Lindeberg theorem for Gibbs-Markov dynamics

NASA Astrophysics Data System (ADS)

Denker, Manfred; Senti, Samuel; Zhang, Xuan

2017-12-01

A dynamical array consists of a family of functions \\{ fn, i: 1≤slant i≤slant k_n, n≥slant 1\\} and a family of initial times \\{τn, i: 1≤slant i≤slant k_n, n≥slant 1\\} . For a dynamical system (X, T) we identify distributional limits for sums of the form for suitable (non-random) constants s_n>0 and an, i\\in { R} . We derive a Lindeberg-type central limit theorem for dynamical arrays. Applications include new central limit theorems for functions which are not locally Lipschitz continuous and central limit theorems for statistical functions of time series obtained from Gibbs-Markov systems. Our results, which hold for more general dynamics, are stated in the context of Gibbs-Markov dynamical systems for convenience.

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.

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.

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.

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.

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.

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

NASA Astrophysics Data System (ADS)

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

2012-01-01

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

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 Chains for Investigating and Predicting Migration: A Case from Southwestern China

NASA Astrophysics Data System (ADS)

Qin, Bo; Wang, Yiyu; Xu, Haoming

2018-03-01

In order to accurately predict the population’s happiness, this paper conducted two demographic surveys on a new district of a city in western China, and carried out a dynamic analysis using related mathematical methods. This paper argues that the migration of migrants in the city will change the pattern of spatial distribution of human resources in the city and thus affect the social and economic development in all districts. The migration status of the population will change randomly with the passage of time, so it can be predicted and analyzed through the Markov process. The Markov process provides the local government and decision-making bureau a valid basis for the dynamic analysis of the mobility of migrants in the city as well as the ways for promoting happiness of local people’s lives.

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.

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.

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.

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.

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.

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.

DNA motif alignment by evolving a population of Markov chains.

PubMed

Bi, Chengpeng

2009-01-30

Deciphering cis-regulatory elements or de novo motif-finding in genomes still remains elusive although much algorithmic effort has been expended. The Markov chain Monte Carlo (MCMC) method such as Gibbs motif samplers has been widely employed to solve the de novo motif-finding problem through sequence local alignment. Nonetheless, the MCMC-based motif samplers still suffer from local maxima like EM. Therefore, as a prerequisite for finding good local alignments, these motif algorithms are often independently run a multitude of times, but without information exchange between different chains. Hence it would be worth a new algorithm design enabling such information exchange. This paper presents a novel motif-finding algorithm by evolving a population of Markov chains with information exchange (PMC), each of which is initialized as a random alignment and run by the Metropolis-Hastings sampler (MHS). It is progressively updated through a series of local alignments stochastically sampled. Explicitly, the PMC motif algorithm performs stochastic sampling as specified by a population-based proposal distribution rather than individual ones, and adaptively evolves the population as a whole towards a global maximum. The alignment information exchange is accomplished by taking advantage of the pooled motif site distributions. A distinct method for running multiple independent Markov chains (IMC) without information exchange, or dubbed as the IMC motif algorithm, is also devised to compare with its PMC counterpart. Experimental studies demonstrate that the performance could be improved if pooled information were used to run a population of motif samplers. The new PMC algorithm was able to improve the convergence and outperformed other popular algorithms tested using simulated and biological motif sequences.

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.

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.

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.

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.

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.

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

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

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.

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

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.

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.

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.

Local randomness: Examples and application

NASA Astrophysics Data System (ADS)

Fu, Honghao; Miller, Carl A.

2018-03-01

When two players achieve a superclassical score at a nonlocal game, their outputs must contain intrinsic randomness. This fact has many useful implications for quantum cryptography. Recently it has been observed [C. Miller and Y. Shi, Quantum Inf. Computat. 17, 0595 (2017)] that such scores also imply the existence of local randomness—that is, randomness known to one player but not to the other. This has potential implications for cryptographic tasks between two cooperating but mistrustful players. In the current paper we bring this notion toward practical realization, by offering near-optimal bounds on local randomness for the CHSH game, and also proving the security of a cryptographic application of local randomness (single-bit certified deletion).

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.

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

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.

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

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.

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.

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.

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.

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

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

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.

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

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.

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.

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.

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.

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

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.

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.

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

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.

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.

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.

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.

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

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.

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

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

PubMed

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

2014-12-19

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

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

NASA Astrophysics Data System (ADS)

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

2014-12-01

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

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

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.

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.

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

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.

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.

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

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.

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.

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

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.

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.

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 .

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.

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.

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.

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

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.

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

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.

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

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.

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.

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

PubMed

Galtier, N; Jean-Marie, A

2004-01-01

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

Markov 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.

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.

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

PubMed

Schmandt, Nicolaus T; Galán, Roberto F

2012-09-14

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

Markov reward processes

NASA Technical Reports Server (NTRS)

Smith, R. M.

1991-01-01

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

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

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.

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.

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.

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

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.

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.

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.

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…

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.

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.

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.

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.

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.

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.

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.

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.

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

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

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.

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

Percolation of localized attack on isolated and interdependent random networks

NASA Astrophysics Data System (ADS)

Shao, Shuai; Huang, Xuqing; Stanley, H. Eugene; Havlin, Shlomo

2014-03-01

Percolation properties of isolated and interdependent random networks have been investigated extensively. The focus of these studies has been on random attacks where each node in network is attacked with the same probability or targeted attack where each node is attacked with a probability being a function of its centrality, such as degree. Here we discuss a new type of realistic attacks which we call a localized attack where a group of neighboring nodes in the networks are attacked. We attack a randomly chosen node, its neighbors, and its neighbor of neighbors and so on, until removing a fraction (1 - p) of the network. This type of attack reflects damages due to localized disasters, such as earthquakes, floods and war zones in real-world networks. We study, both analytically and by simulations the impact of localized attack on percolation properties of random networks with arbitrary degree distributions and discuss in detail random regular (RR) networks, Erdős-Rényi (ER) networks and scale-free (SF) networks. We extend and generalize our theoretical and simulation results of single isolated networks to networks formed of interdependent networks.

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…

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

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.

SAR-based change detection using hypothesis testing and Markov random field modelling

NASA Astrophysics Data System (ADS)

Cao, W.; Martinis, S.

2015-04-01

The objective of this study is to automatically detect changed areas caused by natural disasters from bi-temporal co-registered and calibrated TerraSAR-X data. The technique in this paper consists of two steps: Firstly, an automatic coarse detection step is applied based on a statistical hypothesis test for initializing the classification. The original analytical formula as proposed in the constant false alarm rate (CFAR) edge detector is reviewed and rewritten in a compact form of the incomplete beta function, which is a builtin routine in commercial scientific software such as MATLAB and IDL. Secondly, a post-classification step is introduced to optimize the noisy classification result in the previous step. Generally, an optimization problem can be formulated as a Markov random field (MRF) on which the quality of a classification is measured by an energy function. The optimal classification based on the MRF is related to the lowest energy value. Previous studies provide methods for the optimization problem using MRFs, such as the iterated conditional modes (ICM) algorithm. Recently, a novel algorithm was presented based on graph-cut theory. This method transforms a MRF to an equivalent graph and solves the optimization problem by a max-flow/min-cut algorithm on the graph. In this study this graph-cut algorithm is applied iteratively to improve the coarse classification. At each iteration the parameters of the energy function for the current classification are set by the logarithmic probability density function (PDF). The relevant parameters are estimated by the method of logarithmic cumulants (MoLC). Experiments are performed using two flood events in Germany and Australia in 2011 and a forest fire on La Palma in 2009 using pre- and post-event TerraSAR-X data. The results show convincing coarse classifications and considerable improvement by the graph-cut post-classification step.

Observation uncertainty in reversible Markov chains.

PubMed

Metzner, Philipp; Weber, Marcus; Schütte, Christof

2010-09-01

In many applications one is interested in finding a simplified model which captures the essential dynamical behavior of a real life process. If the essential dynamics can be assumed to be (approximately) memoryless then a reasonable choice for a model is a Markov model whose parameters are estimated by means of Bayesian inference from an observed time series. We propose an efficient Monte Carlo Markov chain framework to assess the uncertainty of the Markov model and related observables. The derived Gibbs sampler allows for sampling distributions of transition matrices subject to reversibility and/or sparsity constraints. The performance of the suggested sampling scheme is demonstrated and discussed for a variety of model examples. The uncertainty analysis of functions of the Markov model under investigation is discussed in application to the identification of conformations of the trialanine molecule via Robust Perron Cluster Analysis (PCCA+) .

A 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.

Localized motion in random matrix decomposition of complex financial systems

NASA Astrophysics Data System (ADS)

Jiang, Xiong-Fei; Zheng, Bo; Ren, Fei; Qiu, Tian

2017-04-01

With the random matrix theory, we decompose the multi-dimensional time series of complex financial systems into a set of orthogonal eigenmode functions, which are classified into the market mode, sector mode, and random mode. In particular, the localized motion generated by the business sectors, plays an important role in financial systems. Both the business sectors and their impact on the stock market are identified from the localized motion. We clarify that the localized motion induces different characteristics of the time correlations for the stock-market index and individual stocks. With a variation of a two-factor model, we reproduce the return-volatility correlations of the eigenmodes.

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/

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

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.

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.

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

Collaborative emitter tracking using Rao-Blackwellized random exchange diffusion particle filtering

NASA Astrophysics Data System (ADS)

Bruno, Marcelo G. S.; Dias, Stiven S.

2014-12-01

We introduce in this paper the fully distributed, random exchange diffusion particle filter (ReDif-PF) to track a moving emitter using multiple received signal strength (RSS) sensors. We consider scenarios with both known and unknown sensor model parameters. In the unknown parameter case, a Rao-Blackwellized (RB) version of the random exchange diffusion particle filter, referred to as the RB ReDif-PF, is introduced. In a simulated scenario with a partially connected network, the proposed ReDif-PF outperformed a PF tracker that assimilates local neighboring measurements only and also outperformed a linearized random exchange distributed extended Kalman filter (ReDif-EKF). Furthermore, the novel ReDif-PF matched the tracking error performance of alternative suboptimal distributed PFs based respectively on iterative Markov chain move steps and selective average gossiping with an inter-node communication cost that is roughly two orders of magnitude lower than the corresponding cost for the Markov chain and selective gossip filters. Compared to a broadcast-based filter which exactly mimics the optimal centralized tracker or its equivalent (exact) consensus-based implementations, ReDif-PF showed a degradation in steady-state error performance. However, compared to the optimal consensus-based trackers, ReDif-PF is better suited for real-time applications since it does not require iterative inter-node communication between measurement arrivals.

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.

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

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.

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.

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.

Many-body localization in Ising models with random long-range interactions

NASA Astrophysics Data System (ADS)

Li, Haoyuan; Wang, Jia; Liu, Xia-Ji; Hu, Hui

2016-12-01

We theoretically investigate the many-body localization phase transition in a one-dimensional Ising spin chain with random long-range spin-spin interactions, Vi j∝|i-j |-α , where the exponent of the interaction range α can be tuned from zero to infinitely large. By using exact diagonalization, we calculate the half-chain entanglement entropy and the energy spectral statistics and use them to characterize the phase transition towards the many-body localization phase at infinite temperature and at sufficiently large disorder strength. We perform finite-size scaling to extract the critical disorder strength and the critical exponent of the divergent localization length. With increasing α , the critical exponent experiences a sharp increase at about αc≃1.2 and then gradually decreases to a value found earlier in a disordered short-ranged interacting spin chain. For α <αc , we find that the system is mostly localized and the increase in the disorder strength may drive a transition between two many-body localized phases. In contrast, for α >αc , the transition is from a thermalized phase to the many-body localization phase. Our predictions could be experimentally tested with an ion-trap quantum emulator with programmable random long-range interactions, or with randomly distributed Rydberg atoms or polar molecules in lattices.

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.

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

NASA Technical Reports Server (NTRS)

English, Thomas

2005-01-01

A standard tool of reliability analysis used at NASA-JSC is the event tree. An event tree is simply a probability tree, with the probabilities determining the next step through the tree specified at each node. The nodal probabilities are determined by a reliability study of the physical system at work for a particular node. The reliability study performed at a node is typically referred to as a fault tree analysis, with the potential of a fault tree existing.for each node on the event tree. When examining an event tree it is obvious why the event tree/fault tree approach has been adopted. Typical event trees are quite complex in nature, and the event tree/fault tree approach provides a systematic and organized approach to reliability analysis. The purpose of this study was two fold. Firstly, we wanted to explore the possibility that a semi-Markov process can create dependencies between sojourn times (the times it takes to transition from one state to the next) that can decrease the uncertainty when estimating time to failures. Using a generalized semi-Markov model, we studied a four element reliability model and were able to demonstrate such sojourn time dependencies. Secondly, we wanted to study the use of semi-Markov processes to introduce a time variable into the event tree diagrams that are commonly developed in PRA (Probabilistic Risk Assessment) analyses. Event tree end states which change with time are more representative of failure scenarios than are the usual static probability-derived end states.

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.

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…

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.

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.

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.

Local polynomial chaos expansion for linear differential equations with high dimensional random inputs

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

Chen, Yi; Jakeman, John; Gittelson, Claude

2015-01-08

In this paper we present a localized polynomial chaos expansion for partial differential equations (PDE) with random inputs. In particular, we focus on time independent linear stochastic problems with high dimensional random inputs, where the traditional polynomial chaos methods, and most of the existing methods, incur prohibitively high simulation cost. Furthermore, the local polynomial chaos method employs a domain decomposition technique to approximate the stochastic solution locally. In each subdomain, a subdomain problem is solved independently and, more importantly, in a much lower dimensional random space. In a postprocesing stage, accurate samples of the original stochastic problems are obtained frommore » the samples of the local solutions by enforcing the correct stochastic structure of the random inputs and the coupling conditions at the interfaces of the subdomains. Overall, the method is able to solve stochastic PDEs in very large dimensions by solving a collection of low dimensional local problems and can be highly efficient. In our paper we present the general mathematical framework of the methodology and use numerical examples to demonstrate the properties of the method.« less

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.

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

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.

Markov chains for testing redundant software

NASA Technical Reports Server (NTRS)

White, Allan L.; Sjogren, Jon A.

1988-01-01

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

Policy Transfer via Markov Logic Networks

NASA Astrophysics Data System (ADS)

Torrey, Lisa; Shavlik, Jude

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

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

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.

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

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

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.

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.

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.

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.

Localized surface plasmon enhanced cellular imaging using random metallic structures

NASA Astrophysics Data System (ADS)

Son, Taehwang; Lee, Wonju; Kim, Donghyun

2017-02-01

We have studied fluorescence cellular imaging with randomly distributed localized near-field induced by silver nano-islands. For the fabrication of nano-islands, a 10-nm silver thin film evaporated on a BK7 glass substrate with an adhesion layer of 2-nm thick chromium. Micrometer sized silver square pattern was defined using e-beam lithography and then the film was annealed at 200°C. Raw images were restored using electric field distribution produced on the surface of random nano-islands. Nano-islands were modeled from SEM images. 488-nm p-polarized light source was set to be incident at 60°. Simulation results show that localized electric fields were created among nano-islands and that their average size was found to be 135 nm. The feasibility was tested using conventional total internal reflection fluorescence microscopy while the angle of incidence was adjusted to maximize field enhancement. Mouse microphage cells were cultured on nano-islands, and actin filaments were selectively stained with FITC-conjugated phalloidin. Acquired images were deconvolved based on linear imaging theory, in which molecular distribution was sampled by randomly distributed localized near-field and blurred by point spread function of far-field optics. The optimum fluorophore distribution was probabilistically estimated by repetitively matching a raw image. The deconvolved images are estimated to have a resolution in the range of 100-150 nm largely determined by the size of localized near-fields. We also discuss and compare the results with images acquired with periodic nano-aperture arrays in various optical configurations to excite localized plasmonic fields and to produce super-resolved molecular images.

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.

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

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

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.

Quantum Enhanced Inference in Markov Logic Networks

NASA Astrophysics Data System (ADS)

Wittek, Peter; Gogolin, Christian

2017-04-01

Markov logic networks (MLNs) reconcile two opposing schools in machine learning and artificial intelligence: causal networks, which account for uncertainty extremely well, and first-order logic, which allows for formal deduction. An MLN is essentially a first-order logic template to generate Markov networks. Inference in MLNs is probabilistic and it is often performed by approximate methods such as Markov chain Monte Carlo (MCMC) Gibbs sampling. An MLN has many regular, symmetric structures that can be exploited at both first-order level and in the generated Markov network. We analyze the graph structures that are produced by various lifting methods and investigate the extent to which quantum protocols can be used to speed up Gibbs sampling with state preparation and measurement schemes. We review different such approaches, discuss their advantages, theoretical limitations, and their appeal to implementations. We find that a straightforward application of a recent result yields exponential speedup compared to classical heuristics in approximate probabilistic inference, thereby demonstrating another example where advanced quantum resources can potentially prove useful in machine learning.

Quantum Enhanced Inference in Markov Logic Networks.

PubMed

Wittek, Peter; Gogolin, Christian

2017-04-19

Markov logic networks (MLNs) reconcile two opposing schools in machine learning and artificial intelligence: causal networks, which account for uncertainty extremely well, and first-order logic, which allows for formal deduction. An MLN is essentially a first-order logic template to generate Markov networks. Inference in MLNs is probabilistic and it is often performed by approximate methods such as Markov chain Monte Carlo (MCMC) Gibbs sampling. An MLN has many regular, symmetric structures that can be exploited at both first-order level and in the generated Markov network. We analyze the graph structures that are produced by various lifting methods and investigate the extent to which quantum protocols can be used to speed up Gibbs sampling with state preparation and measurement schemes. We review different such approaches, discuss their advantages, theoretical limitations, and their appeal to implementations. We find that a straightforward application of a recent result yields exponential speedup compared to classical heuristics in approximate probabilistic inference, thereby demonstrating another example where advanced quantum resources can potentially prove useful in machine learning.

Quantum Enhanced Inference in Markov Logic Networks

PubMed Central

Wittek, Peter; Gogolin, Christian

2017-01-01

Markov logic networks (MLNs) reconcile two opposing schools in machine learning and artificial intelligence: causal networks, which account for uncertainty extremely well, and first-order logic, which allows for formal deduction. An MLN is essentially a first-order logic template to generate Markov networks. Inference in MLNs is probabilistic and it is often performed by approximate methods such as Markov chain Monte Carlo (MCMC) Gibbs sampling. An MLN has many regular, symmetric structures that can be exploited at both first-order level and in the generated Markov network. We analyze the graph structures that are produced by various lifting methods and investigate the extent to which quantum protocols can be used to speed up Gibbs sampling with state preparation and measurement schemes. We review different such approaches, discuss their advantages, theoretical limitations, and their appeal to implementations. We find that a straightforward application of a recent result yields exponential speedup compared to classical heuristics in approximate probabilistic inference, thereby demonstrating another example where advanced quantum resources can potentially prove useful in machine learning. PMID:28422093

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.

Localization on Quantum Graphs with Random Vertex Couplings

NASA Astrophysics Data System (ADS)

Klopp, Frédéric; Pankrashkin, Konstantin

2008-05-01

We consider Schrödinger operators on a class of periodic quantum graphs with randomly distributed Kirchhoff coupling constants at all vertices. We obtain necessary conditions for localization on quantum graphs in terms of finite volume criteria for some energy-dependent discrete Hamiltonians. These conditions hold in the strong disorder limit and at the spectral edges.

Identifying and correcting non-Markov states in peptide conformational dynamics

NASA Astrophysics Data System (ADS)

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

2010-02-01

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

Modeling 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.

Modeling haplotype block variation using Markov chains.

PubMed

Greenspan, G; Geiger, D

2006-04-01

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

Modeling Haplotype Block Variation Using Markov Chains

PubMed Central

Greenspan, G.; Geiger, D.

2006-01-01

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

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.

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

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.

Markov Analysis of Sleep Dynamics

NASA Astrophysics Data System (ADS)

Kim, J. W.; Lee, J.-S.; Robinson, P. A.; Jeong, D.-U.

2009-05-01

A new approach, based on a Markov transition matrix, is proposed to explain frequent sleep and wake transitions during sleep. The matrix is determined by analyzing hypnograms of 113 obstructive sleep apnea patients. Our approach shows that the statistics of sleep can be constructed via a single Markov process and that durations of all states have modified exponential distributions, in contrast to recent reports of a scale-free form for the wake stage and an exponential form for the sleep stage. Hypnograms of the same subjects, but treated with Continuous Positive Airway Pressure, are analyzed and compared quantitatively with the pretreatment ones, suggesting potential clinical applications.

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.

Transition records of stationary Markov chains.

PubMed

Naudts, Jan; Van der Straeten, Erik

2006-10-01

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

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.

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.

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)

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.

Stimulated luminescence emission from localized recombination in randomly distributed defects.

PubMed

Jain, Mayank; Guralnik, Benny; Andersen, Martin Thalbitzer

2012-09-26

We present a new kinetic model describing localized electronic recombination through the excited state of the donor (d) to an acceptor (a) centre in luminescent materials. In contrast to the existing models based on the localized transition model (LTM) of Halperin and Braner (1960 Phys. Rev. 117 408-15) which assumes a fixed d → a tunnelling probability for the entire crystal, our model is based on nearest-neighbour recombination within randomly distributed centres. Such a random distribution can occur through the entire volume or within the defect complexes of the dosimeter, and implies that the tunnelling probability varies with the donor-acceptor (d-a) separation distance. We first develop an 'exact kinetic model' that incorporates this variation in tunnelling probabilities, and evolves both in spatial as well as temporal domains. We then develop a simplified one-dimensional, semi-analytical model that evolves only in the temporal domain. An excellent agreement is observed between thermally and optically stimulated luminescence (TL and OSL) results produced from the two models. In comparison to the first-order kinetic behaviour of the LTM of Halperin and Braner (1960 Phys. Rev. 117 408-15), our model results in a highly asymmetric TL peak; this peak can be understood to derive from a continuum of several first-order TL peaks. Our model also shows an extended power law behaviour for OSL (or prompt luminescence), which is expected from localized recombination mechanisms in materials with random distribution of centres.

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.

Diagonal couplings of quantum Markov chains

NASA Astrophysics Data System (ADS)

Kümmerer, Burkhard; Schwieger, Kay

2016-05-01

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

Markov Chain Ontology Analysis (MCOA)

PubMed Central

2012-01-01

Background Biomedical ontologies have become an increasingly critical lens through which researchers analyze the genomic, clinical and bibliographic data that fuels scientific research. Of particular relevance are methods, such as enrichment analysis, that quantify the importance of ontology classes relative to a collection of domain data. Current analytical techniques, however, remain limited in their ability to handle many important types of structural complexity encountered in real biological systems including class overlaps, continuously valued data, inter-instance relationships, non-hierarchical relationships between classes, semantic distance and sparse data. Results In this paper, we describe a methodology called Markov Chain Ontology Analysis (MCOA) and illustrate its use through a MCOA-based enrichment analysis application based on a generative model of gene activation. MCOA models the classes in an ontology, the instances from an associated dataset and all directional inter-class, class-to-instance and inter-instance relationships as a single finite ergodic Markov chain. The adjusted transition probability matrix for this Markov chain enables the calculation of eigenvector values that quantify the importance of each ontology class relative to other classes and the associated data set members. On both controlled Gene Ontology (GO) data sets created with Escherichia coli, Drosophila melanogaster and Homo sapiens annotations and real gene expression data extracted from the Gene Expression Omnibus (GEO), the MCOA enrichment analysis approach provides the best performance of comparable state-of-the-art methods. Conclusion A methodology based on Markov chain models and network analytic metrics can help detect the relevant signal within large, highly interdependent and noisy data sets and, for applications such as enrichment analysis, has been shown to generate superior performance on both real and simulated data relative to existing state-of-the-art approaches

Markov Chain Ontology Analysis (MCOA).

PubMed

Frost, H Robert; McCray, Alexa T

2012-02-03

Biomedical ontologies have become an increasingly critical lens through which researchers analyze the genomic, clinical and bibliographic data that fuels scientific research. Of particular relevance are methods, such as enrichment analysis, that quantify the importance of ontology classes relative to a collection of domain data. Current analytical techniques, however, remain limited in their ability to handle many important types of structural complexity encountered in real biological systems including class overlaps, continuously valued data, inter-instance relationships, non-hierarchical relationships between classes, semantic distance and sparse data. In this paper, we describe a methodology called Markov Chain Ontology Analysis (MCOA) and illustrate its use through a MCOA-based enrichment analysis application based on a generative model of gene activation. MCOA models the classes in an ontology, the instances from an associated dataset and all directional inter-class, class-to-instance and inter-instance relationships as a single finite ergodic Markov chain. The adjusted transition probability matrix for this Markov chain enables the calculation of eigenvector values that quantify the importance of each ontology class relative to other classes and the associated data set members. On both controlled Gene Ontology (GO) data sets created with Escherichia coli, Drosophila melanogaster and Homo sapiens annotations and real gene expression data extracted from the Gene Expression Omnibus (GEO), the MCOA enrichment analysis approach provides the best performance of comparable state-of-the-art methods. A methodology based on Markov chain models and network analytic metrics can help detect the relevant signal within large, highly interdependent and noisy data sets and, for applications such as enrichment analysis, has been shown to generate superior performance on both real and simulated data relative to existing state-of-the-art approaches.

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.

Multiensemble Markov models of molecular thermodynamics and kinetics.

PubMed

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

2016-06-07

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

Multiensemble Markov models of molecular thermodynamics and kinetics

PubMed Central

Wu, Hao; Paul, Fabian; Noé, Frank

2016-01-01

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

Compactness of viral genomes: effect of disperse and localized random mutations

NASA Astrophysics Data System (ADS)

Lošdorfer Božič, Anže; Micheletti, Cristian; Podgornik, Rudolf; Tubiana, Luca

2018-02-01

Genomes of single-stranded RNA viruses have evolved to optimize several concurrent properties. One of them is the architecture of their genomic folds, which must not only feature precise structural elements at specific positions, but also allow for overall spatial compactness. The latter was shown to be disrupted by random synonymous mutations, a disruption which can consequently negatively affect genome encapsidation. In this study, we use three mutation schemes with different degrees of locality to mutate the genomes of phage MS2 and Brome Mosaic virus in order to understand the observed sensitivity of the global compactness of their folds. We find that mutating local stretches of their genomes’ sequence or structure is less disruptive to their compactness compared to inducing randomly-distributed mutations. Our findings are indicative of a mechanism for the conservation of compactness acting on a global scale of the genomes, and have several implications for understanding the interplay between local and global architecture of viral RNA genomes.

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.

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.

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

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.

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.

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 .

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.

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”.

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.

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.

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.

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.

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 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.

FAST TRACK COMMUNICATION Local randomness in Hardy's correlations: implications from the information causality principle

NASA Astrophysics Data System (ADS)

Rajjak Gazi, MD.; Rai, Ashutosh; Kunkri, Samir; Rahaman, Ramij

2010-11-01

Study of non-local correlations in terms of Hardy's argument has been quite popular in quantum mechanics. Hardy's non-locality argument depends on some kind of asymmetry, but a two-qubit maximally entangled state, being symmetric, does not exhibit this kind of non-locality. Here we ask the following question: can this feature be explained by some principle outside quantum mechanics? The no-signaling condition does not provide a solution. But, interestingly, the information causality principle (Pawlowski et al 2009 Nature 461 1101) offers an explanation. It shows that any generalized probability theory which gives completely random results for local dichotomic observable, cannot provide Hardy's non-local correlation if it is restricted by a necessary condition for respecting the information causality principle. In fact, the applied necessary condition imposes even more restrictions on the local randomness of measured observable. Still, there are some restrictions imposed by quantum mechanics that are not reproduced from the considered information causality condition.

Markov and semi-Markov processes as a failure rate

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

Grabski, Franciszek

2016-06-08

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

Source Localization in Wireless Sensor Networks with Randomly Distributed Elements under Multipath Propagation Conditions

DTIC Science & Technology

2009-03-01

IN WIRELESS SENSOR NETWORKS WITH RANDOMLY DISTRIBUTED ELEMENTS UNDER MULTIPATH PROPAGATION CONDITIONS by Georgios Tsivgoulis March 2009...COVERED Engineer’s Thesis 4. TITLE Source Localization in Wireless Sensor Networks with Randomly Distributed Elements under Multipath Propagation...the non-line-of-sight information. 15. NUMBER OF PAGES 111 14. SUBJECT TERMS Wireless Sensor Network , Direction of Arrival, DOA, Random

Noise can speed convergence in Markov chains.

PubMed

Franzke, Brandon; Kosko, Bart

2011-10-01

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

Prophylactic treatment of local reactions to i.v. vinorelbine: a randomized study.

PubMed

Quant, Eva; Bergman, Bengt

2012-08-01

Local reactions on the site of infusion are common with i.v. vinorelbine treatment. The study aims were to evaluate whether an i.v. saline infusion or steroid injection, or the combination of these measures, could decrease vinorelbine-related local reactions and to study to what extent such reactions actually occur. Patients with lung cancer and planned chemotherapy containing i.v. vinorelbine were randomized in a 2 × 2 factorial design to receive either 4 mg betamethasone or placebo i.v. prior to and either 20 or 250 ml saline infusion following the vinorelbine infusion. Local infusion site signs and symptoms were recorded during and 1 h after the vinorelbine infusion and collected by a study-specific diary 24-48 h following each treatment course. A total of 79 patients were randomized and evaluable. Local infusion site signs, symptoms and reactions occurred in 63% of all patients (49% during vinorelbine monotherapy courses), with local pain being most frequently reported. Pre-treatment with i.v. betamethasone was associated with a reduced risk of local pain (5/38 vs. 20/39; p < 0.001) or any symptoms (14/38 vs. 29/39; p = 0.01) compared with placebo during the 48 h following the vinorelbine infusion. The reduced pain effect was seen both during vinorelbine monotherapy courses and during combination chemotherapy with carboplatin. In contrast, there was no difference between post-treatment infusion with 20 or 250 ml saline with regard to local signs or symptoms. Local infusion site side effects are common with i.v. vinorelbine. Pre-treatment with 4 mg betamethasone i.v. is associated with a reduced risk of local symptoms or reactions, local pain in particular.

Diffusion, subdiffusion, and localization of active colloids in random post lattices

NASA Astrophysics Data System (ADS)

Morin, Alexandre; Lopes Cardozo, David; Chikkadi, Vijayakumar; Bartolo, Denis

2017-10-01

Combining experiments and theory, we address the dynamics of self-propelled particles in crowded environments. We first demonstrate that motile colloids cruising at constant speed through random lattices undergo a smooth transition from diffusive to subdiffusive to localized dynamics upon increasing the obstacle density. We then elucidate the nature of these transitions by performing extensive simulations constructed from a detailed analysis of the colloid-obstacle interactions. We evidence that repulsion at a distance and hard-core interactions both contribute to slowing down the long-time diffusion of the colloids. In contrast, the localization transition stems solely from excluded-volume interactions and occurs at the void-percolation threshold. Within this critical scenario, equivalent to that of the random Lorentz gas, genuine asymptotic subdiffusion is found only at the critical density where the motile particles explore a fractal maze.

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.

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.

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

NASA Astrophysics Data System (ADS)

Ruebeck, Joshua B.; James, Ryan G.; Mahoney, John R.; Crutchfield, James P.

2018-01-01

Understanding the generative mechanism of a natural system is a vital component of the scientific method. Here, we investigate one of the fundamental steps toward this goal by presenting the minimal generator of an arbitrary binary Markov process. This is a class of processes whose predictive model is well known. Surprisingly, the generative model requires three distinct topologies for different regions of parameter space. We show that a previously proposed generator for a particular set of binary Markov processes is, in fact, not minimal. Our results shed the first quantitative light on the relative (minimal) costs of prediction and generation. We find, for instance, that the difference between prediction and generation is maximized when the process is approximately independently, identically distributed.

Metadynamics Enhanced Markov Modeling of Protein Dynamics.

PubMed

Biswas, Mithun; Lickert, Benjamin; Stock, Gerhard

2018-05-31

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

Temperature scaling method for Markov chains.

PubMed

Crosby, Lonnie D; Windus, Theresa L

2009-01-22

The use of ab initio potentials in Monte Carlo simulations aimed at investigating the nucleation kinetics of water clusters is complicated by the computational expense of the potential energy determinations. Furthermore, the common desire to investigate the temperature dependence of kinetic properties leads to an urgent need to reduce the expense of performing simulations at many different temperatures. A method is detailed that allows a Markov chain (obtained via Monte Carlo) at one temperature to be scaled to other temperatures of interest without the need to perform additional large simulations. This Markov chain temperature-scaling (TeS) can be generally applied to simulations geared for numerous applications. This paper shows the quality of results which can be obtained by TeS and the possible quantities which may be extracted from scaled Markov chains. Results are obtained for a 1-D analytical potential for which the exact solutions are known. Also, this method is applied to water clusters consisting of between 2 and 5 monomers, using Dynamical Nucleation Theory to determine the evaporation rate constant for monomer loss. Although ab initio potentials are not utilized in this paper, the benefit of this method is made apparent by using the Dang-Chang polarizable classical potential for water to obtain statistical properties at various temperatures.

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

Exact goodness-of-fit tests for Markov chains.

PubMed

Besag, J; Mondal, D

2013-06-01

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

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.

Dual nature of localization in guiding systems with randomly corrugated boundaries: Anderson-type versus entropic

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

Tarasov, Yu.V., E-mail: yutarasov@ire.kharkov.ua; Shostenko, L.D.

A unified theory for the conductance of an infinitely long multimode quantum wire whose finite segment has randomly rough lateral boundaries is developed. It enables one to rigorously take account of all feasible mechanisms of wave scattering, both related to boundary roughness and to contacts between the wire rough section and the perfect leads within the same technical frameworks. The rough part of the conducting wire is shown to act as a mode-specific randomly modulated effective potential barrier whose height is governed essentially by the asperity slope. The mean height of the barrier, which is proportional to the average slopemore » squared, specifies the number of conducting channels. Under relatively small asperity amplitude this number can take on arbitrary small, up to zero, values if the asperities are sufficiently sharp. The consecutive channel cut-off that arises when the asperity sharpness increases can be regarded as a kind of localization, which is not related to the disorder per se but rather is of entropic or (equivalently) geometric origin. The fluctuating part of the effective barrier results in two fundamentally different types of guided wave scattering, viz., inter- and intramode scattering. The intermode scattering is shown to be for the most part very strong except in the cases of (a) extremely smooth asperities, (b) excessively small length of the corrugated segment, and (c) the asperities sharp enough for only one conducting channel to remain in the wire. Under strong intermode scattering, a new set of conducting channels develops in the corrugated waveguide, which have the form of asymptotically decoupled extended modes subject to individual solely intramode random potentials. In view of this fact, two transport regimes only are realizable in randomly corrugated multimode waveguides, specifically, the ballistic and the localized regime, the latter characteristic of one-dimensional random systems. Two kinds of localization are thus

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.

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.

Local random configuration-tree theory for string repetition and facilitated dynamics of glass

NASA Astrophysics Data System (ADS)

Lam, Chi-Hang

2018-02-01

We derive a microscopic theory of glassy dynamics based on the transport of voids by micro-string motions, each of which involves particles arranged in a line hopping simultaneously displacing one another. Disorder is modeled by a random energy landscape quenched in the configuration space of distinguishable particles, but transient in the physical space as expected for glassy fluids. We study the evolution of local regions with m coupled voids. At a low temperature, energetically accessible local particle configurations can be organized into a random tree with nodes and edges denoting configurations and micro-string propagations respectively. Such trees defined in the configuration space naturally describe systems defined in two- or three-dimensional physical space. A micro-string propagation initiated by a void can facilitate similar motions by other voids via perturbing the random energy landscape, realizing path interactions between voids or equivalently string interactions. We obtain explicit expressions of the particle diffusion coefficient and a particle return probability. Under our approximation, as temperature decreases, random trees of energetically accessible configurations exhibit a sequence of percolation transitions in the configuration space, with local regions containing fewer coupled voids entering the non-percolating immobile phase first. Dynamics is dominated by coupled voids of an optimal group size, which increases as temperature decreases. Comparison with a distinguishable-particle lattice model (DPLM) of glass shows very good quantitative agreements using only two adjustable parameters related to typical energy fluctuations and the interaction range of the micro-strings.

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.

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.

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.

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.

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.

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

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

NASA Astrophysics Data System (ADS)

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

2012-04-01

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

Conditioned Limit Theorems for Some Null Recurrent Markov Processes

DTIC Science & Technology

1976-08-01

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

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.

Diffusive and localization behavior of electromagnetic waves in a two-dimensional random medium

NASA Astrophysics Data System (ADS)

Wang, Ken Kang-Hsin; Ye, Zhen

2003-10-01

In this paper, we discuss the transport phenomena of electromagnetic waves in a two-dimensional random system which is composed of arrays of electrical dipoles, following the model presented earlier by Erdogan et al. [J. Opt. Soc. Am. B 10, 391 (1993)]. A set of self-consistent equations is presented, accounting for the multiple scattering in the system, and is then solved numerically. A strong localization regime is discovered in the frequency domain. The transport properties within, near the edge of, and nearly outside the localization regime are investigated for different parameters such as filling factor and system size. The results show that within the localization regime, waves are trapped near the transmitting source. Meanwhile, the diffusive waves follow an intuitive but expected picture. That is, they increase with traveling path as more and more random scattering incurs, followed by a saturation, then start to decay exponentially when the travelling path is large enough, signifying the localization effect. For the cases where the frequencies are near the boundary of or outside the localization regime, the results of diffusive waves are compared with the diffusion approximation, showing less encouraging agreement as in other systems [Asatryan et al., Phys. Rev. E 67, 036605 (2003)].

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

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

Influence of credit scoring on the dynamics of Markov chain

NASA Astrophysics Data System (ADS)

Galina, Timofeeva

2015-11-01

Markov processes are widely used to model the dynamics of a credit portfolio and forecast the portfolio risk and profitability. In the Markov chain model the loan portfolio is divided into several groups with different quality, which determined by presence of indebtedness and its terms. It is proposed that dynamics of portfolio shares is described by a multistage controlled system. The article outlines mathematical formalization of controls which reflect the actions of the bank's management in order to improve the loan portfolio quality. The most important control is the organization of approval procedure of loan applications. The credit scoring is studied as a control affecting to the dynamic system. Different formalizations of "good" and "bad" consumers are proposed in connection with the Markov chain model.

Band gaps and localization of surface water waves over large-scale sand waves with random fluctuations

NASA Astrophysics Data System (ADS)

Zhang, Yu; Li, Yan; Shao, Hao; Zhong, Yaozhao; Zhang, Sai; Zhao, Zongxi

2012-06-01

Band structure and wave localization are investigated for sea surface water waves over large-scale sand wave topography. Sand wave height, sand wave width, water depth, and water width between adjacent sand waves have significant impact on band gaps. Random fluctuations of sand wave height, sand wave width, and water depth induce water wave localization. However, random water width produces a perfect transmission tunnel of water waves at a certain frequency so that localization does not occur no matter how large a disorder level is applied. Together with theoretical results, the field experimental observations in the Taiwan Bank suggest band gap and wave localization as the physical mechanism of sea surface water wave propagating over natural large-scale sand waves.

Image segmentation using hidden Markov Gauss mixture models.

PubMed

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

2007-07-01

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

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.

Local spatiotemporal time-frequency peak filtering method for seismic random noise reduction

NASA Astrophysics Data System (ADS)

Liu, Yanping; Dang, Bo; Li, Yue; Lin, Hongbo

2014-12-01

To achieve a higher level of seismic random noise suppression, the Radon transform has been adopted to implement spatiotemporal time-frequency peak filtering (TFPF) in our previous studies. Those studies involved performing TFPF in full-aperture Radon domain, including linear Radon and parabolic Radon. Although the superiority of this method to the conventional TFPF has been tested through processing on synthetic seismic models and field seismic data, there are still some limitations in the method. Both full-aperture linear Radon and parabolic Radon are applicable and effective for some relatively simple situations (e.g., curve reflection events with regular geometry) but inapplicable for complicated situations such as reflection events with irregular shapes, or interlaced events with quite different slope or curvature parameters. Therefore, a localized approach to the application of the Radon transform must be applied. It would serve the filter method better by adapting the transform to the local character of the data variations. In this article, we propose an idea that adopts the local Radon transform referred to as piecewise full-aperture Radon to realize spatiotemporal TFPF, called local spatiotemporal TFPF. Through experiments on synthetic seismic models and field seismic data, this study demonstrates the advantage of our method in seismic random noise reduction and reflection event recovery for relatively complicated situations of seismic data.

Optimized mixed Markov models for motif identification

PubMed Central

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

2006-01-01

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

Operations and support cost modeling using Markov chains

NASA Technical Reports Server (NTRS)

Unal, Resit

1989-01-01

Systems for future missions will be selected with life cycle costs (LCC) as a primary evaluation criterion. This reflects the current realization that only systems which are considered affordable will be built in the future due to the national budget constaints. Such an environment calls for innovative cost modeling techniques which address all of the phases a space system goes through during its life cycle, namely: design and development, fabrication, operations and support; and retirement. A significant portion of the LCC for reusable systems are generated during the operations and support phase (OS). Typically, OS costs can account for 60 to 80 percent of the total LCC. Clearly, OS costs are wholly determined or at least strongly influenced by decisions made during the design and development phases of the project. As a result OS costs need to be considered and estimated early in the conceptual phase. To be effective, an OS cost estimating model needs to account for actual instead of ideal processes by associating cost elements with probabilities. One approach that may be suitable for OS cost modeling is the use of the Markov Chain Process. Markov chains are an important method of probabilistic analysis for operations research analysts but they are rarely used for life cycle cost analysis. This research effort evaluates the use of Markov Chains in LCC analysis by developing OS cost model for a hypothetical reusable space transportation vehicle (HSTV) and suggests further uses of the Markov Chain process as a design-aid tool.

Markov chain model for demersal fish catch analysis in Indonesia

NASA Astrophysics Data System (ADS)

Firdaniza; Gusriani, N.

2018-03-01

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

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.

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.

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.

Identification and Simulation of Subsurface Soil patterns using hidden Markov random fields and remote sensing and geophysical EMI data sets

NASA Astrophysics Data System (ADS)

Wang, Hui; Wellmann, Florian; Verweij, Elizabeth; von Hebel, Christian; van der Kruk, Jan

2017-04-01

Lateral and vertical spatial heterogeneity of subsurface properties such as soil texture and structure influences the available water and resource supply for crop growth. High-resolution mapping of subsurface structures using non-invasive geo-referenced geophysical measurements, like electromagnetic induction (EMI), enables a characterization of 3D soil structures, which have shown correlations to remote sensing information of the crop states. The benefit of EMI is that it can return 3D subsurface information, however the spatial dimensions are limited due to the labor intensive measurement procedure. Although active and passive sensors mounted on air- or space-borne platforms return 2D images, they have much larger spatial dimensions. Combining both approaches provides us with a potential pathway to extend the detailed 3D geophysical information to a larger area by using remote sensing information. In this study, we aim at extracting and providing insights into the spatial and statistical correlation of the geophysical and remote sensing observations of the soil/vegetation continuum system. To this end, two key points need to be addressed: 1) how to detect and recognize the geometric patterns (i.e., spatial heterogeneity) from multiple data sets, and 2) how to quantitatively describe the statistical correlation between remote sensing information and geophysical measurements. In the current study, the spatial domain is restricted to shallow depths up to 3 meters, and the geostatistical database contains normalized difference vegetation index (NDVI) derived from RapidEye satellite images and apparent electrical conductivities (ECa) measured from multi-receiver EMI sensors for nine depths of exploration ranging from 0-2.7 m. The integrated data sets are mapped into both the physical space (i.e. the spatial domain) and feature space (i.e. a two-dimensional space framed by the NDVI and the ECa data). Hidden Markov Random Fields (HMRF) are employed to model the

Radioactive Seed Localization or Wire-guided Localization of Nonpalpable Invasive and In Situ Breast Cancer: A Randomized, Multicenter, Open-label Trial.

PubMed

Langhans, Linnea; Tvedskov, Tove F; Klausen, Thomas L; Jensen, Maj-Britt; Talman, Maj-Lis; Vejborg, Ilse; Benian, Cemil; Roslind, Anne; Hermansen, Jonas; Oturai, Peter S; Bentzon, Niels; Kroman, Niels

2017-07-01

To compare the rate of positive resection margins between radioactive seed localization (RSL) and wire-guided localization (WGL) after breast conserving surgery (BCS). WGL is the current standard for localization of nonpalpable breast lesions in BCS, but there are several difficulties related to the method. From January 1, 2014 to February 4, 2016, patients with nonpalpable invasive breast cancer or DCIS visible on ultrasound were enrolled in this randomized, multicenter, open-label clinical trial, and randomly assigned to RSL or WGL. The primary outcome was margin status after BCS. Secondary outcomes were duration of the surgical procedure, weight of surgical specimen, and patients' pain perception. Analyses were performed by intention-to-treat (ITT) and per protocol. Out of 444 eligible patients, 413 lesions representing 409 patients were randomized; 207 to RSL and 206 to WGL. Twenty-three did not meet inclusion criteria, chose to withdraw, or had a change in surgical management and were excluded. The remaining 390 lesions constituted the ITT population. Here, resection margins were positive in 23 cases (11.8%) in the RSL group compared with 26 cases (13.3%) in the WGL group (P = 0.65). The per-protocol analysis revealed no difference in margin status (P = 0.62). There were no significant differences in the duration of the surgical procedure (P = 0.12), weight of the surgical specimen (P = 0.54) or the patients' pain perception (P = 0.28). RSL offers a major logistic advantage, as localization can be done several days before surgery without any increase in positive resection margins compared with WGL.

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.

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

NASA Astrophysics Data System (ADS)

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

2012-04-01

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

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.

Finding exact constants in a Markov model of Zipfs law generation

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

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.

Towards automatic Markov reliability modeling of computer architectures

NASA Technical Reports Server (NTRS)

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

1986-01-01

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

A Markov Random Field Framework for Protein Side-Chain Resonance Assignment

NASA Astrophysics Data System (ADS)

Zeng, Jianyang; Zhou, Pei; Donald, Bruce Randall

Nuclear magnetic resonance (NMR) spectroscopy plays a critical role in structural genomics, and serves as a primary tool for determining protein structures, dynamics and interactions in physiologically-relevant solution conditions. The current speed of protein structure determination via NMR is limited by the lengthy time required in resonance assignment, which maps spectral peaks to specific atoms and residues in the primary sequence. Although numerous algorithms have been developed to address the backbone resonance assignment problem [68,2,10,37,14,64,1,31,60], little work has been done to automate side-chain resonance assignment [43, 48, 5]. Most previous attempts in assigning side-chain resonances depend on a set of NMR experiments that record through-bond interactions with side-chain protons for each residue. Unfortunately, these NMR experiments have low sensitivity and limited performance on large proteins, which makes it difficult to obtain enough side-chain resonance assignments. On the other hand, it is essential to obtain almost all of the side-chain resonance assignments as a prerequisite for high-resolution structure determination. To overcome this deficiency, we present a novel side-chain resonance assignment algorithm based on alternative NMR experiments measuring through-space interactions between protons in the protein, which also provide crucial distance restraints and are normally required in high-resolution structure determination. We cast the side-chain resonance assignment problem into a Markov Random Field (MRF) framework, and extend and apply combinatorial protein design algorithms to compute the optimal solution that best interprets the NMR data. Our MRF framework captures the contact map information of the protein derived from NMR spectra, and exploits the structural information available from the backbone conformations determined by orientational restraints and a set of discretized side-chain conformations (i.e., rotamers). A Hausdorff

Dynamical Localization for Discrete and Continuous Random Schrödinger Operators

NASA Astrophysics Data System (ADS)

Germinet, F.; De Bièvre, S.

We show for a large class of random Schrödinger operators Ho on and on that dynamical localization holds, i.e. that, with probability one, for a suitable energy interval I and for q a positive real, Here ψ is a function of sufficiently rapid decrease, and PI(Ho) is the spectral projector of Ho corresponding to the interval I. The result is obtained through the control of the decay of the eigenfunctions of Ho and covers, in the discrete case, the Anderson tight-binding model with Bernoulli potential (dimension ν = 1) or singular potential (ν > 1), and in the continuous case Anderson as well as random Landau Hamiltonians.

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

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...

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.

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.

Droplet localization in the random XXZ model and its manifestations

NASA Astrophysics Data System (ADS)

Elgart, A.; Klein, A.; Stolz, G.

2018-01-01

We examine many-body localization properties for the eigenstates that lie in the droplet sector of the random-field spin- \\frac 1 2 XXZ chain. These states satisfy a basic single cluster localization property (SCLP), derived in Elgart et al (2018 J. Funct. Anal. (in press)). This leads to many consequences, including dynamical exponential clustering, non-spreading of information under the time evolution, and a zero velocity Lieb-Robinson bound. Since SCLP is only applicable to the droplet sector, our definitions and proofs do not rely on knowledge of the spectral and dynamical characteristics of the model outside this regime. Rather, to allow for a possible mobility transition, we adapt the notion of restricting the Hamiltonian to an energy window from the single particle setting to the many body context.

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

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.

Document Ranking Based upon Markov Chains.

ERIC Educational Resources Information Center

Danilowicz, Czeslaw; Balinski, Jaroslaw

2001-01-01

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

Inelastic collapse and near-wall localization of randomly accelerated particles.

PubMed

Belan, S; Chernykh, A; Lebedev, V; Falkovich, G

2016-05-01

Inelastic collapse of stochastic trajectories of a randomly accelerated particle moving in half-space z>0 has been discovered by McKean [J. Math. Kyoto Univ. 2, 227 (1963)] and then independently rediscovered by Cornell et al. [Phys. Rev. Lett. 81, 1142 (1998)PRLTAO0031-900710.1103/PhysRevLett.81.1142]. The essence of this phenomenon is that the particle arrives at the wall at z=0 with zero velocity after an infinite number of inelastic collisions if the restitution coefficient β of particle velocity is smaller than the critical value β_{c}=exp(-π/sqrt[3]). We demonstrate that inelastic collapse takes place also in a wide class of models with spatially inhomogeneous random forcing and, what is more, that the critical value β_{c} is universal. That class includes an important case of inertial particles in wall-bounded random flows. To establish how inelastic collapse influences the particle distribution, we derive the exact equilibrium probability density function ρ(z,v) for the particle position and velocity. The equilibrium distribution exists only at β<β_{c} and indicates that inelastic collapse does not necessarily imply near-wall localization.

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

PubMed

Malyshkina, Nataliya V; Mannering, Fred L

2010-01-01

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

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

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

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.

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.

MC3: Multi-core Markov-chain Monte Carlo code

NASA Astrophysics Data System (ADS)

Cubillos, Patricio; Harrington, Joseph; Lust, Nate; Foster, AJ; Stemm, Madison; Loredo, Tom; Stevenson, Kevin; Campo, Chris; Hardin, Matt; Hardy, Ryan

2016-10-01

MC3 (Multi-core Markov-chain Monte Carlo) is a Bayesian statistics tool that can be executed from the shell prompt or interactively through the Python interpreter with single- or multiple-CPU parallel computing. It offers Markov-chain Monte Carlo (MCMC) posterior-distribution sampling for several algorithms, Levenberg-Marquardt least-squares optimization, and uniform non-informative, Jeffreys non-informative, or Gaussian-informative priors. MC3 can share the same value among multiple parameters and fix the value of parameters to constant values, and offers Gelman-Rubin convergence testing and correlated-noise estimation with time-averaging or wavelet-based likelihood estimation methods.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

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.

Bayesian seismic tomography by parallel interacting Markov chains

NASA Astrophysics Data System (ADS)

Gesret, Alexandrine; Bottero, Alexis; Romary, Thomas; Noble, Mark; Desassis, Nicolas

2014-05-01

The velocity field estimated by first arrival traveltime tomography is commonly used as a starting point for further seismological, mineralogical, tectonic or similar analysis. In order to interpret quantitatively the results, the tomography uncertainty values as well as their spatial distribution are required. The estimated velocity model is obtained through inverse modeling by minimizing an objective function that compares observed and computed traveltimes. This step is often performed by gradient-based optimization algorithms. The major drawback of such local optimization schemes, beyond the possibility of being trapped in a local minimum, is that they do not account for the multiple possible solutions of the inverse problem. They are therefore unable to assess the uncertainties linked to the solution. Within a Bayesian (probabilistic) framework, solving the tomography inverse problem aims at estimating the posterior probability density function of velocity model using a global sampling algorithm. Markov chains Monte-Carlo (MCMC) methods are known to produce samples of virtually any distribution. In such a Bayesian inversion, the total number of simulations we can afford is highly related to the computational cost of the forward model. Although fast algorithms have been recently developed for computing first arrival traveltimes of seismic waves, the complete browsing of the posterior distribution of velocity model is hardly performed, especially when it is high dimensional and/or multimodal. In the latter case, the chain may even stay stuck in one of the modes. In order to improve the mixing properties of classical single MCMC, we propose to make interact several Markov chains at different temperatures. This method can make efficient use of large CPU clusters, without increasing the global computational cost with respect to classical MCMC and is therefore particularly suited for Bayesian inversion. The exchanges between the chains allow a precise sampling of the

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.

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.

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.

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.

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

Metastable Distributions of Markov Chains with Rare Transitions

NASA Astrophysics Data System (ADS)

Freidlin, M.; Koralov, L.

2017-06-01

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

Evaluation of Usability Utilizing Markov Models

ERIC Educational Resources Information Center

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

2012-01-01

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

Markov Chain Estimation of Avian Seasonal Fecundity

EPA Science Inventory

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

Simulation study of localization of electromagnetic waves in two-dimensional random dipolar systems.

PubMed

Wang, Ken Kang-Hsin; Ye, Zhen

2003-12-01

We study the propagation and scattering of electromagnetic waves by random arrays of dipolar cylinders in a uniform medium. A set of self-consistent equations, incorporating all orders of multiple scattering of the electromagnetic waves, is derived from first principles and then solved numerically for electromagnetic fields. For certain ranges of frequencies, spatially localized electromagnetic waves appear in such a simple but realistic disordered system. Dependence of localization on the frequency, radiation damping, and filling factor is shown. The spatial behavior of the total, coherent, and diffusive waves is explored in detail, and found to comply with a physical intuitive picture. A phase diagram characterizing localization is presented, in agreement with previous investigations on other systems.

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.

Improved longitudinal gray and white matter atrophy assessment via application of a 4-dimensional hidden Markov random field model.

PubMed

Dwyer, Michael G; Bergsland, Niels; Zivadinov, Robert

2014-04-15

SIENA and similar techniques have demonstrated the utility of performing "direct" measurements as opposed to post-hoc comparison of cross-sectional data for the measurement of whole brain (WB) atrophy over time. However, gray matter (GM) and white matter (WM) atrophy are now widely recognized as important components of neurological disease progression, and are being actively evaluated as secondary endpoints in clinical trials. Direct measures of GM/WM change with advantages similar to SIENA have been lacking. We created a robust and easily-implemented method for direct longitudinal analysis of GM/WM atrophy, SIENAX multi-time-point (SIENAX-MTP). We built on the basic halfway-registration and mask composition components of SIENA to improve the raw output of FMRIB's FAST tissue segmentation tool. In addition, we created LFAST, a modified version of FAST incorporating a 4th dimension in its hidden Markov random field model in order to directly represent time. The method was validated by scan-rescan, simulation, comparison with SIENA, and two clinical effect size comparisons. All validation approaches demonstrated improved longitudinal precision with the proposed SIENAX-MTP method compared to SIENAX. For GM, simulation showed better correlation with experimental volume changes (r=0.992 vs. 0.941), scan-rescan showed lower standard deviations (3.8% vs. 8.4%), correlation with SIENA was more robust (r=0.70 vs. 0.53), and effect sizes were improved by up to 68%. Statistical power estimates indicated a potential drop of 55% in the number of subjects required to detect the same treatment effect with SIENAX-MTP vs. SIENAX. The proposed direct GM/WM method significantly improves on the standard SIENAX technique by trading a small amount of bias for a large reduction in variance, and may provide more precise data and additional statistical power in longitudinal studies. Copyright © 2013 Elsevier Inc. All rights reserved.

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

PubMed

Sung, Minje; Soyer, Refik; Nhan, Nguyen

2007-07-10

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

[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.

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

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.

Acupuncture at local and distal points for chronic shoulder pain: study protocol for a randomized controlled trial.

PubMed

Fu, Qing-Nan; Shi, Guang-Xia; Li, Qian-Qian; He, Tian; Liu, Bao-Zhen; Sun, San-Feng; Wang, Jun; Tan, Cheng; Yang, Bo-Feng; Liu, Cun-Zhi

2014-04-17

Chronic shoulder pain (CSP) is the third most common type of musculoskeletal pain. It has a major impact on health-related quality of life. In Chinese medicine, CSP is considered one of the conditions most amenable to treatment with acupuncture. The purpose of this study is to evaluate the efficacy of local acupoints in combination with distal acupoints in pain relief and shoulder function improvement in CSP patients. This is a multicenter, single blind, factorial randomized controlled clinical trial. A total of 164 participants will be randomly allocated to four different groups: Group A will receive acupuncture at local acupoints in combination with distal acupoint. Group B will receive acupuncture at local acupoints in combination with distal non-acupoint. Group C will receive acupuncture at local non-acupoints in combination with distal acupoint. Group D will receive acupuncture at local non-acupoints in combination with distal non-acupoint. Each group will receive 12 treatments of acupuncture one to three times per week for six weeks in total. The primary outcome is shoulder pain intensity, which is graded using a 100 -mm Visual Analogue Scale. The assessment is at baseline (before treatment initiation), 6 weeks after the first acupuncture, 10 weeks after the first acupuncture and 18 weeks after the first acupuncture. This trial will be helpful in identifying whether acupuncture at local acupoints in combination with distal acupoints may be more effective than needling points separately. International Standard Randomized Controlled Trial Number Register: ISRCTN61861069 (http://www.controlled-trials.com).

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.

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.

Predictive Rate-Distortion for Infinite-Order Markov Processes

NASA Astrophysics Data System (ADS)

Marzen, Sarah E.; Crutchfield, James P.

2016-06-01

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

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.

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.

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.

Monitoring volcano activity through Hidden Markov Model

NASA Astrophysics Data System (ADS)

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

2013-12-01

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

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.

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.

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

PubMed

van Rosmalen, Joost; Toy, Mehlika; O'Mahony, James F

2013-08-01

Markov models are a simple and powerful tool for analyzing the health and economic effects of health care interventions. These models are usually evaluated in discrete time using cohort analysis. The use of discrete time assumes that changes in health states occur only at the end of a cycle period. Discrete-time Markov models only approximate the process of disease progression, as clinical events typically occur in continuous time. The approximation can yield biased cost-effectiveness estimates for Markov models with long cycle periods and if no half-cycle correction is made. The purpose of this article is to present an overview of methods for evaluating Markov models in continuous time. These methods use mathematical results from stochastic process theory and control theory. The methods are illustrated using an applied example on the cost-effectiveness of antiviral therapy for chronic hepatitis B. The main result is a mathematical solution for the expected time spent in each state in a continuous-time Markov model. It is shown how this solution can account for age-dependent transition rates and discounting of costs and health effects, and how the concept of tunnel states can be used to account for transition rates that depend on the time spent in a state. The applied example shows that the continuous-time model yields more accurate results than the discrete-time model but does not require much computation time and is easily implemented. In conclusion, continuous-time Markov models are a feasible alternative to cohort analysis and can offer several theoretical and practical advantages.

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.

Economic outcomes of maintenance gefitinib for locally advanced/metastatic non-small-cell lung cancer with unknown EGFR mutations: a semi-Markov model analysis.

PubMed

Zeng, Xiaohui; Li, Jianhe; Peng, Liubao; Wang, Yunhua; Tan, Chongqing; Chen, Gannong; Wan, Xiaomin; Lu, Qiong; Yi, Lidan

2014-01-01

Maintenance gefitinib significantly prolonged progression-free survival (PFS) compared with placebo in patients from eastern Asian with locally advanced/metastatic non-small-cell lung cancer (NSCLC) after four chemotherapeutic cycles (21 days per cycle) of first-line platinum-based combination chemotherapy without disease progression. The objective of the current study was to evaluate the cost-effectiveness of maintenance gefitinib therapy after four chemotherapeutic cycle's stand first-line platinum-based chemotherapy for patients with locally advanced or metastatic NSCLC with unknown EGFR mutations, from a Chinese health care system perspective. A semi-Markov model was designed to evaluate cost-effectiveness of the maintenance gefitinib treatment. Two-parametric Weibull and Log-logistic distribution were fitted to PFS and overall survival curves independently. One-way and probabilistic sensitivity analyses were conducted to assess the stability of the model designed. The model base-case analysis suggested that maintenance gefitinib would increase benefits in a 1, 3, 6 or 10-year time horizon, with incremental $184,829, $19,214, $19,328, and $21,308 per quality-adjusted life-year (QALY) gained, respectively. The most sensitive influential variable in the cost-effectiveness analysis was utility of PFS plus rash, followed by utility of PFS plus diarrhoea, utility of progressed disease, price of gefitinib, cost of follow-up treatment in progressed survival state, and utility of PFS on oral therapy. The price of gefitinib is the most significant parameter that could reduce the incremental cost per QALY. Probabilistic sensitivity analysis indicated that the cost-effective probability of maintenance gefitinib was zero under the willingness-to-pay (WTP) threshold of $16,349 (3 × per-capita gross domestic product of China). The sensitivity analyses all suggested that the model was robust. Maintenance gefitinib following first-line platinum-based chemotherapy for patients

Markov chain Monte Carlo estimation of quantum states

NASA Astrophysics Data System (ADS)

Diguglielmo, James; Messenger, Chris; Fiurášek, Jaromír; Hage, Boris; Samblowski, Aiko; Schmidt, Tabea; Schnabel, Roman

2009-03-01

We apply a Bayesian data analysis scheme known as the Markov chain Monte Carlo to the tomographic reconstruction of quantum states. This method yields a vector, known as the Markov chain, which contains the full statistical information concerning all reconstruction parameters including their statistical correlations with no a priori assumptions as to the form of the distribution from which it has been obtained. From this vector we can derive, e.g., the marginal distributions and uncertainties of all model parameters, and also of other quantities such as the purity of the reconstructed state. We demonstrate the utility of this scheme by reconstructing the Wigner function of phase-diffused squeezed states. These states possess non-Gaussian statistics and therefore represent a nontrivial case of tomographic reconstruction. We compare our results to those obtained through pure maximum-likelihood and Fisher information approaches.

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.

Markov Chains For Testing Redundant Software

NASA Technical Reports Server (NTRS)

White, Allan L.; Sjogren, Jon A.

1990-01-01

Preliminary design developed for validation experiment that addresses problems unique to assuring extremely high quality of multiple-version programs in process-control software. Approach takes into account inertia of controlled system in sense it takes more than one failure of control program to cause controlled system to fail. Verification procedure consists of two steps: experimentation (numerical simulation) and computation, with Markov model for each step.

Hidden Markov models for character recognition.

PubMed

Vlontzos, J A; Kung, S Y

1992-01-01

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

A simplified parsimonious higher order multivariate Markov chain model

NASA Astrophysics Data System (ADS)

Wang, Chao; Yang, Chuan-sheng

2017-09-01

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

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.

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

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

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

Recursive utility in a Markov environment with stochastic growth.

PubMed

Hansen, Lars Peter; Scheinkman, José A

2012-07-24

Recursive utility models that feature investor concerns about the intertemporal composition of risk are used extensively in applied research in macroeconomics and asset pricing. These models represent preferences as the solution to a nonlinear forward-looking difference equation with a terminal condition. In this paper we study infinite-horizon specifications of this difference equation in the context of a Markov environment. We establish a connection between the solution to this equation and to an arguably simpler Perron-Frobenius eigenvalue equation of the type that occurs in the study of large deviations for Markov processes. By exploiting this connection, we establish existence and uniqueness results. Moreover, we explore a substantive link between large deviation bounds for tail events for stochastic consumption growth and preferences induced by recursive utility.

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.

The Markov process admits a consistent steady-state thermodynamic formalism

NASA Astrophysics Data System (ADS)

Peng, Liangrong; Zhu, Yi; Hong, Liu

2018-01-01

The search for a unified formulation for describing various non-equilibrium processes is a central task of modern non-equilibrium thermodynamics. In this paper, a novel steady-state thermodynamic formalism was established for general Markov processes described by the Chapman-Kolmogorov equation. Furthermore, corresponding formalisms of steady-state thermodynamics for the master equation and Fokker-Planck equation could be rigorously derived in mathematics. To be concrete, we proved that (1) in the limit of continuous time, the steady-state thermodynamic formalism for the Chapman-Kolmogorov equation fully agrees with that for the master equation; (2) a similar one-to-one correspondence could be established rigorously between the master equation and Fokker-Planck equation in the limit of large system size; (3) when a Markov process is restrained to one-step jump, the steady-state thermodynamic formalism for the Fokker-Planck equation with discrete state variables also goes to that for master equations, as the discretization step gets smaller and smaller. Our analysis indicated that general Markov processes admit a unified and self-consistent non-equilibrium steady-state thermodynamic formalism, regardless of underlying detailed models.

Information Entropy Production of Maximum Entropy Markov Chains from Spike Trains

NASA Astrophysics Data System (ADS)

Cofré, Rodrigo; Maldonado, Cesar

2018-01-01

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

Chirp- and random-based coded ultrasonic excitation for localized blood-brain barrier opening

PubMed Central

Kamimura, HAS; Wang, S; Wu, S-Y; Karakatsani, ME; Acosta, C; Carneiro, AAO; Konofagou, EE

2015-01-01

Chirp- and random-based coded excitation methods have been proposed to reduce standing wave formation and improve focusing of transcranial ultrasound. However, no clear evidence has been shown to support the benefits of these ultrasonic excitation sequences in vivo. This study evaluates the chirp and periodic selection of random frequency (PSRF) coded-excitation methods for opening the blood-brain barrier (BBB) in mice. Three groups of mice (n=15) were injected with polydisperse microbubbles and sonicated in the caudate putamen using the chirp/PSRF coded (bandwidth: 1.5-1.9 MHz, peak negative pressure: 0.52 MPa, duration: 30 s) or standard ultrasound (frequency: 1.5 MHz, pressure: 0.52 MPa, burst duration: 20 ms, duration: 5 min) sequences. T1-weighted contrast-enhanced MRI scans were performed to quantitatively analyze focused ultrasound induced BBB opening. The mean opening volumes evaluated from the MRI were 9.38±5.71 mm3, 8.91±3.91 mm3 and 35.47 ± 5.10 mm3 for the chirp, random and regular sonications, respectively. The mean cavitation levels were 55.40±28.43 V.s, 63.87±29.97 V.s and 356.52±257.15 V.s for the chirp, random and regular sonications, respectively. The chirp and PSRF coded pulsing sequences improved the BBB opening localization by inducing lower cavitation levels and smaller opening volumes compared to results of the regular sonication technique. Larger bandwidths were associated with more focused targeting but were limited by the frequency response of the transducer, the skull attenuation and the microbubbles optimal frequency range. The coded methods could therefore facilitate highly localized drug delivery as well as benefit other transcranial ultrasound techniques that use higher pressure levels and higher precision to induce the necessary bioeffects in a brain region while avoiding damage to the surrounding healthy tissue. PMID:26394091

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

A tridiagonal parsimonious higher order multivariate Markov chain model

NASA Astrophysics Data System (ADS)

Wang, Chao; Yang, Chuan-sheng

2017-09-01

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

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.

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Sentiment classification technology based on Markov logic networks

NASA Astrophysics Data System (ADS)

He, Hui; Li, Zhigang; Yao, Chongchong; Zhang, Weizhe

2016-07-01

With diverse online media emerging, there is a growing concern of sentiment classification problem. At present, text sentiment classification mainly utilizes supervised machine learning methods, which feature certain domain dependency. On the basis of Markov logic networks (MLNs), this study proposed a cross-domain multi-task text sentiment classification method rooted in transfer learning. Through many-to-one knowledge transfer, labeled text sentiment classification, knowledge was successfully transferred into other domains, and the precision of the sentiment classification analysis in the text tendency domain was improved. The experimental results revealed the following: (1) the model based on a MLN demonstrated higher precision than the single individual learning plan model. (2) Multi-task transfer learning based on Markov logical networks could acquire more knowledge than self-domain learning. The cross-domain text sentiment classification model could significantly improve the precision and efficiency of text sentiment classification.

Estimation in a semi-Markov transformation model

PubMed Central

Dabrowska, Dorota M.

2012-01-01

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

Self-Organizing Hidden Markov Model Map (SOHMMM).

PubMed

Ferles, Christos; Stafylopatis, Andreas

2013-12-01

A hybrid approach combining the Self-Organizing Map (SOM) and the Hidden Markov Model (HMM) is presented. The Self-Organizing Hidden Markov Model Map (SOHMMM) establishes a cross-section between the theoretic foundations and algorithmic realizations of its constituents. The respective architectures and learning methodologies are fused in an attempt to meet the increasing requirements imposed by the properties of deoxyribonucleic acid (DNA), ribonucleic acid (RNA), and protein chain molecules. The fusion and synergy of the SOM unsupervised training and the HMM dynamic programming algorithms bring forth a novel on-line gradient descent unsupervised learning algorithm, which is fully integrated into the SOHMMM. Since the SOHMMM carries out probabilistic sequence analysis with little or no prior knowledge, it can have a variety of applications in clustering, dimensionality reduction and visualization of large-scale sequence spaces, and also, in sequence discrimination, search and classification. Two series of experiments based on artificial sequence data and splice junction gene sequences demonstrate the SOHMMM's characteristics and capabilities. Copyright © 2013 Elsevier Ltd. All rights reserved.

Markov State Models of gene regulatory networks.

PubMed

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

2017-02-06

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

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.

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

NASA Astrophysics Data System (ADS)

Wang, Yong; Hu, Zhen; Wang, Ying

2017-05-01

As the restaurant delivery robot is often in a dynamic and complex environment, including the chairs inadvertently moved to the channel and customers coming and going. The traditional Markov decision process path planning algorithm is not save, the robot is very close to the table and chairs. To solve this problem, this paper proposes the Markov Decision Process with a penalty term called MDPPT path planning algorithm according to the traditional Markov decision process (MDP). For MDP, if the restaurant delivery robot bumps into an obstacle, the reward it receives is part of the current status reward. For the MDPPT, the reward it receives not only the part of the current status but also a negative constant term. Simulation results show that the MDPPT algorithm can plan a more secure path.

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.

A Markov game theoretic data fusion approach for cyber situational awareness

NASA Astrophysics Data System (ADS)

Shen, Dan; Chen, Genshe; Cruz, Jose B., Jr.; Haynes, Leonard; Kruger, Martin; Blasch, Erik

2007-04-01

This paper proposes an innovative data-fusion/ data-mining game theoretic situation awareness and impact assessment approach for cyber network defense. Alerts generated by Intrusion Detection Sensors (IDSs) or Intrusion Prevention Sensors (IPSs) are fed into the data refinement (Level 0) and object assessment (L1) data fusion components. High-level situation/threat assessment (L2/L3) data fusion based on Markov game model and Hierarchical Entity Aggregation (HEA) are proposed to refine the primitive prediction generated by adaptive feature/pattern recognition and capture new unknown features. A Markov (Stochastic) game method is used to estimate the belief of each possible cyber attack pattern. Game theory captures the nature of cyber conflicts: determination of the attacking-force strategies is tightly coupled to determination of the defense-force strategies and vice versa. Also, Markov game theory deals with uncertainty and incompleteness of available information. A software tool is developed to demonstrate the performance of the high level information fusion for cyber network defense situation and a simulation example shows the enhanced understating of cyber-network defense.

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

PubMed Central

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

2016-01-01

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

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

PubMed

Rosta, Edina; Hummer, Gerhard

2015-01-13

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

Random matrix theory and cross-correlations in global financial indices and local stock market indices

NASA Astrophysics Data System (ADS)

Nobi, Ashadun; Maeng, Seong Eun; Ha, Gyeong Gyun; Lee, Jae Woo

2013-02-01

We analyzed cross-correlations between price fluctuations of global financial indices (20 daily stock indices over the world) and local indices (daily indices of 200 companies in the Korean stock market) by using random matrix theory (RMT). We compared eigenvalues and components of the largest and the second largest eigenvectors of the cross-correlation matrix before, during, and after the global financial the crisis in the year 2008. We find that the majority of its eigenvalues fall within the RMT bounds [ λ -, λ +], where λ - and λ + are the lower and the upper bounds of the eigenvalues of random correlation matrices. The components of the eigenvectors for the largest positive eigenvalues indicate the identical financial market mode dominating the global and local indices. On the other hand, the components of the eigenvector corresponding to the second largest eigenvalue are positive and negative values alternatively. The components before the crisis change sign during the crisis, and those during the crisis change sign after the crisis. The largest inverse participation ratio (IPR) corresponding to the smallest eigenvector is higher after the crisis than during any other periods in the global and local indices. During the global financial the crisis, the correlations among the global indices and among the local stock indices are perturbed significantly. However, the correlations between indices quickly recover the trends before the crisis.

A comparison of random draw and locally neutral models for the avifauna of an English woodland.

PubMed

Dolman, Andrew M; Blackburn, Tim M

2004-06-03

Explanations for patterns observed in the structure of local assemblages are frequently sought with reference to interactions between species, and between species and their local environment. However, analyses of null models, where non-interactive local communities are assembled from regional species pools, have demonstrated that much of the structure of local assemblages remains in simulated assemblages where local interactions have been excluded. Here we compare the ability of two null models to reproduce the breeding bird community of Eastern Wood, a 16-hectare woodland in England, UK. A random draw model, in which there is complete annual replacement of the community by immigrants from the regional pool, is compared to a locally neutral community model, in which there are two additional parameters describing the proportion of the community replaced annually (per capita death rate) and the proportion of individuals recruited locally rather than as immigrants from the regional pool. Both the random draw and locally neutral model are capable of reproducing with significant accuracy several features of the observed structure of the annual Eastern Wood breeding bird community, including species relative abundances, species richness and species composition. The two additional parameters present in the neutral model result in a qualitatively more realistic representation of the Eastern Wood breeding bird community, particularly of its dynamics through time. The fact that these parameters can be varied, allows for a close quantitative fit between model and observed communities to be achieved, particularly with respect to annual species richness and species accumulation through time. The presence of additional free parameters does not detract from the qualitative improvement in the model and the neutral model remains a model of local community structure that is null with respect to species differences at the local scale. The ability of this locally neutral model to

Recursive utility in a Markov environment with stochastic growth

PubMed Central

Hansen, Lars Peter; Scheinkman, José A.

2012-01-01

Recursive utility models that feature investor concerns about the intertemporal composition of risk are used extensively in applied research in macroeconomics and asset pricing. These models represent preferences as the solution to a nonlinear forward-looking difference equation with a terminal condition. In this paper we study infinite-horizon specifications of this difference equation in the context of a Markov environment. We establish a connection between the solution to this equation and to an arguably simpler Perron–Frobenius eigenvalue equation of the type that occurs in the study of large deviations for Markov processes. By exploiting this connection, we establish existence and uniqueness results. Moreover, we explore a substantive link between large deviation bounds for tail events for stochastic consumption growth and preferences induced by recursive utility. PMID:22778428

Strong disorder real-space renormalization for the many-body-localized phase of random Majorana models

NASA Astrophysics Data System (ADS)

Monthus, Cécile

2018-03-01

For the many-body-localized phase of random Majorana models, a general strong disorder real-space renormalization procedure known as RSRG-X (Pekker et al 2014 Phys. Rev. X 4 011052) is described to produce the whole set of excited states, via the iterative construction of the local integrals of motion (LIOMs). The RG rules are then explicitly derived for arbitrary quadratic Hamiltonians (free-fermions models) and for the Kitaev chain with local interactions involving even numbers of consecutive Majorana fermions. The emphasis is put on the advantages of the Majorana language over the usual quantum spin language to formulate unified RSRG-X rules.

Using Markov Chain Analyses in Counselor Education Research

ERIC Educational Resources Information Center

Duys, David K.; Headrick, Todd C.

2004-01-01

This study examined the efficacy of an infrequently used statistical analysis in counselor education research. A Markov chain analysis was used to examine hypothesized differences between students' use of counseling skills in an introductory course. Thirty graduate students participated in the study. Independent raters identified the microskills…

Numerical methods in Markov chain modeling

NASA Technical Reports Server (NTRS)

Philippe, Bernard; Saad, Youcef; Stewart, William J.

1989-01-01

Several methods for computing stationary probability distributions of Markov chains are described and compared. The main linear algebra problem consists of computing an eigenvector of a sparse, usually nonsymmetric, matrix associated with a known eigenvalue. It can also be cast as a problem of solving a homogeneous singular linear system. Several methods based on combinations of Krylov subspace techniques are presented. The performance of these methods on some realistic problems are compared.

Magnetic localization and orientation of the capsule endoscope based on a random complex algorithm.

PubMed

He, Xiaoqi; Zheng, Zizhao; Hu, Chao

2015-01-01

The development of the capsule endoscope has made possible the examination of the whole gastrointestinal tract without much pain. However, there are still some important problems to be solved, among which, one important problem is the localization of the capsule. Currently, magnetic positioning technology is a suitable method for capsule localization, and this depends on a reliable system and algorithm. In this paper, based on the magnetic dipole model as well as magnetic sensor array, we propose nonlinear optimization algorithms using a random complex algorithm, applied to the optimization calculation for the nonlinear function of the dipole, to determine the three-dimensional position parameters and two-dimensional direction parameters. The stability and the antinoise ability of the algorithm is compared with the Levenberg-Marquart algorithm. The simulation and experiment results show that in terms of the error level of the initial guess of magnet location, the random complex algorithm is more accurate, more stable, and has a higher "denoise" capacity, with a larger range for initial guess values.

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.

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

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

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

Exploring Mass Perception with Markov Chain Monte Carlo

ERIC Educational Resources Information Center

Cohen, Andrew L.; Ross, Michael G.

2009-01-01

Several previous studies have examined the ability to judge the relative mass of objects in idealized collisions. With a newly developed technique of psychological Markov chain Monte Carlo sampling (A. N. Sanborn & T. L. Griffiths, 2008), this work explores participants; perceptions of different collision mass ratios. The results reveal…

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

NASA Astrophysics Data System (ADS)

Demirer, Nazli

The control of systems with autonomous mobile agents has been a point of interest recently, with many applications like surveillance, coverage, searching over an area with probabilistic target locations or exploring an area. In all of these applications, the main goal of the swarm is to distribute itself over an operational space to achieve mission objectives specified by the density of swarm. This research focuses on the problem of controlling the distribution of multi-agent systems considering a hierarchical control structure where the whole swarm coordination is achieved at the high-level and individual vehicle/agent control is managed at the low-level. High-level coordination algorithms uses macroscopic models that describes the collective behavior of the whole swarm and specify the agent motion commands, whose execution will lead to the desired swarm behavior. The low-level control laws execute the motion to follow these commands at the agent level. The main objective of this research is to develop high-level decision control policies and algorithms to achieve physically realizable commanding of the agents by imposing mission constraints on the distribution. We also make some connections with decentralized low-level motion control. This dissertation proposes a Markov chain based method to control the density distribution of the whole system where the implementation can be achieved in a decentralized manner with no communication between agents since establishing communication with large number of agents is highly challenging. The ultimate goal is to guide the overall density distribution of the system to a prescribed steady-state desired distribution while satisfying desired transition and safety constraints. Here, the desired distribution is determined based on the mission requirements, for example in the application of area search, the desired distribution should match closely with the probabilistic target locations. The proposed method is applicable for both

Short-term outcomes of local infiltration anaesthetic in total knee arthroplasty: a randomized controlled double-blinded controlled trial.

PubMed

Mulford, Jonathan S; Watson, Anna; Broe, David; Solomon, Michael; Loefler, Andreas; Harris, Ian

2016-03-01

The primary objective of the study was to determine if local infiltration anaesthetic (LIA) reduced total length of hospital stay in total knee arthroplasty (TKA) patients. The study also examined whether LIA improves early pain management, patient satisfaction and range of motion in TKA patients. We conducted a randomized controlled double-blinded study. Fifty patients undergoing TKA were randomized to receive either placebo or LIA at the time of surgery and on the first day post-operatively. Pain scores, level of satisfaction and range of motion were recorded preoperatively and post-operatively. There was no statistical difference between the groups for length of stay, post-operative pain scores, satisfaction scores or range of motion 6 weeks post-operatively. This randomized double-blinded trial did not demonstrate a decrease in pain or reduction of length of stay due to local infiltration analgesia. © 2015 Royal Australasian College of Surgeons.

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.

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

PubMed

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

2012-04-01

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

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.

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.

Operational Markov Condition for Quantum Processes

NASA Astrophysics Data System (ADS)

Pollock, Felix A.; Rodríguez-Rosario, César; Frauenheim, Thomas; Paternostro, Mauro; Modi, Kavan

2018-01-01

We derive a necessary and sufficient condition for a quantum process to be Markovian which coincides with the classical one in the relevant limit. Our condition unifies all previously known definitions for quantum Markov processes by accounting for all potentially detectable memory effects. We then derive a family of measures of non-Markovianity with clear operational interpretations, such as the size of the memory required to simulate a process or the experimental falsifiability of a Markovian hypothesis.

Randomized clinical trial of local anesthetic versus a combination of local anesthetic with self-hypnosis in the management of pediatric procedure-related pain.

PubMed

Liossi, Christina; White, Paul; Hatira, Popi

2006-05-01

A prospective controlled trial was conducted to compare the efficacy of an analgesic cream (eutectic mixture of local anesthetics, or EMLA) with a combination of EMLA with hypnosis in the relief of lumbar puncture-induced pain and anxiety in 45 pediatric cancer patients (age 6-16 years). The study also explored whether young patients can be taught and can use hypnosis independently as well as whether the therapeutic benefit depends on hypnotizability. Patients were randomized to 1 of 3 groups: local anesthetic, local anesthetic plus hypnosis, and local anesthetic plus attention. Results confirmed that patients in the local anesthetic plus hypnosis group reported less anticipatory anxiety and less procedure-related pain and anxiety and that they were rated as demonstrating less behavioral distress during the procedure. The level of hypnotizability was significantly associated with the magnitude of treatment benefit, and this benefit was maintained when patients used hypnosis independently. 2006 APA, all rights reserved

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

USGS Publications Warehouse

Williams, B.K.

1988-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

Limiting Distributions of Functionals of Markov Chains.

DTIC Science & Technology

1984-08-01

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

Antipersistent Markov behavior in foreign exchange markets

NASA Astrophysics Data System (ADS)

Baviera, Roberto; Pasquini, Michele; Serva, Maurizio; Vergni, Davide; Vulpiani, Angelo

2002-09-01

A quantitative check of efficiency in US dollar/Deutsche mark exchange rates is developed using high-frequency (tick by tick) data. The antipersistent Markov behavior of log-price fluctuations of given size implies, in principle, the possibility of a statistical forecast. We introduce and measure the available information of the quote sequence, and we show how it can be profitable following a particular trading rule.

Markov Decision Process Measurement Model.

PubMed

LaMar, Michelle M

2018-03-01

Within-task actions can provide additional information on student competencies but are challenging to model. This paper explores the potential of using a cognitive model for decision making, the Markov decision process, to provide a mapping between within-task actions and latent traits of interest. Psychometric properties of the model are explored, and simulation studies report on parameter recovery within the context of a simple strategy game. The model is then applied to empirical data from an educational game. Estimates from the model are found to correlate more strongly with posttest results than a partial-credit IRT model based on outcome data alone.

Asteroid mass estimation with Markov-chain Monte Carlo

NASA Astrophysics Data System (ADS)

Siltala, L.; Granvik, M.

2017-09-01

We have developed a new Markov-chain Monte Carlo-based algorithm for asteroid mass estimation based on mutual encounters and tested it for several different asteroids. Our results are in line with previous literature values but suggest that uncertainties of prior estimates may be misleading as a consequence of using linearized methods.

Building Higher-Order Markov Chain Models with EXCEL

ERIC Educational Resources Information Center

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

2004-01-01

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

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

PubMed

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

2017-12-01

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

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

PubMed

Berlow, Noah; Pal, Ranadip

2011-01-01

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

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

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

Baldi, P.

1995-12-31

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

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

PubMed

Zhu, George; Lizotte, Dan; Hoey, Jesse

2014-05-01

To demonstrate the feasibility of using stochastic simulation methods for the solution of a large-scale Markov decision process model of on-line patient admissions scheduling. The problem of admissions scheduling is modeled as a Markov decision process in which the states represent numbers of patients using each of a number of resources. We investigate current state-of-the-art real time planning methods to compute solutions to this Markov decision process. Due to the complexity of the model, traditional model-based planners are limited in scalability since they require an explicit enumeration of the model dynamics. To overcome this challenge, we apply sample-based planners along with efficient simulation techniques that given an initial start state, generate an action on-demand while avoiding portions of the model that are irrelevant to the start state. We also propose a novel variant of a popular sample-based planner that is particularly well suited to the elective admissions problem. Results show that the stochastic simulation methods allow for the problem size to be scaled by a factor of almost 10 in the action space, and exponentially in the state space. We have demonstrated our approach on a problem with 81 actions, four specialities and four treatment patterns, and shown that we can generate solutions that are near-optimal in about 100s. Sample-based planners are a viable alternative to state-based planners for large Markov decision process models of elective admissions scheduling. Copyright © 2014 Elsevier B.V. All rights reserved.

Hidden Markov models for evolution and comparative genomics analysis.

PubMed

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

2013-01-01

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

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

PubMed

Li, Yan; Dong, Zigang

2016-06-27

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

Radiative transfer calculated from a Markov chain formalism

NASA Technical Reports Server (NTRS)

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

1978-01-01

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

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

PubMed

Zhao, Zhibiao

2011-06-01

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

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

PubMed Central

Zhao, Zhibiao

2011-01-01

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

A Langevin equation for the rates of currency exchange based on the Markov analysis

NASA Astrophysics Data System (ADS)

Farahpour, F.; Eskandari, Z.; Bahraminasab, A.; Jafari, G. R.; Ghasemi, F.; Sahimi, Muhammad; Reza Rahimi Tabar, M.

2007-11-01

We propose a method for analyzing the data for the rates of exchange of various currencies versus the U.S. dollar. The method analyzes the return time series of the data as a Markov process, and develops an effective equation which reconstructs it. We find that the Markov time scale, i.e., the time scale over which the data are Markov-correlated, is one day for the majority of the daily exchange rates that we analyze. We derive an effective Langevin equation to describe the fluctuations in the rates. The equation contains two quantities, D and D, representing the drift and diffusion coefficients, respectively. We demonstrate how the two coefficients are estimated directly from the data, without using any assumptions or models for the underlying stochastic time series that represent the daily rates of exchange of various currencies versus the U.S. dollar.

SU-G-IeP4-03: Cone Beam X-Ray Luminescence Computed Tomography Based On Generalized Gaussian Markov Random Field

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

Zhang, G; Xing, L

2016-06-15

Purpose: Cone beam X-ray luminescence computed tomography (CB-XLCT), which aims to achieve molecular and functional imaging by X-rays, has recently been proposed as a new imaging modality. However, the inverse problem of CB-XLCT is seriously ill-conditioned, hindering us to achieve good image quality. In this work, a novel reconstruction method based on Bayesian theory is proposed to tackle this problem Methods: Bayesian theory provides a natural framework for utilizing various kinds of available prior information to improve the reconstruction image quality. A generalized Gaussian Markov random field (GGMRF) model is proposed here to construct the prior model of the Bayesianmore » theory. The most important feature of GGMRF model is the adjustable shape parameter p, which can be continuously adjusted from 1 to 2. The reconstruction image tends to have more edge-preserving property when p is slide to 1, while having more noise tolerance property when p is slide to 2, just like the behavior of L1 and L2 regularization methods, respectively. The proposed method provides a flexible regularization framework to adapt to a wide range of applications. Results: Numerical simulations were implemented to test the performance of the proposed method. The Digimouse atlas were employed to construct a three-dimensional mouse model, and two small cylinders were placed inside to serve as the targets. Reconstruction results show that the proposed method tends to obtain better spatial resolution with a smaller shape parameter, while better signal-to-noise image with a larger shape parameter. Quantitative indexes, contrast-to-noise ratio (CNR) and full-width at half-maximum (FWHM), were used to assess the performance of the proposed method, and confirmed its effectiveness in CB-XLCT reconstruction. Conclusion: A novel reconstruction method for CB-XLCT is proposed based on GGMRF model, which enables an adjustable performance tradeoff between L1 and L2 regularization methods. Numerical

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.

Intelligent classifier for dynamic fault patterns based on hidden Markov model

NASA Astrophysics Data System (ADS)

Xu, Bo; Feng, Yuguang; Yu, Jinsong

2006-11-01

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

Discrete-element modeling of nacre-like materials: Effects of random microstructures on strain localization and mechanical performance

NASA Astrophysics Data System (ADS)

Abid, Najmul; Mirkhalaf, Mohammad; Barthelat, Francois

2018-03-01

Natural materials such as nacre, collagen, and spider silk are composed of staggered stiff and strong inclusions in a softer matrix. This type of hybrid microstructure results in remarkable combinations of stiffness, strength, and toughness and it now inspires novel classes of high-performance composites. However, the analytical and numerical approaches used to predict and optimize the mechanics of staggered composites often neglect statistical variations and inhomogeneities, which may have significant impacts on modulus, strength, and toughness. Here we present an analysis of localization using small representative volume elements (RVEs) and large scale statistical volume elements (SVEs) based on the discrete element method (DEM). DEM is an efficient numerical method which enabled the evaluation of more than 10,000 microstructures in this study, each including about 5,000 inclusions. The models explore the combined effects of statistics, inclusion arrangement, and interface properties. We find that statistical variations have a negative effect on all properties, in particular on the ductility and energy absorption because randomness precipitates the localization of deformations. However, the results also show that the negative effects of random microstructures can be offset by interfaces with large strain at failure accompanied by strain hardening. More specifically, this quantitative study reveals an optimal range of interface properties where the interfaces are the most effective at delaying localization. These findings show how carefully designed interfaces in bioinspired staggered composites can offset the negative effects of microstructural randomness, which is inherent to most current fabrication methods.

Discrete Latent Markov Models for Normally Distributed Response Data

ERIC Educational Resources Information Center

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

2005-01-01

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

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

NASA Astrophysics Data System (ADS)

Mathai, J.; Mujumdar, P.

2017-12-01

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

Improved estimates of partial volume coefficients from noisy brain MRI using spatial context.

PubMed

Manjón, José V; Tohka, Jussi; Robles, Montserrat

2010-11-01

This paper addresses the problem of accurate voxel-level estimation of tissue proportions in the human brain magnetic resonance imaging (MRI). Due to the finite resolution of acquisition systems, MRI voxels can contain contributions from more than a single tissue type. The voxel-level estimation of this fractional content is known as partial volume coefficient estimation. In the present work, two new methods to calculate the partial volume coefficients under noisy conditions are introduced and compared with current similar methods. Concretely, a novel Markov Random Field model allowing sharp transitions between partial volume coefficients of neighbouring voxels and an advanced non-local means filtering technique are proposed to reduce the errors due to random noise in the partial volume coefficient estimation. In addition, a comparison was made to find out how the different methodologies affect the measurement of the brain tissue type volumes. Based on the obtained results, the main conclusions are that (1) both Markov Random Field modelling and non-local means filtering improved the partial volume coefficient estimation results, and (2) non-local means filtering was the better of the two strategies for partial volume coefficient estimation. Copyright 2010 Elsevier Inc. 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…

Neyman, Markov processes and survival analysis.

PubMed

Yang, Grace

2013-07-01

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

Randomized controlled trial of local progesterone vs corticosteroid injection for carpal tunnel syndrome.

PubMed

Raeissadat, S A; Shahraeeni, S; Sedighipour, L; Vahdatpour, B

2017-10-01

A number of studies have demonstrated the neuroprotective effects of progesterone and its influence on the recovery after neural injury. Few studies investigated the efficacy of local progesterone in carpal tunnel syndrome. The objective of this study was to compare the long-term effects of progesterone vs corticosteroid local injections in patients with mild and moderate carpal tunnel syndrome. In this randomized clinical trial, 78 patients with carpal tunnel syndrome were assigned to two groups. Patients were treated with a single local injection of triamcinolone acetonide in one group and single local injection of hydroxy progesterone in the other group. Variables including pain (based on visual analogue scale), symptom severity, and functional status (based on Bostone/Levine symptom severity and functional status scale) and nerve conduction study were evaluated before and 6 months after the treatments. All outcome measures including pain and electrophysiologic findings, improved in both groups and there were no meaningful differences between two groups regarding mentioned variables except for functional outcome, which was significantly better in progesterone compared with corticosteroid group at 6-month follow-up (P=.04). The efficacy of progesterone local injection in mild and moderate CTS is equal and somehow superior to corticosteroid injection for relieving symptoms and improving functional and electrophysiologic findings at long-term follow-up. © 2017 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

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

NASA Technical Reports Server (NTRS)

Bole, Brian; Goebel, Kai; Vachtsevanos, George

2012-01-01

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

Quantitative risk stratification in Markov chains with limiting conditional distributions.

PubMed

Chan, David C; Pollett, Philip K; Weinstein, Milton C

2009-01-01

Many clinical decisions require patient risk stratification. The authors introduce the concept of limiting conditional distributions, which describe the equilibrium proportion of surviving patients occupying each disease state in a Markov chain with death. Such distributions can quantitatively describe risk stratification. The authors first establish conditions for the existence of a positive limiting conditional distribution in a general Markov chain and describe a framework for risk stratification using the limiting conditional distribution. They then apply their framework to a clinical example of a treatment indicated for high-risk patients, first to infer the risk of patients selected for treatment in clinical trials and then to predict the outcomes of expanding treatment to other populations of risk. For the general chain, a positive limiting conditional distribution exists only if patients in the earliest state have the lowest combined risk of progression or death. The authors show that in their general framework, outcomes and population risk are interchangeable. For the clinical example, they estimate that previous clinical trials have selected the upper quintile of patient risk for this treatment, but they also show that expanded treatment would weakly dominate this degree of targeted treatment, and universal treatment may be cost-effective. Limiting conditional distributions exist in most Markov models of progressive diseases and are well suited to represent risk stratification quantitatively. This framework can characterize patient risk in clinical trials and predict outcomes for other populations of risk.

No-signaling, perfect bipartite dichotomic correlations and local randomness

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

Seevinck, M. P.

2011-03-28

The no-signaling constraint on bi-partite correlations is reviewed. It is shown that in order to obtain non-trivial Bell-type inequalities that discern no-signaling correlations from more general ones, one must go beyond considering expectation values of products of observables only. A new set of nontrivial no-signaling inequalities is derived which have a remarkably close resemblance to the CHSH inequality, yet are fundamentally different. A set of inequalities by Roy and Singh and Avis et al., which is claimed to be useful for discerning no-signaling correlations, is shown to be trivially satisfied by any correlation whatsoever. Finally, using the set of newlymore » derived no-signaling inequalities a result with potential cryptographic consequences is proven: if different parties use identical devices, then, once they have perfect correlations at spacelike separation between dichotomic observables, they know that because of no-signaling the local marginals cannot but be completely random.« less

Statistical significance test for transition matrices of atmospheric Markov chains

NASA Technical Reports Server (NTRS)

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

1990-01-01

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

Medical imaging feasibility in body fluids using Markov chains

NASA Astrophysics Data System (ADS)

Kavehrad, M.; Armstrong, A. D.

2017-02-01

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

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.

Autologous whole blood versus corticosteroid local injection in treatment of plantar fasciitis: A randomized, controlled multicenter clinical trial.

PubMed

Karimzadeh, Afshin; Raeissadat, Seyed Ahmad; Erfani Fam, Saleh; Sedighipour, Leyla; Babaei-Ghazani, Arash

2017-03-01

Plantar fasciitis is the most common cause of heel pain. Local injection modalities are among treatment options in patients with resistant pain. The aim of the present study was to evaluate the effect of local autologous whole blood compared with corticosteroid local injection in treatment of plantar fasciitis. In this randomized controlled multicenter study, 36 patients with chronic plantar fasciitis were recruited. Patients were allocated randomly into three treatment groups: local autologous blood, local corticosteroid injection, and control groups receiving no injection. Patients were assessed with visual analog scale (VAS), pressure pain threshold (PPT), and plantar fasciitis pain/disability scale (PFPS) before treatment, as well as 4 and 12 weeks post therapy. Variables of pain and function improved significantly in both corticosteroid and autologous blood groups compared to control group. At 4 weeks following treatment, patients in corticosteroid group had significantly lower levels of pain than patients in autologous blood and control groups (higher PPT level, lower PFPS, and VAS). After 12 weeks of treatment, both corticosteroid and autologous blood groups had lower average levels of pain than control group. The corticosteroid group showed an early sharp and then more gradual improvement in pain scores, but autologous blood group had a steady gradual drop in pain. Autologous whole blood and corticosteroid local injection can both be considered as effective methods in the treatment of chronic plantar fasciitis. These treatments decrease pain and significantly improve function compared to no treatment.

An 'adding' algorithm for the Markov chain formalism for radiation transfer

NASA Technical Reports Server (NTRS)

Esposito, L. W.

1979-01-01

An adding algorithm is presented, that extends the Markov chain method and considers a preceding calculation as a single state of a new Markov chain. This method takes advantage of the description of the radiation transport as a stochastic process. Successive application of this procedure makes calculation possible for any optical depth without increasing the size of the linear system used. It is determined that the time required for the algorithm is comparable to that for a doubling calculation for homogeneous atmospheres. For an inhomogeneous atmosphere the new method is considerably faster than the standard adding routine. It is concluded that the algorithm is efficient, accurate, and suitable for smaller computers in calculating the diffuse intensity scattered by an inhomogeneous planetary atmosphere.

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.

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.

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

PubMed

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

2018-05-01

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

Adaptive Localization of Focus Point Regions via Random Patch Probabilistic Density from Whole-Slide, Ki-67-Stained Brain Tumor Tissue

PubMed Central

Alomari, Yazan M.; MdZin, Reena Rahayu

2015-01-01

Analysis of whole-slide tissue for digital pathology images has been clinically approved to provide a second opinion to pathologists. Localization of focus points from Ki-67-stained histopathology whole-slide tissue microscopic images is considered the first step in the process of proliferation rate estimation. Pathologists use eye pooling or eagle-view techniques to localize the highly stained cell-concentrated regions from the whole slide under microscope, which is called focus-point regions. This procedure leads to a high variety of interpersonal observations and time consuming, tedious work and causes inaccurate findings. The localization of focus-point regions can be addressed as a clustering problem. This paper aims to automate the localization of focus-point regions from whole-slide images using the random patch probabilistic density method. Unlike other clustering methods, random patch probabilistic density method can adaptively localize focus-point regions without predetermining the number of clusters. The proposed method was compared with the k-means and fuzzy c-means clustering methods. Our proposed method achieves a good performance, when the results were evaluated by three expert pathologists. The proposed method achieves an average false-positive rate of 0.84% for the focus-point region localization error. Moreover, regarding RPPD used to localize tissue from whole-slide images, 228 whole-slide images have been tested; 97.3% localization accuracy was achieved. PMID:25793010

Random local temporal structure of category fluency responses.

PubMed

Meyer, David J; Messer, Jason; Singh, Tanya; Thomas, Peter J; Woyczynski, Wojbor A; Kaye, Jeffrey; Lerner, Alan J

2012-04-01

The Category Fluency Test (CFT) provides a sensitive measurement of cognitive capabilities in humans related to retrieval from semantic memory. In particular, it is widely used to assess progress of cognitive impairment in patients with dementia. Previous research shows that, in the first approximation, the intensity of tested individuals' responses within a standard 60-s test period decays exponentially with time, with faster decay rates for more cognitively impaired patients. Such decay rate can then be viewed as a global (macro) diagnostic parameter of each test. In the present paper we focus on the statistical properties of the properly de-trended time intervals between consecutive responses (inter-call times) in the Category Fluency Test. In a sense, those properties reflect the local (micro) structure of the response generation process. We find that a good approximation for the distribution of the de-trended inter-call times is provided by the Weibull Distribution, a probability distribution that appears naturally in this context as a distribution of a minimum of independent random quantities and is the standard tool in industrial reliability theory. This insight leads us to a new interpretation of the concept of "navigating a semantic space" via patient responses.

On the utility of the multi-level algorithm for the solution of nearly completely decomposable Markov chains

NASA Technical Reports Server (NTRS)

Leutenegger, Scott T.; Horton, Graham

1994-01-01

Recently the Multi-Level algorithm was introduced as a general purpose solver for the solution of steady state Markov chains. In this paper, we consider the performance of the Multi-Level algorithm for solving Nearly Completely Decomposable (NCD) Markov chains, for which special-purpose iteractive aggregation/disaggregation algorithms such as the Koury-McAllister-Stewart (KMS) method have been developed that can exploit the decomposability of the the Markov chain. We present experimental results indicating that the general-purpose Multi-Level algorithm is competitive, and can be significantly faster than the special-purpose KMS algorithm when Gauss-Seidel and Gaussian Elimination are used for solving the individual blocks.

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.

The cutoff phenomenon in finite Markov chains.

PubMed Central

Diaconis, P

1996-01-01

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

Crossing over...Markov meets Mendel.

PubMed

Mneimneh, Saad

2012-01-01

Chromosomal crossover is a biological mechanism to combine parental traits. It is perhaps the first mechanism ever taught in any introductory biology class. The formulation of crossover, and resulting recombination, came about 100 years after Mendel's famous experiments. To a great extent, this formulation is consistent with the basic genetic findings of Mendel. More importantly, it provides a mathematical insight for his two laws (and corrects them). From a mathematical perspective, and while it retains similarities, genetic recombination guarantees diversity so that we do not rapidly converge to the same being. It is this diversity that made the study of biology possible. In particular, the problem of genetic mapping and linkage-one of the first efforts towards a computational approach to biology-relies heavily on the mathematical foundation of crossover and recombination. Nevertheless, as students we often overlook the mathematics of these phenomena. Emphasizing the mathematical aspect of Mendel's laws through crossover and recombination will prepare the students to make an early realization that biology, in addition to being experimental, IS a computational science. This can serve as a first step towards a broader curricular transformation in teaching biological sciences. I will show that a simple and modern treatment of Mendel's laws using a Markov chain will make this step possible, and it will only require basic college-level probability and calculus. My personal teaching experience confirms that students WANT to know Markov chains because they hear about them from bioinformaticists all the time. This entire exposition is based on three homework problems that I designed for a course in computational biology. A typical reader is, therefore, an instructional staff member or a student in a computational field (e.g., computer science, mathematics, statistics, computational biology, bioinformatics). However, other students may easily follow by omitting the

Crossing Over…Markov Meets Mendel

PubMed Central

Mneimneh, Saad

2012-01-01

Chromosomal crossover is a biological mechanism to combine parental traits. It is perhaps the first mechanism ever taught in any introductory biology class. The formulation of crossover, and resulting recombination, came about 100 years after Mendel's famous experiments. To a great extent, this formulation is consistent with the basic genetic findings of Mendel. More importantly, it provides a mathematical insight for his two laws (and corrects them). From a mathematical perspective, and while it retains similarities, genetic recombination guarantees diversity so that we do not rapidly converge to the same being. It is this diversity that made the study of biology possible. In particular, the problem of genetic mapping and linkage—one of the first efforts towards a computational approach to biology—relies heavily on the mathematical foundation of crossover and recombination. Nevertheless, as students we often overlook the mathematics of these phenomena. Emphasizing the mathematical aspect of Mendel's laws through crossover and recombination will prepare the students to make an early realization that biology, in addition to being experimental, IS a computational science. This can serve as a first step towards a broader curricular transformation in teaching biological sciences. I will show that a simple and modern treatment of Mendel's laws using a Markov chain will make this step possible, and it will only require basic college-level probability and calculus. My personal teaching experience confirms that students WANT to know Markov chains because they hear about them from bioinformaticists all the time. This entire exposition is based on three homework problems that I designed for a course in computational biology. A typical reader is, therefore, an instructional staff member or a student in a computational field (e.g., computer science, mathematics, statistics, computational biology, bioinformatics). However, other students may easily follow by omitting the

Animal vocal sequences: not the Markov chains we thought they were

PubMed Central

Kershenbaum, Arik; Bowles, Ann E.; Freeberg, Todd M.; Jin, Dezhe Z.; Lameira, Adriano R.; Bohn, Kirsten

2014-01-01

Many animals produce vocal sequences that appear complex. Most researchers assume that these sequences are well characterized as Markov chains (i.e. that the probability of a particular vocal element can be calculated from the history of only a finite number of preceding elements). However, this assumption has never been explicitly tested. Furthermore, it is unclear how language could evolve in a single step from a Markovian origin, as is frequently assumed, as no intermediate forms have been found between animal communication and human language. Here, we assess whether animal taxa produce vocal sequences that are better described by Markov chains, or by non-Markovian dynamics such as the ‘renewal process’ (RP), characterized by a strong tendency to repeat elements. We examined vocal sequences of seven taxa: Bengalese finches Lonchura striata domestica, Carolina chickadees Poecile carolinensis, free-tailed bats Tadarida brasiliensis, rock hyraxes Procavia capensis, pilot whales Globicephala macrorhynchus, killer whales Orcinus orca and orangutans Pongo spp. The vocal systems of most of these species are more consistent with a non-Markovian RP than with the Markovian models traditionally assumed. Our data suggest that non-Markovian vocal sequences may be more common than Markov sequences, which must be taken into account when evaluating alternative hypotheses for the evolution of signalling complexity, and perhaps human language origins. PMID:25143037

Animal vocal sequences: not the Markov chains we thought they were.

PubMed

Kershenbaum, Arik; Bowles, Ann E; Freeberg, Todd M; Jin, Dezhe Z; Lameira, Adriano R; Bohn, Kirsten

2014-10-07

Many animals produce vocal sequences that appear complex. Most researchers assume that these sequences are well characterized as Markov chains (i.e. that the probability of a particular vocal element can be calculated from the history of only a finite number of preceding elements). However, this assumption has never been explicitly tested. Furthermore, it is unclear how language could evolve in a single step from a Markovian origin, as is frequently assumed, as no intermediate forms have been found between animal communication and human language. Here, we assess whether animal taxa produce vocal sequences that are better described by Markov chains, or by non-Markovian dynamics such as the 'renewal process' (RP), characterized by a strong tendency to repeat elements. We examined vocal sequences of seven taxa: Bengalese finches Lonchura striata domestica, Carolina chickadees Poecile carolinensis, free-tailed bats Tadarida brasiliensis, rock hyraxes Procavia capensis, pilot whales Globicephala macrorhynchus, killer whales Orcinus orca and orangutans Pongo spp. The vocal systems of most of these species are more consistent with a non-Markovian RP than with the Markovian models traditionally assumed. Our data suggest that non-Markovian vocal sequences may be more common than Markov sequences, which must be taken into account when evaluating alternative hypotheses for the evolution of signalling complexity, and perhaps human language origins. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

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

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

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

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

1999-11-15

We introduce upper and lower envelopes for sets of measures on an arbitrary topological space, which are then used to give a tightness criterion. These concepts are applied to show the existence of optimal policies for a class of Markov control processes.

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

DTIC Science & Technology

2013-03-01

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

An abstract specification language for Markov reliability models

NASA Technical Reports Server (NTRS)

Butler, R. W.

1985-01-01

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

An abstract language for specifying Markov reliability models

NASA Technical Reports Server (NTRS)

Butler, Ricky W.

1986-01-01

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

Variable context Markov chains for HIV protease cleavage site prediction.

PubMed

Oğul, Hasan

2009-06-01

Deciphering the knowledge of HIV protease specificity and developing computational tools for detecting its cleavage sites in protein polypeptide chain are very desirable for designing efficient and specific chemical inhibitors to prevent acquired immunodeficiency syndrome. In this study, we developed a generative model based on a generalization of variable order Markov chains (VOMC) for peptide sequences and adapted the model for prediction of their cleavability by certain proteases. The new method, called variable context Markov chains (VCMC), attempts to identify the context equivalence based on the evolutionary similarities between individual amino acids. It was applied for HIV-1 protease cleavage site prediction problem and shown to outperform existing methods in terms of prediction accuracy on a common dataset. In general, the method is a promising tool for prediction of cleavage sites of all proteases and encouraged to be used for any kind of peptide classification problem as well.

Pattern statistics on Markov chains and sensitivity to parameter estimation.

PubMed

Nuel, Grégory

2006-10-17

In order to compute pattern statistics in computational biology a Markov model is commonly used to take into account the sequence composition. Usually its parameter must be estimated. The aim of this paper is to determine how sensitive these statistics are to parameter estimation, and what are the consequences of this variability on pattern studies (finding the most over-represented words in a genome, the most significant common words to a set of sequences,...). In the particular case where pattern statistics (overlap counting only) computed through binomial approximations we use the delta-method to give an explicit expression of sigma, the standard deviation of a pattern statistic. This result is validated using simulations and a simple pattern study is also considered. We establish that the use of high order Markov model could easily lead to major mistakes due to the high sensitivity of pattern statistics to parameter estimation.

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.

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

PubMed Central

Liu, Zengkai; Liu, Yonghong; Cai, Baoping

2014-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

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

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

Hybrid Discrete-Continuous Markov Decision Processes

NASA Technical Reports Server (NTRS)

Feng, Zhengzhu; Dearden, Richard; Meuleau, Nicholas; Washington, Rich

2003-01-01

This paper proposes a Markov decision process (MDP) model that features both discrete and continuous state variables. We extend previous work by Boyan and Littman on the mono-dimensional time-dependent MDP to multiple dimensions. We present the principle of lazy discretization, and piecewise constant and linear approximations of the model. Having to deal with several continuous dimensions raises several new problems that require new solutions. In the (piecewise) linear case, we use techniques from partially- observable MDPs (POMDPS) to represent value functions as sets of linear functions attached to different partitions of the state space.

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

PubMed Central

Rechner, Steffen; Berger, Annabell

2016-01-01

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

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

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

PubMed

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

2014-01-01

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

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

PubMed Central

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

2014-01-01

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

Effect of Facilitation of Local Maternal-and-Newborn Stakeholder Groups on Neonatal Mortality: Cluster-Randomized Controlled Trial

PubMed Central

Persson, Lars Åke; Nga, Nguyen T.; Målqvist, Mats; Thi Phuong Hoa, Dinh; Eriksson, Leif; Wallin, Lars; Selling, Katarina; Huy, Tran Q.; Duc, Duong M.; Tiep, Tran V.; Thi Thu Thuy, Vu; Ewald, Uwe

2013-01-01

Background Facilitation of local women's groups may reportedly reduce neonatal mortality. It is not known whether facilitation of groups composed of local health care staff and politicians can improve perinatal outcomes. We hypothesised that facilitation of local stakeholder groups would reduce neonatal mortality (primary outcome) and improve maternal, delivery, and newborn care indicators (secondary outcomes) in Quang Ninh province, Vietnam. Methods and Findings In a cluster-randomized design 44 communes were allocated to intervention and 46 to control. Laywomen facilitated monthly meetings during 3 years in groups composed of health care staff and key persons in the communes. A problem-solving approach was employed. Births and neonatal deaths were monitored, and interviews were performed in households of neonatal deaths and of randomly selected surviving infants. A latent period before effect is expected in this type of intervention, but this timeframe was not pre-specified. Neonatal mortality rate (NMR) from July 2008 to June 2011 was 16.5/1,000 (195 deaths per 11,818 live births) in the intervention communes and 18.4/1,000 (194 per 10,559 live births) in control communes (adjusted odds ratio [OR] 0.96 [95% CI 0.73–1.25]). There was a significant downward time trend of NMR in intervention communes (p = 0.003) but not in control communes (p = 0.184). No significant difference in NMR was observed during the first two years (July 2008 to June 2010) while the third year (July 2010 to June 2011) had significantly lower NMR in intervention arm: adjusted OR 0.51 (95% CI 0.30–0.89). Women in intervention communes more frequently attended antenatal care (adjusted OR 2.27 [95% CI 1.07–4.8]). Conclusions A randomized facilitation intervention with local stakeholder groups composed of primary care staff and local politicians working for three years with a perinatal problem-solving approach resulted in increased attendance to antenatal care and reduced neonatal

Students' Progress throughout Examination Process as a Markov Chain

ERIC Educational Resources Information Center

Hlavatý, Robert; Dömeová, Ludmila

2014-01-01

The paper is focused on students of Mathematical methods in economics at the Czech university of life sciences (CULS) in Prague. The idea is to create a model of students' progress throughout the whole course using the Markov chain approach. Each student has to go through various stages of the course requirements where his success depends on the…

Symbolic Heuristic Search for Factored Markov Decision Processes

NASA Technical Reports Server (NTRS)

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

2003-01-01

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

Theory and Applications of Weakly Interacting Markov Processes

DTIC Science & Technology

2018-02-03

Moderate deviation principles for stochastic dynamical systems. Boston University, Math Colloquium, March 27, 2015. • Moderate Deviation Principles for...Markov chain approximation method. Submitted. [8] E. Bayraktar and M. Ludkovski. Optimal trade execution in illiquid markets. Math . Finance, 21(4):681...701, 2011. [9] E. Bayraktar and M. Ludkovski. Liquidation in limit order books with controlled intensity. Math . Finance, 24(4):627–650, 2014. [10] P.D

Semi-Markov Approach to the Shipping Safety Modelling

NASA Astrophysics Data System (ADS)

Guze, Sambor; Smolarek, Leszek

2012-02-01

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

Tumor propagation model using generalized hidden Markov model

NASA Astrophysics Data System (ADS)

Park, Sun Young; Sargent, Dustin

2017-02-01

Tumor tracking and progression analysis using medical images is a crucial task for physicians to provide accurate and efficient treatment plans, and monitor treatment response. Tumor progression is tracked by manual measurement of tumor growth performed by radiologists. Several methods have been proposed to automate these measurements with segmentation, but many current algorithms are confounded by attached organs and vessels. To address this problem, we present a new generalized tumor propagation model considering time-series prior images and local anatomical features using a Hierarchical Hidden Markov model (HMM) for tumor tracking. First, we apply the multi-atlas segmentation technique to identify organs/sub-organs using pre-labeled atlases. Second, we apply a semi-automatic direct 3D segmentation method to label the initial boundary between the lesion and neighboring structures. Third, we detect vessels in the ROI surrounding the lesion. Finally, we apply the propagation model with the labeled organs and vessels to accurately segment and measure the target lesion. The algorithm has been designed in a general way to be applicable to various body parts and modalities. In this paper, we evaluate the proposed algorithm on lung and lung nodule segmentation and tracking. We report the algorithm's performance by comparing the longest diameter and nodule volumes using the FDA lung Phantom data and a clinical dataset.

Stochastic effects in EUV lithography: random, local CD variability, and printing failures

NASA Astrophysics Data System (ADS)

De Bisschop, Peter

2017-10-01

Stochastic effects in lithography are usually quantified through local CD variability metrics, such as line-width roughness or local CD uniformity (LCDU), and these quantities have been measured and studied intensively, both in EUV and optical lithography. Next to the CD-variability, stochastic effects can also give rise to local, random printing failures, such as missing contacts or microbridges in spaces. When these occur, there often is no (reliable) CD to be measured locally, and then such failures cannot be quantified with the usual CD-measuring techniques. We have developed algorithms to detect such stochastic printing failures in regular line/space (L/S) or contact- or dot-arrays from SEM images, leading to a stochastic failure metric that we call NOK (not OK), which we consider a complementary metric to the CD-variability metrics. This paper will show how both types of metrics can be used to experimentally quantify dependencies of stochastic effects to, e.g., CD, pitch, resist, exposure dose, etc. As it is also important to be able to predict upfront (in the OPC verification stage of a production-mask tape-out) whether certain structures in the layout are likely to have a high sensitivity to stochastic effects, we look into the feasibility of constructing simple predictors, for both stochastic CD-variability and printing failure, that can be calibrated for the process and exposure conditions used and integrated into the standard OPC verification flow. Finally, we briefly discuss the options to reduce stochastic variability and failure, considering the entire patterning ecosystem.

Continuous time random walk with local particle-particle interaction

NASA Astrophysics Data System (ADS)

Xu, Jianping; Jiang, Guancheng

2018-05-01

The continuous time random walk (CTRW) is often applied to the study of particle motion in disordered media. Yet most such applications do not allow for particle-particle (walker-walker) interaction. In this paper, we consider a CTRW with particle-particle interaction; however, for simplicity, we restrain the interaction to be local. The generalized Chapman-Kolmogorov equation is modified by introducing a perturbation function that fluctuates around 1, which models the effect of interaction. Subsequently, a time-fractional nonlinear advection-diffusion equation is derived from this walking system. Under the initial condition of condensed particles at the origin and the free-boundary condition, we numerically solve this equation with both attractive and repulsive particle-particle interactions. Moreover, a Monte Carlo simulation is devised to verify the results of the above numerical work. The equation and the simulation unanimously predict that this walking system converges to the conventional one in the long-time limit. However, for systems where the free-boundary condition and long-time limit are not simultaneously satisfied, this convergence does not hold.

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.

Pattern statistics on Markov chains and sensitivity to parameter estimation

PubMed Central

Nuel, Grégory

2006-01-01

Background: In order to compute pattern statistics in computational biology a Markov model is commonly used to take into account the sequence composition. Usually its parameter must be estimated. The aim of this paper is to determine how sensitive these statistics are to parameter estimation, and what are the consequences of this variability on pattern studies (finding the most over-represented words in a genome, the most significant common words to a set of sequences,...). Results: In the particular case where pattern statistics (overlap counting only) computed through binomial approximations we use the delta-method to give an explicit expression of σ, the standard deviation of a pattern statistic. This result is validated using simulations and a simple pattern study is also considered. Conclusion: We establish that the use of high order Markov model could easily lead to major mistakes due to the high sensitivity of pattern statistics to parameter estimation. PMID:17044916

Identification of observer/Kalman filter Markov parameters: Theory and experiments

NASA Technical Reports Server (NTRS)

Juang, Jer-Nan; Phan, Minh; Horta, Lucas G.; Longman, Richard W.

1991-01-01

An algorithm to compute Markov parameters of an observer or Kalman filter from experimental input and output data is discussed. The Markov parameters can then be used for identification of a state space representation, with associated Kalman gain or observer gain, for the purpose of controller design. The algorithm is a non-recursive matrix version of two recursive algorithms developed in previous works for different purposes. The relationship between these other algorithms is developed. The new matrix formulation here gives insight into the existence and uniqueness of solutions of certain equations and gives bounds on the proper choice of observer order. It is shown that if one uses data containing noise, and seeks the fastest possible deterministic observer, the deadbeat observer, one instead obtains the Kalman filter, which is the fastest possible observer in the stochastic environment. Results are demonstrated in numerical studies and in experiments on an ten-bay truss structure.

Local infiltration anesthesia with steroids in total knee arthroplasty: A systematic review of randomized control trials.

PubMed

Tran, Jonathan; Schwarzkopf, Ran

2015-10-01

Local infiltration anesthesia (LIA) with anesthetics, steroids, NSAIDS, and epinephrine has been shown to be effective in reducing total knee arthroplasty (TKA) postoperative pain. This systematic review explores the functional outcomes of randomized control trials that have compared the use of LIA with and without steroids during TKA. Five studies with 412 patients met the inclusion criteria, 228 received local infiltration anesthesia with steroids (LIAS) and 184 received local infiltration anesthesia without steroids (LIAWS). The use of LIAS in management of postoperative TKA pain has been shown to decrease the length of hospital stay, time required to achieve straight leg raise, and pro-inflammatory signals in patients. Although there is no overwhelming data to suggest LIAS improves postoperative TKA pain, current literature does support its effectiveness in producing other favorable surgical outcomes.

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

A coupled hidden Markov model for disease interactions

PubMed Central

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

2013-01-01

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

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

PubMed

Molitor, John

2012-03-01

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

Weighted Markov chains for forecasting and analysis in Incidence of infectious diseases in jiangsu Province, China☆

PubMed Central

Peng, Zhihang; Bao, Changjun; Zhao, Yang; Yi, Honggang; Xia, Letian; Yu, Hao; Shen, Hongbing; Chen, Feng

2010-01-01

This paper first applies the sequential cluster method to set up the classification standard of infectious disease incidence state based on the fact that there are many uncertainty characteristics in the incidence course. Then the paper presents a weighted Markov chain, a method which is used to predict the future incidence state. This method assumes the standardized self-coefficients as weights based on the special characteristics of infectious disease incidence being a dependent stochastic variable. It also analyzes the characteristics of infectious diseases incidence via the Markov chain Monte Carlo method to make the long-term benefit of decision optimal. Our method is successfully validated using existing incidents data of infectious diseases in Jiangsu Province. In summation, this paper proposes ways to improve the accuracy of the weighted Markov chain, specifically in the field of infection epidemiology. PMID:23554632

Weighted Markov chains for forecasting and analysis in Incidence of infectious diseases in jiangsu Province, China.

PubMed

Peng, Zhihang; Bao, Changjun; Zhao, Yang; Yi, Honggang; Xia, Letian; Yu, Hao; Shen, Hongbing; Chen, Feng

2010-05-01

This paper first applies the sequential cluster method to set up the classification standard of infectious disease incidence state based on the fact that there are many uncertainty characteristics in the incidence course. Then the paper presents a weighted Markov chain, a method which is used to predict the future incidence state. This method assumes the standardized self-coefficients as weights based on the special characteristics of infectious disease incidence being a dependent stochastic variable. It also analyzes the characteristics of infectious diseases incidence via the Markov chain Monte Carlo method to make the long-term benefit of decision optimal. Our method is successfully validated using existing incidents data of infectious diseases in Jiangsu Province. In summation, this paper proposes ways to improve the accuracy of the weighted Markov chain, specifically in the field of infection epidemiology.

A Markov model of the Indus script

PubMed Central

Rao, Rajesh P. N.; Yadav, Nisha; Vahia, Mayank N.; Joglekar, Hrishikesh; Adhikari, R.; Mahadevan, Iravatham

2009-01-01

Although no historical information exists about the Indus civilization (flourished ca. 2600–1900 B.C.), archaeologists have uncovered about 3,800 short samples of a script that was used throughout the civilization. The script remains undeciphered, despite a large number of attempts and claimed decipherments over the past 80 years. Here, we propose the use of probabilistic models to analyze the structure of the Indus script. The goal is to reveal, through probabilistic analysis, syntactic patterns that could point the way to eventual decipherment. We illustrate the approach using a simple Markov chain model to capture sequential dependencies between signs in the Indus script. The trained model allows new sample texts to be generated, revealing recurring patterns of signs that could potentially form functional subunits of a possible underlying language. The model also provides a quantitative way of testing whether a particular string belongs to the putative language as captured by the Markov model. Application of this test to Indus seals found in Mesopotamia and other sites in West Asia reveals that the script may have been used to express different content in these regions. Finally, we show how missing, ambiguous, or unreadable signs on damaged objects can be filled in with most likely predictions from the model. Taken together, our results indicate that the Indus script exhibits rich synactic structure and the ability to represent diverse content. both of which are suggestive of a linguistic writing system rather than a nonlinguistic symbol system. PMID:19666571

Hypnosis and Local Anesthesia for Dental Pain Relief-Alternative or Adjunct Therapy?-A Randomized, Clinical-Experimental Crossover Study.

PubMed

Wolf, Thomas Gerhard; Wolf, Dominik; Callaway, Angelika; Below, Dagna; d'Hoedt, Bernd; Willershausen, Brita; Daubländer, Monika

2016-01-01

This prospective randomized clinical crossover trial was designed to compare hypnosis and local anesthesia for experimental dental pain relief. Pain thresholds of the dental pulp were determined. A targeted standardized pain stimulus was applied and rated on the Visual Analogue Scale (0-10). The pain threshold was lower under hypnosis (58.3 ± 17.3, p < .001), maximal (80.0) under local anesthesia. The pain stimulus was scored higher under hypnosis (3.9 ± 3.8) than with local anesthesia (0.0, p < .001). Local anesthesia was superior to hypnosis and is a safe and effective method for pain relief in dentistry. Hypnosis seems to produce similar effects observed under sedation. It can be used in addition to local anesthesia and in individual cases as an alternative for pain control in dentistry.

Many-body localization in a long range XXZ model with random-field

NASA Astrophysics Data System (ADS)

Li, Bo

2016-12-01

Many-body localization (MBL) in a long range interaction XXZ model with random field are investigated. Using the exact diagonal method, the MBL phase diagram with different tuning parameters and interaction range is obtained. It is found that the phase diagram of finite size results supplies strong evidence to confirm that the threshold interaction exponent α = 2. The tuning parameter Δ can efficiently change the MBL edge in high energy density stats, thus the system can be controlled to transfer from thermal phase to MBL phase by changing Δ. The energy level statistics data are consistent with result of the MBL phase diagram. However energy level statistics data cannot detect the thermal phase correctly in extreme long range case.

Covariate adjustment of event histories estimated from Markov chains: the additive approach.

PubMed

Aalen, O O; Borgan, O; Fekjaer, H

2001-12-01

Markov chain models are frequently used for studying event histories that include transitions between several states. An empirical transition matrix for nonhomogeneous Markov chains has previously been developed, including a detailed statistical theory based on counting processes and martingales. In this article, we show how to estimate transition probabilities dependent on covariates. This technique may, e.g., be used for making estimates of individual prognosis in epidemiological or clinical studies. The covariates are included through nonparametric additive models on the transition intensities of the Markov chain. The additive model allows for estimation of covariate-dependent transition intensities, and again a detailed theory exists based on counting processes. The martingale setting now allows for a very natural combination of the empirical transition matrix and the additive model, resulting in estimates that can be expressed as stochastic integrals, and hence their properties are easily evaluated. Two medical examples will be given. In the first example, we study how the lung cancer mortality of uranium miners depends on smoking and radon exposure. In the second example, we study how the probability of being in response depends on patient group and prophylactic treatment for leukemia patients who have had a bone marrow transplantation. A program in R and S-PLUS that can carry out the analyses described here has been developed and is freely available on the Internet.

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

NASA Astrophysics Data System (ADS)

Gan, Tingyue; Cameron, Maria

2017-06-01

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

Long-range memory and non-Markov statistical effects in human sensorimotor coordination

NASA Astrophysics Data System (ADS)

M. Yulmetyev, Renat; Emelyanova, Natalya; Hänggi, Peter; Gafarov, Fail; Prokhorov, Alexander

2002-12-01

In this paper, the non-Markov statistical processes and long-range memory effects in human sensorimotor coordination are investigated. The theoretical basis of this study is the statistical theory of non-stationary discrete non-Markov processes in complex systems (Phys. Rev. E 62, 6178 (2000)). The human sensorimotor coordination was experimentally studied by means of standard dynamical tapping test on the group of 32 young peoples with tap numbers up to 400. This test was carried out separately for the right and the left hand according to the degree of domination of each brain hemisphere. The numerical analysis of the experimental results was made with the help of power spectra of the initial time correlation function, the memory functions of low orders and the first three points of the statistical spectrum of non-Markovity parameter. Our observations demonstrate, that with the regard to results of the standard dynamic tapping-test it is possible to divide all examinees into five different dynamic types. We have introduced the conflict coefficient to estimate quantitatively the order-disorder effects underlying life systems. The last one reflects the existence of disbalance between the nervous and the motor human coordination. The suggested classification of the neurophysiological activity represents the dynamic generalization of the well-known neuropsychological types and provides the new approach in a modern neuropsychology.

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.

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

EPA Science Inventory

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

A Markov chain model for reliability growth and decay

NASA Technical Reports Server (NTRS)

Siegrist, K.

1982-01-01

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

Modeling Driver Behavior near Intersections in Hidden Markov Model

PubMed Central

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

2016-01-01

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

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

NASA Astrophysics Data System (ADS)

Turner, Sean; Galelli, Stefano; Wilcox, Karen

2015-04-01

Water reservoir systems are often affected by recurring large-scale ocean-atmospheric anomalies, known as teleconnections, that cause prolonged periods of climatological drought. Accurate forecasts of these events -- at lead times in the order of weeks and months -- may enable reservoir operators to take more effective release decisions to improve the performance of their systems. In practice this might mean a more reliable water supply system, a more profitable hydropower plant or a more sustainable environmental release policy. To this end, climate indices, which represent the oscillation of the ocean-atmospheric system, might be gainfully employed within reservoir operating models that adapt the reservoir operation as a function of the climate condition. This study develops a Stochastic Dynamic Programming (SDP) approach that can incorporate climate indices using a Hidden Markov Model. The model simulates the climatic regime as a hidden state following a Markov chain, with the state transitions driven by variation in climatic indices, such as the Southern Oscillation Index. Time series analysis of recorded streamflow data reveals the parameters of separate autoregressive models that describe the inflow to the reservoir under three representative climate states ("normal", "wet", "dry"). These models then define inflow transition probabilities for use in a classic SDP approach. The key advantage of the Hidden Markov Model is that it allows conditioning the operating policy not only on the reservoir storage and the antecedent inflow, but also on the climate condition, thus potentially allowing adaptability to a broader range of climate conditions. In practice, the reservoir operator would effect a water release tailored to a specific climate state based on available teleconnection data and forecasts. The approach is demonstrated on the operation of a realistic, stylised water reservoir with carry-over capacity in South-East Australia. Here teleconnections relating

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

PubMed

Li, Yao; Hu, Lili

2015-11-14

A new method of the stochastic simulation algorithm (SSA), named the Hashing-Leaping method (HLM), for exact simulations of a class of Markov jump processes, is presented in this paper. The HLM has a conditional constant computational cost per event, which is independent of the number of exponential clocks in the Markov process. The main idea of the HLM is to repeatedly implement a hash-table-like bucket sort algorithm for all times of occurrence covered by a time step with length τ. This paper serves as an introduction to this new SSA method. We introduce the method, demonstrate its implementation, analyze its properties, and compare its performance with three other commonly used SSA methods in four examples. Our performance tests and CPU operation statistics show certain advantages of the HLM for large scale problems.

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

NASA Astrophysics Data System (ADS)

Dharmaraja, Selvamuthu; Pasricha, Puneet; Tardelli, Paola

2017-11-01

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

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

PubMed

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

2014-02-01

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

Dynamic Bandwidth Provisioning Using Markov Chain Based on RSVP

DTIC Science & Technology

2013-09-01

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

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.

Data-driven confounder selection via Markov and Bayesian networks.

PubMed

Häggström, Jenny

2018-06-01

To unbiasedly estimate a causal effect on an outcome unconfoundedness is often assumed. If there is sufficient knowledge on the underlying causal structure then existing confounder selection criteria can be used to select subsets of the observed pretreatment covariates, X, sufficient for unconfoundedness, if such subsets exist. Here, estimation of these target subsets is considered when the underlying causal structure is unknown. The proposed method is to model the causal structure by a probabilistic graphical model, for example, a Markov or Bayesian network, estimate this graph from observed data and select the target subsets given the estimated graph. The approach is evaluated by simulation both in a high-dimensional setting where unconfoundedness holds given X and in a setting where unconfoundedness only holds given subsets of X. Several common target subsets are investigated and the selected subsets are compared with respect to accuracy in estimating the average causal effect. The proposed method is implemented with existing software that can easily handle high-dimensional data, in terms of large samples and large number of covariates. The results from the simulation study show that, if unconfoundedness holds given X, this approach is very successful in selecting the target subsets, outperforming alternative approaches based on random forests and LASSO, and that the subset estimating the target subset containing all causes of outcome yields smallest MSE in the average causal effect estimation. © 2017, The International Biometric Society.

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

PubMed

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

2015-01-01

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

Clustered Numerical Data Analysis Using Markov Lie Monoid Based Networks

NASA Astrophysics Data System (ADS)

Johnson, Joseph

2016-03-01

We have designed and build an optimal numerical standardization algorithm that links numerical values with their associated units, error level, and defining metadata thus supporting automated data exchange and new levels of artificial intelligence (AI). The software manages all dimensional and error analysis and computational tracing. Tables of entities verses properties of these generalized numbers (called ``metanumbers'') support a transformation of each table into a network among the entities and another network among their properties where the network connection matrix is based upon a proximity metric between the two items. We previously proved that every network is isomorphic to the Lie algebra that generates continuous Markov transformations. We have also shown that the eigenvectors of these Markov matrices provide an agnostic clustering of the underlying patterns. We will present this methodology and show how our new work on conversion of scientific numerical data through this process can reveal underlying information clusters ordered by the eigenvalues. We will also show how the linking of clusters from different tables can be used to form a ``supernet'' of all numerical information supporting new initiatives in AI.

The application of Markov decision process in restaurant delivery robot

NASA Astrophysics Data System (ADS)

Wang, Yong; Hu, Zhen; Wang, Ying

2017-05-01

As the restaurant delivery robot is often in a dynamic and complex environment, including the chairs inadvertently moved to the channel and customers coming and going. The traditional path planning algorithm is not very ideal. To solve this problem, this paper proposes the Markov dynamic state immediate reward (MDR) path planning algorithm according to the traditional Markov decision process. First of all, it uses MDR to plan a global path, then navigates along this path. When the sensor detects there is no obstructions in front state, increase its immediate state reward value; when the sensor detects there is an obstacle in front, plan a global path that can avoid obstacle with the current position as the new starting point and reduce its state immediate reward value. This continues until the target is reached. When the robot learns for a period of time, it can avoid those places where obstacles are often present when planning the path. By analyzing the simulation experiment, the algorithm has achieved good results in the global path planning under the dynamic environment.

Bayesian tomography by interacting Markov chains

NASA Astrophysics Data System (ADS)

Romary, T.

2017-12-01

In seismic tomography, we seek to determine the velocity of the undergound from noisy first arrival travel time observations. In most situations, this is an ill posed inverse problem that admits several unperfect solutions. Given an a priori distribution over the parameters of the velocity model, the Bayesian formulation allows to state this problem as a probabilistic one, with a solution under the form of a posterior distribution. The posterior distribution is generally high dimensional and may exhibit multimodality. Moreover, as it is known only up to a constant, the only sensible way to addressthis problem is to try to generate simulations from the posterior. The natural tools to perform these simulations are Monte Carlo Markov chains (MCMC). Classical implementations of MCMC algorithms generally suffer from slow mixing: the generated states are slow to enter the stationary regime, that is to fit the observations, and when one mode of the posterior is eventually identified, it may become difficult to visit others. Using a varying temperature parameter relaxing the constraint on the data may help to enter the stationary regime. Besides, the sequential nature of MCMC makes them ill fitted toparallel implementation. Running a large number of chains in parallel may be suboptimal as the information gathered by each chain is not mutualized. Parallel tempering (PT) can be seen as a first attempt to make parallel chains at different temperatures communicate but only exchange information between current states. In this talk, I will show that PT actually belongs to a general class of interacting Markov chains algorithm. I will also show that this class enables to design interacting schemes that can take advantage of the whole history of the chain, by authorizing exchanges toward already visited states. The algorithms will be illustrated with toy examples and an application to first arrival traveltime tomography.

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.

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

PubMed

Herbei, Radu; Kubatko, Laura

2013-03-26

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

Recombination Processes and Nonlinear Markov Chains.

PubMed

Pirogov, Sergey; Rybko, Alexander; Kalinina, Anastasia; Gelfand, Mikhail

2016-09-01

Bacteria are known to exchange genetic information by horizontal gene transfer. Since the frequency of homologous recombination depends on the similarity between the recombining segments, several studies examined whether this could lead to the emergence of subspecies. Most of them simulated fixed-size Wright-Fisher populations, in which the genetic drift should be taken into account. Here, we use nonlinear Markov processes to describe a bacterial population evolving under mutation and recombination. We consider a population structure as a probability measure on the space of genomes. This approach implies the infinite population size limit, and thus, the genetic drift is not assumed. We prove that under these conditions, the emergence of subspecies is impossible.

Parallel algorithms for simulating continuous time Markov chains

NASA Technical Reports Server (NTRS)

Nicol, David M.; Heidelberger, Philip

1992-01-01

We have previously shown that the mathematical technique of uniformization can serve as the basis of synchronization for the parallel simulation of continuous-time Markov chains. This paper reviews the basic method and compares five different methods based on uniformization, evaluating their strengths and weaknesses as a function of problem characteristics. The methods vary in their use of optimism, logical aggregation, communication management, and adaptivity. Performance evaluation is conducted on the Intel Touchstone Delta multiprocessor, using up to 256 processors.

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

PubMed

Zhang, Chao; Tao, Dacheng

2012-12-01

Many existing results on statistical learning theory are based on the assumption that samples are independently and identically distributed (i.i.d.). However, the assumption of i.i.d. samples is not suitable for practical application to problems in which samples are time dependent. In this paper, we are mainly concerned with the empirical risk minimization (ERM) based learning process for time-dependent samples drawn from a continuous-time Markov chain. This learning process covers many kinds of practical applications, e.g., the prediction for a time series and the estimation of channel state information. Thus, it is significant to study its theoretical properties including the generalization bound, the asymptotic convergence, and the rate of convergence. It is noteworthy that, since samples are time dependent in this learning process, the concerns of this paper cannot (at least straightforwardly) be addressed by existing methods developed under the sample i.i.d. assumption. We first develop a deviation inequality for a sequence of time-dependent samples drawn from a continuous-time Markov chain and present a symmetrization inequality for such a sequence. By using the resultant deviation inequality and symmetrization inequality, we then obtain the generalization bounds of the ERM-based learning process for time-dependent samples drawn from a continuous-time Markov chain. Finally, based on the resultant generalization bounds, we analyze the asymptotic convergence and the rate of convergence of the learning process.

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

Simplification of irreversible Markov chains by removal of states with fast leaving rates.

PubMed

Jia, Chen

2016-07-07

In the recent work of Ullah et al. (2012a), the authors developed an effective method to simplify reversible Markov chains by removal of states with low equilibrium occupancies. In this paper, we extend this result to irreversible Markov chains. We show that an irreversible chain can be simplified by removal of states with fast leaving rates. Moreover, we reveal that the irreversibility of the chain will always decrease after model simplification. This suggests that although model simplification can retain almost all the dynamic information of the chain, it will lose some thermodynamic information as a trade-off. Examples from biology are also given to illustrate the main results of this paper. Copyright © 2016 Elsevier Ltd. All rights reserved.

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

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

Locally adaptive methods for KDE-based random walk models of reactive transport in porous media

NASA Astrophysics Data System (ADS)

Sole-Mari, G.; Fernandez-Garcia, D.

2017-12-01

Random Walk Particle Tracking (RWPT) coupled with Kernel Density Estimation (KDE) has been recently proposed to simulate reactive transport in porous media. KDE provides an optimal estimation of the area of influence of particles which is a key element to simulate nonlinear chemical reactions. However, several important drawbacks can be identified: (1) the optimal KDE method is computationally intensive and thereby cannot be used at each time step of the simulation; (2) it does not take advantage of the prior information about the physical system and the previous history of the solute plume; (3) even if the kernel is optimal, the relative error in RWPT simulations typically increases over time as the particle density diminishes by dilution. To overcome these problems, we propose an adaptive branching random walk methodology that incorporates the physics, the particle history and maintains accuracy with time. The method allows particles to efficiently split and merge when necessary as well as to optimally adapt their local kernel shape without having to recalculate the kernel size. We illustrate the advantage of the method by simulating complex reactive transport problems in randomly heterogeneous porous media.

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

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

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

2015-11-14

A new method of the stochastic simulation algorithm (SSA), named the Hashing-Leaping method (HLM), for exact simulations of a class of Markov jump processes, is presented in this paper. The HLM has a conditional constant computational cost per event, which is independent of the number of exponential clocks in the Markov process. The main idea of the HLM is to repeatedly implement a hash-table-like bucket sort algorithm for all times of occurrence covered by a time step with length τ. This paper serves as an introduction to this new SSA method. We introduce the method, demonstrate its implementation, analyze itsmore » properties, and compare its performance with three other commonly used SSA methods in four examples. Our performance tests and CPU operation statistics show certain advantages of the HLM for large scale problems.« less

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

PubMed

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

2012-09-25

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

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

PubMed Central

2012-01-01

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

Dynamical decoupling of local transverse random telegraph noise in a two-qubit gate

NASA Astrophysics Data System (ADS)

D'Arrigo, A.; Falci, G.; Paladino, E.

2015-10-01

Achieving high-fidelity universal two-qubit gates is a central requisite of any implementation of quantum information processing. The presence of spurious fluctuators of various physical origin represents a limiting factor for superconducting nanodevices. Operating qubits at optimal points, where the qubit-fluctuator interaction is transverse with respect to the single qubit Hamiltonian, considerably improved single qubit gates. Further enhancement has been achieved by dynamical decoupling (DD). In this article we investigate DD of transverse random telegraph noise acting locally on each of the qubits forming an entangling gate. Our analysis is based on the exact numerical solution of the stochastic Schrödinger equation. We evaluate the gate error under local periodic, Carr-Purcell and Uhrig DD sequences. We find that a threshold value of the number, n, of pulses exists above which the gate error decreases with a sequence-specific power-law dependence on n. Below threshold, DD may even increase the error with respect to the unconditioned evolution, a behaviour reminiscent of the anti-Zeno effect.

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.

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

NASA Astrophysics Data System (ADS)

Figueiredo, Danilo Zucolli; Costa, Oswaldo Luiz do Valle

2017-10-01

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

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

NASA Astrophysics Data System (ADS)

Izvekov, Sergei

2017-01-01

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

Application of Markov Models for Analysis of Development of Psychological Characteristics

ERIC Educational Resources Information Center

Kuravsky, Lev S.; Malykh, Sergey B.

2004-01-01

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