of the surface position. A full two-way coupled mode solution is used to derive the stochastic differential equation for the second order statistics in a Markov approximation.

Mapping of uncertainty relations between continuous and discrete time

NASA Astrophysics Data System (ADS)

Chiuchiú, Davide; Pigolotti, Simone

2018-03-01

Lower bounds on fluctuations of thermodynamic currents depend on the nature of time, discrete or continuous. To understand the physical reason, we compare current fluctuations in discrete-time Markov chains and continuous-time master equations. We prove that current fluctuations in the master equations are always more likely, due to random timings of transitions. This comparison leads to a mapping of the moments of a current between discrete and continuous time. We exploit this mapping to obtain uncertainty bounds. Our results reduce the quests for uncertainty bounds in discrete and continuous time to a single problem.

Mapping of uncertainty relations between continuous and discrete time.

PubMed

Chiuchiù, Davide; Pigolotti, Simone

2018-03-01

Lower bounds on fluctuations of thermodynamic currents depend on the nature of time, discrete or continuous. To understand the physical reason, we compare current fluctuations in discrete-time Markov chains and continuous-time master equations. We prove that current fluctuations in the master equations are always more likely, due to random timings of transitions. This comparison leads to a mapping of the moments of a current between discrete and continuous time. We exploit this mapping to obtain uncertainty bounds. Our results reduce the quests for uncertainty bounds in discrete and continuous time to a single problem.

Leadership, personality and social feedback

PubMed Central

Ang, Tzo Zen; Sweetman, Gemma; Johnstone, Rufus A; Manica, Andrea

2009-01-01

In a recent paper, we showed that leadership arises from individual behavioral differences in pairs of foraging stickleback (Gasterosteus aculeatus). Foraging data from randomly combined pairs of fish were analyzed using Markov Chain models to infer the individual movement rules underlying joint behavior. While both fish responded to partner movement, bolder individuals were the least responsive and showed greater individual initiative. Shy partners were more faithful followers and were also found to bring about greater leadership tendencies in their bold partners. The ability of such followers to inspire bolder fish suggests that leadership may be dependent on individual temperament differences, reinforced by social feedback. PMID:19721883

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

PubMed

Malyshkina, Nataliya V; Mannering, Fred L

2009-07-01

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

The generalization ability of SVM classification based on Markov sampling.

PubMed

Xu, Jie; Tang, Yuan Yan; Zou, Bin; Xu, Zongben; Li, Luoqing; Lu, Yang; Zhang, Baochang

2015-06-01

The previously known works studying the generalization ability of support vector machine classification (SVMC) algorithm are usually based on the assumption of independent and identically distributed samples. In this paper, we go far beyond this classical framework by studying the generalization ability of SVMC based on uniformly ergodic Markov chain (u.e.M.c.) samples. We analyze the excess misclassification error of SVMC based on u.e.M.c. samples, and obtain the optimal learning rate of SVMC for u.e.M.c. We also introduce a new Markov sampling algorithm for SVMC to generate u.e.M.c. samples from given dataset, and present the numerical studies on the learning performance of SVMC based on Markov sampling for benchmark datasets. The numerical studies show that the SVMC based on Markov sampling not only has better generalization ability as the number of training samples are bigger, but also the classifiers based on Markov sampling are sparsity when the size of dataset is bigger with regard to the input dimension.

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

NASA Astrophysics Data System (ADS)

Ye, Jing; Dang, Yaoguo; Li, Bingjun

2018-01-01

Grey-Markov forecasting model is a combination of grey prediction model and Markov chain which show obvious optimization effects for data sequences with characteristics of non-stationary and volatility. However, the state division process in traditional Grey-Markov forecasting model is mostly based on subjective real numbers that immediately affects the accuracy of forecasting values. To seek the solution, this paper introduces the central-point triangular whitenization weight function in state division to calculate possibilities of research values in each state which reflect preference degrees in different states in an objective way. On the other hand, background value optimization is applied in the traditional grey model to generate better fitting data. By this means, the improved Grey-Markov forecasting model is built. Finally, taking the grain production in Henan Province as an example, it verifies this model's validity by comparing with GM(1,1) based on background value optimization and the traditional Grey-Markov forecasting model.

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

PubMed

Dixit, Purushottam D; Dill, Ken A

2018-02-13

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

Phasic Triplet Markov Chains.

PubMed

El Yazid Boudaren, Mohamed; Monfrini, Emmanuel; Pieczynski, Wojciech; Aïssani, Amar

2014-11-01

Hidden Markov chains have been shown to be inadequate for data modeling under some complex conditions. In this work, we address the problem of statistical modeling of phenomena involving two heterogeneous system states. Such phenomena may arise in biology or communications, among other fields. Namely, we consider that a sequence of meaningful words is to be searched within a whole observation that also contains arbitrary one-by-one symbols. Moreover, a word may be interrupted at some site to be carried on later. Applying plain hidden Markov chains to such data, while ignoring their specificity, yields unsatisfactory results. The Phasic triplet Markov chain, proposed in this paper, overcomes this difficulty by means of an auxiliary underlying process in accordance with the triplet Markov chains theory. Related Bayesian restoration techniques and parameters estimation procedures according to the new model are then described. Finally, to assess the performance of the proposed model against the conventional hidden Markov chain model, experiments are conducted on synthetic and real data.

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

PubMed

Galtier, N; Jean-Marie, A

2004-01-01

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

Local Approximation and Hierarchical Methods for Stochastic Optimization

NASA Astrophysics Data System (ADS)

Cheng, Bolong

In this thesis, we present local and hierarchical approximation methods for two classes of stochastic optimization problems: optimal learning and Markov decision processes. For the optimal learning problem class, we introduce a locally linear model with radial basis function for estimating the posterior mean of the unknown objective function. The method uses a compact representation of the function which avoids storing the entire history, as is typically required by nonparametric methods. We derive a knowledge gradient policy with the locally parametric model, which maximizes the expected value of information. We show the policy is asymptotically optimal in theory, and experimental works suggests that the method can reliably find the optimal solution on a range of test functions. For the Markov decision processes problem class, we are motivated by an application where we want to co-optimize a battery for multiple revenue, in particular energy arbitrage and frequency regulation. The nature of this problem requires the battery to make charging and discharging decisions at different time scales while accounting for the stochastic information such as load demand, electricity prices, and regulation signals. Computing the exact optimal policy becomes intractable due to the large state space and the number of time steps. We propose two methods to circumvent the computation bottleneck. First, we propose a nested MDP model that structure the co-optimization problem into smaller sub-problems with reduced state space. This new model allows us to understand how the battery behaves down to the two-second dynamics (that of the frequency regulation market). Second, we introduce a low-rank value function approximation for backward dynamic programming. This new method only requires computing the exact value function for a small subset of the state space and approximate the entire value function via low-rank matrix completion. We test these methods on historical price data from the PJM Interconnect and show that it outperforms the baseline approach used in the industry.

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.

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…

Sampling rare fluctuations of discrete-time Markov chains

NASA Astrophysics Data System (ADS)

Whitelam, Stephen

2018-03-01

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

Sampling rare fluctuations of discrete-time Markov chains.

PubMed

Whitelam, Stephen

2018-03-01

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

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

NASA Astrophysics Data System (ADS)

Jamaluddin, Fadhilah; Rahim, Rahela Abdul

2015-12-01

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

Decentralized learning in Markov games.

PubMed

Vrancx, Peter; Verbeeck, Katja; Nowé, Ann

2008-08-01

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

NonMarkov Ito Processes with 1- state memory

NASA Astrophysics Data System (ADS)

McCauley, Joseph L.

2010-08-01

A Markov process, by definition, cannot depend on any previous state other than the last observed state. An Ito process implies the Fokker-Planck and Kolmogorov backward time partial differential eqns. for transition densities, which in turn imply the Chapman-Kolmogorov eqn., but without requiring the Markov condition. We present a class of Ito process superficially resembling Markov processes, but with 1-state memory. In finance, such processes would obey the efficient market hypothesis up through the level of pair correlations. These stochastic processes have been mislabeled in recent literature as 'nonlinear Markov processes'. Inspired by Doob and Feller, who pointed out that the ChapmanKolmogorov eqn. is not restricted to Markov processes, we exhibit a Gaussian Ito transition density with 1-state memory in the drift coefficient that satisfies both of Kolmogorov's partial differential eqns. and also the Chapman-Kolmogorov eqn. In addition, we show that three of the examples from McKean's seminal 1966 paper are also nonMarkov Ito processes. Last, we show that the transition density of the generalized Black-Scholes type partial differential eqn. describes a martingale, and satisfies the ChapmanKolmogorov eqn. This leads to the shortest-known proof that the Green function of the Black-Scholes eqn. with variable diffusion coefficient provides the so-called martingale measure of option pricing.

Hydrogeophysical Assessment of Aquifer Uncertainty Using Simulated Annealing driven MRF-Based Stochastic Joint Inversion

NASA Astrophysics Data System (ADS)

Oware, E. K.

2017-12-01

Geophysical quantification of hydrogeological parameters typically involve limited noisy measurements coupled with inadequate understanding of the target phenomenon. Hence, a deterministic solution is unrealistic in light of the largely uncertain inputs. Stochastic imaging (SI), in contrast, provides multiple equiprobable realizations that enable probabilistic assessment of aquifer properties in a realistic manner. Generation of geologically realistic prior models is central to SI frameworks. Higher-order statistics for representing prior geological features in SI are, however, usually borrowed from training images (TIs), which may produce undesirable outcomes if the TIs are unpresentatitve of the target structures. The Markov random field (MRF)-based SI strategy provides a data-driven alternative to TI-based SI algorithms. In the MRF-based method, the simulation of spatial features is guided by Gibbs energy (GE) minimization. Local configurations with smaller GEs have higher likelihood of occurrence and vice versa. The parameters of the Gibbs distribution for computing the GE are estimated from the hydrogeophysical data, thereby enabling the generation of site-specific structures in the absence of reliable TIs. In Metropolis-like SI methods, the variance of the transition probability controls the jump-size. The procedure is a standard Markov chain Monte Carlo (McMC) method when a constant variance is assumed, and becomes simulated annealing (SA) when the variance (cooling temperature) is allowed to decrease gradually with time. We observe that in certain problems, the large variance typically employed at the beginning to hasten burn-in may be unideal for sampling at the equilibrium state. The powerfulness of SA stems from its flexibility to adaptively scale the variance at different stages of the sampling. Degeneration of results were reported in a previous implementation of the MRF-based SI strategy based on a constant variance. Here, we present an updated version of the algorithm based on SA that appears to resolve the degeneration problem with seemingly improved results. We illustrate the performance of the SA version with a joint inversion of time-lapse concentration and electrical resistivity measurements in a hypothetical trinary hydrofacies aquifer characterization problem.

Markov-state model for CO2 binding with carbonic anhydrase under confinement

NASA Astrophysics Data System (ADS)

Chen, Gong; Xu, Weina; Lu, Diannan; Wu, Jianzhong; Liu, Zheng

2018-01-01

Enzyme immobilization with a nanostructure material can enhance its stability and facilitate reusability. However, the apparent activity is often compromised due to additional diffusion barriers and complex interactions with the substrates and solvent molecules. The present study elucidates the effects of the surface hydrophobicity of nano-confinement on CO2 diffusion to the active site of human carbonic anhydrase II (CA), an enzyme that is able to catalyze CO2 hydration at extremely high turnover rates. Using the Markov-state model in combination with coarse-grained molecular dynamics simulations, we demonstrate that a hydrophobic cage increases CO2 local density but hinders its diffusion towards the active site of CA under confinement. By contrast, a hydrophilic cage hinders CO2 adsorption but promotes its binding with CA. An optimal surface hydrophobicity can be identified to maximize both the CO2 occupation probability and the diffusion rate. The simulation results offer insight into understanding enzyme performance under nano-confinement and help us to advance broader applications of CA for CO2 absorption and recovery.

A decision aid for intensity-modulated radiation-therapy plan selection in prostate cancer based on a prognostic Bayesian network and a Markov model.

PubMed

Smith, Wade P; Doctor, Jason; Meyer, Jürgen; Kalet, Ira J; Phillips, Mark H

2009-06-01

The prognosis of cancer patients treated with intensity-modulated radiation-therapy (IMRT) is inherently uncertain, depends on many decision variables, and requires that a physician balance competing objectives: maximum tumor control with minimal treatment complications. In order to better deal with the complex and multiple objective nature of the problem we have combined a prognostic probabilistic model with multi-attribute decision theory which incorporates patient preferences for outcomes. The response to IMRT for prostate cancer was modeled. A Bayesian network was used for prognosis for each treatment plan. Prognoses included predicting local tumor control, regional spread, distant metastases, and normal tissue complications resulting from treatment. A Markov model was constructed and used to calculate a quality-adjusted life-expectancy which aids in the multi-attribute decision process. Our method makes explicit the tradeoffs patients face between quality and quantity of life. This approach has advantages over current approaches because with our approach risks of health outcomes and patient preferences determine treatment decisions.

MCMC genome rearrangement.

PubMed

Miklós, István

2003-10-01

As more and more genomes have been sequenced, genomic data is rapidly accumulating. Genome-wide mutations are believed more neutral than local mutations such as substitutions, insertions and deletions, therefore phylogenetic investigations based on inversions, transpositions and inverted transpositions are less biased by the hypothesis on neutral evolution. Although efficient algorithms exist for obtaining the inversion distance of two signed permutations, there is no reliable algorithm when both inversions and transpositions are considered. Moreover, different type of mutations happen with different rates, and it is not clear how to weight them in a distance based approach. We introduce a Markov Chain Monte Carlo method to genome rearrangement based on a stochastic model of evolution, which can estimate the number of different evolutionary events needed to sort a signed permutation. The performance of the method was tested on simulated data, and the estimated numbers of different types of mutations were reliable. Human and Drosophila mitochondrial data were also analysed with the new method. The mixing time of the Markov Chain is short both in terms of CPU times and number of proposals. The source code in C is available on request from the author.

Reference-free error estimation for multiple measurement methods.

PubMed

Madan, Hennadii; Pernuš, Franjo; Špiclin, Žiga

2018-01-01

We present a computational framework to select the most accurate and precise method of measurement of a certain quantity, when there is no access to the true value of the measurand. A typical use case is when several image analysis methods are applied to measure the value of a particular quantitative imaging biomarker from the same images. The accuracy of each measurement method is characterized by systematic error (bias), which is modeled as a polynomial in true values of measurand, and the precision as random error modeled with a Gaussian random variable. In contrast to previous works, the random errors are modeled jointly across all methods, thereby enabling the framework to analyze measurement methods based on similar principles, which may have correlated random errors. Furthermore, the posterior distribution of the error model parameters is estimated from samples obtained by Markov chain Monte-Carlo and analyzed to estimate the parameter values and the unknown true values of the measurand. The framework was validated on six synthetic and one clinical dataset containing measurements of total lesion load, a biomarker of neurodegenerative diseases, which was obtained with four automatic methods by analyzing brain magnetic resonance images. The estimates of bias and random error were in a good agreement with the corresponding least squares regression estimates against a reference.

Random access with adaptive packet aggregation in LTE/LTE-A.

PubMed

Zhou, Kaijie; Nikaein, Navid

While random access presents a promising solution for efficient uplink channel access, the preamble collision rate can significantly increase when massive number of devices simultaneously access the channel. To address this issue and improve the reliability of the random access, an adaptive packet aggregation method is proposed. With the proposed method, a device does not trigger a random access for every single packet. Instead, it starts a random access when the number of aggregated packets reaches a given threshold. This method reduces the packet collision rate at the expense of an extra latency, which is used to accumulate multiple packets into a single transmission unit. Therefore, the tradeoff between packet loss rate and channel access latency has to be carefully selected. We use semi-Markov model to derive the packet loss rate and channel access latency as functions of packet aggregation number. Hence, the optimal amount of aggregated packets can be found, which keeps the loss rate below the desired value while minimizing the access latency. We also apply for the idea of packet aggregation for power saving, where a device aggregates as many packets as possible until the latency constraint is reached. Simulations are carried out to evaluate our methods. We find that the packet loss rate and/or power consumption are significantly reduced with the proposed method.

Mum, why do you keep on growing? Impacts of environmental variability on optimal growth and reproduction allocation strategies of annual plants.

PubMed

De Lara, Michel

2006-05-01

In their 1990 paper Optimal reproductive efforts and the timing of reproduction of annual plants in randomly varying environments, Amir and Cohen considered stochastic environments consisting of i.i.d. sequences in an optimal allocation discrete-time model. We suppose here that the sequence of environmental factors is more generally described by a Markov chain. Moreover, we discuss the connection between the time interval of the discrete-time dynamic model and the ability of the plant to rebuild completely its vegetative body (from reserves). We formulate a stochastic optimization problem covering the so-called linear and logarithmic fitness (corresponding to variation within and between years), which yields optimal strategies. For "linear maximizers'', we analyse how optimal strategies depend upon the environmental variability type: constant, random stationary, random i.i.d., random monotonous. We provide general patterns in terms of targets and thresholds, including both determinate and indeterminate growth. We also provide a partial result on the comparison between ;"linear maximizers'' and "log maximizers''. Numerical simulations are provided, allowing to give a hint at the effect of different mathematical assumptions.

Noise, chaos, and (ɛ, τ)-entropy per unit time

NASA Astrophysics Data System (ADS)

Gaspard, Pierre; Wang, Xiao-Jing

1993-12-01

The degree of dynamical randomness of different time processes is characterized in terms of the (ε, τ)-entropy per unit time. The (ε, τ)-entropy is the amount of information generated per unit time, at different scales τ of time and ε of the observables. This quantity generalizes the Kolmogorov-Sinai entropy per unit time from deterministic chaotic processes, to stochastic processes such as fluctuations in mesoscopic physico-chemical phenomena or strong turbulence in macroscopic spacetime dynamics. The random processes that are characterized include chaotic systems, Bernoulli and Markov chains, Poisson and birth-and-death processes, Ornstein-Uhlenbeck and Yaglom noises, fractional Brownian motions, different regimes of hydrodynamical turbulence, and the Lorentz-Boltzmann process of nonequilibrium statistical mechanics. We also extend the (ε, τ)-entropy to spacetime processes like cellular automata, Conway's game of life, lattice gas automata, coupled maps, spacetime chaos in partial differential equations, as well as the ideal, the Lorentz, and the hard sphere gases. Through these examples it is demonstrated that the (ε, τ)-entropy provides a unified quantitative measure of dynamical randomness to both chaos and noises, and a method to detect transitions between dynamical states of different degrees of randomness as a parameter of the system is varied.

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

PubMed

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

2000-03-01

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

Filling of Cloud-Induced Gaps for Land Use and Land Cover Classifications Around Refugee Camps

NASA Astrophysics Data System (ADS)

Braun, Andreas; Hagensieker, Ron; Hochschild, Volker

2016-08-01

Clouds cover is one of the main constraints in the field of optical remote sensing. Especially the use of multispectral imagery is affected by either fully obscured data or parts of the image which remain unusable. This study compares four algorithms for the filling of cloud induced gaps in classified land cover products based on Markov Random Fields (MRF), Random Forest (RF), Closest Spectral Fit (CSF) operators. They are tested on a classified image of Sentinel-2 where artificial clouds are filled by information derived from a scene of Sentinel-1. The approaches rely on different mathematical principles and therefore produced results varying in both pattern and quality. Overall accuracies for the filled areas range from 57 to 64 %. Best results are achieved by CSF, however some classes (e.g. sands and grassland) remain critical through all approaches.

Boosting association rule mining in large datasets via Gibbs sampling.

PubMed

Qian, Guoqi; Rao, Calyampudi Radhakrishna; Sun, Xiaoying; Wu, Yuehua

2016-05-03

Current algorithms for association rule mining from transaction data are mostly deterministic and enumerative. They can be computationally intractable even for mining a dataset containing just a few hundred transaction items, if no action is taken to constrain the search space. In this paper, we develop a Gibbs-sampling-induced stochastic search procedure to randomly sample association rules from the itemset space, and perform rule mining from the reduced transaction dataset generated by the sample. Also a general rule importance measure is proposed to direct the stochastic search so that, as a result of the randomly generated association rules constituting an ergodic Markov chain, the overall most important rules in the itemset space can be uncovered from the reduced dataset with probability 1 in the limit. In the simulation study and a real genomic data example, we show how to boost association rule mining by an integrated use of the stochastic search and the Apriori algorithm.

Entropy of finite random binary sequences with weak long-range correlations.

PubMed

Melnik, S S; Usatenko, O V

2014-11-01

We study the N-step binary stationary ergodic Markov chain and analyze its differential entropy. Supposing that the correlations are weak we express the conditional probability function of the chain through the pair correlation function and represent the entropy as a functional of the pair correlator. Since the model uses the two-point correlators instead of the block probability, it makes it possible to calculate the entropy of strings at much longer distances than using standard methods. A fluctuation contribution to the entropy due to finiteness of random chains is examined. This contribution can be of the same order as its regular part even at the relatively short lengths of subsequences. A self-similar structure of entropy with respect to the decimation transformations is revealed for some specific forms of the pair correlation function. Application of the theory to the DNA sequence of the R3 chromosome of Drosophila melanogaster is presented.

Entropy of finite random binary sequences with weak long-range correlations

NASA Astrophysics Data System (ADS)

Melnik, S. S.; Usatenko, O. V.

2014-11-01

We study the N -step binary stationary ergodic Markov chain and analyze its differential entropy. Supposing that the correlations are weak we express the conditional probability function of the chain through the pair correlation function and represent the entropy as a functional of the pair correlator. Since the model uses the two-point correlators instead of the block probability, it makes it possible to calculate the entropy of strings at much longer distances than using standard methods. A fluctuation contribution to the entropy due to finiteness of random chains is examined. This contribution can be of the same order as its regular part even at the relatively short lengths of subsequences. A self-similar structure of entropy with respect to the decimation transformations is revealed for some specific forms of the pair correlation function. Application of the theory to the DNA sequence of the R3 chromosome of Drosophila melanogaster is presented.

Almost sure convergence in quantum spin glasses

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

Buzinski, David, E-mail: dab197@case.edu; Meckes, Elizabeth, E-mail: elizabeth.meckes@case.edu

2015-12-15

Recently, Keating, Linden, and Wells [Markov Processes Relat. Fields 21(3), 537-555 (2015)] showed that the density of states measure of a nearest-neighbor quantum spin glass model is approximately Gaussian when the number of particles is large. The density of states measure is the ensemble average of the empirical spectral measure of a random matrix; in this paper, we use concentration of measure and entropy techniques together with the result of Keating, Linden, and Wells to show that in fact the empirical spectral measure of such a random matrix is almost surely approximately Gaussian itself with no ensemble averaging. We alsomore » extend this result to a spherical quantum spin glass model and to the more general coupling geometries investigated by Erdős and Schröder [Math. Phys., Anal. Geom. 17(3-4), 441–464 (2014)].« less

A prior feature SVM – MRF based method for mouse brain segmentation

PubMed Central

Wu, Teresa; Bae, Min Hyeok; Zhang, Min; Pan, Rong; Badea, Alexandra

2012-01-01

We introduce an automated method, called prior feature Support Vector Machine- Markov Random Field (pSVMRF), to segment three-dimensional mouse brain Magnetic Resonance Microscopy (MRM) images. Our earlier work, extended MRF (eMRF) integrated Support Vector Machine (SVM) and Markov Random Field (MRF) approaches, leading to improved segmentation accuracy; however, the computation of eMRF is very expensive, which may limit its performance on segmentation and robustness. In this study pSVMRF reduces training and testing time for SVM, while boosting segmentation performance. Unlike the eMRF approach, where MR intensity information and location priors are linearly combined, pSVMRF combines this information in a nonlinear fashion, and enhances the discriminative ability of the algorithm. We validate the proposed method using MR imaging of unstained and actively stained mouse brain specimens, and compare segmentation accuracy with two existing methods: eMRF and MRF. C57BL/6 mice are used for training and testing, using cross validation. For formalin fixed C57BL/6 specimens, pSVMRF outperforms both eMRF and MRF. The segmentation accuracy for C57BL/6 brains, stained or not, was similar for larger structures like hippocampus and caudate putamen, (~87%), but increased substantially for smaller regions like susbtantia nigra (from 78.36% to 91.55%), and anterior commissure (from ~50% to ~80%). To test segmentation robustness against increased anatomical variability we add two strains, BXD29 and a transgenic mouse model of Alzheimer’s Disease. Segmentation accuracy for new strains is 80% for hippocampus, and caudate putamen, indicating that pSVMRF is a promising approach for phenotyping mouse models of human brain disorders. PMID:21988893

A prior feature SVM-MRF based method for mouse brain segmentation.

PubMed

Wu, Teresa; Bae, Min Hyeok; Zhang, Min; Pan, Rong; Badea, Alexandra

2012-02-01

We introduce an automated method, called prior feature Support Vector Machine-Markov Random Field (pSVMRF), to segment three-dimensional mouse brain Magnetic Resonance Microscopy (MRM) images. Our earlier work, extended MRF (eMRF) integrated Support Vector Machine (SVM) and Markov Random Field (MRF) approaches, leading to improved segmentation accuracy; however, the computation of eMRF is very expensive, which may limit its performance on segmentation and robustness. In this study pSVMRF reduces training and testing time for SVM, while boosting segmentation performance. Unlike the eMRF approach, where MR intensity information and location priors are linearly combined, pSVMRF combines this information in a nonlinear fashion, and enhances the discriminative ability of the algorithm. We validate the proposed method using MR imaging of unstained and actively stained mouse brain specimens, and compare segmentation accuracy with two existing methods: eMRF and MRF. C57BL/6 mice are used for training and testing, using cross validation. For formalin fixed C57BL/6 specimens, pSVMRF outperforms both eMRF and MRF. The segmentation accuracy for C57BL/6 brains, stained or not, was similar for larger structures like hippocampus and caudate putamen, (~87%), but increased substantially for smaller regions like susbtantia nigra (from 78.36% to 91.55%), and anterior commissure (from ~50% to ~80%). To test segmentation robustness against increased anatomical variability we add two strains, BXD29 and a transgenic mouse model of Alzheimer's disease. Segmentation accuracy for new strains is 80% for hippocampus, and caudate putamen, indicating that pSVMRF is a promising approach for phenotyping mouse models of human brain disorders. Copyright © 2011 Elsevier Inc. All rights reserved.

Exponential series approaches for nonparametric graphical models

NASA Astrophysics Data System (ADS)

Janofsky, Eric

Markov Random Fields (MRFs) or undirected graphical models are parsimonious representations of joint probability distributions. This thesis studies high-dimensional, continuous-valued pairwise Markov Random Fields. We are particularly interested in approximating pairwise densities whose logarithm belongs to a Sobolev space. For this problem we propose the method of exponential series which approximates the log density by a finite-dimensional exponential family with the number of sufficient statistics increasing with the sample size. We consider two approaches to estimating these models. The first is regularized maximum likelihood. This involves optimizing the sum of the log-likelihood of the data and a sparsity-inducing regularizer. We then propose a variational approximation to the likelihood based on tree-reweighted, nonparametric message passing. This approximation allows for upper bounds on risk estimates, leverages parallelization and is scalable to densities on hundreds of nodes. We show how the regularized variational MLE may be estimated using a proximal gradient algorithm. We then consider estimation using regularized score matching. This approach uses an alternative scoring rule to the log-likelihood, which obviates the need to compute the normalizing constant of the distribution. For general continuous-valued exponential families, we provide parameter and edge consistency results. As a special case we detail a new approach to sparse precision matrix estimation which has statistical performance competitive with the graphical lasso and computational performance competitive with the state-of-the-art glasso algorithm. We then describe results for model selection in the nonparametric pairwise model using exponential series. The regularized score matching problem is shown to be a convex program; we provide scalable algorithms based on consensus alternating direction method of multipliers (ADMM) and coordinate-wise descent. We use simulations to compare our method to others in the literature as well as the aforementioned TRW estimator.

A new phenotyping pipeline reveals three types of lateral roots and a random branching pattern in two cereals.

PubMed

Passot, Sixtine; Moreno-Ortega, Beatriz; Moukouanga, Daniel; Balsera, Crispulo; Guyomarc'h, Soazig; Lucas, Mikael; Lobet, Guillaume; Laplaze, Laurent; Muller, Bertrand; Guédon, Yann

2018-05-11

Recent progress in root phenotyping has focused mainly on increasing throughput for genetic studies while identifying root developmental patterns has been comparatively underexplored. We introduce a new phenotyping pipeline for producing high-quality spatio-temporal root system development data and identifying developmental patterns within these data. The SmartRoot image analysis system and temporal and spatial statistical models were applied to two cereals, pearl millet (Pennisetum glaucum) and maize (Zea mays). Semi-Markov switching linear models were used to cluster lateral roots based on their growth rate profiles. These models revealed three types of lateral roots with similar characteristics in both species. The first type corresponds to fast and accelerating roots, the second to rapidly arrested roots, and the third to an intermediate type where roots cease elongation after a few days. These types of lateral roots were retrieved in different proportions in a maize mutant affected in auxin signaling, while the first most vigorous type was absent in maize plants exposed to severe shading. Moreover, the classification of growth rate profiles was mirrored by a ranking of anatomical traits in pearl millet. Potential dependencies in the succession of lateral root types along the primary root were then analyzed using variable-order Markov chains. The lateral root type was not influenced by the shootward neighbor root type or by the distance from this root. This random branching pattern of primary roots was remarkably conserved, despite the high variability of root systems in both species. Our phenotyping pipeline opens the door to exploring the genetic variability of lateral root developmental patterns. {copyright, serif} 2018 American Society of Plant Biologists. All rights reserved.

An efficient system for reliably transmitting image and video data over low bit rate noisy channels

NASA Technical Reports Server (NTRS)

Costello, Daniel J., Jr.; Huang, Y. F.; Stevenson, Robert L.

1994-01-01

This research project is intended to develop an efficient system for reliably transmitting image and video data over low bit rate noisy channels. The basic ideas behind the proposed approach are the following: employ statistical-based image modeling to facilitate pre- and post-processing and error detection, use spare redundancy that the source compression did not remove to add robustness, and implement coded modulation to improve bandwidth efficiency and noise rejection. Over the last six months, progress has been made on various aspects of the project. Through our studies of the integrated system, a list-based iterative Trellis decoder has been developed. The decoder accepts feedback from a post-processor which can detect channel errors in the reconstructed image. The error detection is based on the Huber Markov random field image model for the compressed image. The compression scheme used here is that of JPEG (Joint Photographic Experts Group). Experiments were performed and the results are quite encouraging. The principal ideas here are extendable to other compression techniques. In addition, research was also performed on unequal error protection channel coding, subband vector quantization as a means of source coding, and post processing for reducing coding artifacts. Our studies on unequal error protection (UEP) coding for image transmission focused on examining the properties of the UEP capabilities of convolutional codes. The investigation of subband vector quantization employed a wavelet transform with special emphasis on exploiting interband redundancy. The outcome of this investigation included the development of three algorithms for subband vector quantization. The reduction of transform coding artifacts was studied with the aid of a non-Gaussian Markov random field model. This results in improved image decompression. These studies are summarized and the technical papers included in the appendices.

Joint inversion of marine seismic AVA and CSEM data using statistical rock-physics models and Markov random fields: Stochastic inversion of AVA and CSEM data

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

Chen, J.; Hoversten, G.M.

2011-09-15

Joint inversion of seismic AVA and CSEM data requires rock-physics relationships to link seismic attributes to electrical properties. Ideally, we can connect them through reservoir parameters (e.g., porosity and water saturation) by developing physical-based models, such as Gassmann’s equations and Archie’s law, using nearby borehole logs. This could be difficult in the exploration stage because information available is typically insufficient for choosing suitable rock-physics models and for subsequently obtaining reliable estimates of the associated parameters. The use of improper rock-physics models and the inaccuracy of the estimates of model parameters may cause misleading inversion results. Conversely, it is easy tomore » derive statistical relationships among seismic and electrical attributes and reservoir parameters from distant borehole logs. In this study, we develop a Bayesian model to jointly invert seismic AVA and CSEM data for reservoir parameter estimation using statistical rock-physics models; the spatial dependence of geophysical and reservoir parameters are carried out by lithotypes through Markov random fields. We apply the developed model to a synthetic case, which simulates a CO{sub 2} monitoring application. We derive statistical rock-physics relations from borehole logs at one location and estimate seismic P- and S-wave velocity ratio, acoustic impedance, density, electrical resistivity, lithotypes, porosity, and water saturation at three different locations by conditioning to seismic AVA and CSEM data. Comparison of the inversion results with their corresponding true values shows that the correlation-based statistical rock-physics models provide significant information for improving the joint inversion results.« less

Shape-and-behavior encoded tracking of bee dances.

PubMed

Veeraraghavan, Ashok; Chellappa, Rama; Srinivasan, Mandyam

2008-03-01

Behavior analysis of social insects has garnered impetus in recent years and has led to some advances in fields like control systems, flight navigation etc. Manual labeling of insect motions required for analyzing the behaviors of insects requires significant investment of time and effort. In this paper, we propose certain general principles that help in simultaneous automatic tracking and behavior analysis with applications in tracking bees and recognizing specific behaviors exhibited by them. The state space for tracking is defined using position, orientation and the current behavior of the insect being tracked. The position and orientation are parametrized using a shape model while the behavior is explicitly modeled using a three-tier hierarchical motion model. The first tier (dynamics) models the local motions exhibited and the models built in this tier act as a vocabulary for behavior modeling. The second tier is a Markov motion model built on top of the local motion vocabulary which serves as the behavior model. The third tier of the hierarchy models the switching between behaviors and this is also modeled as a Markov model. We address issues in learning the three-tier behavioral model, in discriminating between models, detecting and in modeling abnormal behaviors. Another important aspect of this work is that it leads to joint tracking and behavior analysis instead of the traditional track and then recognize approach. We apply these principles for tracking bees in a hive while they are executing the waggle dance and the round dance.

Driving style recognition method using braking characteristics based on hidden Markov model

PubMed Central

Wu, Chaozhong; Lyu, Nengchao; Huang, Zhen

2017-01-01

Since the advantage of hidden Markov model in dealing with time series data and for the sake of identifying driving style, three driving style (aggressive, moderate and mild) are modeled reasonably through hidden Markov model based on driver braking characteristics to achieve efficient driving style. Firstly, braking impulse and the maximum braking unit area of vacuum booster within a certain time are collected from braking operation, and then general braking and emergency braking characteristics are extracted to code the braking characteristics. Secondly, the braking behavior observation sequence is used to describe the initial parameters of hidden Markov model, and the generation of the hidden Markov model for differentiating and an observation sequence which is trained and judged by the driving style is introduced. Thirdly, the maximum likelihood logarithm could be implied from the observable parameters. The recognition accuracy of algorithm is verified through experiments and two common pattern recognition algorithms. The results showed that the driving style discrimination based on hidden Markov model algorithm could realize effective discriminant of driving style. PMID:28837580

Observation uncertainty in reversible Markov chains.

PubMed

Metzner, Philipp; Weber, Marcus; Schütte, Christof

2010-09-01

In many applications one is interested in finding a simplified model which captures the essential dynamical behavior of a real life process. If the essential dynamics can be assumed to be (approximately) memoryless then a reasonable choice for a model is a Markov model whose parameters are estimated by means of Bayesian inference from an observed time series. We propose an efficient Monte Carlo Markov chain framework to assess the uncertainty of the Markov model and related observables. The derived Gibbs sampler allows for sampling distributions of transition matrices subject to reversibility and/or sparsity constraints. The performance of the suggested sampling scheme is demonstrated and discussed for a variety of model examples. The uncertainty analysis of functions of the Markov model under investigation is discussed in application to the identification of conformations of the trialanine molecule via Robust Perron Cluster Analysis (PCCA+) .

Open Markov Processes and Reaction Networks

NASA Astrophysics Data System (ADS)

Swistock Pollard, Blake Stephen

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

Improved Compressive Sensing of Natural Scenes Using Localized Random Sampling

PubMed Central

Barranca, Victor J.; Kovačič, Gregor; Zhou, Douglas; Cai, David

2016-01-01

Compressive sensing (CS) theory demonstrates that by using uniformly-random sampling, rather than uniformly-spaced sampling, higher quality image reconstructions are often achievable. Considering that the structure of sampling protocols has such a profound impact on the quality of image reconstructions, we formulate a new sampling scheme motivated by physiological receptive field structure, localized random sampling, which yields significantly improved CS image reconstructions. For each set of localized image measurements, our sampling method first randomly selects an image pixel and then measures its nearby pixels with probability depending on their distance from the initially selected pixel. We compare the uniformly-random and localized random sampling methods over a large space of sampling parameters, and show that, for the optimal parameter choices, higher quality image reconstructions can be consistently obtained by using localized random sampling. In addition, we argue that the localized random CS optimal parameter choice is stable with respect to diverse natural images, and scales with the number of samples used for reconstruction. We expect that the localized random sampling protocol helps to explain the evolutionarily advantageous nature of receptive field structure in visual systems and suggests several future research areas in CS theory and its application to brain imaging. PMID:27555464

Optimal choice of word length when comparing two Markov sequences using a χ 2-statistic.

PubMed

Bai, Xin; Tang, Kujin; Ren, Jie; Waterman, Michael; Sun, Fengzhu

2017-10-03

Alignment-free sequence comparison using counts of word patterns (grams, k-tuples) has become an active research topic due to the large amount of sequence data from the new sequencing technologies. Genome sequences are frequently modelled by Markov chains and the likelihood ratio test or the corresponding approximate χ 2 -statistic has been suggested to compare two sequences. However, it is not known how to best choose the word length k in such studies. We develop an optimal strategy to choose k by maximizing the statistical power of detecting differences between two sequences. Let the orders of the Markov chains for the two sequences be r 1 and r 2 , respectively. We show through both simulations and theoretical studies that the optimal k= max(r 1 ,r 2 )+1 for both long sequences and next generation sequencing (NGS) read data. The orders of the Markov chains may be unknown and several methods have been developed to estimate the orders of Markov chains based on both long sequences and NGS reads. We study the power loss of the statistics when the estimated orders are used. It is shown that the power loss is minimal for some of the estimators of the orders of Markov chains. Our studies provide guidelines on choosing the optimal word length for the comparison of Markov sequences.

Anderson localization for radial tree-like random quantum graphs

NASA Astrophysics Data System (ADS)

Hislop, Peter D.; Post, Olaf

We prove that certain random models associated with radial, tree-like, rooted quantum graphs exhibit Anderson localization at all energies. The two main examples are the random length model (RLM) and the random Kirchhoff model (RKM). In the RLM, the lengths of each generation of edges form a family of independent, identically distributed random variables (iid). For the RKM, the iid random variables are associated with each generation of vertices and moderate the current flow through the vertex. We consider extensions to various families of decorated graphs and prove stability of localization with respect to decoration. In particular, we prove Anderson localization for the random necklace model.

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

NASA Astrophysics Data System (ADS)

Starý, Tomáš; Biktashev, Vadim N.

2017-09-01

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

A Probabilistic Model of Local Sequence Alignment That Simplifies Statistical Significance Estimation

PubMed Central

Eddy, Sean R.

2008-01-01

Sequence database searches require accurate estimation of the statistical significance of scores. Optimal local sequence alignment scores follow Gumbel distributions, but determining an important parameter of the distribution (λ) requires time-consuming computational simulation. Moreover, optimal alignment scores are less powerful than probabilistic scores that integrate over alignment uncertainty (“Forward” scores), but the expected distribution of Forward scores remains unknown. Here, I conjecture that both expected score distributions have simple, predictable forms when full probabilistic modeling methods are used. For a probabilistic model of local sequence alignment, optimal alignment bit scores (“Viterbi” scores) are Gumbel-distributed with constant λ = log 2, and the high scoring tail of Forward scores is exponential with the same constant λ. Simulation studies support these conjectures over a wide range of profile/sequence comparisons, using 9,318 profile-hidden Markov models from the Pfam database. This enables efficient and accurate determination of expectation values (E-values) for both Viterbi and Forward scores for probabilistic local alignments. PMID:18516236

Indexed semi-Markov process for wind speed modeling.

NASA Astrophysics Data System (ADS)

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

2012-04-01

The increasing interest in renewable energy leads scientific research to find a better way to recover most of the available energy. Particularly, the maximum energy recoverable from wind is equal to 59.3% of that available (Betz law) at a specific pitch angle and when the ratio between the wind speed in output and in input is equal to 1/3. The pitch angle is the angle formed between the airfoil of the blade of the wind turbine and the wind direction. Old turbine and a lot of that actually marketed, in fact, have always the same invariant geometry of the airfoil. This causes that wind turbines will work with an efficiency that is lower than 59.3%. New generation wind turbines, instead, have a system to variate the pitch angle by rotating the blades. This system able the wind turbines to recover, at different wind speed, always the maximum energy, working in Betz limit at different speed ratios. A powerful system control of the pitch angle allows the wind turbine to recover better the energy in transient regime. A good stochastic model for wind speed is then needed to help both the optimization of turbine design and to assist the system control to predict the value of the wind speed to positioning the blades quickly and correctly. The possibility to have synthetic data of wind speed is a powerful instrument to assist designer to verify the structures of the wind turbines or to estimate the energy recoverable from a specific site. To generate synthetic data, Markov chains of first or higher order are often used [1,2,3]. In particular in [1] is presented a comparison between a first-order Markov chain and a second-order Markov chain. A similar work, but only for the first-order Markov chain, is conduced by [2], presenting the probability transition matrix and comparing the energy spectral density and autocorrelation of real and synthetic wind speed data. A tentative to modeling and to join speed and direction of wind is presented in [3], by using two models, first-order Markov chain with different number of states, and Weibull distribution. All this model use Markov chains to generate synthetic wind speed time series but the search for a better model is still open. Approaching this issue, we applied new models which are generalization of Markov models. More precisely we applied semi-Markov models to generate synthetic wind speed time series. In a previous work we proposed different semi-Markov models, showing their ability to reproduce the autocorrelation structures of wind speed data. In that paper we showed also that the autocorrelation is higher with respect to the Markov model. Unfortunately this autocorrelation was still too small compared to the empirical one. In order to overcome the problem of low autocorrelation, in this paper we propose an indexed semi-Markov model. More precisely we assume that wind speed is described by a discrete time homogeneous semi-Markov process. We introduce a memory index which takes into account the periods of different wind activities. With this model the statistical characteristics of wind speed are faithfully reproduced. The wind is a very unstable phenomenon characterized by a sequence of lulls and sustained speeds, and a good wind generator must be able to reproduce such sequences. To check the validity of the predictive semi-Markovian model, the persistence of synthetic winds were calculated, then averaged and computed. The model is used to generate synthetic time series for wind speed by means of Monte Carlo simulations and the time lagged autocorrelation is used to compare statistical properties of the proposed models with those of real data and also with a time series generated though a simple Markov chain. [1] A. Shamshad, M.A. Bawadi, W.M.W. Wan Hussin, T.A. Majid, S.A.M. Sanusi, First and second order Markov chain models for synthetic generation of wind speed time series, Energy 30 (2005) 693-708. [2] H. Nfaoui, H. Essiarab, A.A.M. Sayigh, A stochastic Markov chain model for simulating wind speed time series at Tangiers, Morocco, Renewable Energy 29 (2004) 1407-1418. [3] F. Youcef Ettoumi, H. Sauvageot, A.-E.-H. Adane, Statistical bivariate modeling of wind using first-order Markov chain and Weibull distribution, Renewable Energy 28 (2003) 1787-1802.

Singular Behavior of the Leading Lyapunov Exponent of a Product of Random {2 × 2} Matrices

NASA Astrophysics Data System (ADS)

Genovese, Giuseppe; Giacomin, Giambattista; Greenblatt, Rafael Leon

2017-05-01

We consider a certain infinite product of random {2 × 2} matrices appearing in the solution of some 1 and 1 + 1 dimensional disordered models in statistical mechanics, which depends on a parameter ɛ > 0 and on a real random variable with distribution {μ}. For a large class of {μ}, we prove the prediction by Derrida and Hilhorst (J Phys A 16:2641, 1983) that the Lyapunov exponent behaves like {C ɛ^{2 α}} in the limit {ɛ \\searrow 0}, where {α \\in (0,1)} and {C > 0} are determined by {μ}. Derrida and Hilhorst performed a two-scale analysis of the integral equation for the invariant distribution of the Markov chain associated to the matrix product and obtained a probability measure that is expected to be close to the invariant one for small {ɛ}. We introduce suitable norms and exploit contractivity properties to show that such a probability measure is indeed close to the invariant one in a sense that implies a suitable control of the Lyapunov exponent.

Semiparametric Bayesian classification with longitudinal markers

PubMed Central

De la Cruz-Mesía, Rolando; Quintana, Fernando A.; Müller, Peter

2013-01-01

Summary We analyse data from a study involving 173 pregnant women. The data are observed values of the β human chorionic gonadotropin hormone measured during the first 80 days of gestational age, including from one up to six longitudinal responses for each woman. The main objective in this study is to predict normal versus abnormal pregnancy outcomes from data that are available at the early stages of pregnancy. We achieve the desired classification with a semiparametric hierarchical model. Specifically, we consider a Dirichlet process mixture prior for the distribution of the random effects in each group. The unknown random-effects distributions are allowed to vary across groups but are made dependent by using a design vector to select different features of a single underlying random probability measure. The resulting model is an extension of the dependent Dirichlet process model, with an additional probability model for group classification. The model is shown to perform better than an alternative model which is based on independent Dirichlet processes for the groups. Relevant posterior distributions are summarized by using Markov chain Monte Carlo methods. PMID:24368871

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

NASA Astrophysics Data System (ADS)

Szczota, Mickael

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

Saccade selection when reward probability is dynamically manipulated using Markov chains

PubMed Central

Lovejoy, Lee P.; Krauzlis, Richard J.

2012-01-01

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

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

PubMed

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

2008-05-01

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

Stochastic Modeling based on Dictionary Approach for the Generation of Daily Precipitation Occurrences

NASA Astrophysics Data System (ADS)

Panu, U. S.; Ng, W.; Rasmussen, P. F.

2009-12-01

The modeling of weather states (i.e., precipitation occurrences) is critical when the historical data are not long enough for the desired analysis. Stochastic models (e.g., Markov Chain and Alternating Renewal Process (ARP)) of the precipitation occurrence processes generally assume the existence of short-term temporal-dependency between the neighboring states while implying the existence of long-term independency (randomness) of states in precipitation records. Existing temporal-dependent models for the generation of precipitation occurrences are restricted either by the fixed-length memory (e.g., the order of a Markov chain model), or by the reining states in segments (e.g., persistency of homogenous states within dry/wet-spell lengths of an ARP). The modeling of variable segment lengths and states could be an arduous task and a flexible modeling approach is required for the preservation of various segmented patterns of precipitation data series. An innovative Dictionary approach has been developed in the field of genome pattern recognition for the identification of frequently occurring genome segments in DNA sequences. The genome segments delineate the biologically meaningful ``words" (i.e., segments with a specific patterns in a series of discrete states) that can be jointly modeled with variable lengths and states. A meaningful “word”, in hydrology, can be referred to a segment of precipitation occurrence comprising of wet or dry states. Such flexibility would provide a unique advantage over the traditional stochastic models for the generation of precipitation occurrences. Three stochastic models, namely, the alternating renewal process using Geometric distribution, the second-order Markov chain model, and the Dictionary approach have been assessed to evaluate their efficacy for the generation of daily precipitation sequences. Comparisons involved three guiding principles namely (i) the ability of models to preserve the short-term temporal-dependency in data through the concepts of autocorrelation, average mutual information, and Hurst exponent, (ii) the ability of models to preserve the persistency within the homogenous dry/wet weather states through analysis of dry/wet-spell lengths between the observed and generated data, and (iii) the ability to assesses the goodness-of-fit of models through the likelihood estimates (i.e., AIC and BIC). Past 30 years of observed daily precipitation records from 10 Canadian meteorological stations were utilized for comparative analyses of the three models. In general, the Markov chain model performed well. The remainders of the models were found to be competitive from one another depending upon the scope and purpose of the comparison. Although the Markov chain model has a certain advantage in the generation of daily precipitation occurrences, the structural flexibility offered by the Dictionary approach in modeling the varied segment lengths of heterogeneous weather states provides a distinct and powerful advantage in the generation of precipitation sequences.

Classification of customer lifetime value models using Markov chain

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

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

PubMed

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

2018-01-01

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

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.

Local dependence in random graph models: characterization, properties and statistical inference

PubMed Central

Schweinberger, Michael; Handcock, Mark S.

2015-01-01

Summary Dependent phenomena, such as relational, spatial and temporal phenomena, tend to be characterized by local dependence in the sense that units which are close in a well-defined sense are dependent. In contrast with spatial and temporal phenomena, though, relational phenomena tend to lack a natural neighbourhood structure in the sense that it is unknown which units are close and thus dependent. Owing to the challenge of characterizing local dependence and constructing random graph models with local dependence, many conventional exponential family random graph models induce strong dependence and are not amenable to statistical inference. We take first steps to characterize local dependence in random graph models, inspired by the notion of finite neighbourhoods in spatial statistics and M-dependence in time series, and we show that local dependence endows random graph models with desirable properties which make them amenable to statistical inference. We show that random graph models with local dependence satisfy a natural domain consistency condition which every model should satisfy, but conventional exponential family random graph models do not satisfy. In addition, we establish a central limit theorem for random graph models with local dependence, which suggests that random graph models with local dependence are amenable to statistical inference. We discuss how random graph models with local dependence can be constructed by exploiting either observed or unobserved neighbourhood structure. In the absence of observed neighbourhood structure, we take a Bayesian view and express the uncertainty about the neighbourhood structure by specifying a prior on a set of suitable neighbourhood structures. We present simulation results and applications to two real world networks with ‘ground truth’. PMID:26560142

Quenched Large Deviations for Simple Random Walks on Percolation Clusters Including Long-Range Correlations

NASA Astrophysics Data System (ADS)

Berger, Noam; Mukherjee, Chiranjib; Okamura, Kazuki

2018-03-01

We prove a quenched large deviation principle (LDP) for a simple random walk on a supercritical percolation cluster (SRWPC) on {Z^d} ({d ≥ 2}). The models under interest include classical Bernoulli bond and site percolation as well as models that exhibit long range correlations, like the random cluster model, the random interlacement and the vacant set of random interlacements (for {d ≥ 3}) and the level sets of the Gaussian free field ({d≥ 3}). Inspired by the methods developed by Kosygina et al. (Commun Pure Appl Math 59:1489-1521, 2006) for proving quenched LDP for elliptic diffusions with a random drift, and by Yilmaz (Commun Pure Appl Math 62(8):1033-1075, 2009) and Rosenbluth (Quenched large deviations for multidimensional random walks in a random environment: a variational formula. Ph.D. thesis, NYU, arXiv:0804.1444v1) for similar results regarding elliptic random walks in random environment, we take the point of view of the moving particle and prove a large deviation principle for the quenched distribution of the pair empirical measures of the environment Markov chain in the non-elliptic case of SRWPC. Via a contraction principle, this reduces easily to a quenched LDP for the distribution of the mean velocity of the random walk and both rate functions admit explicit variational formulas. The main difficulty in our set up lies in the inherent non-ellipticity as well as the lack of translation-invariance stemming from conditioning on the fact that the origin belongs to the infinite cluster. We develop a unifying approach for proving quenched large deviations for SRWPC based on exploiting coercivity properties of the relative entropies in the context of convex variational analysis, combined with input from ergodic theory and invoking geometric properties of the supercritical percolation cluster.

Quenched Large Deviations for Simple Random Walks on Percolation Clusters Including Long-Range Correlations

NASA Astrophysics Data System (ADS)

Berger, Noam; Mukherjee, Chiranjib; Okamura, Kazuki

2017-12-01

We prove a quenched large deviation principle (LDP) for a simple random walk on a supercritical percolation cluster (SRWPC) on {Z^d} ({d ≥ 2} ). The models under interest include classical Bernoulli bond and site percolation as well as models that exhibit long range correlations, like the random cluster model, the random interlacement and the vacant set of random interlacements (for {d ≥ 3} ) and the level sets of the Gaussian free field ({d≥ 3} ). Inspired by the methods developed by Kosygina et al. (Commun Pure Appl Math 59:1489-1521, 2006) for proving quenched LDP for elliptic diffusions with a random drift, and by Yilmaz (Commun Pure Appl Math 62(8):1033-1075, 2009) and Rosenbluth (Quenched large deviations for multidimensional random walks in a random environment: a variational formula. Ph.D. thesis, NYU, arXiv:0804.1444v1) for similar results regarding elliptic random walks in random environment, we take the point of view of the moving particle and prove a large deviation principle for the quenched distribution of the pair empirical measures of the environment Markov chain in the non-elliptic case of SRWPC. Via a contraction principle, this reduces easily to a quenched LDP for the distribution of the mean velocity of the random walk and both rate functions admit explicit variational formulas. The main difficulty in our set up lies in the inherent non-ellipticity as well as the lack of translation-invariance stemming from conditioning on the fact that the origin belongs to the infinite cluster. We develop a unifying approach for proving quenched large deviations for SRWPC based on exploiting coercivity properties of the relative entropies in the context of convex variational analysis, combined with input from ergodic theory and invoking geometric properties of the supercritical percolation cluster.

Spectral Density of Laser Beam Scintillation in Wind Turbulence. Part 1; Theory

NASA Technical Reports Server (NTRS)

Balakrishnan, A. V.

1997-01-01

The temporal spectral density of the log-amplitude scintillation of a laser beam wave due to a spatially dependent vector-valued crosswind (deterministic as well as random) is evaluated. The path weighting functions for normalized spectral moments are derived, and offer a potential new technique for estimating the wind velocity profile. The Tatarskii-Klyatskin stochastic propagation equation for the Markov turbulence model is used with the solution approximated by the Rytov method. The Taylor 'frozen-in' hypothesis is assumed for the dependence of the refractive index on the wind velocity, and the Kolmogorov spectral density is used for the refractive index field.

Detecting duplicate biological entities using Shortest Path Edit Distance.

PubMed

Rudniy, Alex; Song, Min; Geller, James

2010-01-01

Duplicate entity detection in biological data is an important research task. In this paper, we propose a novel and context-sensitive Shortest Path Edit Distance (SPED) extending and supplementing our previous work on Markov Random Field-based Edit Distance (MRFED). SPED transforms the edit distance computational problem to the calculation of the shortest path among two selected vertices of a graph. We produce several modifications of SPED by applying Levenshtein, arithmetic mean, histogram difference and TFIDF techniques to solve subtasks. We compare SPED performance to other well-known distance algorithms for biological entity matching. The experimental results show that SPED produces competitive outcomes.

Stationary properties of maximum-entropy random walks.

PubMed

Dixit, Purushottam D

2015-10-01

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

Sur la vitesse d'extinction d'une population dans un environnement aléatoire.

PubMed

Bacaër, Nicolas

2017-05-01

This study focuses on the speed of extinction of a population living in a random environment that follows a continuous-time Markov chain. Each individual dies or reproduces at a rate that depends on the environment. The number of offspring during reproduction follows a given probability law that also depends on the environment. In the so-called subcritical case where the population goes for sure to extinction, there is an explicit formula for the speed of extinction. In some sense, environmental stochasticity slows down population extinction. Copyright © 2017 Académie des sciences. Published by Elsevier Masson SAS. All rights reserved.

Educational Aspirations: Markov and Poisson Models. Rural Industrial Development Project Working Paper Number 14, August 1971.

ERIC Educational Resources Information Center

Kayser, Brian D.

The fit of educational aspirations of Illinois rural high school youths to 3 related one-parameter mathematical models was investigated. The models used were the continuous-time Markov chain model, the discrete-time Markov chain, and the Poisson distribution. The sample of 635 students responded to questionnaires from 1966 to 1969 as part of an…

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

NASA Astrophysics Data System (ADS)

Nagaev, S. V.

2017-12-01

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

Markov chains and semi-Markov models in time-to-event analysis.

PubMed

Abner, Erin L; Charnigo, Richard J; Kryscio, Richard J

2013-10-25

A variety of statistical methods are available to investigators for analysis of time-to-event data, often referred to as survival analysis. Kaplan-Meier estimation and Cox proportional hazards regression are commonly employed tools but are not appropriate for all studies, particularly in the presence of competing risks and when multiple or recurrent outcomes are of interest. Markov chain models can accommodate censored data, competing risks (informative censoring), multiple outcomes, recurrent outcomes, frailty, and non-constant survival probabilities. Markov chain models, though often overlooked by investigators in time-to-event analysis, have long been used in clinical studies and have widespread application in other fields.

Markov chains and semi-Markov models in time-to-event analysis

PubMed Central

Abner, Erin L.; Charnigo, Richard J.; Kryscio, Richard J.

2014-01-01

A variety of statistical methods are available to investigators for analysis of time-to-event data, often referred to as survival analysis. Kaplan-Meier estimation and Cox proportional hazards regression are commonly employed tools but are not appropriate for all studies, particularly in the presence of competing risks and when multiple or recurrent outcomes are of interest. Markov chain models can accommodate censored data, competing risks (informative censoring), multiple outcomes, recurrent outcomes, frailty, and non-constant survival probabilities. Markov chain models, though often overlooked by investigators in time-to-event analysis, have long been used in clinical studies and have widespread application in other fields. PMID:24818062

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

NASA Astrophysics Data System (ADS)

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

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

Hierarchically Structured Non-Intrusive Sign Language Recognition. Chapter 2

NASA Technical Reports Server (NTRS)

Zieren, Jorg; Zieren, Jorg; Kraiss, Karl-Friedrich

2007-01-01

This work presents a hierarchically structured approach at the nonintrusive recognition of sign language from a monocular frontal view. Robustness is achieved through sophisticated localization and tracking methods, including a combined EM/CAMSHIFT overlap resolution procedure and the parallel pursuit of multiple hypotheses about hands position and movement. This allows handling of ambiguities and automatically corrects tracking errors. A biomechanical skeleton model and dynamic motion prediction using Kalman filters represents high level knowledge. Classification is performed by Hidden Markov Models. 152 signs from German sign language were recognized with an accuracy of 97.6%.

Bayesian linkage and segregation analysis: factoring the problem.

PubMed

Matthysse, S

2000-01-01

Complex segregation analysis and linkage methods are mathematical techniques for the genetic dissection of complex diseases. They are used to delineate complex modes of familial transmission and to localize putative disease susceptibility loci to specific chromosomal locations. The computational problem of Bayesian linkage and segregation analysis is one of integration in high-dimensional spaces. In this paper, three available techniques for Bayesian linkage and segregation analysis are discussed: Markov Chain Monte Carlo (MCMC), importance sampling, and exact calculation. The contribution of each to the overall integration will be explicitly discussed.

Adaptiveness in monotone pseudo-Boolean optimization and stochastic neural computation.

PubMed

Grossi, Giuliano

2009-08-01

Hopfield neural network (HNN) is a nonlinear computational model successfully applied in finding near-optimal solutions of several difficult combinatorial problems. In many cases, the network energy function is obtained through a learning procedure so that its minima are states falling into a proper subspace (feasible region) of the search space. However, because of the network nonlinearity, a number of undesirable local energy minima emerge from the learning procedure, significantly effecting the network performance. In the neural model analyzed here, we combine both a penalty and a stochastic process in order to enhance the performance of a binary HNN. The penalty strategy allows us to gradually lead the search towards states representing feasible solutions, so avoiding oscillatory behaviors or asymptotically instable convergence. Presence of stochastic dynamics potentially prevents the network to fall into shallow local minima of the energy function, i.e., quite far from global optimum. Hence, for a given fixed network topology, the desired final distribution on the states can be reached by carefully modulating such process. The model uses pseudo-Boolean functions both to express problem constraints and cost function; a combination of these two functions is then interpreted as energy of the neural network. A wide variety of NP-hard problems fall in the class of problems that can be solved by the model at hand, particularly those having a monotonic quadratic pseudo-Boolean function as constraint function. That is, functions easily derived by closed algebraic expressions representing the constraint structure and easy (polynomial time) to maximize. We show the asymptotic convergence properties of this model characterizing its state space distribution at thermal equilibrium in terms of Markov chain and give evidence of its ability to find high quality solutions on benchmarks and randomly generated instances of two specific problems taken from the computational graph theory.

Probabilistic multiple sclerosis lesion classification based on modeling regional intensity variability and local neighborhood information.

PubMed

Harmouche, Rola; Subbanna, Nagesh K; Collins, D Louis; Arnold, Douglas L; Arbel, Tal

2015-05-01

In this paper, a fully automatic probabilistic method for multiple sclerosis (MS) lesion classification is presented, whereby the posterior probability density function over healthy tissues and two types of lesions (T1-hypointense and T2-hyperintense) is generated at every voxel. During training, the system explicitly models the spatial variability of the intensity distributions throughout the brain by first segmenting it into distinct anatomical regions and then building regional likelihood distributions for each tissue class based on multimodal magnetic resonance image (MRI) intensities. Local class smoothness is ensured by incorporating neighboring voxel information in the prior probability through Markov random fields. The system is tested on two datasets from real multisite clinical trials consisting of multimodal MRIs from a total of 100 patients with MS. Lesion classification results based on the framework are compared with and without the regional information, as well as with other state-of-the-art methods against the labels from expert manual raters. The metrics for comparison include Dice overlap, sensitivity, and positive predictive rates for both voxel and lesion classifications. Statistically significant improvements in Dice values ( ), for voxel-based and lesion-based sensitivity values ( ), and positive predictive rates ( and respectively) are shown when the proposed method is compared to the method without regional information, and to a widely used method [1]. This holds particularly true in the posterior fossa, an area where classification is very challenging. The proposed method allows us to provide clinicians with accurate tissue labels for T1-hypointense and T2-hyperintense lesions, two types of lesions that differ in appearance and clinical ramifications, and with a confidence level in the classification, which helps clinicians assess the classification results.

Fully Bayesian inference for structural MRI: application to segmentation and statistical analysis of T2-hypointensities.

PubMed

Schmidt, Paul; Schmid, Volker J; Gaser, Christian; Buck, Dorothea; Bührlen, Susanne; Förschler, Annette; Mühlau, Mark

2013-01-01

Aiming at iron-related T2-hypointensity, which is related to normal aging and neurodegenerative processes, we here present two practicable approaches, based on Bayesian inference, for preprocessing and statistical analysis of a complex set of structural MRI data. In particular, Markov Chain Monte Carlo methods were used to simulate posterior distributions. First, we rendered a segmentation algorithm that uses outlier detection based on model checking techniques within a Bayesian mixture model. Second, we rendered an analytical tool comprising a Bayesian regression model with smoothness priors (in the form of Gaussian Markov random fields) mitigating the necessity to smooth data prior to statistical analysis. For validation, we used simulated data and MRI data of 27 healthy controls (age: [Formula: see text]; range, [Formula: see text]). We first observed robust segmentation of both simulated T2-hypointensities and gray-matter regions known to be T2-hypointense. Second, simulated data and images of segmented T2-hypointensity were analyzed. We found not only robust identification of simulated effects but also a biologically plausible age-related increase of T2-hypointensity primarily within the dentate nucleus but also within the globus pallidus, substantia nigra, and red nucleus. Our results indicate that fully Bayesian inference can successfully be applied for preprocessing and statistical analysis of structural MRI data.

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

PubMed

Hettle, Robert; Posnett, John; Borrill, John

2015-01-01

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

Unified framework to evaluate panmixia and migration direction among multiple sampling locations.

PubMed

Beerli, Peter; Palczewski, Michal

2010-05-01

For many biological investigations, groups of individuals are genetically sampled from several geographic locations. These sampling locations often do not reflect the genetic population structure. We describe a framework using marginal likelihoods to compare and order structured population models, such as testing whether the sampling locations belong to the same randomly mating population or comparing unidirectional and multidirectional gene flow models. In the context of inferences employing Markov chain Monte Carlo methods, the accuracy of the marginal likelihoods depends heavily on the approximation method used to calculate the marginal likelihood. Two methods, modified thermodynamic integration and a stabilized harmonic mean estimator, are compared. With finite Markov chain Monte Carlo run lengths, the harmonic mean estimator may not be consistent. Thermodynamic integration, in contrast, delivers considerably better estimates of the marginal likelihood. The choice of prior distributions does not influence the order and choice of the better models when the marginal likelihood is estimated using thermodynamic integration, whereas with the harmonic mean estimator the influence of the prior is pronounced and the order of the models changes. The approximation of marginal likelihood using thermodynamic integration in MIGRATE allows the evaluation of complex population genetic models, not only of whether sampling locations belong to a single panmictic population, but also of competing complex structured population models.

Updating categorical soil maps using limited survey data by Bayesian Markov chain cosimulation.

PubMed

Li, Weidong; Zhang, Chuanrong; Dey, Dipak K; Willig, Michael R

2013-01-01

Updating categorical soil maps is necessary for providing current, higher-quality soil data to agricultural and environmental management but may not require a costly thorough field survey because latest legacy maps may only need limited corrections. This study suggests a Markov chain random field (MCRF) sequential cosimulation (Co-MCSS) method for updating categorical soil maps using limited survey data provided that qualified legacy maps are available. A case study using synthetic data demonstrates that Co-MCSS can appreciably improve simulation accuracy of soil types with both contributions from a legacy map and limited sample data. The method indicates the following characteristics: (1) if a soil type indicates no change in an update survey or it has been reclassified into another type that similarly evinces no change, it will be simply reproduced in the updated map; (2) if a soil type has changes in some places, it will be simulated with uncertainty quantified by occurrence probability maps; (3) if a soil type has no change in an area but evinces changes in other distant areas, it still can be captured in the area with unobvious uncertainty. We concluded that Co-MCSS might be a practical method for updating categorical soil maps with limited survey data.

Updating Categorical Soil Maps Using Limited Survey Data by Bayesian Markov Chain Cosimulation

PubMed Central

Dey, Dipak K.; Willig, Michael R.

2013-01-01

Updating categorical soil maps is necessary for providing current, higher-quality soil data to agricultural and environmental management but may not require a costly thorough field survey because latest legacy maps may only need limited corrections. This study suggests a Markov chain random field (MCRF) sequential cosimulation (Co-MCSS) method for updating categorical soil maps using limited survey data provided that qualified legacy maps are available. A case study using synthetic data demonstrates that Co-MCSS can appreciably improve simulation accuracy of soil types with both contributions from a legacy map and limited sample data. The method indicates the following characteristics: (1) if a soil type indicates no change in an update survey or it has been reclassified into another type that similarly evinces no change, it will be simply reproduced in the updated map; (2) if a soil type has changes in some places, it will be simulated with uncertainty quantified by occurrence probability maps; (3) if a soil type has no change in an area but evinces changes in other distant areas, it still can be captured in the area with unobvious uncertainty. We concluded that Co-MCSS might be a practical method for updating categorical soil maps with limited survey data. PMID:24027447

Replica exchange and expanded ensemble simulations as Gibbs sampling: simple improvements for enhanced mixing.

PubMed

Chodera, John D; Shirts, Michael R

2011-11-21

The widespread popularity of replica exchange and expanded ensemble algorithms for simulating complex molecular systems in chemistry and biophysics has generated much interest in discovering new ways to enhance the phase space mixing of these protocols in order to improve sampling of uncorrelated configurations. Here, we demonstrate how both of these classes of algorithms can be considered as special cases of Gibbs sampling within a Markov chain Monte Carlo framework. Gibbs sampling is a well-studied scheme in the field of statistical inference in which different random variables are alternately updated from conditional distributions. While the update of the conformational degrees of freedom by Metropolis Monte Carlo or molecular dynamics unavoidably generates correlated samples, we show how judicious updating of the thermodynamic state indices--corresponding to thermodynamic parameters such as temperature or alchemical coupling variables--can substantially increase mixing while still sampling from the desired distributions. We show how state update methods in common use can lead to suboptimal mixing, and present some simple, inexpensive alternatives that can increase mixing of the overall Markov chain, reducing simulation times necessary to obtain estimates of the desired precision. These improved schemes are demonstrated for several common applications, including an alchemical expanded ensemble simulation, parallel tempering, and multidimensional replica exchange umbrella sampling.

Discriminative Learning with Markov Logic Networks

DTIC Science & Technology

2009-10-01

Discriminative Learning with Markov Logic Networks Tuyen N. Huynh Department of Computer Sciences University of Texas at Austin Austin, TX 78712...emerging area of research that addresses the problem of learning from noisy structured/relational data. Markov logic networks (MLNs), sets of weighted...TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) University of Texas at Austin,Department of Computer

Prediction of future urban growth using CA-Markov for urban sustainability planning of Banda Aceh, Indonesia

NASA Astrophysics Data System (ADS)

Achmad, A.; Irwansyah, M.; Ramli, I.

2018-03-01

Banda Aceh experienced rapid growth, both physically, socially, and economically, after the Tsunami that devastated it the end of December in 2004. Hence policy controls are needed to direct the pattern of urban growth to achieve sustainable development for the future. The purpose of this paper is to generate a growth model for Banda Aceh using the CA-Markov process. By knowing the changes in land use between 2005 and 2009 from the results of previous research, simulations for 2013, 2019 and 2029 using the application of Idrisi@Selva. CA-Markov models were prepared to determine the quantity of changes. The simulation results showed that, after the Tsunami, the City of Banda Aceh tended to grow towards the coast. For the control of the LUC, the Banda Aceh City government needs to prepare comprehensive and detailed maps and inventory of LUC for the city to provide basic data and information needed for monitoring and evaluation that can be done effectively and efficiently. An institution for monitoring and evaluation of the urban landscape and the LUC should be formed immediately. This institution could consist of representatives from government, academia, community leaders, the private sector and other experts. The findings from this study can be used to start the monitoring and evaluation of future urban growth. Especially for the coastal areas, the local government should immediately prepare special spatial coastal area plans to control growth in those areas and to ensure that the economic benefits from disaster mitigation and coastal protection are preserved. For the development of the city in the future, it is necessary to achieve a balance between economic development, and social welfare with environmental protection and disaster mitigation. iIt will become a big challenge to achieve sustainable development for the future.

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

PubMed

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

2011-10-01

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