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Sample records for local markov random

  1. Local Autoencoding for Parameter Estimation in a Hidden Potts-Markov Random Field.

    PubMed

    Song, Sanming; Si, Bailu; Herrmann, J Michael; Feng, Xisheng

    2016-05-01

    A local-autoencoding (LAE) method is proposed for the parameter estimation in a Hidden Potts-Markov random field model. Due to sampling cost, Markov chain Monte Carlo methods are rarely used in real-time applications. Like other heuristic methods, LAE is based on a conditional independence assumption. It adapts, however, the parameters in a block-by-block style with a simple Hebbian learning rule. Experiments with given label fields show that the LAE is able to converge in far less time than required for a scan. It is also possible to derive an estimate for LAE based on a Cramer–Rao bound that is similar to the classical maximum pseudolikelihood method. As a general algorithm, LAE can be used to estimate the parameters in anisotropic label fields. Furthermore, LAE is not limited to the classical Potts model and can be applied to other types of Potts models by simple label field transformations and straightforward learning rule extensions. Experimental results on image segmentations demonstrate the efficiency and generality of the LAE algorithm. PMID:27019491

  2. A Novel Microaneurysms Detection Method Based on Local Applying of Markov Random Field.

    PubMed

    Ganjee, Razieh; Azmi, Reza; Moghadam, Mohsen Ebrahimi

    2016-03-01

    Diabetic Retinopathy (DR) is one of the most common complications of long-term diabetes. It is a progressive disease and by damaging retina, it finally results in blindness of patients. Since Microaneurysms (MAs) appear as a first sign of DR in retina, early detection of this lesion is an essential step in automatic detection of DR. In this paper, a new MAs detection method is presented. The proposed approach consists of two main steps. In the first step, the MA candidates are detected based on local applying of Markov random field model (MRF). In the second step, these candidate regions are categorized to identify the correct MAs using 23 features based on shape, intensity and Gaussian distribution of MAs intensity. The proposed method is evaluated on DIARETDB1 which is a standard and publicly available database in this field. Evaluation of the proposed method on this database resulted in the average sensitivity of 0.82 for a confidence level of 75 as a ground truth. The results show that our method is able to detect the low contrast MAs with the background while its performance is still comparable to other state of the art approaches. PMID:26779642

  3. Homogeneous Superpixels from Markov Random Walks

    NASA Astrophysics Data System (ADS)

    Perbet, Frank; Stenger, Björn; Maki, Atsuto

    This paper presents a novel algorithm to generate homogeneous superpixels from Markov random walks. We exploit Markov clustering (MCL) as the methodology, a generic graph clustering method based on stochastic flow circulation. In particular, we introduce a graph pruning strategy called compact pruning in order to capture intrinsic local image structure. The resulting superpixels are homogeneous, i.e. uniform in size and compact in shape. The original MCL algorithm does not scale well to a graph of an image due to the square computation of the Markov matrix which is necessary for circulating the flow. The proposed pruning scheme has the advantages of faster computation, smaller memory footprint, and straightforward parallel implementation. Through comparisons with other recent techniques, we show that the proposed algorithm achieves state-of-the-art performance.

  4. Defect Detection Using Hidden Markov Random Fields

    NASA Astrophysics Data System (ADS)

    Dogandžić, Aleksandar; Eua-anant, Nawanat; Zhang, Benhong

    2005-04-01

    We derive an approximate maximum a posteriori (MAP) method for detecting NDE defect signals using hidden Markov random fields (HMRFs). In the proposed HMRF framework, a set of spatially distributed NDE measurements is assumed to form a noisy realization of an underlying random field that has a simple structure with Markovian dependence. Here, the random field describes the defect signals to be estimated or detected. The HMRF models incorporate measurement locations into the statistical analysis, which is important in scenarios where the same defect affects measurements at multiple locations. We also discuss initialization of the proposed HMRF detector and apply to simulated eddy-current data and experimental ultrasonic C-scan data from an inspection of a cylindrical Ti 6-4 billet.

  5. Unmixing hyperspectral images using Markov random fields

    SciTech Connect

    Eches, Olivier; Dobigeon, Nicolas; Tourneret, Jean-Yves

    2011-03-14

    This paper proposes a new spectral unmixing strategy based on the normal compositional model that exploits the spatial correlations between the image pixels. The pure materials (referred to as endmembers) contained in the image are assumed to be available (they can be obtained by using an appropriate endmember extraction algorithm), while the corresponding fractions (referred to as abundances) are estimated by the proposed algorithm. Due to physical constraints, the abundances have to satisfy positivity and sum-to-one constraints. The image is divided into homogeneous distinct regions having the same statistical properties for the abundance coefficients. The spatial dependencies within each class are modeled thanks to Potts-Markov random fields. Within a Bayesian framework, prior distributions for the abundances and the associated hyperparameters are introduced. A reparametrization of the abundance coefficients is proposed to handle the physical constraints (positivity and sum-to-one) inherent to hyperspectral imagery. The parameters (abundances), hyperparameters (abundance mean and variance for each class) and the classification map indicating the classes of all pixels in the image are inferred from the resulting joint posterior distribution. To overcome the complexity of the joint posterior distribution, Markov chain Monte Carlo methods are used to generate samples asymptotically distributed according to the joint posterior of interest. Simulations conducted on synthetic and real data are presented to illustrate the performance of the proposed algorithm.

  6. Multiple testing for neuroimaging via hidden Markov random field.

    PubMed

    Shu, Hai; Nan, Bin; Koeppe, Robert

    2015-09-01

    Traditional voxel-level multiple testing procedures in neuroimaging, mostly p-value based, often ignore the spatial correlations among neighboring voxels and thus suffer from substantial loss of power. We extend the local-significance-index based procedure originally developed for the hidden Markov chain models, which aims to minimize the false nondiscovery rate subject to a constraint on the false discovery rate, to three-dimensional neuroimaging data using a hidden Markov random field model. A generalized expectation-maximization algorithm for maximizing the penalized likelihood is proposed for estimating the model parameters. Extensive simulations show that the proposed approach is more powerful than conventional false discovery rate procedures. We apply the method to the comparison between mild cognitive impairment, a disease status with increased risk of developing Alzheimer's or another dementia, and normal controls in the FDG-PET imaging study of the Alzheimer's Disease Neuroimaging Initiative. PMID:26012881

  7. Learning Markov Random Walks for robust subspace clustering and estimation.

    PubMed

    Liu, Risheng; Lin, Zhouchen; Su, Zhixun

    2014-11-01

    Markov Random Walks (MRW) has proven to be an effective way to understand spectral clustering and embedding. However, due to less global structural measure, conventional MRW (e.g., the Gaussian kernel MRW) cannot be applied to handle data points drawn from a mixture of subspaces. In this paper, we introduce a regularized MRW learning model, using a low-rank penalty to constrain the global subspace structure, for subspace clustering and estimation. In our framework, both the local pairwise similarity and the global subspace structure can be learnt from the transition probabilities of MRW. We prove that under some suitable conditions, our proposed local/global criteria can exactly capture the multiple subspace structure and learn a low-dimensional embedding for the data, in which giving the true segmentation of subspaces. To improve robustness in real situations, we also propose an extension of the MRW learning model based on integrating transition matrix learning and error correction in a unified framework. Experimental results on both synthetic data and real applications demonstrate that our proposed MRW learning model and its robust extension outperform the state-of-the-art subspace clustering methods. PMID:25005156

  8. A Markov Random Field Groupwise Registration Framework for Face Recognition

    PubMed Central

    Liao, Shu; Shen, Dinggang; Chung, Albert C.S.

    2014-01-01

    In this paper, we propose a new framework for tackling face recognition problem. The face recognition problem is formulated as groupwise deformable image registration and feature matching problem. The main contributions of the proposed method lie in the following aspects: (1) Each pixel in a facial image is represented by an anatomical signature obtained from its corresponding most salient scale local region determined by the survival exponential entropy (SEE) information theoretic measure. (2) Based on the anatomical signature calculated from each pixel, a novel Markov random field based groupwise registration framework is proposed to formulate the face recognition problem as a feature guided deformable image registration problem. The similarity between different facial images are measured on the nonlinear Riemannian manifold based on the deformable transformations. (3) The proposed method does not suffer from the generalizability problem which exists commonly in learning based algorithms. The proposed method has been extensively evaluated on four publicly available databases: FERET, CAS-PEAL-R1, FRGC ver 2.0, and the LFW. It is also compared with several state-of-the-art face recognition approaches, and experimental results demonstrate that the proposed method consistently achieves the highest recognition rates among all the methods under comparison. PMID:25506109

  9. Fuzzy Markov random fields versus chains for multispectral image segmentation.

    PubMed

    Salzenstein, Fabien; Collet, Christophe

    2006-11-01

    This paper deals with a comparison of recent statistical models based on fuzzy Markov random fields and chains for multispectral image segmentation. The fuzzy scheme takes into account discrete and continuous classes which model the imprecision of the hidden data. In this framework, we assume the dependence between bands and we express the general model for the covariance matrix. A fuzzy Markov chain model is developed in an unsupervised way. This method is compared with the fuzzy Markovian field model previously proposed by one of the authors. The segmentation task is processed with Bayesian tools, such as the well-known MPM (Mode of Posterior Marginals) criterion. Our goal is to compare the robustness and rapidity for both methods (fuzzy Markov fields versus fuzzy Markov chains). Indeed, such fuzzy-based procedures seem to be a good answer, e.g., for astronomical observations when the patterns present diffuse structures. Moreover, these approaches allow us to process missing data in one or several spectral bands which correspond to specific situations in astronomy. To validate both models, we perform and compare the segmentation on synthetic images and raw multispectral astronomical data. PMID:17063681

  10. Monte Carlo Integration Using Spatial Structure of Markov Random Field

    NASA Astrophysics Data System (ADS)

    Yasuda, Muneki

    2015-03-01

    Monte Carlo integration (MCI) techniques are important in various fields. In this study, a new MCI technique for Markov random fields (MRFs) is proposed. MCI consists of two successive parts: the first involves sampling using a technique such as the Markov chain Monte Carlo method, and the second involves an averaging operation using the obtained sample points. In the averaging operation, a simple sample averaging technique is often employed. The method proposed in this paper improves the averaging operation by addressing the spatial structure of the MRF and is mathematically guaranteed to statistically outperform standard MCI using the simple sample averaging operation. Moreover, the proposed method can be improved in a systematic manner and is numerically verified by numerical simulations using planar Ising models. In the latter part of this paper, the proposed method is applied to the inverse Ising problem and we observe that it outperforms the maximum pseudo-likelihood estimation.

  11. Markov-random-field modeling for linear seismic tomography.

    PubMed

    Kuwatani, Tatsu; Nagata, Kenji; Okada, Masato; Toriumi, Mitsuhiro

    2014-10-01

    We apply the Markov-random-field model to linear seismic tomography and propose a method to estimate the hyperparameters for the smoothness and the magnitude of the noise. Optimal hyperparameters can be determined analytically by minimizing the free energy function, which is defined by marginalizing the evaluation function. In synthetic inversion tests under various settings, the assumed velocity structures are successfully reconstructed, which shows the effectiveness and robustness of the proposed method. The proposed mathematical framework can be applied to inversion problems in various fields in the natural sciences. PMID:25375468

  12. CAUSAL MARKOV RANDOM FIELD FOR BRAIN MR IMAGE SEGMENTATION

    PubMed Central

    Razlighi, Qolamreza R.; Orekhov, Aleksey; Laine, Andrew; Stern, Yaakov

    2013-01-01

    We propose a new Bayesian classifier, based on the recently introduced causal Markov random field (MRF) model, Quadrilateral MRF (QMRF). We use a second order inhomogeneous anisotropic QMRF to model the prior and likelihood probabilities in the maximum a posteriori (MAP) classifier, named here as MAP-QMRF. The joint distribution of QMRF is given in terms of the product of two dimensional clique distributions existing in its neighboring structure. 20 manually labeled human brain MR images are used to train and assess the MAP-QMRF classifier using the jackknife validation method. Comparing the results of the proposed classifier and FreeSurfer on the Dice overlap measure shows an average gain of 1.8%. We have performed a power analysis to demonstrate that this increase in segmentation accuracy substantially reduces the number of samples required to detect a 5% change in volume of a brain region. PMID:23366607

  13. A Markov random field approach for microstructure synthesis

    NASA Astrophysics Data System (ADS)

    Kumar, A.; Nguyen, L.; DeGraef, M.; Sundararaghavan, V.

    2016-03-01

    We test the notion that many microstructures have an underlying stationary probability distribution. The stationary probability distribution is ubiquitous: we know that different windows taken from a polycrystalline microstructure are generally ‘statistically similar’. To enable computation of such a probability distribution, microstructures are represented in the form of undirected probabilistic graphs called Markov Random Fields (MRFs). In the model, pixels take up integer or vector states and interact with multiple neighbors over a window. Using this lattice structure, algorithms are developed to sample the conditional probability density for the state of each pixel given the known states of its neighboring pixels. The sampling is performed using reference experimental images. 2D microstructures are artificially synthesized using the sampled probabilities. Statistical features such as grain size distribution and autocorrelation functions closely match with those of the experimental images. The mechanical properties of the synthesized microstructures were computed using the finite element method and were also found to match the experimental values.

  14. MRFalign: protein homology detection through alignment of Markov random fields.

    PubMed

    Ma, Jianzhu; Wang, Sheng; Wang, Zhiyong; Xu, Jinbo

    2014-03-01

    Sequence-based protein homology detection has been extensively studied and so far the most sensitive method is based upon comparison of protein sequence profiles, which are derived from multiple sequence alignment (MSA) of sequence homologs in a protein family. A sequence profile is usually represented as a position-specific scoring matrix (PSSM) or an HMM (Hidden Markov Model) and accordingly PSSM-PSSM or HMM-HMM comparison is used for homolog detection. This paper presents a new homology detection method MRFalign, consisting of three key components: 1) a Markov Random Fields (MRF) representation of a protein family; 2) a scoring function measuring similarity of two MRFs; and 3) an efficient ADMM (Alternating Direction Method of Multipliers) algorithm aligning two MRFs. Compared to HMM that can only model very short-range residue correlation, MRFs can model long-range residue interaction pattern and thus, encode information for the global 3D structure of a protein family. Consequently, MRF-MRF comparison for remote homology detection shall be much more sensitive than HMM-HMM or PSSM-PSSM comparison. Experiments confirm that MRFalign outperforms several popular HMM or PSSM-based methods in terms of both alignment accuracy and remote homology detection and that MRFalign works particularly well for mainly beta proteins. For example, tested on the benchmark SCOP40 (8353 proteins) for homology detection, PSSM-PSSM and HMM-HMM succeed on 48% and 52% of proteins, respectively, at superfamily level, and on 15% and 27% of proteins, respectively, at fold level. In contrast, MRFalign succeeds on 57.3% and 42.5% of proteins at superfamily and fold level, respectively. This study implies that long-range residue interaction patterns are very helpful for sequence-based homology detection. The software is available for download at http://raptorx.uchicago.edu/download/. A summary of this paper appears in the proceedings of the RECOMB 2014 conference, April 2-5. PMID:24675572

  15. Biomedical image analysis using Markov random fields & efficient linear programing.

    PubMed

    Komodakis, Nikos; Besbes, Ahmed; Glocker, Ben; Paragios, Nikos

    2009-01-01

    Computer-aided diagnosis through biomedical image analysis is increasingly considered in health sciences. This is due to the progress made on the acquisition side, as well as on the processing one. In vivo visualization of human tissues where one can determine both anatomical and functional information is now possible. The use of these images with efficient intelligent mathematical and processing tools allows the interpretation of the tissues state and facilitates the task of the physicians. Segmentation and registration are the two most fundamental tools in bioimaging. The first aims to provide automatic tools for organ delineation from images, while the second focuses on establishing correspondences between observations inter and intra subject and modalities. In this paper, we present some recent results towards a common formulation addressing these problems, called the Markov Random Fields. Such an approach is modular with respect to the application context, can be easily extended to deal with various modalities, provides guarantees on the optimality properties of the obtained solution and is computationally efficient. PMID:19963682

  16. Comparing quantum versus Markov random walk models of judgements measured by rating scales

    PubMed Central

    Wang, Z.; Busemeyer, J. R.

    2016-01-01

    Quantum and Markov random walk models are proposed for describing how people evaluate stimuli using rating scales. To empirically test these competing models, we conducted an experiment in which participants judged the effectiveness of public health service announcements from either their own personal perspective or from the perspective of another person. The order of the self versus other judgements was manipulated, which produced significant sequential effects. The quantum and Markov models were fitted to the data using the same number of parameters, and the model comparison strongly supported the quantum over the Markov model. PMID:26621984

  17. The mean field theory in EM procedures for blind Markov random field image restoration.

    PubMed

    Zhang, J

    1993-01-01

    A Markov random field (MRF) model-based EM (expectation-maximization) procedure for simultaneously estimating the degradation model and restoring the image is described. The MRF is a coupled one which provides continuity (inside regions of smooth gray tones) and discontinuity (at region boundaries) constraints for the restoration problem which is, in general, ill posed. The computational difficulty associated with the EM procedure for MRFs is resolved by using the mean field theory from statistical mechanics. An orthonormal blur decomposition is used to reduce the chances of undesirable locally optimal estimates. Experimental results on synthetic and real-world images show that this approach provides good blur estimates and restored images. The restored images are comparable to those obtained by a Wiener filter in mean-square error, but are most visually pleasing. PMID:18296192

  18. 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.

  19. 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.

  20. 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

  1. A Markov Chain Model for evaluating the effectiveness of randomized surveillance procedures

    SciTech Connect

    Edmunds, T.A.

    1994-01-01

    A Markov Chain Model has been developed to evaluate the effectiveness of randomized surveillance procedures. The model is applicable for surveillance systems that monitor a collection of assets by randomly selecting and inspecting the assets. The model provides an estimate of the detection probability as a function of the amount of time that an adversary would require to steal or sabotage the asset. An interactive computer code has been written to perform the necessary computations.

  2. Fusion of Hidden Markov Random Field models and its Bayesian estimation.

    PubMed

    Destrempes, François; Angers, Jean-François; Mignotte, Max

    2006-10-01

    In this paper, we present a Hidden Markov Random Field (HMRF) data-fusion model. The proposed model is applied to the segmentation of natural images based on the fusion of colors and textons into Julesz ensembles. The corresponding Exploration/ Selection/Estimation (ESE) procedure for the estimation of the parameters is presented. This method achieves the estimation of the parameters of the Gaussian kernels, the mixture proportions, the region labels, the number of regions, and the Markov hyper-parameter. Meanwhile, we present a new proof of the asymptotic convergence of the ESE procedure, based on original finite time bounds for the rate of convergence. PMID:17022259

  3. A multiresolution wavelet analysis and Gaussian Markov random field algorithm for breast cancer screening of digital mammography

    SciTech Connect

    Lee, C.G.; Chen, C.H.

    1996-12-31

    In this paper a novel multiresolution wavelet analysis (MWA) and non-stationary Gaussian Markov random field (GMRF) technique is introduced for the identification of microcalcifications with high accuracy. The hierarchical multiresolution wavelet information in conjunction with the contextual information of the images extracted from GMRF provides a highly efficient technique for microcalcification detection. A Bayesian teaming paradigm realized via the expectation maximization (EM) algorithm was also introduced for edge detection or segmentation of larger lesions recorded on the mammograms. The effectiveness of the approach has been extensively tested with a number of mammographic images provided by a local hospital.

  4. Detection and characterization of regulatory elements using probabilistic conditional random field and hidden Markov models.

    PubMed

    Wang, Hongyan; Zhou, Xiaobo

    2013-04-01

    By altering the electrostatic charge of histones or providing binding sites to protein recognition molecules, Chromatin marks have been proposed to regulate gene expression, a property that has motivated researchers to link these marks to cis-regulatory elements. With the help of next generation sequencing technologies, we can now correlate one specific chromatin mark with regulatory elements (e.g. enhancers or promoters) and also build tools, such as hidden Markov models, to gain insight into mark combinations. However, hidden Markov models have limitation for their character of generative models and assume that a current observation depends only on a current hidden state in the chain. Here, we employed two graphical probabilistic models, namely the linear conditional random field model and multivariate hidden Markov model, to mark gene regions with different states based on recurrent and spatially coherent character of these eight marks. Both models revealed chromatin states that may correspond to enhancers and promoters, transcribed regions, transcriptional elongation, and low-signal regions. We also found that the linear conditional random field model was more effective than the hidden Markov model in recognizing regulatory elements, such as promoter-, enhancer-, and transcriptional elongation-associated regions, which gives us a better choice. PMID:23237214

  5. Markov random field restoration of point correspondences for active shape modeling

    NASA Astrophysics Data System (ADS)

    Hilger, Klaus B.; Paulsen, Rasmus R.; Larsen, Rasmus

    2004-05-01

    In this paper it is described how to build a statistical shape model using a training set with a sparse of landmarks. A well defined model mesh is selected and fitted to all shapes in the training set using thin plate spline warping. This is followed by a projection of the points of the warped model mesh to the target shapes. When this is done by a nearest neighbour projection it can result in folds and inhomogeneities in the correspondence vector field. The novelty in this paper is the use and extension of a Markov random field regularisation of the correspondence field. The correspondence field is regarded as a collection of random variables, and using the Hammersley-Clifford theorem it is proved that it can be treated as a Markov Random Field. The problem of finding the optimal correspondence field is cast into a Bayesian framework for Markov Random Field restoration, where the prior distribution is a smoothness term and the observation model is the curvature of the shapes. The Markov Random Field is optimised using a combination of Gibbs sampling and the Metropolis-Hasting algorithm. The parameters of the model are found using a leave-one-out approach. The method leads to a generative model that produces highly homogeneous polygonised shapes with improved reconstruction capabilities of the training data. Furthermore, the method leads to an overall reduction in the total variance of the resulting point distribution model. The method is demonstrated on a set of human ear canals extracted from 3D-laser scans.

  6. Joint clustering of protein interaction networks through Markov random walk

    PubMed Central

    2014-01-01

    Biological networks obtained by high-throughput profiling or human curation are typically noisy. For functional module identification, single network clustering algorithms may not yield accurate and robust results. In order to borrow information across multiple sources to alleviate such problems due to data quality, we propose a new joint network clustering algorithm ASModel in this paper. We construct an integrated network to combine network topological information based on protein-protein interaction (PPI) datasets and homological information introduced by constituent similarity between proteins across networks. A novel random walk strategy on the integrated network is developed for joint network clustering and an optimization problem is formulated by searching for low conductance sets defined on the derived transition matrix of the random walk, which fuses both topology and homology information. The optimization problem of joint clustering is solved by a derived spectral clustering algorithm. Network clustering using several state-of-the-art algorithms has been implemented to both PPI networks within the same species (two yeast PPI networks and two human PPI networks) and those from different species (a yeast PPI network and a human PPI network). Experimental results demonstrate that ASModel outperforms the existing single network clustering algorithms as well as another recent joint clustering algorithm in terms of complex prediction and Gene Ontology (GO) enrichment analysis. PMID:24565376

  7. Joint clustering of protein interaction networks through Markov random walk.

    PubMed

    Wang, Yijie; Qian, Xiaoning

    2014-01-01

    Biological networks obtained by high-throughput profiling or human curation are typically noisy. For functional module identification, single network clustering algorithms may not yield accurate and robust results. In order to borrow information across multiple sources to alleviate such problems due to data quality, we propose a new joint network clustering algorithm ASModel in this paper. We construct an integrated network to combine network topological information based on protein-protein interaction (PPI) datasets and homological information introduced by constituent similarity between proteins across networks. A novel random walk strategy on the integrated network is developed for joint network clustering and an optimization problem is formulated by searching for low conductance sets defined on the derived transition matrix of the random walk, which fuses both topology and homology information. The optimization problem of joint clustering is solved by a derived spectral clustering algorithm. Network clustering using several state-of-the-art algorithms has been implemented to both PPI networks within the same species (two yeast PPI networks and two human PPI networks) and those from different species (a yeast PPI network and a human PPI network). Experimental results demonstrate that ASModel outperforms the existing single network clustering algorithms as well as another recent joint clustering algorithm in terms of complex prediction and Gene Ontology (GO) enrichment analysis. PMID:24565376

  8. A Hypergraph-Based Reduction for Higher-Order Binary Markov Random Fields.

    PubMed

    Fix, Alexander; Gruber, Aritanan; Boros, Endre; Zabih, Ramin

    2015-07-01

    Higher-order Markov Random Fields, which can capture important properties of natural images, have become increasingly important in computer vision. While graph cuts work well for first-order MRF's, until recently they have rarely been effective for higher-order MRF's. Ishikawa's graph cut technique [1], [2] shows great promise for many higher-order MRF's. His method transforms an arbitrary higher-order MRF with binary labels into a first-order one with the same minima. If all the terms are submodular the exact solution can be easily found; otherwise, pseudoboolean optimization techniques can produce an optimal labeling for a subset of the variables. We present a new transformation with better performance than [1], [2], both theoretically and experimentally. While [1], [2] transforms each higher-order term independently, we use the underlying hypergraph structure of the MRF to transform a group of terms at once. For n binary variables, each of which appears in terms with k other variables, at worst we produce n non-submodular terms, while [1], [2] produces O(nk). We identify a local completeness property under which our method perform even better, and show that under certain assumptions several important vision problems (including common variants of fusion moves) have this property. We show experimentally that our method produces smaller weight of non-submodular edges, and that this metric is directly related to the effectiveness of QPBO [3]. Running on the same field of experts dataset used in [1], [2] we optimally label significantly more variables (96 versus 80 percent) and converge more rapidly to a lower energy. Preliminary experiments suggest that some other higher-order MRF's used in stereo [4] and segmentation [5] are also locally complete and would thus benefit from our work. PMID:26352447

  9. Bayesian Clustering Using Hidden Markov Random Fields in Spatial Population Genetics

    PubMed Central

    François, Olivier; Ancelet, Sophie; Guillot, Gilles

    2006-01-01

    We introduce a new Bayesian clustering algorithm for studying population structure using individually geo-referenced multilocus data sets. The algorithm is based on the concept of hidden Markov random field, which models the spatial dependencies at the cluster membership level. We argue that (i) a Markov chain Monte Carlo procedure can implement the algorithm efficiently, (ii) it can detect significant geographical discontinuities in allele frequencies and regulate the number of clusters, (iii) it can check whether the clusters obtained without the use of spatial priors are robust to the hypothesis of discontinuous geographical variation in allele frequencies, and (iv) it can reduce the number of loci required to obtain accurate assignments. We illustrate and discuss the implementation issues with the Scandinavian brown bear and the human CEPH diversity panel data set. PMID:16888334

  10. Adaptation of the projection-slice theorem for stock valuation estimation using random Markov fields

    NASA Astrophysics Data System (ADS)

    Riasati, Vahid R.

    2009-04-01

    The Projection-Slice Synthetic Discriminant function filter is utilized with Random Markov Fields, RMF to estimate trends that may be used as prediction for stock valuation through the representation of the market behavior as a hidden Markov Model, HMM. In this work, we utilize a set of progressive and contiguous time segments of a given stock, and treat the set as a two dimensional object that has been represented by its one-d projections. The abstract two-D object is thus an incarnation of N-temporal projections. The HMM is then utilized to generate N+1 projections that maximizes the two-dimensional correlation peak between the data and the HMM-generated stochastic processes. This application of the PSDF provides a method of stock valuation prediction via the market stochastic behavior utilized in the filter.

  11. Binary 3-D Markov Chain Random Fields: Finite-size Scaling Analysis of Percolation Properties

    NASA Astrophysics Data System (ADS)

    Harter, T.

    2004-12-01

    Percolation phenomena in random media have been extensively studied in a wide variety of fields in physics, chemistry, engineering, bio-, earth-, and environmental sciences. Most work has focused on uncorrelated random fields. The critical behavior in media with short-range correlations is thought to be identical to that in uncorrelated systems. However, the percolation threshold, pc, which is 0.3116 in uncorrelated media, has been observed to vary with the correlation scale and also with the random field type. Here, we present percolation properties and finite-size scaling effects in three-dimensional binary cubic lattices represented by correlated Markov-chain random fields and compare them to those in sequential Gaussian and sequential indicator random fields. We find that the computed percolation threshold in correlated random fields is significantly lower than in the uncorrelated lattice and decreases with increasing correlation scale. The rate of decrease rapidly flattens out for correlation lengths larger than 2-3 grid-blocks. At correlation scales of 5-6 grid blocks, pc is found to be 0.126 for the Markov chain random fields and slightly higher for sequential Gaussian and indicator random fields. The universal scaling constants for mean cluster size, backbone fraction, and connectivity are found to be consistent with results on uncorrelated lattices. For numerical studies, it is critical to understand finite-size effects on the percolation and associated phase connectivity properties of lattices. We present detailed statistical results on the percolation properties in finite sized lattice and their dependence on correlation scale. We show that appropriate grid resolution and choice of simulation boundaries is critical to properly simulate correlated natural geologic systems, which may display significant finite-size effects.

  12. 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.

  13. Hierarchical Markov random-field modeling for texture classification in chest radiographs

    NASA Astrophysics Data System (ADS)

    Vargas-Voracek, Rene; Floyd, Carey E., Jr.; Nolte, Loren W.; McAdams, Page

    1996-04-01

    A hierarchical Markov random field (MRF) modeling approach is presented for the classification of textures in selected regions of interest (ROIs) of chest radiographs. The procedure integrates possible texture classes and their spatial definition with other components present in an image such as noise and background trend. Classification is performed as a maximum a-posteriori (MAP) estimation of texture class and involves an iterative Gibbs- sampling technique. Two cases are studied: classification of lung parenchyma versus bone and classification of normal lung parenchyma versus miliary tuberculosis (MTB). Accurate classification was obtained for all examined cases showing the potential of the proposed modeling approach for texture analysis of radiographic images.

  14. Classifying Urban Land cover using Spatial Weights: A Comparison of Discriminant Analysis and Markov Random Fields

    NASA Astrophysics Data System (ADS)

    Wentz, E.; Song, Y.

    2011-12-01

    Classifying urban area images is challenging because of the heterogeneous nature of the urban landscape. This means that each pixel represents a mixture of classes with potentially highly variable various spectral values. Land cover classification approaches using ancillary data, such as knowledge based or expert systems, have shown to improve the classification accuracy in urban areas, particularly with medium or low-resolution imagery. This is because information other than the spectral signatures is used to assign pixels to classes. Defining rules is challenging and acquiring appropriate ancillary data may not always be possible. The goal of this study is to compare the results of three approaches to classify urban land cover with medium resolution data with and without ancillary information. We compare discriminant analysis, Markov random fields, and an expert system. Furthermore, we explore whether including spatial weights improves classification accuracy of the discriminant model. Discriminant analysis is a statistical technique used to predict group membership for a pixel based on the linear combination of independent variables. Adding spatial weights to this includes a weighted value for neighboring pixels. Markov random fields represent spatial dependencies through conditional relationships defined using Markov principles. In comparison to using spatial dependencies in neighbouring pixels, strict per pixel statistical analysis, however, does not consider the spatial dependencies among neighbouring pixels. Our study showed that approaches using ancillary data continued to outperform strict spectral classifiers but that using a spatial weight improved the results. Furthermore, results demonstrate that when the discriminant analysis technique works well then the spatially weighted approach works better. However, when the discriminant analysis performs ineffectively, those poor results are magnified. This study suggests that spatial weights improve the

  15. 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.

  16. 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. PMID:27415245

  17. Mixed Markov models

    PubMed Central

    Fridman, Arthur

    2003-01-01

    Markov random fields can encode complex probabilistic relationships involving multiple variables and admit efficient procedures for probabilistic inference. However, from a knowledge engineering point of view, these models suffer from a serious limitation. The graph of a Markov field must connect all pairs of variables that are conditionally dependent even for a single choice of values of the other variables. This makes it hard to encode interactions that occur only in a certain context and are absent in all others. Furthermore, the requirement that two variables be connected unless always conditionally independent may lead to excessively dense graphs, obscuring the independencies present among the variables and leading to computationally prohibitive inference algorithms. Mumford [Mumford, D. (1996) in ICIAM 95, eds. Kirchgassner, K., Marenholtz, O. & Mennicken, R. (Akademie Verlag, Berlin), pp. 233–256] proposed an alternative modeling framework where the graph need not be rigid and completely determined a priori. Mixed Markov models contain node-valued random variables that, when instantiated, augment the graph by a set of transient edges. A single joint probability distribution relates the values of regular and node-valued variables. In this article, we study the analytical and computational properties of mixed Markov models. In particular, we show that positive mixed models have a local Markov property that is equivalent to their global factorization. We also describe a computationally efficient procedure for answering probabilistic queries in mixed Markov models. PMID:12829802

  18. Class-specific weighting for Markov random field estimation: application to medical image segmentation.

    PubMed

    Monaco, James P; Madabhushi, Anant

    2012-12-01

    Many estimation tasks require Bayesian classifiers capable of adjusting their performance (e.g. sensitivity/specificity). In situations where the optimal classification decision can be identified by an exhaustive search over all possible classes, means for adjusting classifier performance, such as probability thresholding or weighting the a posteriori probabilities, are well established. Unfortunately, analogous methods compatible with Markov random fields (i.e. large collections of dependent random variables) are noticeably absent from the literature. Consequently, most Markov random field (MRF) based classification systems typically restrict their performance to a single, static operating point (i.e. a paired sensitivity/specificity). To address this deficiency, we previously introduced an extension of maximum posterior marginals (MPM) estimation that allows certain classes to be weighted more heavily than others, thus providing a means for varying classifier performance. However, this extension is not appropriate for the more popular maximum a posteriori (MAP) estimation. Thus, a strategy for varying the performance of MAP estimators is still needed. Such a strategy is essential for several reasons: (1) the MAP cost function may be more appropriate in certain classification tasks than the MPM cost function, (2) the literature provides a surfeit of MAP estimation implementations, several of which are considerably faster than the typical Markov Chain Monte Carlo methods used for MPM, and (3) MAP estimation is used far more often than MPM. Consequently, in this paper we introduce multiplicative weighted MAP (MWMAP) estimation-achieved via the incorporation of multiplicative weights into the MAP cost function-which allows certain classes to be preferred over others. This creates a natural bias for specific classes, and consequently a means for adjusting classifier performance. Similarly, we show how this multiplicative weighting strategy can be applied to the MPM

  19. 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.

  20. Accelerating Markov chain Monte Carlo simulation by differential evolution with self-adaptive randomized subspace sampling

    SciTech Connect

    Vrugt, Jasper A; Hyman, James M; Robinson, Bruce A; Higdon, Dave; Ter Braak, Cajo J F; Diks, Cees G H

    2008-01-01

    Markov chain Monte Carlo (MCMC) methods have found widespread use in many fields of study to estimate the average properties of complex systems, and for posterior inference in a Bayesian framework. Existing theory and experiments prove convergence of well constructed MCMC schemes to the appropriate limiting distribution under a variety of different conditions. In practice, however this convergence is often observed to be disturbingly slow. This is frequently caused by an inappropriate selection of the proposal distribution used to generate trial moves in the Markov Chain. Here we show that significant improvements to the efficiency of MCMC simulation can be made by using a self-adaptive Differential Evolution learning strategy within a population-based evolutionary framework. This scheme, entitled DiffeRential Evolution Adaptive Metropolis or DREAM, runs multiple different chains simultaneously for global exploration, and automatically tunes the scale and orientation of the proposal distribution in randomized subspaces during the search. Ergodicity of the algorithm is proved, and various examples involving nonlinearity, high-dimensionality, and multimodality show that DREAM is generally superior to other adaptive MCMC sampling approaches. The DREAM scheme significantly enhances the applicability of MCMC simulation to complex, multi-modal search problems.

  1. Localization for random and quasiperiodic potentials

    NASA Astrophysics Data System (ADS)

    Spencer, Thomas

    1988-06-01

    A survey is made of some recent mathematical results and techniques for Schrödinger operators with random and quasiperiodic potentials. A new proof of localization for random potentials, established in collaboration with H. von Dreifus, is sketched.

  2. Multi-fidelity modelling via recursive co-kriging and Gaussian–Markov random fields

    PubMed Central

    Perdikaris, P.; Venturi, D.; Royset, J. O.; Karniadakis, G. E.

    2015-01-01

    We propose a new framework for design under uncertainty based on stochastic computer simulations and multi-level recursive co-kriging. The proposed methodology simultaneously takes into account multi-fidelity in models, such as direct numerical simulations versus empirical formulae, as well as multi-fidelity in the probability space (e.g. sparse grids versus tensor product multi-element probabilistic collocation). We are able to construct response surfaces of complex dynamical systems by blending multiple information sources via auto-regressive stochastic modelling. A computationally efficient machine learning framework is developed based on multi-level recursive co-kriging with sparse precision matrices of Gaussian–Markov random fields. The effectiveness of the new algorithms is demonstrated in numerical examples involving a prototype problem in risk-averse design, regression of random functions, as well as uncertainty quantification in fluid mechanics involving the evolution of a Burgers equation from a random initial state, and random laminar wakes behind circular cylinders. PMID:26345079

  3. Monte-Carlo analysis of rarefied-gas diffusion including variance reduction using the theory of Markov random walks

    NASA Technical Reports Server (NTRS)

    Perlmutter, M.

    1973-01-01

    Molecular diffusion through a rarefied gas is analyzed by using the theory of Markov random walks. The Markov walk is simulated on the computer by using random numbers to find the new states from the appropriate transition probabilities. As the sample molecule during its random walk passes a scoring position, which is a location at which the macroscopic diffusing flow variables such as molecular flux and molecular density are desired, an appropriate payoff is scored. The payoff is a function of the sample molecule velocity. For example, in obtaining the molecular flux across a scoring position, the random walk payoff is the net number of times the scoring position has been crossed in the positive direction. Similarly, when the molecular density is required, the payoff is the sum of the inverse velocity of the sample molecule passing the scoring position. The macroscopic diffusing flow variables are then found from the expected payoff of the random walks.

  4. Face Association for Videos Using Conditional Random Fields and Max-Margin Markov Networks.

    PubMed

    Du, Ming; Chellappa, Rama

    2016-09-01

    We address the video-based face association problem, in which one attempts to extract the face tracks of multiple subjects while maintaining label consistency. Traditional tracking algorithms have difficulty in handling this task, especially when challenging nuisance factors like motion blur, low resolution or significant camera motions are present. We demonstrate that contextual features, in addition to face appearance itself, play an important role in this case. We propose principled methods to combine multiple features using Conditional Random Fields and Max-Margin Markov networks to infer labels for the detected faces. Different from many existing approaches, our algorithms work in online mode and hence have a wider range of applications. We address issues such as parameter learning, inference and handling false positves/negatives that arise in the proposed approach. Finally, we evaluate our approach on several public databases. PMID:26552075

  5. Theory of Distribution Estimation of Hyperparameters in Markov Random Field Models

    NASA Astrophysics Data System (ADS)

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

    2016-06-01

    We investigated the performance of distribution estimation of hyperparameters in Markov random field models proposed by Nakanishi-Ohno et al., J. Phys. A 47, 045001 (2014) when used to evaluate the confidence of data. We analytically calculated the configurational average, with respect to data, of the negative logarithm of the posterior distribution, which is called free energy based on an analogy with statistical mechanics. This configurational average of free energy shrinks as the amount of data increases. Our results theoretically confirm the numerical results from that previous study.

  6. Object-oriented image coding scheme based on DWT and Markov random field

    NASA Astrophysics Data System (ADS)

    Zheng, Lei; Wu, Hsien-Hsun S.; Liu, Jyh-Charn S.; Chan, Andrew K.

    1998-12-01

    In this paper, we introduce an object-oriented image coding algorithm to differentiate regions of interest (ROI) in visual communications. Our scheme is motivated by the fact that in visual communications, image contents (objects) are not equally important. For a given network bandwidth budget, one should give the highest transmission priority to the most interesting object, and serve the remaining ones at lower priorities. We propose a DWT based Multiresolution Markov Random Field technique to segment image objects according to their textures. We show that this technique can effectively distinguish visual objects and assign them different priorities. This scheme can be integrated with our ROI compression coder, the Generalized Self-Similarity Tress codex, for networking applications.

  7. 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.

  8. A Markov random field approach for topology-preserving registration: application to object-based tomographic image interpolation.

    PubMed

    Cordero-Grande, Lucilio; Vegas-Sánchez-Ferrero, Gonzalo; Casaseca-de-la-Higuera, Pablo; Alberola-López, Carlos

    2012-04-01

    This paper proposes a topology-preserving multiresolution elastic registration method based on a discrete Markov random field of deformations and a block-matching procedure. The method is applied to the object-based interpolation of tomographic slices. For that purpose, the fidelity of a given deformation to the data is established by a block-matching strategy based on intensity- and gradient-related features, the smoothness of the transformation is favored by an appropriate prior on the field, and the deformation is guaranteed to maintain the topology by imposing some hard constraints on the local configurations of the field. The resulting deformation is defined as the maximum a posteriori configuration. Additionally, the relative influence of the fidelity and smoothness terms is weighted by the unsupervised estimation of the field parameters. In order to obtain an unbiased interpolation result, the registration is performed both in the forward and backward directions, and the resulting transformations are combined by using the local information content of the deformation. The method is applied to magnetic resonance and computed tomography acquisitions of the brain and the torso. Quantitative comparisons offer an overall improvement in performance with respect to related works in the literature. Additionally, the application of the interpolation method to cardiac magnetic resonance images has shown that the removal of any of the main components of the algorithm results in a decrease in performance which has proven to be statistically significant. PMID:21997265

  9. A recursive model-reduction method for approximate inference in Gaussian Markov random fields.

    PubMed

    Johnson, Jason K; Willsky, Alan S

    2008-01-01

    This paper presents recursive cavity modeling--a principled, tractable approach to approximate, near-optimal inference for large Gauss-Markov random fields. The main idea is to subdivide the random field into smaller subfields, constructing cavity models which approximate these subfields. Each cavity model is a concise, yet faithful, model for the surface of one subfield sufficient for near-optimal inference in adjacent subfields. This basic idea leads to a tree-structured algorithm which recursively builds a hierarchy of cavity models during an "upward pass" and then builds a complementary set of blanket models during a reverse "downward pass." The marginal statistics of individual variables can then be approximated using their blanket models. Model thinning plays an important role, allowing us to develop thinned cavity and blanket models thereby providing tractable approximate inference. We develop a maximum-entropy approach that exploits certain tractable representations of Fisher information on thin chordal graphs. Given the resulting set of thinned cavity models, we also develop a fast preconditioner, which provides a simple iterative method to compute optimal estimates. Thus, our overall approach combines recursive inference, variational learning and iterative estimation. We demonstrate the accuracy and scalability of this approach in several challenging, large-scale remote sensing problems. PMID:18229805

  10. Automatic white matter lesion segmentation using contrast enhanced FLAIR intensity and Markov Random Field.

    PubMed

    Roy, Pallab Kanti; Bhuiyan, Alauddin; Janke, Andrew; Desmond, Patricia M; Wong, Tien Yin; Abhayaratna, Walter P; Storey, Elsdon; Ramamohanarao, Kotagiri

    2015-10-01

    White matter lesions (WMLs) are small groups of dead cells that clump together in the white matter of brain. In this paper, we propose a reliable method to automatically segment WMLs. Our method uses a novel filter to enhance the intensity of WMLs. Then a feature set containing enhanced intensity, anatomical and spatial information is used to train a random forest classifier for the initial segmentation of WMLs. Following that a reliable and robust edge potential function based Markov Random Field (MRF) is proposed to obtain the final segmentation by removing false positive WMLs. Quantitative evaluation of the proposed method is performed on 24 subjects of ENVISion study. The segmentation results are validated against the manual segmentation, performed under the supervision of an expert neuroradiologist. The results show a dice similarity index of 0.76 for severe lesion load, 0.73 for moderate lesion load and 0.61 for mild lesion load. In addition to that we have compared our method with three state of the art methods on 20 subjects of Medical Image Computing and Computer Aided Intervention Society's (MICCAI's) MS lesion challenge dataset, where our method shows better segmentation accuracy compare to the state of the art methods. These results indicate that the proposed method can assist the neuroradiologists in assessing the WMLs in clinical practice. PMID:26398564

  11. Hyperspectral image clustering method based on artificial bee colony algorithm and Markov random fields

    NASA Astrophysics Data System (ADS)

    Sun, Xu; Yang, Lina; Gao, Lianru; Zhang, Bing; Li, Shanshan; Li, Jun

    2015-01-01

    Center-oriented hyperspectral image clustering methods have been widely applied to hyperspectral remote sensing image processing; however, the drawbacks are obvious, including the over-simplicity of computing models and underutilized spatial information. In recent years, some studies have been conducted trying to improve this situation. We introduce the artificial bee colony (ABC) and Markov random field (MRF) algorithms to propose an ABC-MRF-cluster model to solve the problems mentioned above. In this model, a typical ABC algorithm framework is adopted in which cluster centers and iteration conditional model algorithm's results are considered as feasible solutions and objective functions separately, and MRF is modified to be capable of dealing with the clustering problem. Finally, four datasets and two indices are used to show that the application of ABC-cluster and ABC-MRF-cluster methods could help to obtain better image accuracy than conventional methods. Specifically, the ABC-cluster method is superior when used for a higher power of spectral discrimination, whereas the ABC-MRF-cluster method can provide better results when used for an adjusted random index. In experiments on simulated images with different signal-to-noise ratios, ABC-cluster and ABC-MRF-cluster showed good stability.

  12. Prediction coefficient estimation in Markov random fields for iterative x-ray CT reconstruction

    NASA Astrophysics Data System (ADS)

    Wang, Jiao; Sauer, Ken; Thibault, Jean-Baptiste; Yu, Zhou; Bouman, Charles

    2012-02-01

    Bayesian estimation is a statistical approach for incorporating prior information through the choice of an a priori distribution for a random field. A priori image models in Bayesian image estimation are typically low-order Markov random fields (MRFs), effectively penalizing only differences among immediately neighboring voxels. This limits spectral description to a crude low-pass model. For applications where more flexibility in spectral response is desired, potential benefit exists in models which accord higher a priori probability to content in higher frequencies. Our research explores the potential of larger neighborhoods in MRFs to raise the number of degrees of freedom in spectral description. Similarly to classical filter design, the MRF coefficients may be chosen to yield a desired pass-band/stop-band characteristic shape in the a priori model of the images. In this paper, we present an alternative design method, where high-quality sample images are used to estimate the MRF coefficients by fitting them into the spatial correlation of the given ensemble. This method allows us to choose weights that increase the probability of occurrence of strong components at particular spatial frequencies. This allows direct adaptation of the MRFs for different tissue types based on sample images with different frequency content. In this paper, we consider particularly the preservation of detail in bone structure in X-ray CT. Our results show that MRF design can be used to obtain bone emphasis similar to that of conventional filtered back-projection (FBP) with a bone kernel.

  13. Local Random Quantum Circuits are Approximate Polynomial-Designs

    NASA Astrophysics Data System (ADS)

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

    2016-08-01

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

  14. 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

  15. Envelope Synthesis on the Free Surface of a Random Elastic Medium Based on the Markov Approximation

    NASA Astrophysics Data System (ADS)

    Emoto, K.; Sato, H.; Nishimura, T.

    2008-12-01

    Short-period seismograms mostly consist of the waves scattered by random inhomogeneities of the solid earth. For P-waves, the apparent duration is broadened and the transverse amplitude is excited with travel distance increasing. Usually, we observe the seismic waves on the free surface. For the homogeneous medium case, the vertical incident P-wave amplitude is doubled at the free surface; however, for the inhomogeneous medium case it has not been clear how the free surface affects wave amplitudes since the ray directions are widely distributed because of scattering. Here, we develop the synthesis of vector-wave envelopes on the free surface of a random medium. When the wave length is shorter than the correlation distance of 3-D infinite random media, characterized by a Gaussian autocorrelation function, Sato (2006) derives analytical solutions of vector-wave envelopes on the basis of the Markov approximation, which is a stochastic extension of the split stem method to solve the parabolic wave equation. We extend his method for the synthesis of vector-wave envelopes on the free surface of a random medium. In the Markov approximation, Mean square (MS) envelopes are calculated by using the Fourier transform of two-frequency mutual coherence function (TFMCF) with respect to the angular frequency. The TFMCF is statistically defined on the transverse plane, which is perpendicular to the global ray direction. The Fourier transform of the TFMCF with respect to the transverse coordinates gives the angular spectrum that shows the distribution of ray directions. This angular spectrum has a sharp peak in the global ray direction just after the direct wave arrival and gradually increases its width with the lapse time increasing. We can calculate vector-wave envelopes in the infinite space, simply projecting the angular spectrum to each component and integrating it in the wavenumber space. We calculate the vector-wave envelopes on the free surface by multiplying the

  16. Spatio-contextual fuzzy clustering with Markov random field model for change detection in remotely sensed images

    NASA Astrophysics Data System (ADS)

    Subudhi, Badri Narayan; Bovolo, Francesca; Ghosh, Ashish; Bruzzone, Lorenzo

    2014-04-01

    This paper presents a novel spatio-contextual fuzzy clustering algorithm for unsupervised change detection from multispectral and multitemporal remote sensing images. The proposed technique uses fuzzy Gibbs Markov Random Field (GMRF) to model the spatial gray level attributes of the multispectral difference image. The change detection problem is solved using the maximum a posteriori probability (MAP) estimation principle. The MAP estimator of the fuzzy GMRF modeled difference image is found to be exponential in nature. Convergence of conventional fuzzy clustering based search criterion is more likely to lead the clustering solutions to be getting trapped in a local minimum. Hence we adhered to the variable neighborhood searching (VNS) based global convergence criterion for iterative estimation of the fuzzy GMRF parameters. Experiments are carried out on different multispectral and multitemporal remote sensing images. Results confirm the effectiveness of the proposed technique. It is also noticed that the proposed scheme provides better results with less misclassification error as compared to the existing techniques. The computational time taken by the proposed technique is comparable with that of the HTNN scheme.

  17. A new method for direction finding based on Markov random field model

    NASA Astrophysics Data System (ADS)

    Ota, Mamoru; Kasahara, Yoshiya; Goto, Yoshitaka

    2015-07-01

    Investigating the characteristics of plasma waves observed by scientific satellites in the Earth's plasmasphere/magnetosphere is effective for understanding the mechanisms for generating waves and the plasma environment that influences wave generation and propagation. In particular, finding the propagation directions of waves is important for understanding mechanisms of VLF/ELF waves. To find these directions, the wave distribution function (WDF) method has been proposed. This method is based on the idea that observed signals consist of a number of elementary plane waves that define wave energy density distribution. However, the resulting equations constitute an ill-posed problem in which a solution is not determined uniquely; hence, an adequate model must be assumed for a solution. Although many models have been proposed, we have to select the most optimum model for the given situation because each model has its own advantages and disadvantages. In the present study, we propose a new method for direction finding of the plasma waves measured by plasma wave receivers. Our method is based on the assumption that the WDF can be represented by a Markov random field model with inference of model parameters performed using a variational Bayesian learning algorithm. Using computer-generated spectral matrices, we evaluated the performance of the model and compared the results with those obtained from two conventional methods.

  18. 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. PMID:24968171

  19. Context-aware patch-based image inpainting using Markov random field modeling.

    PubMed

    Ružić, Tijana; Pižurica, Aleksandra

    2015-01-01

    In this paper, we first introduce a general approach for context-aware patch-based image inpainting, where textural descriptors are used to guide and accelerate the search for well-matching (candidate) patches. A novel top-down splitting procedure divides the image into variable size blocks according to their context, constraining thereby the search for candidate patches to nonlocal image regions with matching context. This approach can be employed to improve the speed and performance of virtually any (patch-based) inpainting method. We apply this approach to the so-called global image inpainting with the Markov random field (MRF) prior, where MRF encodes a priori knowledge about consistency of neighboring image patches. We solve the resulting optimization problem with an efficient low-complexity inference method. Experimental results demonstrate the potential of the proposed approach in inpainting applications like scratch, text, and object removal. Improvement and significant acceleration of a related global MRF-based inpainting method is also evident. PMID:25420260

  20. A Markov Random Field Model-Based Approach To Image Interpretation

    NASA Astrophysics Data System (ADS)

    Zhang, Jun; Modestino, James W.

    1989-11-01

    In this paper, a Markov random field (MRF) model-based approach to automated image interpretation is described and demonstrated as a region-based scheme. In this approach, an image is first segmented into a collection of disjoint regions which form the nodes of an adjacency graph. Image interpretation is then achieved through assigning object labels, or interpretations, to the segmented regions, or nodes, using domain knowledge, extracted feature measurements and spatial relationships between the various regions. The interpretation labels are modeled as a MRF on the corresponding adjacency graph and the image interpretation problem is formulated as a maximum a posteriori (MAP) estimation rule. Simulated annealing is used to find the best realization, or optimal MAP interpretation. Through the MRF model, this approach also provides a systematic method for organizing and representing domain knowledge through the clique functions of the pdf of the underlying MRF. Results of image interpretation experiments performed on synthetic and real-world images using this approach are described and appear promising.

  1. Segmentation of 2D gel electrophoresis spots using a Markov random field

    NASA Astrophysics Data System (ADS)

    Hoeflich, Christopher S.; Corso, Jason J.

    2009-02-01

    We propose a statistical model-based approach for the segmentation of fragments of DNA as a first step in the automation of the primarily manual process of comparing two or more images resulting from the Restriction Landmark Genomic Scanning (RLGS) method. These 2D gel electrophoresis images are the product of the separation of DNA into fragments that appear as spots on X-ray films. The goal is to find instances where a spot appears in one image and not in another since a missing spot can be correlated with a region of DNA that has been affected by a disease such as cancer. The entire comparison process is typically done manually, which is tedious and very error prone. We pose the problem as the labeling of each image pixel as either a spot or non-spot and use a Markov Random Field (MRF) model and simulated annealing for inference. Neighboring spot labels are then connected to form spot regions. The MRF based model was tested on actual 2D gel electrophoresis images.

  2. Medical image retrieval and analysis by Markov random fields and multi-scale fractal dimension.

    PubMed

    Backes, André Ricardo; Gerhardinger, Leandro Cavaleri; Batista Neto, João do Espírito Santo; Bruno, Odemir Martinez

    2015-02-01

    Many Content-based Image Retrieval (CBIR) systems and image analysis tools employ color, shape and texture (in a combined fashion or not) as attributes, or signatures, to retrieve images from databases or to perform image analysis in general. Among these attributes, texture has turned out to be the most relevant, as it allows the identification of a larger number of images of a different nature. This paper introduces a novel signature which can be used for image analysis and retrieval. It combines texture with complexity extracted from objects within the images. The approach consists of a texture segmentation step, modeled as a Markov Random Field process, followed by the estimation of the complexity of each computed region. The complexity is given by a Multi-scale Fractal Dimension. Experiments have been conducted using an MRI database in both pattern recognition and image retrieval contexts. The results show the accuracy of the proposed method in comparison with other traditional texture descriptors and also indicate how the performance changes as the level of complexity is altered. PMID:25586375

  3. Medical image retrieval and analysis by Markov random fields and multi-scale fractal dimension

    NASA Astrophysics Data System (ADS)

    Backes, André Ricardo; Cavaleri Gerhardinger, Leandro; do Espírito Santo Batista Neto, João; Martinez Bruno, Odemir

    2015-02-01

    Many Content-based Image Retrieval (CBIR) systems and image analysis tools employ color, shape and texture (in a combined fashion or not) as attributes, or signatures, to retrieve images from databases or to perform image analysis in general. Among these attributes, texture has turned out to be the most relevant, as it allows the identification of a larger number of images of a different nature. This paper introduces a novel signature which can be used for image analysis and retrieval. It combines texture with complexity extracted from objects within the images. The approach consists of a texture segmentation step, modeled as a Markov Random Field process, followed by the estimation of the complexity of each computed region. The complexity is given by a Multi-scale Fractal Dimension. Experiments have been conducted using an MRI database in both pattern recognition and image retrieval contexts. The results show the accuracy of the proposed method in comparison with other traditional texture descriptors and also indicate how the performance changes as the level of complexity is altered.

  4. Identifying protein interaction subnetworks by a bagging Markov random field-based method

    PubMed Central

    Chen, Li; Xuan, Jianhua; Riggins, Rebecca B.; Wang, Yue; Clarke, Robert

    2013-01-01

    Identification of differentially expressed subnetworks from protein–protein interaction (PPI) networks has become increasingly important to our global understanding of the molecular mechanisms that drive cancer. Several methods have been proposed for PPI subnetwork identification, but the dependency among network member genes is not explicitly considered, leaving many important hub genes largely unidentified. We present a new method, based on a bagging Markov random field (BMRF) framework, to improve subnetwork identification for mechanistic studies of breast cancer. The method follows a maximum a posteriori principle to form a novel network score that explicitly considers pairwise gene interactions in PPI networks, and it searches for subnetworks with maximal network scores. To improve their robustness across data sets, a bagging scheme based on bootstrapping samples is implemented to statistically select high confidence subnetworks. We first compared the BMRF-based method with existing methods on simulation data to demonstrate its improved performance. We then applied our method to breast cancer data to identify PPI subnetworks associated with breast cancer progression and/or tamoxifen resistance. The experimental results show that not only an improved prediction performance can be achieved by the BMRF approach when tested on independent data sets, but biologically meaningful subnetworks can also be revealed that are relevant to breast cancer and tamoxifen resistance. PMID:23161673

  5. D Classification of Crossroads from Multiple Aerial Images Using Markov Random Fields

    NASA Astrophysics Data System (ADS)

    Kosov, S.; Rottensteiner, F.; Heipke, C.; Leitloff, J.; Hinz, S.

    2012-08-01

    The precise classification and reconstruction of crossroads from multiple aerial images is a challenging problem in remote sensing. We apply the Markov Random Fields (MRF) approach to this problem, a probabilistic model that can be used to consider context in classification. A simple appearance-based model is combined with a probabilistic model of the co-occurrence of class label at neighbouring image sites to distinguish up to 14 different classes that are relevant for scenes containing crossroads. The parameters of these models are learnt from training data. We use multiple overlap aerial images to derive a digital surface model (DSM) and a true orthophoto without moving cars. From the DSM and the orthophoto we derive feature vectors that are used in the classification. One of the features is a car confidence value that is supposed to support the classification when the road surface is occluded by static cars. Our approach is evaluated on a dataset of airborne photos of an urban area by a comparison of the results to reference data. Whereas the method has problems in distinguishing classes having a similar appearance, it is shown to produce promising results if a reduced set of classes is considered, yielding an overall classification accuracy of 74.8%.

  6. Segmentation of complementary DNA microarray images by wavelet-based Markov random field model.

    PubMed

    Athanasiadis, Emmanouil I; Cavouras, Dionisis A; Glotsos, Dimitris Th; Georgiadis, Pantelis V; Kalatzis, Ioannis K; Nikiforidis, George C

    2009-11-01

    A wavelet-based modification of the Markov random field (WMRF) model is proposed for segmenting complementary DNA (cDNA) microarray images. For evaluation purposes, five simulated and a set of five real microarray images were used. The one-level stationary wavelet transform (SWT) of each microarray image was used to form two images, a denoised image, using hard thresholding filter, and a magnitude image, from the amplitudes of the horizontal and vertical components of SWT. Elements from these two images were suitably combined to form the WMRF model for segmenting spots from their background. The WMRF was compared against the conventional MRF and the Fuzzy C means (FCM) algorithms on simulated and real microarray images and their performances were evaluated by means of the segmentation matching factor (SMF) and the coefficient of determination (r2). Additionally, the WMRF was compared against the SPOT and SCANALYZE, and performances were evaluated by the mean absolute error (MAE) and the coefficient of variation (CV). The WMRF performed more accurately than the MRF and FCM (SMF: 92.66, 92.15, and 89.22, r2 : 0.92, 0.90, and 0.84, respectively) and achieved higher reproducibility than the MRF, SPOT, and SCANALYZE (MAE: 497, 1215, 1180, and 503, CV: 0.88, 1.15, 0.93, and 0.90, respectively). PMID:19783509

  7. A wavelet-based Markov random field segmentation model in segmenting microarray experiments.

    PubMed

    Athanasiadis, Emmanouil; Cavouras, Dionisis; Kostopoulos, Spyros; Glotsos, Dimitris; Kalatzis, Ioannis; Nikiforidis, George

    2011-12-01

    In the present study, an adaptation of the Markov Random Field (MRF) segmentation model, by means of the stationary wavelet transform (SWT), applied to complementary DNA (cDNA) microarray images is proposed (WMRF). A 3-level decomposition scheme of the initial microarray image was performed, followed by a soft thresholding filtering technique. With the inverse process, a Denoised image was created. In addition, by using the Amplitudes of the filtered wavelet Horizontal and Vertical images at each level, three different Magnitudes were formed. These images were combined with the Denoised one to create the proposed SMRF segmentation model. For numerical evaluation of the segmentation accuracy, the segmentation matching factor (SMF), the Coefficient of Determination (r(2)), and the concordance correlation (p(c)) were calculated on the simulated images. In addition, the SMRF performance was contrasted to the Fuzzy C Means (FCM), Gaussian Mixture Models (GMM), Fuzzy GMM (FGMM), and the conventional MRF techniques. Indirect accuracy performances were also tested on the experimental images by means of the Mean Absolute Error (MAE) and the Coefficient of Variation (CV). In the latter case, SPOT and SCANALYZE software results were also tested. In the former case, SMRF attained the best SMF, r(2), and p(c) (92.66%, 0.923, and 0.88, respectively) scores, whereas, in the latter case scored MAE and CV, 497 and 0.88, respectively. The results and support the performance superiority of the SMRF algorithm in segmenting cDNA images. PMID:21531035

  8. Segmentation of cone-beam CT using a hidden Markov random field with informative priors

    NASA Astrophysics Data System (ADS)

    Moores, M.; Hargrave, C.; Harden, F.; Mengersen, K.

    2014-03-01

    Cone-beam computed tomography (CBCT) has enormous potential to improve the accuracy of treatment delivery in image-guided radiotherapy (IGRT). To assist radiotherapists in interpreting these images, we use a Bayesian statistical model to label each voxel according to its tissue type. The rich sources of prior information in IGRT are incorporated into a hidden Markov random field model of the 3D image lattice. Tissue densities in the reference CT scan are estimated using inverse regression and then rescaled to approximate the corresponding CBCT intensity values. The treatment planning contours are combined with published studies of physiological variability to produce a spatial prior distribution for changes in the size, shape and position of the tumour volume and organs at risk. The voxel labels are estimated using iterated conditional modes. The accuracy of the method has been evaluated using 27 CBCT scans of an electron density phantom. The mean voxel-wise misclassification rate was 6.2%, with Dice similarity coefficient of 0.73 for liver, muscle, breast and adipose tissue. By incorporating prior information, we are able to successfully segment CBCT images. This could be a viable approach for automated, online image analysis in radiotherapy.

  9. Markov random field based automatic alignment for low SNR imagesfor cryo electron tomography

    SciTech Connect

    Amat, Fernando; Moussavi, Farshid; Comolli, Luis R.; Elidan, Gal; Horowitz, Mark

    2007-07-21

    We present a method for automatic full precision alignmentof the images in a tomographic tilt series. Full-precision automaticalignment of cryo electron microscopy images has remained a difficultchallenge to date, due to the limited electron dose and low imagecontrast. These facts lead to poor signal to noise ratio (SNR) in theimages, which causes automatic feature trackers to generate errors, evenwith high contrast gold particles as fiducial features. To enable fullyautomatic alignment for full-precision reconstructions, we frame theproblem probabilistically as finding the most likely particle tracksgiven a set of noisy images, using contextual information to make thesolution more robust to the noise in each image. To solve this maximumlikelihood problem, we use Markov Random Fields (MRF) to establish thecorrespondence of features in alignment and robust optimization forprojection model estimation. The resultingalgorithm, called RobustAlignment and Projection Estimation for Tomographic Reconstruction, orRAPTOR, has not needed any manual intervention for the difficult datasets we have tried, and has provided sub-pixel alignment that is as goodas the manual approach by an expert user. We are able to automaticallymap complete and partial marker trajectories and thus obtain highlyaccurate image alignment. Our method has been applied to challenging cryoelectron tomographic datasets with low SNR from intact bacterial cells,as well as several plastic section and x-ray datasets.

  10. Image Enhancement and Speckle Reduction of Full Polarimetric SAR Data by Gaussian Markov Random Field

    NASA Astrophysics Data System (ADS)

    Mahdian, M.; Motagh, M.; Akbari, V.

    2013-09-01

    In recent years, the use of Polarimetric Synthetic Aperture Radar (PolSAR) data in different applications dramatically has been increased. In SAR imagery an interference phenomenon with random behavior exists which is called speckle noise. The interpretation of data encounters some troubles due to the presence of speckle which can be considered as a multiplicative noise affecting all coherent imaging systems. Indeed, speckle degrade radiometric resolution of PolSAR images, therefore it is needful to perform speckle filtering on the SAR data type. Markov Random Field (MRF) has proven to be a powerful method for drawing out eliciting contextual information from remotely sensed images. In the present paper, a probability density function (PDF), which is fitted well with the PolSAR data based on the goodness-of-fit test, is first obtained for the pixel-wise analysis. Then the contextual smoothing is achieved with the MRF method. This novel speckle reduction method combines an advanced statistical distribution with spatial contextual information for PolSAR data. These two parts of information are combined based on weighted summation of pixel-wise and contextual models. This approach not only preserves edge information in the images, but also improves signal-to-noise ratio of the results. The method maintains the mean value of original signal in the homogenous areas and preserves the edges of features in the heterogeneous regions. Experiments on real medium resolution ALOS data from Tehran, and also high resolution full polarimetric SAR data over the Oberpfaffenhofen test-site in Germany, demonstrate the effectiveness of the algorithm compared with well-known despeckling methods.

  11. Analysis and Validation of Grid dem Generation Based on Gaussian Markov Random Field

    NASA Astrophysics Data System (ADS)

    Aguilar, F. J.; Aguilar, M. A.; Blanco, J. L.; Nemmaoui, A.; García Lorca, A. M.

    2016-06-01

    Digital Elevation Models (DEMs) are considered as one of the most relevant geospatial data to carry out land-cover and land-use classification. This work deals with the application of a mathematical framework based on a Gaussian Markov Random Field (GMRF) to interpolate grid DEMs from scattered elevation data. The performance of the GMRF interpolation model was tested on a set of LiDAR data (0.87 points/m2) provided by the Spanish Government (PNOA Programme) over a complex working area mainly covered by greenhouses in Almería, Spain. The original LiDAR data was decimated by randomly removing different fractions of the original points (from 10% to up to 99% of points removed). In every case, the remaining points (scattered observed points) were used to obtain a 1 m grid spacing GMRF-interpolated Digital Surface Model (DSM) whose accuracy was assessed by means of the set of previously extracted checkpoints. The GMRF accuracy results were compared with those provided by the widely known Triangulation with Linear Interpolation (TLI). Finally, the GMRF method was applied to a real-world case consisting of filling the LiDAR-derived DSM gaps after manually filtering out non-ground points to obtain a Digital Terrain Model (DTM). Regarding accuracy, both GMRF and TLI produced visually pleasing and similar results in terms of vertical accuracy. As an added bonus, the GMRF mathematical framework makes possible to both retrieve the estimated uncertainty for every interpolated elevation point (the DEM uncertainty) and include break lines or terrain discontinuities between adjacent cells to produce higher quality DTMs.

  12. Fisher informations and local asymptotic normality for continuous-time quantum Markov processes

    NASA Astrophysics Data System (ADS)

    Catana, Catalin; Bouten, Luc; Guţă, Mădălin

    2015-09-01

    We consider the problem of estimating an arbitrary dynamical parameter of an open quantum system in the input-output formalism. For irreducible Markov processes, we show that in the limit of large times the system-output state can be approximated by a quantum Gaussian state whose mean is proportional to the unknown parameter. This approximation holds locally in a neighbourhood of size {t}-1/2 in the parameter space, and provides an explicit expression of the asymptotic quantum Fisher information in terms of the Markov generator. Furthermore we show that additive statistics of the counting and homodyne measurements also satisfy local asymptotic normality and we compute the corresponding classical Fisher informations. The general theory is illustrated with the examples of a two-level system and the atom maser. Our results contribute towards a better understanding of the statistical and probabilistic properties of the output process, with relevance for quantum control engineering, and the theory of non-equilibrium quantum open systems.

  13. Bayesian inference of local trees along chromosomes by the sequential Markov coalescent.

    PubMed

    Zheng, Chaozhi; Kuhner, Mary K; Thompson, Elizabeth A

    2014-05-01

    We propose a genealogy-sampling algorithm, Sequential Markov Ancestral Recombination Tree (SMARTree), that provides an approach to estimation from SNP haplotype data of the patterns of coancestry across a genome segment among a set of homologous chromosomes. To enable analysis across longer segments of genome, the sequence of coalescent trees is modeled via the modified sequential Markov coalescent (Marjoram and Wall, Genetics 7:16, 2006). To assess performance in estimating these local trees, our SMARTree implementation is tested on simulated data. Our base data set is of the SNPs in 10 DNA sequences over 50 kb. We examine the effects of longer sequences and of more sequences, and of a recombination and/or mutational hotspot. The model underlying SMARTree is an approximation to the full recombinant-coalescent distribution. However, in a small trial on simulated data, recovery of local trees was similar to that of LAMARC (Kuhner et al. Genetics 156:1393-1401, 2000a), a sampler which uses the full model. PMID:24817610

  14. 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.

  15. Bayesian inference of local trees along chromosomes by the sequential Markov coalescent

    PubMed Central

    Zheng, Chaozhi; Kuhner, Mary K.

    2014-01-01

    We propose a genealogy sampling algorithm, SMARTree, that provides an approach to estimation from SNP haplotype data of the patterns of coancestry across a genome segment among a set of homologous chromosomes. To enable analysis across longer segments of genome, the sequence of coalescent trees is modeled via the modified sequential Markov coalescent (Marjoram and Wall, 2006). To assess performance in estimating these local trees, our SMARTree implementation is tested on simulated data. Our base data set is of the SNPs in ten DNA sequences over 50kb. We examine the effects of longer sequences and of more sequences, and of a recombination and/or mutational hotspot. The model underlying SMARTree is an approximation to the full recombinant-coalescent distribution. However, in a small trial on simulated data, recovery of local trees was similar to that of LAMARC (Kuhner et al., 2000a), a sampler which uses the full model. PMID:24817610

  16. An automatic water body area monitoring algorithm for satellite images based on Markov Random Fields

    NASA Astrophysics Data System (ADS)

    Elmi, Omid; Tourian, Mohammad J.; Sneeuw, Nico

    2016-04-01

    Our knowledge about spatial and temporal variation of hydrological parameters are surprisingly poor, because most of it is based on in situ stations and the number of stations have reduced dramatically during the past decades. On the other hand, remote sensing techniques have proven their ability to measure different parameters of Earth phenomena. Optical and SAR satellite imagery provide the opportunity to monitor the spatial change in coastline, which can serve as a way to determine the water extent repeatedly in an appropriate time interval. An appropriate classification technique to separate water and land is the backbone of each automatic water body monitoring. Due to changes in the water level, river and lake extent, atmosphere, sunlight radiation and onboard calibration of the satellite over time, most of the pixel-based classification techniques fail to determine accurate water masks. Beyond pixel intensity, spatial correlation between neighboring pixels is another source of information that should be used to decide the label of pixels. Water bodies have strong spatial correlation in satellite images. Therefore including contextual information as additional constraint into the procedure of water body monitoring improves the accuracy of the derived water masks significantly. In this study, we present an automatic algorithm for water body area monitoring based on maximum a posteriori (MAP) estimation of Markov Random Fields (MRF). First we collect all available images from selected case studies during the monitoring period. Then for each image separately we apply a k-means clustering to derive a primary water mask. After that we develop a MRF using pixel values and the primary water mask for each image. Then among the different realizations of the field we select the one that maximizes the posterior estimation. We solve this optimization problem using graph cut techniques. A graph with two terminals is constructed, after which the best labelling structure for

  17. Impact of model order and estimation window for indexing TerraSAR-X images using Gauss Markov random fields

    NASA Astrophysics Data System (ADS)

    Espinoza-Molina, Daniela; Datcu, Mihai

    2010-10-01

    TerraSAR-X is the Synthetic Aperture Radar (SAR) German satellite which provides a high diversity of information due to its high-resolution. TerraSAR-X acquires daily a volume of up to 100 GB of high complexity, multi-mode SAR images, i.e. SpotLight, StripMap, and ScanSAR data, with dual or quad-polarization, and with different look angles. The high and multiple resolutions of the instrument (1m, 3m or 10m) open perspectives for new applications, that were not possible with past lower resolution sensors (20-30m). Mainly the 1m and 3m modes we expect to support a broad range of new applications related to human activities with relevant structures and objects at the 1m scale. Thus, among the most interesting scenes are: urban, industrial, and rural data. In addition, the global coverage and the relatively frequent repeat pass will definitely help to acquire extremely relevant data sets. To analyze the available TerrrSAR-X data we rely on model based methods for feature extraction and despeckling. The image information content is extracted using model-based methods based on Gauss Markov Random Field (GMRF) and Bayesian inference approach. This approach enhances the local adaptation by using a prior model, which learns the image structure and enables to estimate the local description of the structures, acting as primitive feature extraction method. However, the GMRF model-based method uses as input parameters the Model Order (MO) and the size of Estimation Window (EW). The appropriated selection of these parameters allows us to improve the classification and indexing results due to the number of well separated classes could be determined by them. Our belief is that the selection of the MO depends on the kind of information that the image contains, explaining how well the model can recognize complex structures as objects, and according to the size of EW the accuracy of the estimation is determined. In the following, we present an evaluation of the impact of the model

  18. Local volume fraction fluctuations in random media

    SciTech Connect

    Quintanilla, J.; Torquato, S.

    1997-02-01

    Although the volume fraction is a constant for a statistically homogeneous random medium, on a spatially local level it fluctuates. We study the full distribution of volume fraction within an observation window of finite size for models of random media. A formula due to Lu and Torquato for the standard deviation or {open_quotes}coarseness{close_quotes} associated with the {ital local} volume fraction {xi} is extended for the nth moment of {xi} for any n. The distribution function F{sub L} of the local volume fraction of five different model microstructures is evaluated using analytical and computer-simulation methods for a wide range of window sizes and overall volume fractions. On the line, we examine a system of fully penetrable rods and a system of totally impenetrable rods formed by random sequential addition (RSA). In the plane, we study RSA totally impenetrable disks and fully penetrable aligned squares. In three dimensions, we study fully penetrable aligned cubes. In the case of fully penetrable rods, we will also simplify and numerically invert a prior analytical result for the Laplace transform of F{sub L}. In all of these models, we show that, for sufficiently large window sizes, F{sub L} can be reasonably approximated by the normal distribution. {copyright} {ital 1997 American Institute of Physics.}

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

    NASA Astrophysics Data System (ADS)

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

    2016-07-01

    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 field 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.

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

    DOE PAGESBeta

    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

  1. 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

  2. Hidden Markov models that use predicted local structure for fold recognition: alphabets of backbone geometry.

    PubMed

    Karchin, Rachel; Cline, Melissa; Mandel-Gutfreund, Yael; Karplus, Kevin

    2003-06-01

    An important problem in computational biology is predicting the structure of the large number of putative proteins discovered by genome sequencing projects. Fold-recognition methods attempt to solve the problem by relating the target proteins to known structures, searching for template proteins homologous to the target. Remote homologs that may have significant structural similarity are often not detectable by sequence similarities alone. To address this, we incorporated predicted local structure, a generalization of secondary structure, into two-track profile hidden Markov models (HMMs). We did not rely on a simple helix-strand-coil definition of secondary structure, but experimented with a variety of local structure descriptions, following a principled protocol to establish which descriptions are most useful for improving fold recognition and alignment quality. On a test set of 1298 nonhomologous proteins, HMMs incorporating a 3-letter STRIDE alphabet improved fold recognition accuracy by 15% over amino-acid-only HMMs and 23% over PSI-BLAST, measured by ROC-65 numbers. We compared two-track HMMs to amino-acid-only HMMs on a difficult alignment test set of 200 protein pairs (structurally similar with 3-24% sequence identity). HMMs with a 6-letter STRIDE secondary track improved alignment quality by 62%, relative to DALI structural alignments, while HMMs with an STR track (an expanded DSSP alphabet that subdivides strands into six states) improved by 40% relative to CE. PMID:12784210

  3. Precise estimation of pressure-temperature paths from zoned minerals using Markov random field modeling: theory and synthetic inversion

    NASA Astrophysics Data System (ADS)

    Kuwatani, Tatsu; Nagata, Kenji; Okada, Masato; Toriumi, Mitsuhiro

    2012-03-01

    The chemical zoning profile in metamorphic minerals is often used to deduce the pressure-temperature ( P- T) history of rock. However, it remains difficult to restore detailed paths from zoned minerals because thermobarometric evaluation of metamorphic conditions involves several uncertainties, including measurement errors and geological noise. We propose a new stochastic framework for estimating precise P- T paths from a chemical zoning structure using the Markov random field (MRF) model, which is a type of Bayesian stochastic method that is often applied to image analysis. The continuity of pressure and temperature during mineral growth is incorporated by Gaussian Markov chains as prior probabilities in order to apply the MRF model to the P- T path inversion. The most probable P- T path can be obtained by maximizing the posterior probability of the sequential set of P and T given the observed compositions of zoned minerals. Synthetic P- T inversion tests were conducted in order to investigate the effectiveness and validity of the proposed model from zoned Mg-Fe-Ca garnet in the divariant KNCFMASH system. In the present study, the steepest descent method was implemented in order to maximize the posterior probability using the Markov chain Monte Carlo algorithm. The proposed method successfully reproduced the detailed shape of the synthetic P- T path by eliminating appropriately the statistical compositional noises without operator's subjectivity and prior knowledge. It was also used to simultaneously evaluate the uncertainty of pressure, temperature, and mineral compositions for all measurement points. The MRF method may have potential to deal with several geological uncertainties, which cause cumbersome systematic errors, by its Bayesian approach and flexible formalism, so that it comprises potentially powerful tools for various inverse problems in petrology.

  4. Classification of EEG Single Trial Microstates Using Local Global Graphs and Discrete Hidden Markov Models.

    PubMed

    Michalopoulos, Kostas; Zervakis, Michalis; Deiber, Marie-Pierre; Bourbakis, Nikolaos

    2016-09-01

    We present a novel synergistic methodology for the spatio-temporal analysis of single Electroencephalogram (EEG) trials. This new methodology is based on the novel synergy of Local Global Graph (LG graph) to characterize define the structural features of the EEG topography as a global descriptor for robust comparison of dominant topographies (microstates) and Hidden Markov Models (HMM) to model the topographic sequence in a unique way. In particular, the LG graph descriptor defines similarity and distance measures that can be successfully used for the difficult comparison of the extracted LG graphs in the presence of noise. In addition, hidden states represent periods of stationary distribution of topographies that constitute the equivalent of the microstates in the model. The transitions between the different microstates and the formed syntactic patterns can reveal differences in the processing of the input stimulus between different pathologies. We train the HMM model to learn the transitions between the different microstates and express the syntactic patterns that appear in the single trials in a compact and efficient way. We applied this methodology in single trials consisting of normal subjects and patients with Progressive Mild Cognitive Impairment (PMCI) to discriminate these two groups. The classification results show that this approach is capable to efficiently discriminate between control and Progressive MCI single trials. Results indicate that HMMs provide physiologically meaningful results that can be used in the syntactic analysis of Event Related Potentials. PMID:27255799

  5. Image segmentation for automatic particle identification in electron micrographs based on hidden Markov random field models and expectation maximization

    PubMed Central

    Singh, Vivek; Marinescu, Dan C.; Baker, Timothy S.

    2014-01-01

    Three-dimensional reconstruction of large macromolecules like viruses at resolutions below 10 ÅA requires a large set of projection images. Several automatic and semi-automatic particle detection algorithms have been developed along the years. Here we present a general technique designed to automatically identify the projection images of particles. The method is based on Markov random field modelling of the projected images and involves a pre-processing of electron micrographs followed by image segmentation and post-processing. The image is modelled as a coupling of two fields—a Markovian and a non-Markovian. The Markovian field represents the segmented image. The micrograph is the non-Markovian field. The image segmentation step involves an estimation of coupling parameters and the maximum áa posteriori estimate of the realization of the Markovian field i.e, segmented image. Unlike most current methods, no bootstrapping with an initial selection of particles is required. PMID:15065680

  6. A Functional Networks Estimation Method of Resting-State fMRI Using a Hierarchical Markov Random Field

    PubMed Central

    Liu, Wei; Awate, Suyash P.; Anderson, Jeffrey S.; Fletcher, P. Thomas

    2014-01-01

    We propose a hierarchical Markov random field model that estimates both group and subject functional networks simultaneously. The model takes into account the within-subject spatial coherence as well as the between-subject consistency of the network label maps. The statistical dependency between group and subject networks acts as a regularization, which helps the network estimation on both layers. We use Gibbs sampling to approximate the posterior density of the network labels and Monte Carlo expectation maximization to estimate the model parameters. We compare our method with two alternative segmentation methods based on K-Means and normalized cuts, using synthetic and real fMRI data. The experimental results show our proposed model is able to identify both group and subject functional networks with higher accuracy, more robustness, and inter-session consistency. PMID:24954282

  7. Object-oriented Markov random model for classification of high resolution satellite imagery based on wavelet transform

    NASA Astrophysics Data System (ADS)

    Hong, Liang; Liu, Cun; Yang, Kun; Deng, Ming

    2013-07-01

    The high resolution satellite imagery (HRSI) have higher spatial resolution and less spectrum number, so there are some "object with different spectra, different objects with same spectrum" phenomena. The objective of this paper is to utilize the extracted features of high resolution satellite imagery (HRSI) obtained by the wavelet transform(WT) for segmentation. WT provides the spatial and spectral characteristics of a pixel along with its neighbors. The object-oriented Markov random Model in the wavelet domain is proposed in order to segment high resolution satellite imagery (HRSI). The proposed method is made up of three blocks: (1) WT-based feature extrcation.the aim of extraction of feature using WT for original spectral bands is to exploit the spatial and frequency information of the pixels; (2) over-segmentation object generation. Mean-Shift algorithm is employed to obtain over-segmentation objects; (3) classification based on Object-oriented Markov Random Model. Firstly the object adjacent graph (OAG) can be constructed on the over-segmentation objects. Secondly MRF model is easily defined on the OAG, in which WT-based feature of pixels are modeled in the feature field model and the neighbor system, potential cliques and energy functions of OAG are exploited in the labeling model. Experiments are conducted on one HRSI dataset-QuickBird images. We evaluate and compare the proposed approach with the well-known commercial software eCognition(object-based analysis approach) and Maximum Likelihood(ML) based pixels. Experimental results show that the proposed the method in this paper obviously outperforms the other methods.

  8. Weighted maximum posterior marginals for random fields using an ensemble of conditional densities from multiple Markov chain Monte Carlo simulations.

    PubMed

    Monaco, James Peter; Madabhushi, Anant

    2011-07-01

    The ability of classification systems to adjust their performance (sensitivity/specificity) is essential for tasks in which certain errors are more significant than others. For example, mislabeling cancerous lesions as benign is typically more detrimental than mislabeling benign lesions as cancerous. Unfortunately, methods for modifying the performance of Markov random field (MRF) based classifiers are noticeably absent from the literature, and thus most such systems restrict their performance to a single, static operating point (a paired sensitivity/specificity). To address this deficiency we present weighted maximum posterior marginals (WMPM) estimation, an extension of maximum posterior marginals (MPM) estimation. Whereas the MPM cost function penalizes each error equally, the WMPM cost function allows misclassifications associated with certain classes to be weighted more heavily than others. This creates a preference for specific classes, and consequently a means for adjusting classifier performance. Realizing WMPM estimation (like MPM estimation) requires estimates of the posterior marginal distributions. The most prevalent means for estimating these--proposed by Marroquin--utilizes a Markov chain Monte Carlo (MCMC) method. Though Marroquin's method (M-MCMC) yields estimates that are sufficiently accurate for MPM estimation, they are inadequate for WMPM. To more accurately estimate the posterior marginals we present an equally simple, but more effective extension of the MCMC method (E-MCMC). Assuming an identical number of iterations, E-MCMC as compared to M-MCMC yields estimates with higher fidelity, thereby 1) allowing a far greater number and diversity of operating points and 2) improving overall classifier performance. To illustrate the utility of WMPM and compare the efficacies of M-MCMC and E-MCMC, we integrate them into our MRF-based classification system for detecting cancerous glands in (whole-mount or quarter) histological sections of the prostate

  9. a Comparative Study Between Pair-Point Clique and Multi-Point Clique Markov Random Field Models for Land Cover Classification

    NASA Astrophysics Data System (ADS)

    Hu, B.; Li, P.

    2013-07-01

    Markov random field (MRF) is an effective method for description of local spatial-temporal dependence of image and has been widely used in land cover classification and change detection. However, existing studies only use pair-point clique (PPC) to describe spatial dependence of neighbouring pixels, which may not fully quantify complex spatial relations, particularly in high spatial resolution images. In this study, multi-point clique (MPC) is adopted in MRF model to quantitatively express spatial dependence among pixels. A modified least squares fit (LSF) method based on robust estimation is proposed to calculate potential parameters for MRF models with different types. The proposed MPC-MRF method is evaluated and quantitatively compared with traditional PPCMRF in urban land cover classification using high resolution hyperspectral HYDICE data of Washington DC. The experimental results revealed that the proposed MPC-MRF method outperformed the traditional PPC-MRF method in terms of classification details. The MPC-MRF provides a sophisticated way of describing complex spatial dependence for relevant applications.

  10. 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.

  11. A Markov random field-based approach for joint estimation of differentially expressed genes in mouse transcriptome data.

    PubMed

    Lin, Zhixiang; Li, Mingfeng; Sestan, Nenad; Zhao, Hongyu

    2016-04-01

    The statistical methodology developed in this study was motivated by our interest in studying neurodevelopment using the mouse brain RNA-Seq data set, where gene expression levels were measured in multiple layers in the somatosensory cortex across time in both female and male samples. We aim to identify differentially expressed genes between adjacent time points, which may provide insights on the dynamics of brain development. Because of the extremely small sample size (one male and female at each time point), simple marginal analysis may be underpowered. We propose a Markov random field (MRF)-based approach to capitalizing on the between layers similarity, temporal dependency and the similarity between sex. The model parameters are estimated by an efficient EM algorithm with mean field-like approximation. Simulation results and real data analysis suggest that the proposed model improves the power to detect differentially expressed genes than simple marginal analysis. Our method also reveals biologically interesting results in the mouse brain RNA-Seq data set. PMID:26926866

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

    SciTech Connect

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

    2015-04-24

    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.

  13. 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

  14. A Markov model for the temporal dynamics of balanced random networks of finite size

    PubMed Central

    Lagzi, Fereshteh; Rotter, Stefan

    2014-01-01

    The balanced state of recurrent networks of excitatory and inhibitory spiking neurons is characterized by fluctuations of population activity about an attractive fixed point. Numerical simulations show that these dynamics are essentially nonlinear, and the intrinsic noise (self-generated fluctuations) in networks of finite size is state-dependent. Therefore, stochastic differential equations with additive noise of fixed amplitude cannot provide an adequate description of the stochastic dynamics. The noise model should, rather, result from a self-consistent description of the network dynamics. Here, we consider a two-state Markovian neuron model, where spikes correspond to transitions from the active state to the refractory state. Excitatory and inhibitory input to this neuron affects the transition rates between the two states. The corresponding nonlinear dependencies can be identified directly from numerical simulations of networks of leaky integrate-and-fire neurons, discretized at a time resolution in the sub-millisecond range. Deterministic mean-field equations, and a noise component that depends on the dynamic state of the network, are obtained from this model. The resulting stochastic model reflects the behavior observed in numerical simulations quite well, irrespective of the size of the network. In particular, a strong temporal correlation between the two populations, a hallmark of the balanced state in random recurrent networks, are well represented by our model. Numerical simulations of such networks show that a log-normal distribution of short-term spike counts is a property of balanced random networks with fixed in-degree that has not been considered before, and our model shares this statistical property. Furthermore, the reconstruction of the flow from simulated time series suggests that the mean-field dynamics of finite-size networks are essentially of Wilson-Cowan type. We expect that this novel nonlinear stochastic model of the interaction between

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

    PubMed

    Camproux, A C; Tufféry, P

    2005-08-01

    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. PMID:16040198

  16. Coloring random graphs and maximizing local diversity.

    PubMed

    Bounkong, S; van Mourik, J; Saad, D

    2006-11-01

    We study a variation of the graph coloring problem on random graphs of finite average connectivity. Given the number of colors, we aim to maximize the number of different colors at neighboring vertices (i.e., one edge distance) of any vertex. Two efficient algorithms, belief propagation and Walksat, are adapted to carry out this task. We present experimental results based on two types of random graphs for different system sizes and identify the critical value of the connectivity for the algorithms to find a perfect solution. The problem and the suggested algorithms have practical relevance since various applications, such as distributed storage, can be mapped onto this problem. PMID:17280022

  17. 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. PMID:24333394

  18. Improved Compressive Sensing of Natural Scenes Using Localized Random Sampling.

    PubMed

    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

  19. 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

  20. Localization of Spinons in Random Majumdar-Ghosh Chains

    NASA Astrophysics Data System (ADS)

    Lavarélo, Arthur; Roux, Guillaume

    2013-02-01

    We study the effect of disorder on frustrated dimerized spin-1/2 chains at the Majumdar-Ghosh point. Using variational methods and density-matrix renormalization group approaches, we identify two localization mechanisms for spinons which are the deconfined fractional elementary excitations of these chains. The first one belongs to the Anderson localization class and dominates at the random Majumdar-Ghosh point. There, spinons remain gapped and localize in Lifshitz states whose localization length is analytically obtained. The other mechanism is a random confinement mechanism which induces an effective interaction between spinons and brings the chain into a gapless and partially polarized phase for arbitrarily small disorder.

  1. Tuneabilities of localized electromagnetic modes in random nanostructures for random lasing

    NASA Astrophysics Data System (ADS)

    Takeda, S.; Obara, M.

    2010-02-01

    The modal characteristics of localized electromagnetic waves inside random nanostructures are theoretically presented. It is crucial to know the tuneabilities of the localized modes systematically for demonstrating a specific random lasing application. By use of FDTD (Finite-Difference Time-Domain) method, we investigated the impulse response of two-dimensional random nanostructures consisting of closely packed cylindrical dielectric columns, and precisely analyzed the localized modes. We revealed the tuneability of the frequency of the localized modes by controlling the medium configurations: diameter, spatial density, and refractive index of the cylinders. Furthermore, it is found to be able to tune the Q (quality) factors of the localized modes dramatically by controlling simply the system size of the entire medium. The observed Q factors of approximately 1.6×104 were exhibited in our random disordered structures.

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

    PubMed

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

    2015-01-01

    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

  3. 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

  4. Markov random fields reveal an N-terminal double beta-propeller motif as part of a bacterial hybrid two-component sensor system

    PubMed Central

    Menke, Matt; Berger, Bonnie; Cowen, Lenore

    2010-01-01

    The recent explosion in newly sequenced bacterial genomes is outpacing the capacity of researchers to try to assign functional annotation to all the new proteins. Hence, computational methods that can help predict structural motifs provide increasingly important clues in helping to determine how these proteins might function. We introduce a Markov Random Field approach tailored for recognizing proteins that fold into mainly β-structural motifs, and apply it to build recognizers for the β-propeller shapes. As an application, we identify a potential class of hybrid two-component sensor proteins, that we predict contain a double-propeller domain. PMID:20147619

  5. HaplotypeCN: copy number haplotype inference with Hidden Markov Model and localized haplotype clustering.

    PubMed

    Lin, Yen-Jen; Chen, Yu-Tin; Hsu, Shu-Ni; Peng, Chien-Hua; Tang, Chuan-Yi; Yen, Tzu-Chen; Hsieh, Wen-Ping

    2014-01-01

    Copy number variation (CNV) has been reported to be associated with disease and various cancers. Hence, identifying the accurate position and the type of CNV is currently a critical issue. There are many tools targeting on detecting CNV regions, constructing haplotype phases on CNV regions, or estimating the numerical copy numbers. However, none of them can do all of the three tasks at the same time. This paper presents a method based on Hidden Markov Model to detect parent specific copy number change on both chromosomes with signals from SNP arrays. A haplotype tree is constructed with dynamic branch merging to model the transition of the copy number status of the two alleles assessed at each SNP locus. The emission models are constructed for the genotypes formed with the two haplotypes. The proposed method can provide the segmentation points of the CNV regions as well as the haplotype phasing for the allelic status on each chromosome. The estimated copy numbers are provided as fractional numbers, which can accommodate the somatic mutation in cancer specimens that usually consist of heterogeneous cell populations. The algorithm is evaluated on simulated data and the previously published regions of CNV of the 270 HapMap individuals. The results were compared with five popular methods: PennCNV, genoCN, COKGEN, QuantiSNP and cnvHap. The application on oral cancer samples demonstrates how the proposed method can facilitate clinical association studies. The proposed algorithm exhibits comparable sensitivity of the CNV regions to the best algorithm in our genome-wide study and demonstrates the highest detection rate in SNP dense regions. In addition, we provide better haplotype phasing accuracy than similar approaches. The clinical association carried out with our fractional estimate of copy numbers in the cancer samples provides better detection power than that with integer copy number states. PMID:24849202

  6. Local theorems in strengthened form for lattice random variables.

    NASA Technical Reports Server (NTRS)

    Mason, J. D.

    1971-01-01

    Investigation of some conditions which are sufficient for a sequence of independent integral-valued lattice random variables to satisfy a local theorem in strengthened form. A number of theorems giving the conditions under which the investigated sequence satisfies a local theorem in strengthened form are proven with the aid of lemmas derived by Kruglov (1968).

  7. A random matrix model with localization and ergodic transitions

    NASA Astrophysics Data System (ADS)

    Kravtsov, V. E.; Khaymovich, I. M.; Cuevas, E.; Amini, M.

    2015-12-01

    Motivated by the problem of many-body localization and the recent numerical results for the level and eigenfunction statistics on the random regular graphs, a generalization of the Rosenzweig-Porter random matrix model is suggested that possesses two transitions. One of them is the Anderson localization transition from the localized to the extended states. The other one is the ergodic transition from the extended non-ergodic (multifractal) states to the extended ergodic states. We confirm the existence of both transitions by computing the two-level spectral correlation function, the spectrum of multifractality f(α ) and the wave function overlap which consistently demonstrate these two transitions.

  8. Localization of Spinons in Random Majumdar-Ghosh Chains

    NASA Astrophysics Data System (ADS)

    Roux, Guillaume; Lavarelo, Arthur

    2014-03-01

    We study the effect of disorder on frustrated dimerized spin-1/2 chains at the Majumdar-Ghosh point. Using variational methods and density-matrix renormalization group approaches, we identify two localization mechanisms for spinons which are the deconfined fractional elementary excitations of these chains. The first one belongs to the Anderson localization class and dominates at the random Majumdar-Ghosh point. There, spinons remain gapped and localize in Lifshitz states whose localization length is analytically obtained. The other mechanism is a random confinement mechanism which induces an effective interaction between spinons and brings the initially gapped antiferromagnetic chain into a gapless and partially polarized phase for arbitrarily small disorder. This Imry-Ma mechanism induces domains which statistics is analyzed. Last, the connection to the real-space renormalization group method suited for the strong disorder limit is discussed.

  9. Designing for Local and Global Meanings of Randomness

    ERIC Educational Resources Information Center

    Paparistodemou, Efi; Noss, Richard

    2004-01-01

    This research aims to study the ways in which "local" events of randomness, based on experiencing the outcome of individual events, can be developed into "global" understandings that focus on an aggregated view of probability (e.g. probability of an event). The findings reported in the paper are part of a broader study that adopted a strategy of…

  10. Local theorems for nonidentically distributed lattice random variables.

    NASA Technical Reports Server (NTRS)

    Mason, J. D.

    1972-01-01

    Derivation of local limit theorems for a sequence X sub n of independent integral-valued lattice random variables involving only a finite number of distinct nondegenerate distributions. Given appropriate sequences A sub n and B sub n of constants such that 1/B sub n (X sub 1 +

  11. Random matrix analysis of localization properties of gene coexpression network

    NASA Astrophysics Data System (ADS)

    Jalan, Sarika; Solymosi, Norbert; Vattay, Gábor; Li, Baowen

    2010-04-01

    We analyze gene coexpression network under the random matrix theory framework. The nearest-neighbor spacing distribution of the adjacency matrix of this network follows Gaussian orthogonal statistics of random matrix theory (RMT). Spectral rigidity test follows random matrix prediction for a certain range and deviates afterwards. Eigenvector analysis of the network using inverse participation ratio suggests that the statistics of bulk of the eigenvalues of network is consistent with those of the real symmetric random matrix, whereas few eigenvalues are localized. Based on these IPR calculations, we can divide eigenvalues in three sets: (a) The nondegenerate part that follows RMT. (b) The nondegenerate part, at both ends and at intermediate eigenvalues, which deviates from RMT and expected to contain information about important nodes in the network. (c) The degenerate part with zero eigenvalue, which fluctuates around RMT-predicted value. We identify nodes corresponding to the dominant modes of the corresponding eigenvectors and analyze their structural properties.

  12. Extended State to Localization in Random Aperiodic Chains

    NASA Astrophysics Data System (ADS)

    Gao, Hui-Fen; Tao, Rui-Bao

    2006-11-01

    The electronic states in Thus-Morse chain (TMC) and generalized Fibonacci chain (GFC) are studied by solving eigenequation and using transfer matrix method. Two model Hamiltonians are studied. One contains the nearest neighbor (n.n.) hopping terms only and the other has additionally next nearest neighbor (n.n.n.) hopping terms. Based on the transfer matrix method, a criterion of transition from the extended to the localized states is suggested for GFC and TMC. The numerical calculation shows the existence of both extended and localized states in pure aperiodic system. A random potential is introduced to the diagonal term of the Hamiltonian and then the extended states are always changed to be localized. The exponents related to the localization length as a function of randomness are calculated. For different kinds of aperiodic chain, the critical value of randomness for the transition from extended to the localized states are found to be zero, consistent with the case of ordinary one-dimensional systems.

  13. Localization of disordered bosons and magnets in random fields

    SciTech Connect

    Yu, Xiaoquan; Müller, Markus

    2013-10-15

    We study localization properties of disordered bosons and spins in random fields at zero temperature. We focus on two representatives of different symmetry classes, hard-core bosons (XY magnets) and Ising magnets in random transverse fields, and contrast their physical properties. We describe localization properties using a locator expansion on general lattices. For 1d Ising chains, we find non-analytic behavior of the localization length as a function of energy at ω=0, ξ{sup −1}(ω)=ξ{sup −1}(0)+A|ω|{sup α}, with α vanishing at criticality. This contrasts with the much smoother behavior predicted for XY magnets. We use these results to approach the ordering transition on Bethe lattices of large connectivity K, which mimic the limit of high dimensionality. In both models, in the paramagnetic phase with uniform disorder, the localization length is found to have a local maximum at ω=0. For the Ising model, we find activated scaling at the phase transition, in agreement with infinite randomness studies. In the Ising model long range order is found to arise due to a delocalization and condensation initiated at ω=0, without a closing mobility gap. We find that Ising systems establish order on much sparser (fractal) subgraphs than XY models. Possible implications of these results for finite-dimensional systems are discussed. -- Highlights: •Study of localization properties of disordered bosons and spins in random fields. •Comparison between XY magnets (hard-core bosons) and Ising magnets. •Analysis of the nature of the magnetic transition in strong quenched disorder. •Ising magnets: activated scaling, no closing mobility gap at the transition. •Ising order emerges on sparser (fractal) support than XY order.

  14. Fusing Markov random fields with anatomical knowledge and shape-based analysis to segment multiple sclerosis white matter lesions in magnetic resonance images of the brain

    NASA Astrophysics Data System (ADS)

    AlZubi, Stephan; Toennies, Klaus D.; Bodammer, N.; Hinrichs, Herman

    2002-05-01

    This paper proposes an image analysis system to segment multiple sclerosis lesions of magnetic resonance (MR) brain volumes consisting of 3 mm thick slices using three channels (images showing T1-, T2- and PD -weighted contrast). The method uses the statistical model of Markov Random Fields (MRF) both at low and high levels. The neighborhood system used in this MRF is defined in three types: (1) Voxel to voxel: a low-level heterogeneous neighborhood system is used to restore noisy images. (2) Voxel to segment: a fuzzy atlas, which indicates the probability distribution of each tissue type in the brain, is registered elastically with the MRF. It is used by the MRF as a-priori knowledge to correct miss-classified voxels. (3) Segment to segment: Remaining lesion candidates are processed by a feature based classifier that looks at unary and neighborhood information to eliminate more false positives. An expert's manual segmentation was compared with the algorithm.

  15. Prestack inversion based on anisotropic Markov random field-maximum posterior probability inversion and its application to identify shale gas sweet spots

    NASA Astrophysics Data System (ADS)

    Wang, Kang-Ning; Sun, Zan-Dong; Dong, Ning

    2015-12-01

    Economic shale gas production requires hydraulic fracture stimulation to increase the formation permeability. Hydraulic fracturing strongly depends on geomechanical parameters such as Young's modulus and Poisson's ratio. Fracture-prone sweet spots can be predicted by prestack inversion, which is an ill-posed problem; thus, regularization is needed to obtain unique and stable solutions. To characterize gas-bearing shale sedimentary bodies, elastic parameter variations are regarded as an anisotropic Markov random field. Bayesian statistics are adopted for transforming prestack inversion to the maximum posterior probability. Two energy functions for the lateral and vertical directions are used to describe the distribution, and the expectation-maximization algorithm is used to estimate the hyperparameters of the prior probability of elastic parameters. Finally, the inversion yields clear geological boundaries, high vertical resolution, and reasonable lateral continuity using the conjugate gradient method to minimize the objective function. Antinoise and imaging ability of the method were tested using synthetic and real data.

  16. Local Spin Relaxation within the Random Heisenberg Chain

    NASA Astrophysics Data System (ADS)

    Herbrych, J.; Kokalj, J.; Prelovšek, P.

    2013-10-01

    Finite-temperature local dynamical spin correlations Snn(ω) are studied numerically within the random spin-1/2 antiferromagnetic Heisenberg chain. The aim is to explain measured NMR spin-lattice relaxation times in BaCu2(Si0.5Ge0.5)2O7, which is the realization of a random spin chain. In agreement with experiments we find that the distribution of relaxation times within the model shows a very large span similar to the stretched-exponential form. The distribution is strongly reduced with increasing T, but stays finite also in the high-T limit. Anomalous dynamical correlations can be associated with the random singlet concept but not directly with static quantities. Our results also reveal the crucial role of the spin anisotropy (interaction), since the behavior is in contrast with the ones for the XX model, where we do not find any significant T dependence of the distribution.

  17. Non-local MRI denoising using random sampling.

    PubMed

    Hu, Jinrong; Zhou, Jiliu; Wu, Xi

    2016-09-01

    In this paper, we propose a random sampling non-local mean (SNLM) algorithm to eliminate noise in 3D MRI datasets. Non-local means (NLM) algorithms have been implemented efficiently for MRI denoising, but are always limited by high computational complexity. Compared to conventional methods, which raster through the entire search window when computing similarity weights, the proposed SNLM algorithm randomly selects a small subset of voxels which dramatically decreases the computational burden, together with competitive denoising result. Moreover, structure tensor which encapsulates high-order information was introduced as an optimal sampling pattern for further improvement. Numerical experiments demonstrated that the proposed SNLM method can get a good balance between denoising quality and computation efficiency. At a relative sampling ratio (i.e. ξ=0.05), SNLM can remove noise as effectively as full NLM, meanwhile the running time can be reduced to 1/20 of NLM's. PMID:27114338

  18. 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

  19. Localization of wave packets in one-dimensional random potentials

    NASA Astrophysics Data System (ADS)

    Valdes, Juan Pablo Ramírez; Wellens, Thomas

    2016-06-01

    We study the expansion of an initially strongly confined wave packet in a one-dimensional weak random potential with short correlation length. At long times, the expansion of the wave packet comes to a halt due to destructive interferences leading to Anderson localization. We develop an analytical description for the disorder-averaged localized density profile. For this purpose, we employ the diagrammatic method of Berezinskii which we extend to the case of wave packets, present an analytical expression of the Lyapunov exponent which is valid for small as well as for high energies, and, finally, develop a self-consistent Born approximation in order to analytically calculate the energy distribution of our wave packet. By comparison with numerical simulations, we show that our theory describes well the complete localized density profile, not only in the tails but also in the center.

  20. Autoregressive Higher-Order Hidden Markov Models: Exploiting Local Chromosomal Dependencies in the Analysis of Tumor Expression Profiles

    PubMed Central

    Seifert, Michael; Abou-El-Ardat, Khalil; Friedrich, Betty; Klink, Barbara; Deutsch, Andreas

    2014-01-01

    Changes in gene expression programs play a central role in cancer. Chromosomal aberrations such as deletions, duplications and translocations of DNA segments can lead to highly significant positive correlations of gene expression levels of neighboring genes. This should be utilized to improve the analysis of tumor expression profiles. Here, we develop a novel model class of autoregressive higher-order Hidden Markov Models (HMMs) that carefully exploit local data-dependent chromosomal dependencies to improve the identification of differentially expressed genes in tumor. Autoregressive higher-order HMMs overcome generally existing limitations of standard first-order HMMs in the modeling of dependencies between genes in close chromosomal proximity by the simultaneous usage of higher-order state-transitions and autoregressive emissions as novel model features. We apply autoregressive higher-order HMMs to the analysis of breast cancer and glioma gene expression data and perform in-depth model evaluation studies. We find that autoregressive higher-order HMMs clearly improve the identification of overexpressed genes with underlying gene copy number duplications in breast cancer in comparison to mixture models, standard first- and higher-order HMMs, and other related methods. The performance benefit is attributed to the simultaneous usage of higher-order state-transitions in combination with autoregressive emissions. This benefit could not be reached by using each of these two features independently. We also find that autoregressive higher-order HMMs are better able to identify differentially expressed genes in tumors independent of the underlying gene copy number status in comparison to the majority of related methods. This is further supported by the identification of well-known and of previously unreported hotspots of differential expression in glioblastomas demonstrating the efficacy of autoregressive higher-order HMMs for the analysis of individual tumor expression

  1. Many-body localization in the quantum random energy model

    NASA Astrophysics Data System (ADS)

    Laumann, Chris; Pal, Arijeet

    2014-03-01

    The quantum random energy model is a canonical toy model for a quantum spin glass with a well known phase diagram. We show that the model exhibits a many-body localization-delocalization transition at finite energy density which significantly alters the interpretation of the statistical ``frozen'' phase at lower temperature in isolated quantum systems. The transition manifests in many-body level statistics as well as the long time dynamics of on-site observables. CRL thanks the Perimeter Institute for hospitality and support.

  2. Local random potentials of high differentiability to model the Landscape

    SciTech Connect

    Battefeld, T.; Modi, C.

    2015-03-09

    We generate random functions locally via a novel generalization of Dyson Brownian motion, such that the functions are in a desired differentiability class C{sup k}, while ensuring that the Hessian is a member of the Gaussian orthogonal ensemble (other ensembles might be chosen if desired). Potentials in such higher differentiability classes (k≥2) are required/desirable to model string theoretical landscapes, for instance to compute cosmological perturbations (e.g., k=2 for the power-spectrum) or to search for minima (e.g., suitable de Sitter vacua for our universe). Since potentials are created locally, numerical studies become feasible even if the dimension of field space is large (D∼100). In addition to the theoretical prescription, we provide some numerical examples to highlight properties of such potentials; concrete cosmological applications will be discussed in companion publications.

  3. Local random potentials of high differentiability to model the Landscape

    NASA Astrophysics Data System (ADS)

    Battefeld, T.; Modi, C.

    2015-03-01

    We generate random functions locally via a novel generalization of Dyson Brownian motion, such that the functions are in a desired differentiability class Ck, while ensuring that the Hessian is a member of the Gaussian orthogonal ensemble (other ensembles might be chosen if desired). Potentials in such higher differentiability classes (k>= 2) are required/desirable to model string theoretical landscapes, for instance to compute cosmological perturbations (e.g., k=2 for the power-spectrum) or to search for minima (e.g., suitable de Sitter vacua for our universe). Since potentials are created locally, numerical studies become feasible even if the dimension of field space is large (0D~ 10). In addition to the theoretical prescription, we provide some numerical examples to highlight properties of such potentials; concrete cosmological applications will be discussed in companion publications.

  4. Three-dimensional multiphase segmentation of X-ray CT data of porous materials using a Bayesian Markov random field framework

    SciTech Connect

    Kulkarni, Ramaprasad; Tuller, Markus; Fink, Wolfgang; Wildschild, Dorthe

    2012-07-27

    Advancements in noninvasive imaging methods such as X-ray computed tomography (CT) have led to a recent surge of applications in porous media research with objectives ranging from theoretical aspects of pore-scale fluid and interfacial dynamics to practical applications such as enhanced oil recovery and advanced contaminant remediation. While substantial efforts and resources have been devoted to advance CT technology, microscale analysis, and fluid dynamics simulations, the development of efficient and stable three-dimensional multiphase image segmentation methods applicable to large data sets is lacking. To eliminate the need for wet-dry or dual-energy scans, image alignment, and subtraction analysis, commonly applied in X-ray micro-CT, a segmentation method based on a Bayesian Markov random field (MRF) framework amenable to true three-dimensional multiphase processing was developed and evaluated. Furthermore, several heuristic and deterministic combinatorial optimization schemes required to solve the labeling problem of the MRF image model were implemented and tested for computational efficiency and their impact on segmentation results. Test results for three grayscale data sets consisting of dry glass beads, partially saturated glass beads, and partially saturated crushed tuff obtained with synchrotron X-ray micro-CT demonstrate great potential of the MRF image model for three-dimensional multiphase segmentation. While our results are promising and the developed algorithm is stable and computationally more efficient than other commonly applied porous media segmentation models, further potential improvements exist for fully automated operation.

  5. Semi-Markov Graph Dynamics

    PubMed Central

    Raberto, Marco; Rapallo, Fabio; Scalas, Enrico

    2011-01-01

    In this paper, we outline a model of graph (or network) dynamics based on two ingredients. The first ingredient is a Markov chain on the space of possible graphs. The second ingredient is a semi-Markov counting process of renewal type. The model consists in subordinating the Markov chain to the semi-Markov counting process. In simple words, this means that the chain transitions occur at random time instants called epochs. The model is quite rich and its possible connections with algebraic geometry are briefly discussed. Moreover, for the sake of simplicity, we focus on the space of undirected graphs with a fixed number of nodes. However, in an example, we present an interbank market model where it is meaningful to use directed graphs or even weighted graphs. PMID:21887245

  6. No-signaling, perfect bipartite dichotomic correlations and local randomness

    SciTech Connect

    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 newly 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.

  7. Nonlinear Markov processes

    NASA Astrophysics Data System (ADS)

    Frank, T. D.

    2008-06-01

    Some elementary properties and examples of Markov processes are reviewed. It is shown that the definition of the Markov property naturally leads to a classification of Markov processes into linear and nonlinear ones.

  8. 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

    SciTech Connect

    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 to 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.

  9. Incorporating uncertanity into Markov random field classification with the combine use of optical and SAR images and aduptive fuzzy mean vector

    NASA Astrophysics Data System (ADS)

    Welikanna, D. R.; Tamura, M.; Susaki, J.

    2014-09-01

    A Markov Random Field (MRF) model accounting for the classification uncertainty using multisource satellite images and an adaptive fuzzy class mean vector is proposed in this study. The work also highlights the initialization of the class values for an MRF based classification for synthetic aperture radar (SAR) images using optical data. The model uses the contextual information from the optical image pixels and the SAR pixel intensity with corresponding fuzzy grade of memberships respectively, in the classification mechanism. Sub pixel class fractions estimated using Singular Value Decomposition (SVD) from the optical image initializes the class arrangement for the MRF process. Pair-site interactions of the pixels are used to model the prior energy from the initial class arrangement. Fuzzy class mean vector from the SAR intensity pixels is calculated using Fuzzy C-means (FCM) partitioning. Conditional probability for each class was determined by a Gamma distribution for the SAR image. Simulated annealing (SA) to minimize the global energy was executed using a logarithmic and power-law combined annealing schedule. Proposed technique was tested using an Advanced Land Observation Satellite (ALOS) phased array type L-band SAR (PALSAR) and Advanced Visible and Near-Infrared Radiometer-2 (AVNIR-2) data set over a disaster effected urban region in Japan. Proposed method and the conventional MRF results were evaluated with neural network (NN) and support vector machine (SVM) based classifications. The results suggest the possible integration of an adaptive fuzzy class mean vector and multisource data is promising for imprecise class discrimination using a MRF based classification.

  10. 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.

  11. Randomized discrepancy bounded local search for transmission expansion planning

    SciTech Connect

    Bent, Russell W; Daniel, William B

    2010-11-23

    In recent years the transmission network expansion planning problem (TNEP) has become increasingly complex. As the TNEP is a non-linear and non-convex optimization problem, researchers have traditionally focused on approximate models of power flows to solve the TNEP. Existing approaches are often tightly coupled to the approximation choice. Until recently these approximations have produced results that are straight-forward to adapt to the more complex (real) problem. However, the power grid is evolving towards a state where the adaptations are no longer easy (e.g. large amounts of limited control, renewable generation) and necessitates new approaches. Recent work on deterministic Discrepancy Bounded Local Search (DBLS) has shown it to be quite effective in addressing this question. DBLS encapsulates the complexity of power flow modeling in a black box that may be queried for information about the quality of proposed expansions. In this paper, we propose a randomization strategy that builds on DBLS and dramatically increases the computational efficiency of the algorithm.

  12. The defect-induced localization in many positions of the quantum random walk

    NASA Astrophysics Data System (ADS)

    Chen, Tian; Zhang, Xiangdong

    2016-05-01

    We study the localization of probability distribution in a discrete quantum random walk on an infinite chain. With a phase defect introduced in any position of the quantum random walk (QRW), we have found that the localization of the probability distribution in the QRW emerges. Different localized behaviors of the probability distribution in the QRW are presented when the defect occupies different positions. Given that the coefficients of the localized stationary eigenstates relies on the coin operator, we reveal that when the defect occupies different positions, the amplitude of localized probability distribution in the QRW exhibits a non-trivial dependence on the coin operator.

  13. The defect-induced localization in many positions of the quantum random walk.

    PubMed

    Chen, Tian; Zhang, Xiangdong

    2016-01-01

    We study the localization of probability distribution in a discrete quantum random walk on an infinite chain. With a phase defect introduced in any position of the quantum random walk (QRW), we have found that the localization of the probability distribution in the QRW emerges. Different localized behaviors of the probability distribution in the QRW are presented when the defect occupies different positions. Given that the coefficients of the localized stationary eigenstates relies on the coin operator, we reveal that when the defect occupies different positions, the amplitude of localized probability distribution in the QRW exhibits a non-trivial dependence on the coin operator. PMID:27216697

  14. The defect-induced localization in many positions of the quantum random walk

    PubMed Central

    Chen, Tian; Zhang, Xiangdong

    2016-01-01

    We study the localization of probability distribution in a discrete quantum random walk on an infinite chain. With a phase defect introduced in any position of the quantum random walk (QRW), we have found that the localization of the probability distribution in the QRW emerges. Different localized behaviors of the probability distribution in the QRW are presented when the defect occupies different positions. Given that the coefficients of the localized stationary eigenstates relies on the coin operator, we reveal that when the defect occupies different positions, the amplitude of localized probability distribution in the QRW exhibits a non-trivial dependence on the coin operator. PMID:27216697

  15. 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

  16. Elucid—exploring the local universe with the reconstructed initial density field. I. Hamiltonian Markov chain Monte Carlo method with particle mesh dynamics

    SciTech Connect

    Wang, Huiyuan; Mo, H. J.; Yang, Xiaohu; Lin, W. P.; Jing, Y. P.

    2014-10-10

    Simulating the evolution of the local universe is important for studying galaxies and the intergalactic medium in a way free of cosmic variance. Here we present a method to reconstruct the initial linear density field from an input nonlinear density field, employing the Hamiltonian Markov Chain Monte Carlo (HMC) algorithm combined with Particle-mesh (PM) dynamics. The HMC+PM method is applied to cosmological simulations, and the reconstructed linear density fields are then evolved to the present day with N-body simulations. These constrained simulations accurately reproduce both the amplitudes and phases of the input simulations at various z. Using a PM model with a grid cell size of 0.75 h {sup –1} Mpc and 40 time steps in the HMC can recover more than half of the phase information down to a scale k ∼ 0.85 h Mpc{sup –1} at high z and to k ∼ 3.4 h Mpc{sup –1} at z = 0, which represents a significant improvement over similar reconstruction models in the literature, and indicates that our model can reconstruct the formation histories of cosmic structures over a large dynamical range. Adopting PM models with higher spatial and temporal resolutions yields even better reconstructions, suggesting that our method is limited more by the availability of computer resource than by principle. Dynamic models of structure evolution adopted in many earlier investigations can induce non-Gaussianity in the reconstructed linear density field, which in turn can cause large systematic deviations in the predicted halo mass function. Such deviations are greatly reduced or absent in our reconstruction.

  17. Quantification of deterministic matched-field source localization error in the face of random model inputs

    NASA Astrophysics Data System (ADS)

    Daly, Peter M.; Hebenstreit, Gerald T.

    2003-04-01

    Deterministic source localization using matched-field processing (MFP) has yielded good results in propagation scenarios where the nonrandom model parameter input assumption is valid. In many shallow water environments, inputs to acoustic propagation models may be better represented using random distributions rather than fixed quantities. One can estimate the negative effect of random source inputs on deterministic MFP by (1) obtaining a realistic statistical representation of a signal model parameter, then (2) using the mean of the parameter as input to the MFP signal model (the so-called ``replica vector''), (3) synthesizing a source signal using multiple realizations of the random parameter, and (4) estimating the source localization error by correlating the synthesized signal vector with the replica vector over a three dimensional space. This approach allows one to quantify deterministic localization error introduced by random model parameters, including sound velocity profile, hydrophone locations, and sediment thickness and speed. [Work supported by DARPA Advanced Technology Office.

  18. High-order local spatial context modeling by spatialized random forest.

    PubMed

    Ni, Bingbing; Yan, Shuicheng; Wang, Meng; Kassim, Ashraf A; Tian, Qi

    2013-02-01

    In this paper, we propose a novel method for spatial context modeling toward boosting visual discriminating power. We are particularly interested in how to model high-order local spatial contexts instead of the intensively studied second-order spatial contexts, i.e., co-occurrence relations. Motivated by the recent success of random forest in learning discriminative visual codebook, we present a spatialized random forest (SRF) approach, which can encode an unlimited length of high-order local spatial contexts. By spatially random neighbor selection and random histogram-bin partition during the tree construction, the SRF can explore much more complicated and informative local spatial patterns in a randomized manner. Owing to the discriminative capability test for the random partition in each tree node's split process, a set of informative high-order local spatial patterns are derived, and new images are then encoded by counting the occurrences of such discriminative local spatial patterns. Extensive comparison experiments on face recognition and object/scene classification clearly demonstrate the superiority of the proposed spatial context modeling method over other state-of-the-art approaches for this purpose. PMID:23060330

  19. Local hidden variable models for entangled quantum States using finite shared randomness.

    PubMed

    Bowles, Joseph; Hirsch, Flavien; Quintino, Marco Túlio; Brunner, Nicolas

    2015-03-27

    The statistics of local measurements performed on certain entangled states can be reproduced using a local hidden variable (LHV) model. While all known models make use of an infinite amount of shared randomness, we show that essentially all entangled states admitting a LHV model can be simulated with finite shared randomness. Our most economical model simulates noisy two-qubit Werner states using only log_{2}(12)≃3.58 bits of shared randomness. We also discuss the case of positive operator valued measures, and the simulation of nonlocal states with finite shared randomness and finite communication. Our work represents a first step towards quantifying the cost of LHV models for entangled quantum states. PMID:25860723

  20. 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.

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

    SciTech Connect

    Chen, Yi; Jakeman, John; Gittelson, Claude; Xiu, Dongbin

    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 from 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.

  2. 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

  3. Hidden Markov model using Dirichlet process for de-identification.

    PubMed

    Chen, Tao; Cullen, Richard M; Godwin, Marshall

    2015-12-01

    For the 2014 i2b2/UTHealth de-identification challenge, we introduced a new non-parametric Bayesian hidden Markov model using a Dirichlet process (HMM-DP). The model intends to reduce task-specific feature engineering and to generalize well to new data. In the challenge we developed a variational method to learn the model and an efficient approximation algorithm for prediction. To accommodate out-of-vocabulary words, we designed a number of feature functions to model such words. The results show the model is capable of understanding local context cues to make correct predictions without manual feature engineering and performs as accurately as state-of-the-art conditional random field models in a number of categories. To incorporate long-range and cross-document context cues, we developed a skip-chain conditional random field model to align the results produced by HMM-DP, which further improved the performance. PMID:26407642

  4. Reconstruction of seismic data with missing traces based on local random sampling and curvelet transform

    NASA Astrophysics Data System (ADS)

    Liu, Wei; Cao, Siyuan; Li, Guofa; He, Yuan

    2015-04-01

    It is likely to yield seismic data with missing traces in field data acquisition, however, the subsequent processing requires complete seismic data; therefore, it is more necessary to reconstruct missing traces in seismic data. The reconstruction of seismic data becomes a sparse optimization problem based on sparsity of seismic data in curvelet transform domain and the gradient projection algorithm is employed to solve it. To overcome the limitations of uncontrolled random sampling, the local random sampling is presented in the paper; it can not only control the size of the sampling gaps effectively, but also keep the randomness of the sampling. The numerical modeling shows that the reconstructed result of local random sampling is better than that of traditional random sampling and jitter sampling. In addition, the proposed approach is also applied to pre-stack shot gather and stacked section, the field examples indicate that this method is effective and applicable for the reconstruction of seismic data with missing traces again. Furthermore, this approach can provide satisfactory result for the following processing on seismic data.

  5. Markov information sources

    NASA Technical Reports Server (NTRS)

    Massey, J. L.

    1975-01-01

    A regular Markov source is defined as the output of a deterministic, but noisy, channel driven by the state sequence of a regular finite-state Markov chain. The rate of such a source is the per letter uncertainty of its digits. The well-known result that the rate of a unifilar regular Markov source is easily calculable is demonstrated, where unifilarity means that the present state of the Markov chain and the next output of the deterministic channel uniquely determine the next state. At present, there is no known method to calculate the rate of a nonunifilar source. Two tentative approaches to this unsolved problem are given, namely source identical twins and the master-slave source, which appear to shed some light on the question of rate calculation for a nonunifilar source.

  6. 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.

  7. The use of negative pressure wound therapy for random local flaps at the ankle region.

    PubMed

    Goldstein, Jesse A; Iorio, Matthew L; Brown, Benjamin; Attinger, Christopher E

    2010-01-01

    Local random flaps are seldom used for reconstruction of complex ankle wounds because of concern for flap failure attributable to vascular compromise and tissue edema. Negative pressure wound therapy has been shown to improve perfusion and limit tissue edema. The objective of this study was to demonstrate the utility of negative pressure wound therapy in improving outcomes for local flaps of the ankle. Ten consecutive patients presenting with complex ankle wounds and reconstructed using local flaps were treated with negative pressure wound therapy postoperatively. Type of flap, immediate and long-term outcomes, and complications were assessed. Seventeen local flaps were performed on 10 patients to reconstruct their ankle wounds. Mean follow up was 88 days. All flaps healed without tissue compromise or necrosis. Only one partial dehiscence and no infections were observed. This study demonstrates that negative pressure therapy may contribute to the viability of random local flaps by decreasing venous congestion. Our experience using negative pressure wound therapy on local flaps suggests that it may serve as a useful adjunct to ensure successful closure of high-risk wounds. PMID:20801691

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

    SciTech Connect

    Tarasov, Yu.V. Shostenko, L.D.

    2015-05-15

    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 slope 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 shown to

  9. Large deviations for Markov processes with resetting.

    PubMed

    Meylahn, Janusz M; Sabhapandit, Sanjib; Touchette, Hugo

    2015-12-01

    Markov processes restarted or reset at random times to a fixed state or region in space have been actively studied recently in connection with random searches, foraging, and population dynamics. Here we study the large deviations of time-additive functions or observables of Markov processes with resetting. By deriving a renewal formula linking generating functions with and without resetting, we are able to obtain the rate function of such observables, characterizing the likelihood of their fluctuations in the long-time limit. We consider as an illustration the large deviations of the area of the Ornstein-Uhlenbeck process with resetting. Other applications involving diffusions, random walks, and jump processes with resetting or catastrophes are discussed. PMID:26764673

  10. Local search methods based on variable focusing for random K -satisfiability

    NASA Astrophysics Data System (ADS)

    Lemoy, Rémi; Alava, Mikko; Aurell, Erik

    2015-01-01

    We introduce variable focused local search algorithms for satisfiabiliity problems. Usual approaches focus uniformly on unsatisfied clauses. The methods described here work by focusing on random variables in unsatisfied clauses. Variants are considered where variables are selected uniformly and randomly or by introducing a bias towards picking variables participating in several unsatistified clauses. These are studied in the case of the random 3-SAT problem, together with an alternative energy definition, the number of variables in unsatisfied constraints. The variable-based focused Metropolis search (V-FMS) is found to be quite close in performance to the standard clause-based FMS at optimal noise. At infinite noise, instead, the threshold for the linearity of solution times with instance size is improved by picking preferably variables in several UNSAT clauses. Consequences for algorithmic design are discussed.

  11. Local search methods based on variable focusing for random K-satisfiability.

    PubMed

    Lemoy, Rémi; Alava, Mikko; Aurell, Erik

    2015-01-01

    We introduce variable focused local search algorithms for satisfiabiliity problems. Usual approaches focus uniformly on unsatisfied clauses. The methods described here work by focusing on random variables in unsatisfied clauses. Variants are considered where variables are selected uniformly and randomly or by introducing a bias towards picking variables participating in several unsatistified clauses. These are studied in the case of the random 3-SAT problem, together with an alternative energy definition, the number of variables in unsatisfied constraints. The variable-based focused Metropolis search (V-FMS) is found to be quite close in performance to the standard clause-based FMS at optimal noise. At infinite noise, instead, the threshold for the linearity of solution times with instance size is improved by picking preferably variables in several UNSAT clauses. Consequences for algorithmic design are discussed. PMID:25679737

  12. The random-motion theorem in a local cosmology with dark energy

    NASA Astrophysics Data System (ADS)

    Chernin, A. D.; Dolgachev, V. P.; Domozhilova, L. M.; Teerikorpi, P.; Valtonen, M. Yu.

    2010-03-01

    It is shown that the random-motion theorem in cosmology proven in the early 1960s can be generalized to take into account the presence of a uniform dark-energy background. The role of the dark energy is substantial: its repulsive force exceeds the gravitational force due to darkmatter and baryons, both on the scale of the Universe as a whole and on local scales of about 1 Mpc. The generalized random-motion theorem has the form of a differential equation relating the kinetic energy of the random motion and the potential energy of the particles due to their own gravitational field and the repulsive dark-energy field. One consequence of the generalized theorem is a virial relation containing the potential energy in the repulsive field.

  13. Existence of Anderson localization of classical waves in a random two-component medium

    SciTech Connect

    Soukoulis, C.M.; Economou, E.N.; Grest, G.S.; Cohen, M.H.

    1989-01-30

    An exact mapping of the classical wave problem to that of electronic motion is utilized together with extensive numerical results to examine the question of the existence of genuine localization (i.e., one occurring when both components have real positive dielectric constants) of classical waves in random binary alloys A/sub 1-//sub x/B/sub x/. We find that scalar waves do exhibit localization. We have also developed a coherent potential approximation which for x<0.2 gives results not that much different from the numerical ones. This result can be easily generalized to electromagnetic fields as well.

  14. 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)].

  15. 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. PMID:26353069

  16. 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.

  17. Distribution of the Height of Local Maxima of Gaussian Random Fields*

    PubMed Central

    Cheng, Dan; Schwartzman, Armin

    2015-01-01

    Let {f(t) : t ∈ T} be a smooth Gaussian random field over a parameter space T, where T may be a subset of Euclidean space or, more generally, a Riemannian manifold. We provide a general formula for the distribution of the height of a local maximum P{f(t0)>u∣t0 is a local maximum of f(t)} when f is non-stationary. Moreover, we establish asymptotic approximations for the overshoot distribution of a local maximum P{f(t0)>u+v∣t0 is a local maximum of f(t) and f(t0) > v} as v → ∞. Assuming further that f is isotropic, we apply techniques from random matrix theory related to the Gaussian orthogonal ensemble to compute such conditional probabilities explicitly when T is Euclidean or a sphere of arbitrary dimension. Such calculations are motivated by the statistical problem of detecting peaks in the presence of smooth Gaussian noise. PMID:26478714

  18. Continuous time random walks for non-local radial solute transport

    NASA Astrophysics Data System (ADS)

    Dentz, Marco; Kang, Peter K.; Le Borgne, Tanguy

    2015-08-01

    This study formulates and analyzes continuous time random walk (CTRW) models in radial flow geometries for the quantification of non-local solute transport induced by heterogeneous flow distributions and by mobile-immobile mass transfer processes. To this end we derive a general CTRW framework in radial coordinates starting from the random walk equations for radial particle positions and times. The particle density, or solute concentration is governed by a non-local radial advection-dispersion equation (ADE). Unlike in CTRWs for uniform flow scenarios, particle transition times here depend on the radial particle position, which renders the CTRW non-stationary. As a consequence, the memory kernel characterizing the non-local ADE, is radially dependent. Based on this general formulation, we derive radial CTRW implementations that (i) emulate non-local radial transport due to heterogeneous advection, (ii) model multirate mass transfer (MRMT) between mobile and immobile continua, and (iii) quantify both heterogeneous advection in a mobile region and mass transfer between mobile and immobile regions. The expected solute breakthrough behavior is studied using numerical random walk particle tracking simulations. This behavior is analyzed by explicit analytical expressions for the asymptotic solute breakthrough curves. We observe clear power-law tails of the solute breakthrough for broad (power-law) distributions of particle transit times (heterogeneous advection) and particle trapping times (MRMT model). The combined model displays two distinct time regimes. An intermediate regime, in which the solute breakthrough is dominated by the particle transit times in the mobile zones, and a late time regime that is governed by the distribution of particle trapping times in immobile zones. These radial CTRW formulations allow for the identification of heterogeneous advection and mobile-immobile processes as drivers of anomalous transport, under conditions relevant for field tracer

  19. Localization of directed polymers in random media due to a columnar defect

    NASA Astrophysics Data System (ADS)

    Lee, Jong-Dae; Kim, Jin Min; Lee, Jae Hwan

    2015-04-01

    We investigate the localization of directed polymers in random media due to the presence of an attractive columnar defect at the center of a two-dimensional substrate. If the defect's strength is too weak to affect the polymers, the localization length of the polymers exhibits a power-law behavior as a function of the polymer length, as in the case of no defect. When the defect's strength is greater than a critical value, the localization length approaches a finite value, thereby yielding a localization length exponent (or liberation exponent) ν ⊥ = 1.8004(31). The correlation length, which is perpendicular to the localization length, is defined as the distance over which the polymer is localized by the defect. The correlation length exponent ν ‖ = 2.881(5) is estimated from the data collapse via the scaling relation ζ = ν ⊥/ ν ‖, where ζ = 5/8 represents the wandering exponent. In addition, we measure the number of times that the optimal path passes through the defect, because that number increases as the defect's strength increases. This measurement yields a new critical exponent λ = 0.59.

  20. Markov Processes: Linguistics and Zipf's Law

    NASA Astrophysics Data System (ADS)

    Kanter, I.; Kessler, D. A.

    1995-05-01

    It is shown that a 2-parameter random Markov process constructed with N states and biased random transitions gives rise to a stationary distribution where the probabilities of occurrence of the states, P\\(k\\), k = 1,...,N, exhibit the following three universal behaviors which characterize biological sequences and texts in natural languages: (a) the rank-ordered frequencies of occurrence of words are given by Zipf's law P\\(k\\)~1/kρ, where ρ\\(k\\) is slowly increasing for small k; (b) the frequencies of occurrence of letters are given by P\\(k\\) = A-Dln\\(k\\); and (c) long-range correlations are observed over long but finite intervals, as a result of the quasiergodicity of the Markov process.

  1. Critical Casimir force in the presence of random local adsorption preference.

    PubMed

    Parisen Toldin, Francesco

    2015-03-01

    We study the critical Casimir force for a film geometry in the Ising universality class. We employ a homogeneous adsorption preference on one of the confining surfaces, while the opposing surface exhibits quenched random disorder, leading to a random local adsorption preference. Disorder is characterized by a parameter p, which measures, on average, the portion of the surface that prefers one component, so that p=0,1 correspond to homogeneous adsorption preference. By means of Monte Carlo simulations of an improved Hamiltonian and finite-size scaling analysis, we determine the critical Casimir force. We show that by tuning the disorder parameter p, the system exhibits a crossover between an attractive and a repulsive force. At p=1/2, disorder allows to effectively realize Dirichlet boundary conditions, which are generically not accessible in classical fluids. Our results are relevant for the experimental realizations of the critical Casimir force in binary liquid mixtures. PMID:25871052

  2. Critical Casimir force in the presence of random local adsorption preference

    NASA Astrophysics Data System (ADS)

    Toldin, Francesco Parisen

    2015-03-01

    We study the critical Casimir force for a film geometry in the Ising universality class. We employ a homogeneous adsorption preference on one of the confining surfaces, while the opposing surface exhibits quenched random disorder, leading to a random local adsorption preference. Disorder is characterized by a parameter p , which measures, on average, the portion of the surface that prefers one component, so that p =0 ,1 correspond to homogeneous adsorption preference. By means of Monte Carlo simulations of an improved Hamiltonian and finite-size scaling analysis, we determine the critical Casimir force. We show that by tuning the disorder parameter p , the system exhibits a crossover between an attractive and a repulsive force. At p =1 /2 , disorder allows to effectively realize Dirichlet boundary conditions, which are generically not accessible in classical fluids. Our results are relevant for the experimental realizations of the critical Casimir force in binary liquid mixtures.

  3. 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.

  4. Local anesthetic infusion pumps improve postoperative pain after inguinal hernia repair: a randomized trial.

    PubMed

    Sanchez, Barry; Waxman, Kenneth; Tatevossian, Raymond; Gamberdella, Marla; Read, Bruce

    2004-11-01

    Pain after an open inguinal hernia repair may be significant. In fact, some surgeons feel that the pain after open repair justifies a laparoscopic approach. The purpose of this study was to determine if the use of local anesthetic infusion pumps would reduce postoperative pain after open inguinal hernia repair. We performed a prospective, double-blind randomized study of 45 open plug and patch inguinal hernia repairs. Patients were randomized to receive either 0.25 per cent bupivicaine or saline solution via an elastomeric infusion pump (ON-Q) for 48 hours, at 2 cc/h. The catheters were placed in the subcutaneous tissue and removed on postoperative day 3. Both groups were prescribed hydrocodone to use in the postoperative period at the prescribed dosage as needed for pain. Interviews were conducted on postoperative days 3 and 7, and patient's questionnaires, including pain scores, amount of pain medicine used, and any complications, were collected accordingly. During the first 5 postoperative days, postoperative pain was assessed using a visual analog scale. Twenty-three repairs were randomized to the bupivicaine group and 22 repairs randomized to the placebo group. In the bupivicaine group, there was a significant decrease in postoperative pain on postoperative days 2 through 5 with P values <0.05. This significant difference continued through postoperative day 5, 2 days after the infusion pumps were removed. Patients who had bupivicaine instilled in their infusion pump had statistically significant lower subjective pain scores on postoperative days 2 through 5. This significant difference continued even after the infusion pumps were removed. Local anesthetic infusion pumps significantly decreased the amount of early postoperative pain. Pain relief persisted for 2 days after catheter and pump removal. PMID:15586515

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

    PubMed

    Kamimura, H A S; Wang, S; Wu, S-Y; Karakatsani, M E; Acosta, C; Carneiro, A A O; Konofagou, E E

    2015-10-01

    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 mm3, mm3and mm3 for the chirp, random and regular sonications, respectively. The mean cavitation levels were V.s, V.s and 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

  6. How breadth of degree distribution influences network robustness: Comparing localized and random attacks

    NASA Astrophysics Data System (ADS)

    Yuan, Xin; Shao, Shuai; Stanley, H. Eugene; Havlin, Shlomo

    2015-09-01

    The stability of networks is greatly influenced by their degree distributions and in particular by their breadth. Networks with broader degree distributions are usually more robust to random failures but less robust to localized attacks. To better understand the effect of the breadth of the degree distribution we study two models in which the breadth is controlled and compare their robustness against localized attacks (LA) and random attacks (RA). We study analytically and by numerical simulations the cases where the degrees in the networks follow a bi-Poisson distribution, P (k ) =α e-λ1λ/1kk ! +(1 -α ) e-λ2λ/2kk ! ,α ∈[0 ,1 ] , and a Gaussian distribution, P (k ) =A exp(-(k/-μ) 22 σ2 ), with a normalization constant A where k ≥0 . In the bi-Poisson distribution the breadth is controlled by the values of α , λ1, and λ2, while in the Gaussian distribution it is controlled by the standard deviation, σ . We find that only when α =0 or α =1 , i.e., degrees obeying a pure Poisson distribution, are LA and RA the same. In all other cases networks are more vulnerable under LA than under RA. For a Gaussian distribution with an average degree μ fixed, we find that when σ2 is smaller than μ the network is more vulnerable against random attack. When σ2 is larger than μ , however, the network becomes more vulnerable against localized attack. Similar qualitative results are also shown for interdependent networks.

  7. 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.

  8. Local random quantum circuits: Ensemble completely positive maps and swap algebras

    SciTech Connect

    Zanardi, Paolo

    2014-08-15

    We define different classes of local random quantum circuits (L-RQC) and show that (a) statistical properties of L-RQC are encoded into an associated family of completely positive maps and (b) average purity dynamics can be described by the action of these maps on operator algebras of permutations (swap algebras). An exactly solvable one-dimensional case is analyzed to illustrate the power of the swap algebra formalism. More in general, we prove short time area-law bounds on average purity for uncorrelated L-RQC and infinite time results for both the uncorrelated and correlated cases.

  9. MODELING PAVEMENT DETERIORATION PROCESSES BY POISSON HIDDEN MARKOV MODELS

    NASA Astrophysics Data System (ADS)

    Nam, Le Thanh; Kaito, Kiyoyuki; Kobayashi, Kiyoshi; Okizuka, Ryosuke

    In pavement management, it is important to estimate lifecycle cost, which is composed of the expenses for repairing local damages, including potholes, and repairing and rehabilitating the surface and base layers of pavements, including overlays. In this study, a model is produced under the assumption that the deterioration process of pavement is a complex one that includes local damages, which occur frequently, and the deterioration of the surface and base layers of pavement, which progresses slowly. The variation in pavement soundness is expressed by the Markov deterioration model and the Poisson hidden Markov deterioration model, in which the frequency of local damage depends on the distribution of pavement soundness, is formulated. In addition, the authors suggest a model estimation method using the Markov Chain Monte Carlo (MCMC) method, and attempt to demonstrate the applicability of the proposed Poisson hidden Markov deterioration model by studying concrete application cases.

  10. In vivo MRI based prostate cancer localization with random forests and auto-context model.

    PubMed

    Qian, Chunjun; Wang, Li; Gao, Yaozong; Yousuf, Ambereen; Yang, Xiaoping; Oto, Aytekin; Shen, Dinggang

    2016-09-01

    Prostate cancer is one of the major causes of cancer death for men. Magnetic resonance (MR) imaging is being increasingly used as an important modality to localize prostate cancer. Therefore, localizing prostate cancer in MRI with automated detection methods has become an active area of research. Many methods have been proposed for this task. However, most of previous methods focused on identifying cancer only in the peripheral zone (PZ), or classifying suspicious cancer ROIs into benign tissue and cancer tissue. Few works have been done on developing a fully automatic method for cancer localization in the entire prostate region, including central gland (CG) and transition zone (TZ). In this paper, we propose a novel learning-based multi-source integration framework to directly localize prostate cancer regions from in vivo MRI. We employ random forests to effectively integrate features from multi-source images together for cancer localization. Here, multi-source images include initially the multi-parametric MRIs (i.e., T2, DWI, and dADC) and later also the iteratively-estimated and refined tissue probability map of prostate cancer. Experimental results on 26 real patient data show that our method can accurately localize cancerous sections. The higher section-based evaluation (SBE), combined with the ROC analysis result of individual patients, shows that the proposed method is promising for in vivo MRI based prostate cancer localization, which can be used for guiding prostate biopsy, targeting the tumor in focal therapy planning, triage and follow-up of patients with active surveillance, as well as the decision making in treatment selection. The common ROC analysis with the AUC value of 0.832 and also the ROI-based ROC analysis with the AUC value of 0.883 both illustrate the effectiveness of our proposed method. PMID:27048995

  11. 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.

  12. Absence of localized acoustic waves in a scale-free correlated random system.

    PubMed

    Costa, A E B; de Moura, F A B F

    2011-02-16

    We numerically study the propagation of acoustic waves in a one-dimensional medium with a scale-free long-range correlated elasticity distribution. The random elasticity distribution is assumed to have a power spectrum S(k) ∼ 1/k(α). By using a transfer-matrix method we solve the discrete version of the scalar wave equation and compute the localization length. In addition, we apply a second-order finite-difference method for both the time and spatial variables and study the nature of the waves that propagate in the chain. Our numerical data indicate the presence of extended acoustic waves for a high degree of correlations. In contrast with local correlations, we numerically demonstrate that scale-free correlations promote a stable phase of free acoustic waves in the thermodynamic limit. PMID:21406919

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

    NASA Astrophysics Data System (ADS)

    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), 10.1103/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 βc=exp(-π /√{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 βc 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 <βc and indicates that inelastic collapse does not necessarily imply near-wall localization.

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

    PubMed Central

    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. PMID:25914561

  15. Random local binary pattern based label learning for multi-atlas segmentation

    NASA Astrophysics Data System (ADS)

    Zhu, Hancan; Cheng, Hewei; Fan, Yong

    2015-03-01

    Multi-atlas segmentation method has attracted increasing attention in the field of medical image segmentation. It segments the target image by combining warped atlas labels according to a label fusion strategy, usually based on the intensity information of the target and atlas images. However, it has been demonstrated that image intensity information itself is not discriminative enough for distinguishing different subcortical structures in brain magnetic resonance (MR) images. Recent advance in multi-atlas based segmentation has witnessed success of label fusion methods built on informative image features. The key component in these methods is the image feature extraction. Conventional image feature extraction methods, such as textural feature extraction, are built on manually designed image filters and their performance varies when applied to different segmentation problems. In this paper, we propose a random local binary pattern (RLBP) method to generate image features in a random fashion. Based on RLBP features, we use a local learning strategy to fuse labels in multi-atlas based segmentation. Our method has been validated for segmenting hippocampus from MR images. The experiment results have demonstrated that our method can achieve competitive segmentation performance as the state-of-the-art methods.

  16. Anisotropy of the monomer random walk in a polymer melt: local-order and connectivity effects.

    PubMed

    Bernini, S; Leporini, D

    2016-05-11

    The random walk of a bonded monomer in a polymer melt is anisotropic due to local order and bond connectivity. We investigate both effects by molecular-dynamics simulations on melts of fully-flexible linear chains ranging from dimers (M  =  2) up to entangled polymers (M  =  200). The corresponding atomic liquid is also considered a reference system. To disentangle the influence of the local geometry and the bond arrangements, and to reveal their interplay, we define suitable measures of the anisotropy emphasising either the former or the latter aspect. Connectivity anisotropy, as measured by the correlation between the initial bond orientation and the direction of the subsequent monomer displacement, shows a slight enhancement due to the local order at times shorter than the structural relaxation time. At intermediate times-when the monomer displacement is comparable to the bond length-a pronounced peak and then decays slowly as t (-1/2), becoming negligible when the displacement is as large as about five bond lengths, i.e. about four monomer diameters or three Kuhn lengths. Local-geometry anisotropy, as measured by the correlation between the initial orientation of a characteristic axis of the Voronoi cell and the subsequent monomer dynamics, is affected at shorter times than the structural relaxation time by the cage shape with antagonistic disturbance by the connectivity. Differently, at longer times, the connectivity favours the persistence of the local-geometry anisotropy, which vanishes when the monomer displacement exceeds the bond length. Our results strongly suggest that the sole consideration of the local order is not enough to understand the microscopic origin of the rattling amplitude of the trapped monomer in the cage of the neighbours. PMID:27070080

  17. Anisotropy of the monomer random walk in a polymer melt: local-order and connectivity effects

    NASA Astrophysics Data System (ADS)

    Bernini, S.; Leporini, D.

    2016-05-01

    The random walk of a bonded monomer in a polymer melt is anisotropic due to local order and bond connectivity. We investigate both effects by molecular-dynamics simulations on melts of fully-flexible linear chains ranging from dimers (M  =  2) up to entangled polymers (M  =  200). The corresponding atomic liquid is also considered a reference system. To disentangle the influence of the local geometry and the bond arrangements, and to reveal their interplay, we define suitable measures of the anisotropy emphasising either the former or the latter aspect. Connectivity anisotropy, as measured by the correlation between the initial bond orientation and the direction of the subsequent monomer displacement, shows a slight enhancement due to the local order at times shorter than the structural relaxation time. At intermediate times—when the monomer displacement is comparable to the bond length—a pronounced peak and then decays slowly as t ‑1/2, becoming negligible when the displacement is as large as about five bond lengths, i.e. about four monomer diameters or three Kuhn lengths. Local-geometry anisotropy, as measured by the correlation between the initial orientation of a characteristic axis of the Voronoi cell and the subsequent monomer dynamics, is affected at shorter times than the structural relaxation time by the cage shape with antagonistic disturbance by the connectivity. Differently, at longer times, the connectivity favours the persistence of the local-geometry anisotropy, which vanishes when the monomer displacement exceeds the bond length. Our results strongly suggest that the sole consideration of the local order is not enough to understand the microscopic origin of the rattling amplitude of the trapped monomer in the cage of the neighbours.

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

    NASA Astrophysics Data System (ADS)

    Kamimura, H. A. S.; Wang, S.; Wu, S.-Y.; Karakatsani, M. E.; Acosta, C.; Carneiro, A. A. O.; Konofagou, E. E.

    2015-10-01

    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 mm3and 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.

  19. Rank-Driven Markov Processes

    NASA Astrophysics Data System (ADS)

    Grinfeld, Michael; Knight, Philip A.; Wade, Andrew R.

    2012-01-01

    We study a class of Markovian systems of N elements taking values in [0,1] that evolve in discrete time t via randomized replacement rules based on the ranks of the elements. These rank-driven processes are inspired by variants of the Bak-Sneppen model of evolution, in which the system represents an evolutionary `fitness landscape' and which is famous as a simple model displaying self-organized criticality. Our main results are concerned with long-time large- N asymptotics for the general model in which, at each time step, K randomly chosen elements are discarded and replaced by independent U[0,1] variables, where the ranks of the elements to be replaced are chosen, independently at each time step, according to a distribution κ N on {1,2,…, N} K . Our main results are that, under appropriate conditions on κ N , the system exhibits threshold behavior at s ∗∈[0,1], where s ∗ is a function of κ N , and the marginal distribution of a randomly selected element converges to U[ s ∗,1] as t→∞ and N→∞. Of this class of models, results in the literature have previously been given for special cases only, namely the `mean-field' or `random neighbor' Bak-Sneppen model. Our proofs avoid the heuristic arguments of some of the previous work and use Foster-Lyapunov ideas. Our results extend existing results and establish their natural, more general context. We derive some more specialized results for the particular case where K=2. One of our technical tools is a result on convergence of stationary distributions for families of uniformly ergodic Markov chains on increasing state-spaces, which may be of independent interest.

  20. Equivalent Markov processes under gauge group

    NASA Astrophysics Data System (ADS)

    Caruso, M.; Jarne, C.

    2015-11-01

    We have studied Markov processes on denumerable state space and continuous time. We found that all these processes are connected via gauge transformations. We have used this result before as a method to resolve equations, included the case in a previous work in which the sample space is time-dependent [Phys. Rev. E 90, 022125 (2014), 10.1103/PhysRevE.90.022125]. We found a general solution through dilation of the state space, although the prior probability distribution of the states defined in this new space takes smaller values with respect to that in the initial problem. The gauge (local) group of dilations modifies the distribution on the dilated space to restore the original process. In this work, we show how the Markov process in general could be linked via gauge (local) transformations, and we present some illustrative examples for this result.

  1. Equivalent Markov processes under gauge group.

    PubMed

    Caruso, M; Jarne, C

    2015-11-01

    We have studied Markov processes on denumerable state space and continuous time. We found that all these processes are connected via gauge transformations. We have used this result before as a method to resolve equations, included the case in a previous work in which the sample space is time-dependent [Phys. Rev. E 90, 022125 (2014)]. We found a general solution through dilation of the state space, although the prior probability distribution of the states defined in this new space takes smaller values with respect to that in the initial problem. The gauge (local) group of dilations modifies the distribution on the dilated space to restore the original process. In this work, we show how the Markov process in general could be linked via gauge (local) transformations, and we present some illustrative examples for this result. PMID:26651671

  2. k -core percolation on complex networks: Comparing random, localized, and targeted attacks

    NASA Astrophysics Data System (ADS)

    Yuan, Xin; Dai, Yang; Stanley, H. Eugene; Havlin, Shlomo

    2016-06-01

    The type of malicious attack inflicting on networks greatly influences their stability under ordinary percolation in which a node fails when it becomes disconnected from the giant component. Here we study its generalization, k -core percolation, in which a node fails when it loses connection to a threshold k number of neighbors. We study and compare analytically and by numerical simulations of k -core percolation the stability of networks under random attacks (RA), localized attacks (LA) and targeted attacks (TA), respectively. By mapping a network under LA or TA into an equivalent network under RA, we find that in both single and interdependent networks, TA exerts the greatest damage to the core structure of a network. We also find that for Erdős-Rényi (ER) networks, LA and RA exert equal damage to the core structure, whereas for scale-free (SF) networks, LA exerts much more damage than RA does to the core structure.

  3. Many-body localization phase transition: A simplified strong-randomness approximate renormalization group

    NASA Astrophysics Data System (ADS)

    Zhang, Liangsheng; Zhao, Bo; Devakul, Trithep; Huse, David A.

    2016-06-01

    We present a simplified strong-randomness renormalization group (RG) that captures some aspects of the many-body localization (MBL) phase transition in generic disordered one-dimensional systems. This RG can be formulated analytically and is mathematically equivalent to a domain coarsening model that has been previously solved. The critical fixed-point distribution and critical exponents (that satisfy the Chayes inequality) are thus obtained analytically or to numerical precision. This reproduces some, but not all, of the qualitative features of the MBL phase transition that are indicated by previous numerical work and approximate RG studies: our RG might serve as a "zeroth-order" approximation for future RG studies. One interesting feature that we highlight is that the rare Griffiths regions are fractal. For thermal Griffiths regions within the MBL phase, this feature might be qualitatively correctly captured by our RG. If this is correct beyond our approximations, then these Griffiths effects are stronger than has been previously assumed.

  4. Fuzzy overlapping community detection based on local random walk and multidimensional scaling

    NASA Astrophysics Data System (ADS)

    Wang, Wenjun; Liu, Dong; Liu, Xiao; Pan, Lin

    2013-12-01

    A fuzzy overlapping community is an important kind of overlapping community in which each node belongs to each community to different extents. It exists in many real networks but how to identify a fuzzy overlapping community is still a challenging task. In this work, the concept of local random walk and a new distance metric are introduced. Based on the new distance measurement, the dissimilarity index between each node of a network is calculated firstly. Then in order to keep the original node distance as much as possible, the network structure is mapped into low-dimensional space by the multidimensional scaling (MDS). Finally, the fuzzy c-means clustering is employed to find fuzzy communities in a network. The experimental results show that the proposed algorithm is effective and efficient to identify the fuzzy overlapping communities in both artificial networks and real-world networks.

  5. Modeling of nonlinear microscopy of localized field enhancements in random metal nanostructures

    NASA Astrophysics Data System (ADS)

    Beermann, Jonas; Bozhevolnyi, Sergey I.; Coello, Victor

    2006-03-01

    Nonlinear microscopy of localized field enhancements in random metal nanostructures with a tightly focused laser beam scanning over a sample surface is modeled by making use of analytic representations of the Green dyadic in the near- and far-field regions, with the latter being approximated by the part describing the scattering via excitation of surface plasmon polaritons. The developed approach is applied to scanning second-harmonic (SH) microscopy of small gold spheres placed randomly on a gold surface. We calculate self-consistent fundamental harmonic (FH) and SH field distributions at the illuminated sample surface and, thereby, FH and SH images for different polarization configurations of the illuminating and detected fields. The simulated images bear close resemblance to the images obtained experimentally, exhibiting similar sensitivity to the wavelength and polarization, as well as sensitivity to the scattering configuration. We verify directly our conjecture that very bright spots in the SH images occur due to the spatial overlap of properly polarized FH and SH eigenmodes. Applications and further improvements of the developed model are discussed.

  6. Influence of interface and random arrangement of inclusions on local stresses in composite materials

    SciTech Connect

    Al-Ostaz, A.; Jasiuk, I.

    1995-12-31

    The analysis of the local stress fields in composite materials is a very important and complex problem in micromechanics. There are many factors which influence the stress fields: the material properties of constituents, the shape and relative size of reinforcement (inclusions), the boundary conditions at the inclusion-matrix interfaces, and other. A fundamental problem in micromechanics is one involving a single inclusion. Perhaps the most famous result dealing with a single inclusion is due to Eshelby (1957), who found that the stress in an ellipsoidal and perfectly bonded inclusion is uniform, under a constant loading. However, when two or more inclusions are present, the stress fields are more complex and so is their evaluation. The additional complexity is added when the bonding at the inclusion-matrix interface is not perfect. In this paper we study the joint effect of random geometric arrangement and matrix-inclusion interface in composites by using experimental, numerical, and analytical approaches. We conduct the experiments on model composites consisting of copper inclusions and photoelastic epoxy matrix. We use this very idealized composite system because of its easy handling characteristics and isotropic properties of components. Also, the measurements are facilitated due to the larger scale of the specimen. We prepare specimens with several random arrangements of inclusions, several volume fractions, and different interface conditions. We vary the interfaces by using several types of coatings and include perfectly bonded and debonding cases. In this paper we study the local stress fields in the above model composites by using the photoelasticity method. Additionally, we conduct the finite element calculations for the composite systems with the same geometry and material properties. Also, we employ analytical techniques in the studies of simple geometries.

  7. Predicting local Soil- and Land-units with Random Forest in the Senegalese Sahel

    NASA Astrophysics Data System (ADS)

    Grau, Tobias; Brandt, Martin; Samimi, Cyrus

    2013-04-01

    MODIS (MCD12Q1) or Globcover are often the only available global land-cover products, however ground-truthing in the Sahel of Senegal has shown that most classes do have any agreement with actual land-cover making those products unusable in any local application. We suggest a methodology, which models local Wolof land- and soil-types in an area in the Senegalese Ferlo around Linguère at different scales. In a first step, interviews with the local population were conducted to ascertain the local denotation of soil units, as well as their agricultural use and woody vegetation mainly growing on them. "Ndjor" are soft sand soils with mainly Combretum glutinosum trees. They are suitable for groundnuts and beans while millet is grown on hard sand soils ("Bardjen") dominated by Balanites aegyptiaca and Acacia tortilis. "Xur" are clayey depressions with a high diversity of tree species. Lateritic pasture sites with dense woody vegetation (mostly Pterocarpus lucens and Guiera senegalensis) have never been used for cropping and are called "All". In a second step, vegetation and soil parameters of 85 plots (~1 ha) were surveyed in the field. 28 different soil parameters are clustered into 4 classes using the WARD algorithm. Here, 81% agree with the local classification. Then, an ordination (NMDS) with 2 dimensions and a stress-value of 9.13% was calculated using the 28 soil parameters. It shows several significant relationships between the soil classes and the fitted environmental parameters which are derived from field data, a digital elevation model, Landsat and RapidEye imagery as well as TRMM rainfall data. Landsat's band 5 reflectance values (1.55 - 1.75 µm) of mean dry season image (2000-2010) has a R² of 0.42 and is the most important of 9 significant variables (5%-level). A random forest classifier is then used to extrapolate the 4 classes to the whole study area based on the 9 significant environmental parameters. At a resolution of 30 m the OBB (out-of-bag) error

  8. Adjuvant chemo- and hormonal therapy in locally advanced breast cancer: a randomized clinical study

    SciTech Connect

    Schaake-Koning, C.; van der Linden, E.H.; Hart, G.; Engelsman, E.

    1985-10-01

    Between 1977 and 1980, 118 breast cancer patients with locally advanced disease, T3B-4, any N, M0 or T1-3, tumor positive axillary apex biopsy, were randomized to one of three arms: I: radiotherapy (RT) to the breast and adjacent lymph node areas; II: RT followed by 12 cycles of cyclophosphamide, methotrexate, 5 fluorouracil (CMF) and tamoxifen during the chemotherapy period; III: 2 cycles of adriamycin and vincristine (AV), alternated with 2 cycles of CMF, then RT, followed by another 4 cycles of AV, alternated with 4 CMF; tamoxifen during the entire treatment period. The median follow-up period was 5 1/2 years. The adjuvant chemo- and hormonal therapy did not improve the overall survival; the 5-year survival was 37% for all three treatment arms. There was no statistically significant difference in RFS between the three modalities, nor when arm I was compared to arm II and III together. LR was not statistically different over the three treatment arms. In 18 of the 24 patients with LR, distant metastases appeared within a few months from the local recurrence. The menopausal status did not influence the treatment results. Dose reduction in more than 4 cycles of chemotherapy was accompanied by better results. In conclusion: adjuvant chemo- and hormonal therapy did not improve RFS and overall survival. These findings do not support the routine use of adjuvant chemo- and endocrine therapy for inoperable breast cancer.

  9. 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.

  10. Phase transitions in Hidden Markov Models

    NASA Astrophysics Data System (ADS)

    Bechhoefer, John; Lathouwers, Emma

    In Hidden Markov Models (HMMs), a Markov process is not directly accessible. In the simplest case, a two-state Markov model ``emits'' one of two ``symbols'' at each time step. We can think of these symbols as noisy measurements of the underlying state. With some probability, the symbol implies that the system is in one state when it is actually in the other. The ability to judge which state the system is in sets the efficiency of a Maxwell demon that observes state fluctuations in order to extract heat from a coupled reservoir. The state-inference problem is to infer the underlying state from such noisy measurements at each time step. We show that there can be a phase transition in such measurements: for measurement error rates below a certain threshold, the inferred state always matches the observation. For higher error rates, there can be continuous or discontinuous transitions to situations where keeping a memory of past observations improves the state estimate. We can partly understand this behavior by mapping the HMM onto a 1d random-field Ising model at zero temperature. We also present more recent work that explores a larger parameter space and more states. Research funded by NSERC, Canada.

  11. Effect of local anesthesia on atypical odontalgia--a randomized controlled trial.

    PubMed

    List, Thomas; Leijon, Göran; Helkimo, Martti; Oster, Anders; Svensson, Peter

    2006-06-01

    The aim of the study was to evaluate the analgesic effect of lidocaine in a double-blind, controlled multi-center study on patients with atypical odontalgia (AO)--a possible orofacial neuropathic pain condition. Thirty-five consecutive AO patients (range 31-81 years) with a mean pain duration of 7.2 years (range 1-30 years) were recruited from four different orofacial pain clinics in Sweden. In a randomized cross-over design, 1.5 ml local anesthesia (20mg/ml lidocaine and 12.5 microg/ml adrenaline) or 1.5 ml saline (9 mg/ml NaCl solution) (placebo) was injected to block the painful area. The VAS pain scores showed an overall effect of time (ANOVA: P<0.001) and treatment (ANOVA: P=0.018) with a significant interaction between the factors (ANOVA: P<0.001). Overall, VAS pain relief was significantly greater at 15-120 min following the lidocaine injections compared to the placebo injections (Tukey: P<0.05). All patients demonstrated significant disturbances in somatosensory function on the painful side compared to the non-painful side as revealed by quantitative sensory tests, however, only one significant inverse correlation was found between percentage pain relief and the magnitude of brush-evoked allodynia (Spearman: P<0.01). In conclusion, AO patients experienced significant, but not complete, pain relief from administration of local anesthetics compared with placebo. The findings indicate that the spontaneous pain in AO patients only to some extent is dependent on peripheral afferent inputs and that sensitization of higher order neurons may be involved in the pathophysiology of AO. PMID:16564621

  12. Exact electronic spectra and inverse localization lengths in one-dimensional random systems I. Random alloy, liquid metal and liquid alloy

    NASA Astrophysics Data System (ADS)

    Nieuwenhuizen, T. M.

    1983-07-01

    Analytic continuations into the complex energy plane of Dyson-Schmidt type of equations for the calculation of the density of states are constructed for a random alloy model, a liquid metal and for a liquid alloy. In all these models the characteristic function follows from the solution of this equation. Its imaginary part yields the accumulated density of states and its real part is a measure for the inverse of the localization length of the eigenfunctions. The equations have been solved exactly for some distributions of the random variables. In the random alloy case the strengths of the delta-potentials have an exponential distribution. They may also have finite, exponentially distributed values with probability 0 ⪕ p ⪕ 1 and be infinite with probability q = 1 - p. In the liquid metal the liquid particles are assumed to behave like hard rods. This implies an exponential distribution of the distances between the particles. The common electronic potential may be arbitrary, but is assumed to vanish outside the rods. In the one-dimensional liquid alloy there is, apart from positional randomness of the liquid particles, a distribution of the strengths of the electronic delta-potentials. For Cauchy distributions an argument of Lloyd is extended to obtain the characteristic function from the one in the model with equal strengths. For the case of a liquid of point particles a three parameter class of distributions of the strengths is shown to yield a solution in the form of known functions of the equation mentioned above. For several cases numerical calculations of the density of states and the inverse localization length of the eigenfunctions are presented and discussed. New results are found: exponential decay of the density of states near special energies in the random alloy and liquid metal; divergence of the density of states at certain energies with non-classical exponent {1}/{3} in the random alloy if the average of the potential strengths vanishes

  13. Markov counting models for correlated binary responses.

    PubMed

    Crawford, Forrest W; Zelterman, Daniel

    2015-07-01

    We propose a class of continuous-time Markov counting processes for analyzing correlated binary data and establish a correspondence between these models and sums of exchangeable Bernoulli random variables. Our approach generalizes many previous models for correlated outcomes, admits easily interpretable parameterizations, allows different cluster sizes, and incorporates ascertainment bias in a natural way. We demonstrate several new models for dependent outcomes and provide algorithms for computing maximum likelihood estimates. We show how to incorporate cluster-specific covariates in a regression setting and demonstrate improved fits to well-known datasets from familial disease epidemiology and developmental toxicology. PMID:25792624

  14. 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.

  15. Local Infiltration Analgesia reduces pain and hospital stay after primary TKA: randomized controlled double blind trial.

    PubMed

    Vaishya, Raju; Wani, Ajaz Majeed; Vijay, Vipul

    2015-12-01

    Postoperative analgesia following Total Knee Arthroplasty (TKA) with the use of parenteral opioids or epidural analgesia can be associated with important side effects. Good perioperative analgesia facilitates faster rehabilitation, improves patient satisfaction, and may reduce the hospital stay. We investigated the analgesic effect of a locally injected mixture of drugs, in a double blinded RCT in 80 primary TKA. They were randomized either to receive a periarticular mixture of drugs containing bupivacaine, ketorolac, morphine, and adrenalline or to receive normal saline. Visual analog scores (VAS) for pain (at rest and during activity) and for patient satisfaction and range of motion were recorded postoperatively. The patients who had received the periarticular injection used significantly less the Patient Controlled Analgesia (PCA) after the surgery as compared to the control group. In addition, they had lower VAS for pain during rest and activity and higher visual analog scores for patient satisfaction 72 hours postoperatively. No major complication related to the drugs was observed. Intraoperative periarticular injection with multimodal drugs following TKA can significantly reduce the postoperative pain and hence the requirements for PCA and hospital stay, with no apparent risks. PMID:26790796

  16. Markov chain for estimating human mitochondrial DNA mutation pattern

    NASA Astrophysics Data System (ADS)

    Vantika, Sandy; Pasaribu, Udjianna S.

    2015-12-01

    The Markov chain was proposed to estimate the human mitochondrial DNA mutation pattern. One DNA sequence was taken randomly from 100 sequences in Genbank. The nucleotide transition matrix and mutation transition matrix were estimated from this sequence. We determined whether the states (mutation/normal) are recurrent or transient. The results showed that both of them are recurrent.

  17. 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. PMID:16719602

  18. Near-field-assisted localization: effect of size and filling factor of randomly distributed zinc oxide nanoneedles on multiple scattering and localization of light

    NASA Astrophysics Data System (ADS)

    Silies, Martin; Mascheck, Manfred; Leipold, David; Kollmann, Heiko; Schmidt, Slawa; Sartor, Janos; Yatsui, Takashi; Kitamura, Kokoro; Ohtsu, Motoicho; Kalt, Heinz; Runge, Erich; Lienau, Christoph

    2016-07-01

    We investigate the influence of the diameter and the filling factor of randomly arranged ZnO nanoneedles on the multiple scattering and localization of light in disordered dielectrics. Coherent, ultra-broadband second-harmonic (SH) microscopy is used to probe the spatial localization of light in representative nm-sized ZnO arrays of needles. We observe strong fluctuations of the SH intensity inside different ZnO needle geometries. Comparison of the SH intensity distributions with predictions based on a one-parameter scaling model indicate that SH fluctuations can be taken as a quantitative measure for the degree of localization. Interestingly, the strongest localization signatures are found for densely packed arrays of thin needles with diameters in the range of only 30 nm range, despite the small scattering cross section of these needles. FDTD simulations indicate that in this case coupling of electric near-fields between neighbouring needles governs the localization.

  19. Effects of Preoperative Local Estrogen in Postmenopausal Women With Prolapse: A Randomized Trial

    PubMed Central

    Good, Meadow M.; Roshanravan, Shayzreen M.; Shi, Haolin; Schaffer, Joseph I.; Singh, Ravinder J.; Word, R. Ann

    2014-01-01

    Context: Pelvic organ prolapse (POP) increases in prevalence with age; recurrence after surgical repair is common. Objective: The objective of the study was to determine the effects of local estrogen treatment on connective tissue synthesis and breakdown in the vaginal wall of postmenopausal women planning surgical repair of POP. Design: This was a randomized trial. Setting: The study was conducted at an academic tertiary medical center. Patients or Other Participants: Postmenopausal women with a uterus and symptomatic anterior and/or apical prolapse at stage 2 or greater participated in the study. Intervention: Estrogen (Premarin) or placebo cream for 6 weeks preoperatively was the intervention. Main Outcome Measures: Full-thickness anterior apical vaginal wall biopsies were obtained at the time of hysterectomy and analyzed for mucosa and muscularis thickness, connective tissue synthesis, and degradation. Serum levels of estrone and 17β-estradiol were analyzed at baseline and the day of surgery using highly sensitive liquid chromatography-tandem mass spectrometry. Results: Fifteen women per group (n = 30 total) were randomized; 13 per group underwent surgery. Among drug-adherent participants (n = 8 estrogen, n = 13 placebo), epithelial and muscularis thickness was increased 1.8- and 2.7-fold (P = .002 and P =.088, respectively) by estrogen. Collagen types 1α1 and 1α2 mRNA increased 6.0- and 1.8-fold in the vaginal muscularis (P < .05 for both); collagen type Ia protein increased 9-fold in the muscularis (P = .012), whereas collagen III was not changed significantly. MMP-12 (human macrophage elastase) mRNA was suppressed in the vaginal mucosa from estrogen-treated participants (P = .011), and matrix metalloprotease-9 activity was decreased 6-fold in the mucosa and 4-fold in the muscularis (P = .02). Consistent with menopausal norms, serum estrone and 17β-estradiol were low and did not differ among the two groups. Conclusions: Vaginal estrogen application for 6

  20. 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.

  1. 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. PMID:18632387

  2. Analysis of (1+1) evolutionary algorithm and randomized local search with memory.

    PubMed

    Sung, Chi Wan; Yuen, Shiu Yin

    2011-01-01

    This paper considers the scenario of the (1+1) evolutionary algorithm (EA) and randomized local search (RLS) with memory. Previously explored solutions are stored in memory until an improvement in fitness is obtained; then the stored information is discarded. This results in two new algorithms: (1+1) EA-m (with a raw list and hash table option) and RLS-m+ (and RLS-m if the function is a priori known to be unimodal). These two algorithms can be regarded as very simple forms of tabu search. Rigorous theoretical analysis of the expected time to find the globally optimal solutions for these algorithms is conducted for both unimodal and multimodal functions. A unified mathematical framework, involving the new concept of spatially invariant neighborhood, is proposed. Under this framework, both (1+1) EA with standard uniform mutation and RLS can be considered as particular instances and in the most general cases, all functions can be considered to be unimodal. Under this framework, it is found that for unimodal functions, the improvement by memory assistance is always positive but at most by one half. For multimodal functions, the improvement is significant; for functions with gaps and another hard function, the order of growth is reduced; for at least one example function, the order can change from exponential to polynomial. Empirical results, with a reasonable fitness evaluation time assumption, verify that (1+1) EA-m and RLS-m+ are superior to their conventional counterparts. Both new algorithms are promising for use in a memetic algorithm. In particular, RLS-m+ makes the previously impractical RLS practical, and surprisingly, does not require any extra memory in actual implementation. PMID:20868262

  3. Lower bound for the spatial extent of localized modes in photonic-crystal waveguides with small random imperfections

    NASA Astrophysics Data System (ADS)

    Faggiani, Rémi; Baron, Alexandre; Zang, Xiaorun; Lalouat, Loïc; Schulz, Sebastian A.; O’Regan, Bryan; Vynck, Kevin; Cluzel, Benoît; de Fornel, Frédérique; Krauss, Thomas F.; Lalanne, Philippe

    2016-06-01

    Light localization due to random imperfections in periodic media is paramount in photonics research. The group index is known to be a key parameter for localization near photonic band edges, since small group velocities reinforce light interaction with imperfections. Here, we show that the size of the smallest localized mode that is formed at the band edge of a one-dimensional periodic medium is driven instead by the effective photon mass, i.e. the flatness of the dispersion curve. Our theoretical prediction is supported by numerical simulations, which reveal that photonic-crystal waveguides can exhibit surprisingly small localized modes, much smaller than those observed in Bragg stacks thanks to their larger effective photon mass. This possibility is demonstrated experimentally with a photonic-crystal waveguide fabricated without any intentional disorder, for which near-field measurements allow us to distinctly observe a wavelength-scale localized mode despite the smallness (~1/1000 of a wavelength) of the fabrication imperfections.

  4. 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.

  5. Bibliometric Application of Markov Chains.

    ERIC Educational Resources Information Center

    Pao, Miranda Lee; McCreery, Laurie

    1986-01-01

    A rudimentary description of Markov Chains is presented in order to introduce its use to describe and to predict authors' movements among subareas of the discipline of ethnomusicology. Other possible applications are suggested. (Author)

  6. Tight asymptotic key rate for the Bennett-Brassard 1984 protocol with local randomization and device imprecisions

    NASA Astrophysics Data System (ADS)

    Woodhead, Erik

    2014-08-01

    Local randomization is a preprocessing procedure in which one of the legitimate parties of a quantum key distribution (QKD) scheme adds noise to their version of the key and was found by Kraus et al. [Phys. Rev. Lett. 95, 080501 (2005), 10.1103/PhysRevLett.95.080501] to improve the security of certain QKD protocols. In this article, the improvement yielded by local randomization is derived for an imperfect implementation of the Bennett-Brassard 1984 (BB84) QKD protocol, in which the source emits four given but arbitrary pure states and the detector performs arbitrarily aligned measurements. Specifically, this is achieved by modifying an approach to analyzing the security of imperfect variants of the BB84 protocol against collective attacks, introduced in [Phys. Rev. A 88, 012331 (2013), 10.1103/PhysRevA.88.012331], to include the additional preprocessing step. The previously known improvement to the threshold channel noise, from 11% to 12.41%, is recovered in the special case of an ideal BB84 implementation and becomes more pronounced in the case of a nonideal source. Finally, the bound derived for the asymptotic key rate, both with and without local randomization, is shown to be tight with the particular source characterization used. This is demonstrated by the explicit construction of a family of source states and optimal attacks for which the key-rate bound is attained with equality.

  7. Robust 3D object localization and pose estimation for random bin picking with the 3DMaMa algorithm

    NASA Astrophysics Data System (ADS)

    Skotheim, Øystein; Thielemann, Jens T.; Berge, Asbjørn; Sommerfelt, Arne

    2010-02-01

    Enabling robots to automatically locate and pick up randomly placed and oriented objects from a bin is an important challenge in factory automation, replacing tedious and heavy manual labor. A system should be able to recognize and locate objects with a predefined shape and estimate the position with the precision necessary for a gripping robot to pick it up. We describe a system that consists of a structured light instrument for capturing 3D data and a robust approach for object location and pose estimation. The method does not depend on segmentation of range images, but instead searches through pairs of 2D manifolds to localize candidates for object match. This leads to an algorithm that is not very sensitive to scene complexity or the number of objects in the scene. Furthermore, the strategy for candidate search is easily reconfigurable to arbitrary objects. Experiments reported in this paper show the utility of the method on a general random bin picking problem, in this paper exemplified by localization of car parts with random position and orientation. Full pose estimation is done in less than 380 ms per image. We believe that the method is applicable for a wide range of industrial automation problems where precise localization of 3D objects in a scene is needed.

  8. Adiabatic condition and the quantum hitting time of Markov chains

    SciTech Connect

    Krovi, Hari; Ozols, Maris; Roland, Jeremie

    2010-08-15

    We present an adiabatic quantum algorithm for the abstract problem of searching marked vertices in a graph, or spatial search. Given a random walk (or Markov chain) P on a graph with a set of unknown marked vertices, one can define a related absorbing walk P{sup '} where outgoing transitions from marked vertices are replaced by self-loops. We build a Hamiltonian H(s) from the interpolated Markov chain P(s)=(1-s)P+sP{sup '} and use it in an adiabatic quantum algorithm to drive an initial superposition over all vertices to a superposition over marked vertices. The adiabatic condition implies that, for any reversible Markov chain and any set of marked vertices, the running time of the adiabatic algorithm is given by the square root of the classical hitting time. This algorithm therefore demonstrates a novel connection between the adiabatic condition and the classical notion of hitting time of a random walk. It also significantly extends the scope of previous quantum algorithms for this problem, which could only obtain a full quadratic speedup for state-transitive reversible Markov chains with a unique marked vertex.

  9. 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.

  10. Localization phenomenon in gaps of the spectrum of random lattice operators

    NASA Astrophysics Data System (ADS)

    Figotin, Alexander; Klein, Abel

    1994-06-01

    We consider a class of random lattice operators including Schrödinger operators of the form H=-Δ+w+gv, where w(x) is a real-valued periodic function, g is a positive constant, and v(x),x∈ℤ d , are independent, identically distributed real random variables. We prove that if the operator -Δ+ w has gaps in the spectrum and g is sufficiently small, then the operator H develops pure point spectrum with exponentially decaying eigenfunctions in a vicinity of the gaps.

  11. Universality of the local eigenvalue statistics for a class of unitary invariant random matrix ensembles

    SciTech Connect

    Pastur, L. |; Shcherbina, M.

    1997-01-01

    This paper is devoted to the rigorous proof of the universality conjecture of random matrix theory, according to which the limiting eigenvalue statistics of n x n random matrices within spectral intervals of O(n{sup -1}) is determined by the type of matrix (real symmetric, Hermitian, or quaternion real) and by the density of states. We prove this conjecture for a certain class of the Hermitian matrix ensembles that arise in the quantum field theory and have the unitary invariant distribution defined by a certain function (the potential in the quantum field theory) satisfying some regularity conditions.

  12. Latent Variable Model for Learning in Pairwise Markov Networks

    PubMed Central

    Amizadeh, Saeed; Hauskrecht, Milos

    2011-01-01

    Pairwise Markov Networks (PMN) are an important class of Markov networks which, due to their simplicity, are widely used in many applications such as image analysis, bioinformatics, sensor networks, etc. However, learning of Markov networks from data is a challenging task; there are many possible structures one must consider and each of these structures comes with its own parameters making it easy to overfit the model with limited data. To deal with the problem, recent learning methods build upon the L1 regularization to express the bias towards sparse network structures. In this paper, we propose a new and more flexible framework that let us bias the structure, that can, for example, encode the preference to networks with certain local substructures which as a whole exhibit some special global structure. We experiment with and show the benefit of our framework on two types of problems: learning of modular networks and learning of traffic networks models. PMID:22228193

  13. Assessment of optimized Markov models in protein fold classification.

    PubMed

    Lampros, Christos; Simos, Thomas; Exarchos, Themis P; Exarchos, Konstantinos P; Papaloukas, Costas; Fotiadis, Dimitrios I

    2014-08-01

    Protein fold classification is a challenging task strongly associated with the determination of proteins' structure. In this work, we tested an optimization strategy on a Markov chain and a recently introduced Hidden Markov Model (HMM) with reduced state-space topology. The proteins with unknown structure were scored against both these models. Then the derived scores were optimized following a local optimization method. The Protein Data Bank (PDB) and the annotation of the Structural Classification of Proteins (SCOP) database were used for the evaluation of the proposed methodology. The results demonstrated that the fold classification accuracy of the optimized HMM was substantially higher compared to that of the Markov chain or the reduced state-space HMM approaches. The proposed methodology achieved an accuracy of 41.4% on fold classification, while Sequence Alignment and Modeling (SAM), which was used for comparison, reached an accuracy of 38%. PMID:25152041

  14. Microwave conductance in random waveguides in the cross-over to Anderson localization and single-parameter scaling

    PubMed Central

    Shi, Zhou; Wang, Jing; Genack, Azriel Z.

    2014-01-01

    The nature of transport of electrons and classical waves in disordered systems depends upon the proximity to the Anderson localization transition between freely diffusing and localized waves. The suppression of average transport and the enhancement of relative fluctuations in conductance in one-dimensional samples with lengths greatly exceeding the localization length, , are related in the single-parameter scaling (SPS) theory of localization. However, the difficulty of producing an ensemble of statistically equivalent samples in which the electron wave function is temporally coherent has so-far precluded the experimental demonstration of SPS. Here we demonstrate SPS in random multichannel systems for the transmittance T of microwave radiation, which is the analog of the dimensionless conductance. We show that for , a single eigenvalue of the transmission matrix (TM) dominates transmission, and the distribution of the is Gaussian with a variance equal to the average of , as conjectured by SPS. For samples in the cross-over to localization, , we find a one-sided distribution for . This anomalous distribution is explained in terms of a charge model for the eigenvalues of the TM τ in which the Coulomb interaction between charges mimics the repulsion between the eigenvalues of TM. We show in the localization limit that the joint distribution of T and the effective number of transmission eigenvalues determines the probability distributions of intensity and total transmission for a single-incident channel. PMID:24516156

  15. Transport of localized and extended excitations in chains embedded with randomly distributed linear and nonlinear n -mers

    NASA Astrophysics Data System (ADS)

    López-González, Dany; Molina, Mario I.

    2016-03-01

    We examine the transport of extended and localized excitations in one-dimensional linear chains populated by linear and nonlinear symmetric identical n -mers (with n =3 , 4, 5, and 6), randomly distributed. First, we examine the transmission of plane waves across a single linear n -mer, paying attention to its resonances, and looking for parameters that allow resonances to merge. Within this parameter regime we examine the transmission of plane waves through a disordered and nonlinear segment composed by n -mers randomly placed inside a linear chain. It is observed that nonlinearity tends to inhibit the transmission, which decays as a power law at long segment lengths. This behavior still holds when the n -mer parameters do not obey the resonance condition. On the other hand, the mean square displacement exponent of an initially localized excitation does not depend on nonlinearity at long propagation distances z , and shows a superdiffusive behavior ˜z1.8 for all n -mers, when parameters obey the resonance merging condition; otherwise the exponent reverts back to the random dimer model value ˜z1.5 .

  16. 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.

  17. Non-Amontons-Coulomb local friction law of randomly rough contact interfaces with rubber

    NASA Astrophysics Data System (ADS)

    Nguyen, Danh Toan; Wandersman, Elie; Prevost, Alexis; Le Chenadec, Yohan; Fretigny, Christian; Chateauminois, Antoine

    2013-12-01

    We report on measurements of the local friction law at a multi-contact interface formed between a smooth rubber and statistically rough glass lenses, under steady-state friction. Using contact imaging, surface displacements are measured, and inverted to extract both distributions of frictional shear stress and contact pressure with a spatial resolution of about 10\\ \\mu\\text{m} . For a glass surface whose topography is self-affine with a Gaussian height asperity distribution, the local frictional shear stress is found to vary sub-linearly with the local contact pressure over the whole investigated pressure range. Such sub-linear behavior is also evidenced for a surface with a non-Gaussian height asperity distribution, demonstrating that, for such multi-contact interfaces, Amontons-Coulomb's friction law does not prevail at the local scale.

  18. 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…

  19. SU-D-201-06: Random Walk Algorithm Seed Localization Parameters in Lung Positron Emission Tomography (PET) Images

    SciTech Connect

    Soufi, M; Asl, A Kamali; Geramifar, P

    2015-06-15

    Purpose: The objective of this study was to find the best seed localization parameters in random walk algorithm application to lung tumor delineation in Positron Emission Tomography (PET) images. Methods: PET images suffer from statistical noise and therefore tumor delineation in these images is a challenging task. Random walk algorithm, a graph based image segmentation technique, has reliable image noise robustness. Also its fast computation and fast editing characteristics make it powerful for clinical purposes. We implemented the random walk algorithm using MATLAB codes. The validation and verification of the algorithm have been done by 4D-NCAT phantom with spherical lung lesions in different diameters from 20 to 90 mm (with incremental steps of 10 mm) and different tumor to background ratios of 4:1 and 8:1. STIR (Software for Tomographic Image Reconstruction) has been applied to reconstruct the phantom PET images with different pixel sizes of 2×2×2 and 4×4×4 mm{sup 3}. For seed localization, we selected pixels with different maximum Standardized Uptake Value (SUVmax) percentages, at least (70%, 80%, 90% and 100%) SUVmax for foreground seeds and up to (20% to 55%, 5% increment) SUVmax for background seeds. Also, for investigation of algorithm performance on clinical data, 19 patients with lung tumor were studied. The resulted contours from algorithm have been compared with nuclear medicine expert manual contouring as ground truth. Results: Phantom and clinical lesion segmentation have shown that the best segmentation results obtained by selecting the pixels with at least 70% SUVmax as foreground seeds and pixels up to 30% SUVmax as background seeds respectively. The mean Dice Similarity Coefficient of 94% ± 5% (83% ± 6%) and mean Hausdorff Distance of 1 (2) pixels have been obtained for phantom (clinical) study. Conclusion: The accurate results of random walk algorithm in PET image segmentation assure its application for radiation treatment planning and

  20. Randomized clinical trial of local infiltration plus patient-controlled opiate analgesia vs. epidural analgesia following liver resection surgery

    PubMed Central

    Revie, Erica J; McKeown, Dermot W; Wilson, John A; Garden, O James; Wigmore, Stephen J

    2012-01-01

    Objectives Epidural analgesia is recommended for the provision of analgesia following major abdominal surgery. Continuous local anaesthetic wound infiltration may be an effective alternative. A prospective randomized trial was undertaken to compare these two methods following open liver resection. The primary outcome was length of time required to fulfil criteria for discharge from hospital. Methods Patients undergoing open liver resection were randomized to receive either epidural (EP group) or local anaesthetic wound infiltration plus patient-controlled opiate analgesia (WI group) for the first 2 days postoperatively. All other care followed a standardized enhanced recovery protocol. Time to fulfil discharge criteria, pain scores, physical activity measurements and complications were recorded. Results Between August 2009 and July 2010, 65 patients were randomized to EP (n= 32) or WI (n= 33). The mean time required to fulfil discharge criteria was 4.5 days (range: 2.5–63.5 days) in the WI group and 6.0 days (range: 3.0–42.5 days) in the EP group (P= 0.044). During the first 48 h following surgery, pain scores were significantly lower in the EP group both at rest and on movement. Resting pain scores within both groups were rated as mild (range: 0–3). There was no significant difference between the groups in time to first mobilization or overall complication rate (48.5% in the WI group vs. 58.1% in the EP group; P= 0.443). Conclusions Local anaesthetic wound infiltration combined with patient-controlled opiate analgesia reduces the length of time required to fulfil criteria for discharge from hospital compared with epidural analgesia following open liver resection. Epidural analgesia provides superior analgesia, but does not confer benefits in terms of faster mobilization or recovery. PMID:22882198

  1. Relativistic Weierstrass random walks.

    PubMed

    Saa, Alberto; Venegeroles, Roberto

    2010-08-01

    The Weierstrass random walk is a paradigmatic Markov chain giving rise to a Lévy-type superdiffusive behavior. It is well known that special relativity prevents the arbitrarily high velocities necessary to establish a superdiffusive behavior in any process occurring in Minkowski spacetime, implying, in particular, that any relativistic Markov chain describing spacetime phenomena must be essentially Gaussian. Here, we introduce a simple relativistic extension of the Weierstrass random walk and show that there must exist a transition time t{c} delimiting two qualitative distinct dynamical regimes: the (nonrelativistic) superdiffusive Lévy flights, for tt{c} . Implications of this crossover between different diffusion regimes are discussed for some explicit examples. The study of such an explicit and simple Markov chain can shed some light on several results obtained in much more involved contexts. PMID:20866862

  2. Lower bound for the spatial extent of localized modes in photonic-crystal waveguides with small random imperfections.

    PubMed

    Faggiani, Rémi; Baron, Alexandre; Zang, Xiaorun; Lalouat, Loïc; Schulz, Sebastian A; O'Regan, Bryan; Vynck, Kevin; Cluzel, Benoît; de Fornel, Frédérique; Krauss, Thomas F; Lalanne, Philippe

    2016-01-01

    Light localization due to random imperfections in periodic media is paramount in photonics research. The group index is known to be a key parameter for localization near photonic band edges, since small group velocities reinforce light interaction with imperfections. Here, we show that the size of the smallest localized mode that is formed at the band edge of a one-dimensional periodic medium is driven instead by the effective photon mass, i.e. the flatness of the dispersion curve. Our theoretical prediction is supported by numerical simulations, which reveal that photonic-crystal waveguides can exhibit surprisingly small localized modes, much smaller than those observed in Bragg stacks thanks to their larger effective photon mass. This possibility is demonstrated experimentally with a photonic-crystal waveguide fabricated without any intentional disorder, for which near-field measurements allow us to distinctly observe a wavelength-scale localized mode despite the smallness (~1/1000 of a wavelength) of the fabrication imperfections. PMID:27246902

  3. Lower bound for the spatial extent of localized modes in photonic-crystal waveguides with small random imperfections

    PubMed Central

    Faggiani, Rémi; Baron, Alexandre; Zang, Xiaorun; Lalouat, Loïc; Schulz, Sebastian A.; O’Regan, Bryan; Vynck, Kevin; Cluzel, Benoît; de Fornel, Frédérique; Krauss, Thomas F.; Lalanne, Philippe

    2016-01-01

    Light localization due to random imperfections in periodic media is paramount in photonics research. The group index is known to be a key parameter for localization near photonic band edges, since small group velocities reinforce light interaction with imperfections. Here, we show that the size of the smallest localized mode that is formed at the band edge of a one-dimensional periodic medium is driven instead by the effective photon mass, i.e. the flatness of the dispersion curve. Our theoretical prediction is supported by numerical simulations, which reveal that photonic-crystal waveguides can exhibit surprisingly small localized modes, much smaller than those observed in Bragg stacks thanks to their larger effective photon mass. This possibility is demonstrated experimentally with a photonic-crystal waveguide fabricated without any intentional disorder, for which near-field measurements allow us to distinctly observe a wavelength-scale localized mode despite the smallness (~1/1000 of a wavelength) of the fabrication imperfections. PMID:27246902

  4. Wave propagation through random media: A local method of small perturbations based on the Helmholtz equation

    NASA Technical Reports Server (NTRS)

    Grosse, Ralf

    1990-01-01

    Propagation of sound through the turbulent atmosphere is a statistical problem. The randomness of the refractive index field causes sound pressure fluctuations. Although no general theory to predict sound pressure statistics from given refractive index statistics exists, there are several approximate solutions to the problem. The most common approximation is the parabolic equation method. Results obtained by this method are restricted to small refractive index fluctuations and to small wave lengths. While the first condition is generally met in the atmosphere, it is desirable to overcome the second. A generalization of the parabolic equation method with respect to the small wave length restriction is presented.

  5. 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.

  6. Sunspots and ENSO relationship using Markov method

    NASA Astrophysics Data System (ADS)

    Hassan, Danish; Iqbal, Asif; Ahmad Hassan, Syed; Abbas, Shaheen; Ansari, Muhammad Rashid Kamal

    2016-01-01

    The various techniques have been used to confer the existence of significant relations between the number of Sunspots and different terrestrial climate parameters such as rainfall, temperature, dewdrops, aerosol and ENSO etc. Improved understanding and modelling of Sunspots variations can explore the information about the related variables. This study uses a Markov chain method to find the relations between monthly Sunspots and ENSO data of two epochs (1996-2009 and 1950-2014). Corresponding transition matrices of both data sets appear similar and it is qualitatively evaluated by high values of 2-dimensional correlation found between transition matrices of ENSO and Sunspots. The associated transition diagrams show that each state communicates with the others. Presence of stronger self-communication (between same states) confirms periodic behaviour among the states. Moreover, closeness found in the expected number of visits from one state to the other show the existence of a possible relation between Sunspots and ENSO data. Moreover, perfect validation of dependency and stationary tests endorses the applicability of the Markov chain analyses on Sunspots and ENSO data. This shows that a significant relation between Sunspots and ENSO data exists. Improved understanding and modelling of Sunspots variations can help to explore the information about the related variables. This study can be useful to explore the influence of ENSO related local climatic variability.

  7. A nonrandomized cohort and a randomized study of local control of large hepatocarcinoma by targeting intratumoral lactic acidosis

    PubMed Central

    Chao, Ming; Wu, Hao; Jin, Kai; Li, Bin; Wu, Jianjun; Zhang, Guangqiang; Yang, Gong; Hu, Xun

    2016-01-01

    Study design: Previous works suggested that neutralizing intratumoral lactic acidosis combined with glucose deprivation may deliver an effective approach to control tumor. We did a pilot clinical investigation, including a nonrandomized (57 patients with large HCC) and a randomized controlled (20 patients with large HCC) studies. Methods: The patients were treated with transarterial chemoembolization (TACE) with or without bicarbonate local infusion into tumor. Results: In the nonrandomized controlled study, geometric mean of viable tumor residues (VTR) in TACE with bicarbonate was 6.4-fold lower than that in TACE without bicarbonate (7.1% [95% CI: 4.6%–10.9%] vs 45.6% [28.9%–72.0%]; p<0.0001). This difference was recapitulated by a subsequent randomized controlled study. TACE combined with bicarbonate yielded a 100% objective response rate (ORR), whereas the ORR treated with TACE alone was 44.4% (nonrandomized) and 63.6% (randomized). The survival data suggested that bicarbonate may bring survival benefit. Conclusion: Bicarbonate markedly enhances the anticancer activity of TACE. Clinical trail registration: ChiCTR-IOR-14005319. DOI: http://dx.doi.org/10.7554/eLife.15691.001 PMID:27481188

  8. Classification of acoustic emission signals using wavelets and Random Forests : Application to localized corrosion

    NASA Astrophysics Data System (ADS)

    Morizet, N.; Godin, N.; Tang, J.; Maillet, E.; Fregonese, M.; Normand, B.

    2016-03-01

    This paper aims to propose a novel approach to classify acoustic emission (AE) signals deriving from corrosion experiments, even if embedded into a noisy environment. To validate this new methodology, synthetic data are first used throughout an in-depth analysis, comparing Random Forests (RF) to the k-Nearest Neighbor (k-NN) algorithm. Moreover, a new evaluation tool called the alter-class matrix (ACM) is introduced to simulate different degrees of uncertainty on labeled data for supervised classification. Then, tests on real cases involving noise and crevice corrosion are conducted, by preprocessing the waveforms including wavelet denoising and extracting a rich set of features as input of the RF algorithm. To this end, a software called RF-CAM has been developed. Results show that this approach is very efficient on ground truth data and is also very promising on real data, especially for its reliability, performance and speed, which are serious criteria for the chemical industry.

  9. Reconstructing local population dynamics in noisy metapopulations--the role of random catastrophes and Allee effects.

    PubMed

    Hart, Edmund M; Avilés, Leticia

    2014-01-01

    Reconstructing the dynamics of populations is complicated by the different types of stochasticity experienced by populations, in particular if some forms of stochasticity introduce bias in parameter estimation in addition to error. Identification of systematic biases is critical when determining whether the intrinsic dynamics of populations are stable or unstable and whether or not populations exhibit an Allee effect, i.e., a minimum size below which deterministic extinction should follow. Using a simulation model that allows for Allee effects and a range of intrinsic dynamics, we investigated how three types of stochasticity--demographic, environmental, and random catastrophes--affect our ability to reconstruct the intrinsic dynamics of populations. Demographic stochasticity aside, which is only problematic in small populations, we find that environmental stochasticity--positive and negative environmental fluctuations--caused increased error in parameter estimation, but bias was rarely problematic, except at the highest levels of noise. Random catastrophes, events causing large-scale mortality and likely to be more common than usually recognized, caused immediate bias in parameter estimates, in particular when Allee effects were large. In the latter case, population stability was predicted when endogenous dynamics were actually unstable and the minimum viable population size was overestimated in populations with small or non-existent Allee effects. Catastrophes also generally increased extinction risk, in particular when endogenous Allee effects were large. We propose a method for identifying data points likely resulting from catastrophic events when such events have not been recorded. Using social spider colonies (Anelosimus spp.) as models for populations, we show that after known or suspected catastrophes are accounted for, reconstructed growth parameters are consistent with intrinsic dynamical instability and substantial Allee effects. Our results are

  10. Reconstructing Local Population Dynamics in Noisy Metapopulations—The Role of Random Catastrophes and Allee Effects

    PubMed Central

    Hart, Edmund M.; Avilés, Leticia

    2014-01-01

    Reconstructing the dynamics of populations is complicated by the different types of stochasticity experienced by populations, in particular if some forms of stochasticity introduce bias in parameter estimation in addition to error. Identification of systematic biases is critical when determining whether the intrinsic dynamics of populations are stable or unstable and whether or not populations exhibit an Allee effect, i.e., a minimum size below which deterministic extinction should follow. Using a simulation model that allows for Allee effects and a range of intrinsic dynamics, we investigated how three types of stochasticity—demographic, environmental, and random catastrophes— affect our ability to reconstruct the intrinsic dynamics of populations. Demographic stochasticity aside, which is only problematic in small populations, we find that environmental stochasticity—positive and negative environmental fluctuations—caused increased error in parameter estimation, but bias was rarely problematic, except at the highest levels of noise. Random catastrophes, events causing large-scale mortality and likely to be more common than usually recognized, caused immediate bias in parameter estimates, in particular when Allee effects were large. In the latter case, population stability was predicted when endogenous dynamics were actually unstable and the minimum viable population size was overestimated in populations with small or non-existent Allee effects. Catastrophes also generally increased extinction risk, in particular when endogenous Allee effects were large. We propose a method for identifying data points likely resulting from catastrophic events when such events have not been recorded. Using social spider colonies (Anelosimus spp.) as models for populations, we show that after known or suspected catastrophes are accounted for, reconstructed growth parameters are consistent with intrinsic dynamical instability and substantial Allee effects. Our results are

  11. Localized Piezoelectric Alveolar Decortication for Orthodontic Treatment in Adults: A Randomized Controlled Trial.

    PubMed

    Charavet, C; Lecloux, G; Bruwier, A; Rompen, E; Maes, N; Limme, M; Lambert, F

    2016-08-01

    This randomized controlled trial aimed to evaluate the benefits and clinical outcomes of piezocision, which is a minimally invasive approach to corticotomy that is used in orthodontic treatments. Twenty-four adult patients presenting with mild overcrowdings were randomly allocated to either a control group that was treated with conventional orthodontics or a test group that received piezo-assisted orthodontics. The piezocisions were performed 1 wk week after the placement of the orthodontic appliances. Neither grafting material nor sutures were used. All patients were followed every 2 wk, and archwires were changed only when they were no longer active. The periods required for the completion of the overall orthodontic treatments were calculated, and the periodontal parameters were evaluated at baseline and at the end of the orthodontic treatment. Patient-centered outcomes were assessed with a visual analog scale; analgesic use following the procedures was also recorded. The patient characteristics were similar between the 2 groups. The overall treatment time was significantly reduced by 43% in the piezocision group as compared with the control group. In both groups, periodontal parameters (i.e., recession depth, pocket depth, plaque index, and papilla bleeding index) remained unchanged between the baseline and treatment completion time points. No increase in root resorption was observed in either group. Scars were observed in 50% of the patients in the piezocision group. Analgesic consumption was similar following orthodontic appliance placement and piezocision surgery. Patient satisfaction was significantly better in the piezocision group than in the control group. In these conditions, the piezocision technique seemed to be effective in accelerating orthodontic tooth movement. No gingival recessions were observed. The risk of residual scars might limit the indications for piezocision in patients with a high smile line (ClinicalTrials.gov NCT02590835). PMID

  12. Quality control of radiation therapy in multi-institutional randomized clinical trial for localized prostate cancer

    SciTech Connect

    Hafermann, M.D.; Gibbons, R.P.; Murphy, G.P.

    1988-02-01

    The National Prostatic Cancer Project (NPCP) from 1978 through 1985 compared definitive radiation therapy for Stages B2, C, D1 lesions in those who received only radiation treatment to those who received two years of additional cyclophosphamide (Cytoxan) or estramustine phosphate (Emcyt) chemotherapy. Two hundred fifty-four patients were entered and 229 evaluated for compliance of the spatial localization of the prostate through review of the simulation and port films. In 78 per cent this was satisfactory, whereas in 12 per cent it was unsatisfactory, and another 10 per cent were not evaluable. The principle cause of an unsatisfactory rating was failure to adequately cover the prostatic target volume, especially the apex which was found to be variable in location. Routine use of retrograde urethrocystography is urged as part of the localization method in patients to receive definitive external beam radiation therapy for prostate cancer. The role and impact of quality assurance programs for radiotherapy in cooperative clinical study groups is reviewed and discussed.

  13. Combined radiotherapy and chemotherapy versus radiotherapy alone in locally advanced epidermoid bronchogenic carcinoma. A randomized study

    SciTech Connect

    Trovo, M.G.; Minatel, E.; Veronesi, A.; Roncadin, M.; De Paoli, A.; Franchin, G.; Magri, D.M.; Tirelli, U.; Carbone, A.; Grigoletto, E. )

    1990-02-01

    Between June 1980 and December 1983, 111 patients with inoperable epidermoid bronchogenic carcinoma (limited disease) were entered into a randomized trial comparing radiotherapy alone versus radiotherapy and combination chemotherapy with cyclophosphamide, Adriamycin (doxorubicin), methotrexate, and procarbazine. Thirty-five of 62 (56.4%) patients treated with 4500 rad in 15 fractions in 3 weeks and 19 of 49 (38.8%) patients treated with the same radiation treatment and chemotherapy had an objective response. The difference in response rate was not significant (P = 0.900). Median time to progression was 5.9 and 7.02 months, respectively, for the radiation treatment and the combined treatment. Median survival was 11.74 and 10.03 months, respectively, without statistically significant differences between the two groups of patients. The toxicity was acceptable and no treatment-related death occurred in either treatment schedule. In this study no significant superiority of combined radiotherapy and chemotherapy treatment over radiation therapy alone was evidenced. Whether different chemotherapy regimens may prove more effective in this context should be clarified by further studies.

  14. Semi-automatic medical image segmentation with adaptive local statistics in Conditional Random Fields framework.

    PubMed

    Hu, Yu-Chi J; Grossberg, Michael D; Mageras, Gikas S

    2008-01-01

    Planning radiotherapy and surgical procedures usually require onerous manual segmentation of anatomical structures from medical images. In this paper we present a semi-automatic and accurate segmentation method to dramatically reduce the time and effort required of expert users. This is accomplished by giving a user an intuitive graphical interface to indicate samples of target and non-target tissue by loosely drawing a few brush strokes on the image. We use these brush strokes to provide the statistical input for a Conditional Random Field (CRF) based segmentation. Since we extract purely statistical information from the user input, we eliminate the need of assumptions on boundary contrast previously used by many other methods, A new feature of our method is that the statistics on one image can be reused on related images without registration. To demonstrate this, we show that boundary statistics provided on a few 2D slices of volumetric medical data, can be propagated through the entire 3D stack of images without using the geometric correspondence between images. In addition, the image segmentation from the CRF can be formulated as a minimum s-t graph cut problem which has a solution that is both globally optimal and fast. The combination of a fast segmentation and minimal user input that is reusable, make this a powerful technique for the segmentation of medical images. PMID:19163362

  15. Full eigenvalues of the Markov matrix for scale-free polymer networks

    NASA Astrophysics Data System (ADS)

    Zhang, Zhongzhi; Guo, Xiaoye; Lin, Yuan

    2014-08-01

    Much important information about the structural and dynamical properties of complex systems can be extracted from the eigenvalues and eigenvectors of a Markov matrix associated with random walks performed on these systems, and spectral methods have become an indispensable tool in the complex system analysis. In this paper, we study the Markov matrix of a class of scale-free polymer networks. We present an exact analytical expression for all the eigenvalues and determine explicitly their multiplicities. We then use the obtained eigenvalues to derive an explicit formula for the random target access time for random walks on the studied networks. Furthermore, based on the link between the eigenvalues of the Markov matrix and the number of spanning trees, we confirm the validity of the obtained eigenvalues and their corresponding degeneracies.

  16. Plume mapping via hidden Markov methods.

    PubMed

    Farrell, J A; Pang, Shuo; Li, Wei

    2003-01-01

    This paper addresses the problem of mapping likely locations of a chemical source using an autonomous vehicle operating in a fluid flow. The paper reviews biological plume-tracing concepts, reviews previous strategies for vehicle-based plume tracing, and presents a new plume mapping approach based on hidden Markov methods (HMM). HMM provide efficient algorithms for predicting the likelihood of odor detection versus position, the likelihood of source location versus position, the most likely path taken by the odor to a given location, and the path between two points most likely to result in odor detection. All four are useful for solving the odor source localization problem using an autonomous vehicle. The vehicle is assumed to be capable of detecting above threshold chemical concentration and sensing the fluid flow velocity at the vehicle location. The fluid flow is assumed to vary with space and time, and to have a high Reynolds number (Re>10). PMID:18238238

  17. Experiments with central-limit properties of spatial samples from locally covariant random fields

    USGS Publications Warehouse

    Barringer, T.H.; Smith, T.E.

    1992-01-01

    When spatial samples are statistically dependent, the classical estimator of sample-mean standard deviation is well known to be inconsistent. For locally dependent samples, however, consistent estimators of sample-mean standard deviation can be constructed. The present paper investigates the sampling properties of one such estimator, designated as the tau estimator of sample-mean standard deviation. In particular, the asymptotic normality properties of standardized sample means based on tau estimators are studied in terms of computer experiments with simulated sample-mean distributions. The effects of both sample size and dependency levels among samples are examined for various value of tau (denoting the size of the spatial kernel for the estimator). The results suggest that even for small degrees of spatial dependency, the tau estimator exhibits significantly stronger normality properties than does the classical estimator of standardized sample means. ?? 1992.

  18. 70 Gy Versus 80 Gy in Localized Prostate Cancer: 5-Year Results of GETUG 06 Randomized Trial;Prostate cancer; Dose escalation; Conformal radiotherapy; Randomized trial

    SciTech Connect

    Beckendorf, Veronique; Guerif, Stephane; Le Prise, Elisabeth; Cosset, Jean-Marc; Bougnoux, Agnes; Chauvet, Bruno; Salem, Naji; Chapet, Olivier; Bourdain, Sylvain; Bachaud, Jean-Marc; Maingon, Philippe; Hannoun-Levi, Jean-Michel; Malissard, Luc; Simon, Jean-Marc; Pommier, Pascal; Hay, Men; Dubray, Bernard; Lagrange, Jean-Leon; Luporsi, Elisabeth; Bey, Pierre

    2011-07-15

    Purpose: To perform a randomized trial comparing 70 and 80 Gy radiotherapy for prostate cancer. Patients and Methods: A total of 306 patients with localized prostate cancer were randomized. No androgen deprivation was allowed. The primary endpoint was biochemical relapse according to the modified 1997-American Society for Therapeutic Radiology and Oncology and Phoenix definitions. Toxicity was graded using the Radiation Therapy Oncology Group 1991 criteria and the late effects on normal tissues-subjective, objective, management, analytic scales (LENT-SOMA) scales. The patients' quality of life was scored using the European Organization for Research and Treatment of Cancer Quality of Life Questionnaire 30-item cancer-specific and 25-item prostate-specific modules. Results: The median follow-up was 61 months. According to the 1997-American Society for Therapeutic Radiology and Oncology definition, the 5-year biochemical relapse rate was 39% and 28% in the 70- and 80-Gy arms, respectively (p = .036). Using the Phoenix definition, the 5-year biochemical relapse rate was 32% and 23.5%, respectively (p = .09). The subgroup analysis showed a better biochemical outcome for the higher dose group with an initial prostate-specific antigen level >15 ng/mL. At the last follow-up date, 26 patients had died, 10 of their disease and none of toxicity, with no differences between the two arms. According to the Radiation Therapy Oncology Group scale, the Grade 2 or greater rectal toxicity rate was 14% and 19.5% for the 70- and 80-Gy arms (p = .22), respectively. The Grade 2 or greater urinary toxicity was 10% at 70 Gy and 17.5% at 80 Gy (p = .046). Similar results were observed using the LENT-SOMA scale. Bladder toxicity was more frequent at 80 Gy than at 70 Gy (p = .039). The quality-of-life questionnaire results before and 5 years after treatment were available for 103 patients with no differences found between the 70- and 80-Gy arms. Conclusion: High-dose radiotherapy provided a

  19. On the entropy of a hidden Markov process⋆

    PubMed Central

    Jacquet, Philippe; Seroussi, Gadiel; Szpankowski, Wojciech

    2008-01-01

    We study the entropy rate of a hidden Markov process (HMP) defined by observing the output of a binary symmetric channel whose input is a first-order binary Markov process. Despite the simplicity of the models involved, the characterization of this entropy is a long standing open problem. By presenting the probability of a sequence under the model as a product of random matrices, one can see that the entropy rate sought is equal to a top Lyapunov exponent of the product. This offers an explanation for the elusiveness of explicit expressions for the HMP entropy rate, as Lyapunov exponents are notoriously difficult to compute. Consequently, we focus on asymptotic estimates, and apply the same product of random matrices to derive an explicit expression for a Taylor approximation of the entropy rate with respect to the parameter of the binary symmetric channel. The accuracy of the approximation is validated against empirical simulation results. We also extend our results to higher-order Markov processes and to Rényi entropies of any order. PMID:19169438

  20. Isotropic Markov semigroups on ultra-metric spaces

    NASA Astrophysics Data System (ADS)

    Bendikov, A. D.; Grigor'yan, A. A.; Pittet, Ch; Woess, W.

    2014-08-01

    Let (X,d) be a separable ultra-metric space with compact balls. Given a reference measure μ on X and a distance distribution function σ on \\lbrack 0,∞), a symmetric Markov semigroup \\{Pt\\}t≥slant 0 acting in L2(X,μ ) is constructed. Let \\{Xt\\} be the corresponding Markov process. The authors obtain upper and lower bounds for its transition density and its Green function, give a transience criterion, estimate its moments, and describe the Markov generator L and its spectrum, which is pure point. In the particular case when X={Q}pn, where {Q}p is the field of p-adic numbers, the construction recovers the Taibleson Laplacian (spectral multiplier), and one can also apply the theory to the study of the Vladimirov Laplacian. Even in this well-established setting, several of the results are new. The paper also describes the relation between the processes involved and Kigami's jump processes on the boundary of a tree which are induced by a random walk. In conclusion, examples illustrating the interplay between the fractional derivatives and random walks are provided. Bibliography: 66 titles.

  1. High-order hidden Markov model for piecewise linear processes and applications to speech recognition.

    PubMed

    Lee, Lee-Min; Jean, Fu-Rong

    2016-08-01

    The hidden Markov models have been widely applied to systems with sequential data. However, the conditional independence of the state outputs will limit the output of a hidden Markov model to be a piecewise constant random sequence, which is not a good approximation for many real processes. In this paper, a high-order hidden Markov model for piecewise linear processes is proposed to better approximate the behavior of a real process. A parameter estimation method based on the expectation-maximization algorithm was derived for the proposed model. Experiments on speech recognition of noisy Mandarin digits were conducted to examine the effectiveness of the proposed method. Experimental results show that the proposed method can reduce the recognition error rate compared to a baseline hidden Markov model. PMID:27586781

  2. Adjunctive Systemic and Local Antimicrobial Therapy in the Surgical Treatment of Peri-implantitis: A Randomized Controlled Clinical Trial.

    PubMed

    Carcuac, O; Derks, J; Charalampakis, G; Abrahamsson, I; Wennström, J; Berglundh, T

    2016-01-01

    The aim of the present randomized controlled clinical trial was to investigate the adjunctive effect of systemic antibiotics and the local use of chlorhexidine for implant surface decontamination in the surgical treatment of peri-implantitis. One hundred patients with severe peri-implantitis were recruited. Surgical therapy was performed with or without adjunctive systemic antibiotics or the local use of chlorhexidine for implant surface decontamination. Treatment outcomes were evaluated at 1 y. A binary logistic regression analysis was used to identify factors influencing the probability of treatment success, that is, probing pocket depth ≤5 mm, absence of bleeding/suppuration on probing, and no additional bone loss. Treatment success was obtained in 45% of all implants but was higher in implants with a nonmodified surface (79%) than those with a modified surface (34%). The local use of chlorhexidine had no overall effect on treatment outcomes. While adjunctive systemic antibiotics had no impact on treatment success at implants with a nonmodified surface, a positive effect on treatment success was observed at implants with a modified surface. The likelihood for treatment success using adjunctive systemic antibiotics in patients with implants with a modified surface, however, was low. As the effect of adjunctive systemic antibiotics depended on implant surface characteristics, recommendations for their use in the surgical treatment of peri-implantitis should be based on careful assessments of the targeted implant (ClinicalTrials.gov NCT01857804). PMID:26285807

  3. Directed polymer in a random medium of dimension 1+3: multifractal properties at the localization-delocalization transition.

    PubMed

    Monthus, Cécile; Garel, Thomas

    2007-05-01

    We consider the model of the directed polymer in a random medium of dimension 1+3 , and investigate its multifractal properties at the localization-delocalization transition. In close analogy with models of the quantum Anderson localization transition, where the multifractality of critical wavefunctions is well established, we analyze the statistics of the position weights w{L}(r[over]) of the endpoint of the polymer of length L via the moments [equation: see text]. We measure the generalized exponents tau(q) and tau[over](q) governing the decay of the typical values [equation: see text] and disorder-averaged values Y{q}(L)[over] approximately L{-tau[over](q)} , respectively. To understand the difference between these exponents, tau(q) not equal to tau[over](q) above some threshold q>q{c} approximately 2 , we compute the probability distributions of [equation: see text] over the samples: We find that these distributions becomes scale invariant with a power-law tail 1/y{1+x{q}} . These results thus correspond to the Evers-Mirlin scenario [Phys. Rev. Lett. 84, 3690 (2000)] for the statistics of inverse participation ratios at the Anderson localization transitions. Finally, the finite-size scaling analysis in the critical region yields the correlation length exponent nu approximately 2 . PMID:17677037

  4. Multiple pattern matching: a Markov chain approach.

    PubMed

    Lladser, Manuel E; Betterton, M D; Knight, Rob

    2008-01-01

    RNA motifs typically consist of short, modular patterns that include base pairs formed within and between modules. Estimating the abundance of these patterns is of fundamental importance for assessing the statistical significance of matches in genomewide searches, and for predicting whether a given function has evolved many times in different species or arose from a single common ancestor. In this manuscript, we review in an integrated and self-contained manner some basic concepts of automata theory, generating functions and transfer matrix methods that are relevant to pattern analysis in biological sequences. We formalize, in a general framework, the concept of Markov chain embedding to analyze patterns in random strings produced by a memoryless source. This conceptualization, together with the capability of automata to recognize complicated patterns, allows a systematic analysis of problems related to the occurrence and frequency of patterns in random strings. The applications we present focus on the concept of synchronization of automata, as well as automata used to search for a finite number of keywords (including sets of patterns generated according to base pairing rules) in a general text. PMID:17668213

  5. Stochastic algorithms for Markov models estimation with intermittent missing data.

    PubMed

    Deltour, I; Richardson, S; Le Hesran, J Y

    1999-06-01

    Multistate Markov models are frequently used to characterize disease processes, but their estimation from longitudinal data is often hampered by complex patterns of incompleteness. Two algorithms for estimating Markov chain models in the case of intermittent missing data in longitudinal studies, a stochastic EM algorithm and the Gibbs sampler, are described. The first can be viewed as a random perturbation of the EM algorithm and is appropriate when the M step is straightforward but the E step is computationally burdensome. It leads to a good approximation of the maximum likelihood estimates. The Gibbs sampler is used for a full Bayesian inference. The performances of the two algorithms are illustrated on two simulated data sets. A motivating example concerned with the modelling of the evolution of parasitemia by Plasmodium falciparum (malaria) in a cohort of 105 young children in Cameroon is described and briefly analyzed. PMID:11318215

  6. 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.

  7. 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. PMID:25761965

  8. 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. PMID:17930206

  9. Effectiveness of splinting and splinting plus local steroid injection in severe carpal tunnel syndrome: A Randomized control clinical trial

    PubMed Central

    Khosrawi, Saeid; Emadi, Masoud; Mahmoodian, Amir Ebrahim

    2016-01-01

    Background: The Study aimed to compare the effectiveness of two commonly used conservative treatments, splinting and local steroid injection in improving clinical and nerve conduction findings of the patients with severe carpal tunnel syndrome (CTS). Materials and Methods: In this randomized control clinical trial, the patients with severe CTS selected and randomized in two interventional groups. Group A was prescribed to use full time neutral wrist splint and group B was injected with 40 mg Depo-Medrol and prescribed to use the full time neutral wrist splint for 12 weeks. Clinical and nerve conduction findings of the patients was evaluated at baseline, 4 and 12 weeks after interventions. Results: Twenty-two and 21 patients were allocated in group A and B, respectively. Mean of clinical symptoms and functional status scores, nerve conduction variables and patients’ satisfaction score were not significant between group at baseline and 4 and 12 weeks after intervention. Within the group comparison, there was significant improvement in the patients’ satisfaction, clinical and nerve conduction items between the baseline level and 4 weeks after intervention and between the baseline and 12 weeks after intervention (P < 0.01). The difference was significant for functional status score between 4 and 12 weeks after intervention in group B (P = 0.02). Conclusion: considering some findings regarding the superior effect of splinting plus local steroid injection on functional status scale and median nerve distal motor latency, it seems that using combination therapy could be more effective for long-term period specially in the field of functional improvement of CTS. PMID:26962518

  10. Prospective Randomized Comparison of the Effectiveness of Radiation Therapy and Local Steroid Injection for the Treatment of Plantar Fasciitis

    SciTech Connect

    Canyilmaz, Emine; Canyilmaz, Fatih; Aynaci, Ozlem; Colak, Fatma; Serdar, Lasif; Uslu, Gonca Hanedan; Aynaci, Osman; Yoney, Adnan

    2015-07-01

    Purpose: The purpose of this study was to conduct a randomized trial of radiation therapy for plantar fasciitis and to compare radiation therapy with local steroid injections. Methods and Materials: Between March 2013 and April 2014, 128 patients with plantar fasciitis were randomized to receive radiation therapy (total dose of 6.0 Gy applied in 6 fractions of 1.0 Gy three times a week) or local corticosteroid injections a 1 ml injection of 40 mg methylprednisolone and 0.5 ml 1% lidocaine under the guidance of palpation. The results were measured using a visual analog scale, a modified von Pannewitz scale, and a 5-level function score. The fundamental phase of the study was 3 months, with a follow-up period of up to 6 months. Results: The median follow-up period for all patients was 12.5 months (range, 6.5-18.6 months). For the radiation therapy patients, the median follow-up period was 13 months (range, 6.5-18.5 months), whereas in the palpation-guided (PG) steroid injection arm, it was 12.1 months (range, 6.5-18.6 months). After 3 months, results in the radiation therapy arm were significantly superior to those in the PG steroid injection arm (visual analog scale, P<.001; modified von Pannewitz scale, P<.001; 5-level function score, P<.001). Requirements for a second treatment did not significantly differ between the 2 groups, but the time interval for the second treatment was significantly shorter in the PG steroid injection group (P=.045). Conclusion: This study confirms the superior analgesic effect of radiation therapy compared to mean PG steroid injection on plantar fasciitis for at least 6 months after treatment.