Search

Atherosclerosis, a leading cause of cardiovascular disease, necessitates advanced and innovative modeling techniques to better understand and predict plaque dynamics. The present work presents two distinct hypothetical models inspired by different research fields: the logistic map from chaos theory and Markov models from stochastic processes. The logistic map effectively models the nonlinear progression and sudden changes in plaque stability, reflecting the chaotic nature of atherosclerotic events. In contrast, Markov models, including traditional Markov chains, spatial Markov models, and Markov random fields, provide a probabilistic framework to assess plaque stability and transitions. Spatial Markov models, visualized through heatmaps, highlight the spatial distribution of transition probabilities, emphasizing local interactions and dependencies. Markov random fields incorporate complex spatial interactions, inspired by advances in physics and computational biology, but present challenges in parameter estimation and computational complexity. While these hypothetical models offer promising insights, they require rigorous validation with real-world data to confirm their accuracy and applicability. This study underscores the importance of interdisciplinary approaches in developing theoretical models for atherosclerotic plaques. [ABSTRACT FROM AUTHOR]

We consider the clustering of extremes for stationary regularly varying random fields over arbitrary growing index sets. We study sufficient assumptions on the index set such that the limit of the point processes of the exceedances above a high threshold exists. Under the so-called anti-clustering condition, the extremal dependence is only local. Thus the index set can have a general form compared to previous literature (Basrak and Planinić in Bernoulli 27(2):1371–1408, 2021; Stehr and Rønn-Nielsen in Extremes 24(4):753–795, 2021). However, we cannot describe the clustering of extreme values in terms of the usual spectral tail measure (Wu and Samorodnitsky in Stochastic Process Appl 130(7):4470–4492, 2020) except for hyperrectangles or index sets in the lattice case. Using the recent extension of the spectral measure for star-shaped equipped space (Segers et al. in Extremes 20:539–566, 2017), the Υ -spectral tail measure provides a natural extension that describes the clustering effect in full generality. [ABSTRACT FROM AUTHOR]

We derive analytical formulations relating the spatial covariance (CY) of (log-transformed) hydraulic conductivities to auto- and cross-covariances of porosity (ϕ) and representative soil particle sizes within the framework of the classical Terzaghi model. The latter provides an empirical relationship which is widely used to obtain conductivity estimates. We frame the study within recent stochastic approaches and conceptualize appropriate transformations of ϕ and representative soil particle size as Generalized Sub-Gaussian (GSG) spatially cross-correlated random processes. Consistency of the theoretical framework against sample distributions of ϕ and particle size is assessed through the analysis of field data. A perturbation-based approach yields workable expressions of CY upon truncating the otherwise exact analytical solution at given orders of approximations. Our analytical (truncated) log-conductivity covariance is in agreement with its Monte Carlo-based counterpart. A Global Sensitivity Analysis relying on classical Sobol indices quantifies the relative importance of all parameters embedded in the formulation of CY. We show that parameters driving the GSG nature of the distribution of (transformed) porosity are key to the main features of CY. We also document the relevance of properly capturing emergences of possible cross-correlations between ϕ and representative particle size to reconstruct conductivity fields. [ABSTRACT FROM AUTHOR]

Consider a system of homogeneous interacting diffusive particles labeled by the nodes of a unimodular Galton–Watson tree, where the state of each node evolves infinitesimally like a d-dimensional diffusion whose drift coefficient depends on (the histories of) its own state and the states of neighboring nodes, and whose diffusion coefficient depends only on (the history of) its own state. Under suitable regularity assumptions on the coefficients, an autonomous characterization is obtained for the marginal distribution of the dynamics of the neighborhood of a typical node in terms of a certain local equation, which is a new kind of stochastic differential equation that is nonlinear in the sense of McKean. This equation describes a finite-dimensional non-Markovian stochastic process whose infinitesimal evolution at any time depends not only on the structure and current state of the neighborhood, but also on the conditional law of the current state given the past of the states of neighborhing nodes until that time. Such marginal distributions are of interest because they arise as weak limits of both marginal distributions and empirical measures of interacting diffusions on many sequences of sparse random graphs, including the configuration model and Erdös–Rényi graphs whose average degrees converge to a finite non-zero limit. The results obtained complement classical results in the mean-field regime, which characterize the limiting dynamics of homogeneous interacting diffusions on complete graphs, as the number of nodes goes to infinity, in terms of a corresponding nonlinear Markov process. However, in the sparse graph setting, the topology of the graph strongly influences the dynamics, and the analysis requires a completely different approach. The proofs of existence and uniqueness of the local equation rely on delicate new conditional independence and symmetry properties of particle trajectories on unimodular Galton–Watson trees, as well as judicious use of changes of measure. [ABSTRACT FROM AUTHOR]

The author considers a practical algorithm for estimating an unknown parameter of the mathematical model of a Markov process with local interaction based on the Gibbs distribution. It is proposed to apply the stochastic quasi-gradient method to the maximum likelihood function, which is constructed from the observations of the realizations of the Gibbs field. The obtained results have a wide application scope in the modeling of stochastic processes. [ABSTRACT FROM AUTHOR]

The author considers a practical algorithm for estimating an unknown parameter of the mathematical model of a Markov process with local interaction based on the Gibbs distribution. It is proposed to apply the stochastic quasi-gradient method to the maximum likelihood function, which is constructed from the observations of the realizations of the Gibbs field. The obtained results have a wide application scope in the modeling of stochastic processes. [ABSTRACT FROM AUTHOR]

We present a novel approach named Physics-based Residual Kriging for the statistical prediction of spatially dependent functional data. It incorporates a physical model—expressed by a partial differential equation—within a Universal Kriging setting through a geostatistical modelization of the residuals with respect to the physical model. The approach is extended to deal with sequential problems, where samples of functional data become available along consecutive time intervals, in a context where the physical and stochastic processes generating them evolve, as time intervals succeed one another. An incremental modeling is used to account for both these dynamics and the misfit between previous predictions and actual observations. We apply Physics-based Residual Kriging to forecast production rates of wells operating in a mature reservoir according to a given drilling schedule. We evaluate the predictive errors of the method in two different case studies. The first deals with a single-phase reservoir where production is supported by fluid injection, while the second considers again a single-phase reservoir but the production is driven by rock compaction. [ABSTRACT FROM AUTHOR]

Herein, an image‐processing‐based random field modeling of microstructure in an actual specimen of a unidirectional fiber‐reinforced composite material and multiscale stochastic stress analysis with considering a random fiber arrangement having the random field identified from an actual specimen is described. Multiscale stochastic stress analysis will be effective for evaluation of uncertainty propagation through the different scales in heterogeneous materials. It will be important when a microscopic randomness has a significant influence on apparent material properties. Some mechanical properties of heterogeneous materials take an influence of the microscopic randomness, and such multiscale stochastic analysis has been attracted. In this article, a random field modeling technique for a digital image of microstructure of a unidirectional fiber‐reinforced plastic (FRP) is presented, and the multiscale stochastic stress analysis with considering a random fiber arrangement in FRP based on the random field model identified by the presented method is attempted. For this purpose, a method for generating a set of realizations according to the identified random field is also developed. From the results, effectiveness of the presented approach is discussed. [ABSTRACT FROM AUTHOR]

This article addresses the problem of suitably defining statistical models of languages derived from context-free grammars (CFGs), where the observed strings may be corrupted by noise or other mechanisms. This article uses the concept of a stochastic syntactic process (SSP), which we have introduced in previous work. An SSP is a stochastic process taking values in the set of all parse trees of a CFG. Inference problems such as estimating a parse tree for “noisy” processes are of obvious significance, particularly in the motivating example of metalevel target tracking. This article demonstrates that by careful application of the theory of probability, an SSP can be embedded into a Markov random field (MRF), thus opening up the possibility of the application of advanced machine learning algorithms based on graphical models to inference problems involving sophisticated target behavior at the “meta” level. This article provides a simple example of how a simple CFG can be embedded in an MRF. Extensions to context-sensitive grammars are discussed. [ABSTRACT FROM AUTHOR]

Large deviations for additive path functionals of stochastic processes have attracted significant research interest, in particular in the context of stochastic particle systems and statistical physics. Efficient numerical 'cloning' algorithms have been developed to estimate the scaled cumulant generating function, based on importance sampling via cloning of rare event trajectories. So far, attempts to study the convergence properties of these algorithms in continuous time have led to only partial results for particular cases. Adapting previous results from the literature of particle filters and sequential Monte Carlo methods, we establish a first comprehensive and fully rigorous approach to bound systematic and random errors of cloning algorithms in continuous time. To this end we develop a method to compare different algorithms for particular classes of observables, based on the martingale characterization of stochastic processes. Our results apply to a large class of jump processes on compact state space, and do not involve any time discretization in contrast to previous approaches. This provides a robust and rigorous framework that can also be used to evaluate and improve the efficiency of algorithms. [ABSTRACT FROM AUTHOR]

The geometrical modeling of granular objects is a complex challenge that exists in many scientific fields, such as the modeling of granular materials or rocks and coarse aggregates with applications in civil, mechanical, and chemical engineering. In this paper, a model called SPHERE (Stochastic Process for Highly Effective Radial Expansion) is proposed, which is based on the deformation of an ellipsoid mesh using multiple 3D Gaussian random fields. The model is designed to be flexible (full control over 2D and 3D morphological properties of granular objects), ultra-fast (over 1000 aggregates in less than 5 s), and independent of the mesh and base shape used (as long as it is a star-shaped object). The flexibility of the model and its ability to reflect real data is illustrated using images of latex nanoparticle aggregates. Using 2D measurements on images from a morphogranulometer, a method based on the SPHERE model is proposed to estimate the 3D morphological properties of aggregates. A multiscale optimization process is applied, in particular using a partial reconstruction of 2D shapes from elliptic Fourier descriptors, in order to best reproduce the shape, angularity and texture of the aggregates using the SPHERE model. Validation of the method on 3D printed data shows relative errors of less than 3% for all measured 2D and 3D morphological characteristics, and validation on a population of synthetic objects shows relative errors of less than 6%. The results are compared and discussed with those obtained using other models based on overlapping spheres and show consistency with previous work. Finally, suggestions for improvement are given. [Display omitted] • Proposed SPHERE model uses 3D random fields to deform a mesh. • Model generates >1000 aggregates in <5 s with full morphological flexibility. • 3D printed object and numerical validation using multiscale optimization. • SPHERE can estimate 3D morphological properties from 2D image measurements. • SPHERE's adaptability showcases potential for diverse scientific applications. [ABSTRACT FROM AUTHOR]

Inference of fields defined in space and time from observational data is a core discipline in many scientific areas. This work approaches the problem in a Bayesian framework. The proposed method is based on statistically homogeneous random fields defined in space and time and demonstrates how to reconstruct the field together with its prior correlation structure from data. The prior model of the correlation structure is described in a non‐parametric fashion and solely builds on fundamental physical assumptions such as space‐time homogeneity, locality, and causality. These assumptions are sufficient to successfully infer the field and its prior correlation structure from noisy and incomplete data of a single realization of the process as demonstrated via multiple numerical examples. [ABSTRACT FROM AUTHOR]

In this article, we propose an efficient heterogeneous change detection algorithm based on stochastic distance measure between two $\mathcal {G}_{d}^{0}$ distributions. Due to its flexibility and simplicity, the matrix-variate $\mathcal {G}_{d}^{0}$ distribution has been successfully used to model the multilook polarimetric synthetic aperture radar (PolSAR) data and has been tested for classification, segmentation, and image analysis. Concretely, closed-form expressions for the Kullback–Leibler, Renyi of order $\beta $ , Bhattacharyya, and Hellinger distances are provided to compute the stochastic distance between $\mathcal {G}_{d}^{0}$ distributions. In this context, we resort to the expectation–maximization (EM) to estimate accurately with low complexity for the parameters of the probability distribution of the two multilook polarimetric covariance matrices to be compared. Finally, the performance of the method is compared firstly to the performance of other known distributions, such as the scaled complex Wishart distribution, and secondly to other known statistical tests using simulated and real multilook PolSAR data. [ABSTRACT FROM AUTHOR]

This work presents a Bayesian statistical approach to the multimodal change detection (CD) problem in remote sensing imagery. More precisely, we formulate the multimodal CD problem in the unsupervised Markovian framework. The main novelty of the proposed Markovian model lies in the use of an observation field built up from a pixel pairwise modeling and on the bitemporal heterogeneous satellite image pair. Such modeling allows us to rely instead on a robust visual cue, with the appealing property of being quasi-invariant to the imaging (multi-) modality. To use this observation cue as part of a stochastic likelihood model, we first rely on a preliminary iterative estimation technique that takes into account the variety of the laws in the distribution mixture and estimates the parameters of the Markovian mixture model. Once this estimation step is completed, the Maximum a posteriori (MAP) solution of the change detection map, based on the previously estimated parameters, is then computed with a stochastic optimization process. Experimental results and comparisons involving a mixture of different types of imaging modalities confirm the robustness of the proposed approach. [ABSTRACT FROM AUTHOR]

Multistage stochastic optimization is used to solve many real-life problems where decisions are taken at multiple times. Such problems need the representation of stochastic processes, which are usually approximated by scenario trees. In this article, we implement seven scenario reduction algorithms: three based on random extraction, named Random, and four based on specific distance measures, named Distance-based. Three of the latter are well known in literature while the fourth is a new approach, namely nodal clustering. We compare all the algorithms in terms of computational cost and information cost. The computational cost is measured by the time needed for the reduction, while the information cost is measured by the nested distance between the original and the reduced tree. Moreover, we also formulate and solve a multistage stochastic portfolio selection problem to measure the distance between the optimal solutions and between the optimal objective values of the original and the reduced tree. [ABSTRACT FROM AUTHOR]

This work considers the challenging problem of identifying the statistical properties of random fields from indirect observations. To this end, a Bayesian approach is introduced, whose key step is the nonparametric approximation of the likelihood function from limited information. When the likelihood function is based on the evaluation of an expensive computer code, this work also proposes a method to select iteratively new design points to reduce the uncertainties on the results that are due to the approximation of the likelihood. Two applications are finally presented to illustrate the efficiency of the proposed procedure: a first one based on analytic data, and a second one dealing with the identification of the random elasticity field of an heterogeneous microstructure. [ABSTRACT FROM AUTHOR]

The inverse problem associated with microscopic image reconstruction has attracted much attention and initiated a lot of interest in microscopic image processing. The inverse problem of image reconstruction from noisy and incomplete data is still one of the key factors for realizing the full potential of optical microscopy. We propose to address the inverse problem using Markov random field in the Bayesian domain. This approach has the potential advantage of incorporation of prior knowledge in the reconstruction process through the prior function, thus making the problem well-posed and computationally efficient for three-dimensional (3D) image reconstruction. Image reconstruction on 3D phantom and microscopic specimens shows comparatively noise-free and better-resolved images. The edges and minute features such as islets are well reconstructed. We believe that the proposed image reconstruction methodology will find applications in microscopy and imaging. [ABSTRACT FROM AUTHOR]

Random fields are commonly used for modeling of spatially (or timely) dependent stochastic processes. In this study, we provide a characterization of the intrinsic complexity of a random field in terms of its second order statistics, e.g., the covariance function, based on the Karhumen--Loéve expansion. We then show scaling laws for the intrinsic complexity of a random field in terms of the correlation length as it goes to 0. In the discrete setting, the analogy is approximation of a set of random vectors based on principal component analysis. We provide a precise scaling law when the random vectors have independent and identically distributed entries using random matrix theory as well as when the random vectors have a specific covariance structure. [ABSTRACT FROM AUTHOR]

The paper introduces a dynamic extension of the hybrid random field (HRF), called dynamic HRF (D-HRF). The D-HRF is aimed at the probabilistic graphical modeling of arbitrary-length sequences of sets of (time-dependent) discrete random variables under Markov assumptions. Suitable maximum likelihood algorithms for learning the parameters and the structure of the D-HRF are presented. The D-HRF inherits the computational efficiency and the modeling capabilities of HRFs, subsuming both dynamic Bayesian networks and Markov random fields. The behavior of the D-HRF is first evaluated empirically on synthetic data drawn from probabilistic distributions having known form. Then, D-HRFs (combined with a recurrent autoencoder) are successfully applied to the prediction of the disulfide-bonding state of cysteines from the primary structure of proteins in the Protein Data Bank. [ABSTRACT FROM AUTHOR]

Summary: Embankment slopes composed of spatially variable soils have a variety of different failure modes that are affected by the correlation distances of the material properties and the geometry and total length of the slope. This paper examines the reliability of soil slopes for embankments of different length and uses parallel computing to analyse very long embankments (up to 100 times the embankment height) for a clay soil characterised by a spatially varying undrained shear strength. Based on a series of analyses using the 3D random finite element method (RFEM), it is first shown that the reliability of slopes of various length can be efficiently computed by combining simple probability theory with a detailed 3D RFEM analysis of a representative shorter slope of length 10 times the slope height. RFEM predictions of reliability indices for longer slopes are then compared with results obtained using Vanmarcke's (1977a) simplified 3D method and Calle's (1985) extended 2D approach. It is shown that these methods can give significantly different results, depending on the horizontal scale of fluctuation relative to the slope length, with RFEM predicting a lower slope reliability than the Vanmarcke and Calle solutions in all cases. The differences in the solutions are evaluated and attributed to differences in the assumed and computed failure surface geometries. [ABSTRACT FROM AUTHOR]

Secondly, the positioning of the exogenous processes HT ht in equation (1) seems to me counter-intuitive. [Extracted from the article]

In continuation of the previous work, we now introduced a new algorithm for text embedding based on scan pattern with XOR and texture synthesis. In this work we have considered natural images and the scan pattern and XOR function in three standalone steps have been used to embed text into patching regions from a sample natural image/video transformed and copied to the output and then stitched together along optimal seams to generate a new output. The size of the patch is not chosen before, but instead a graph cut technique is used to determine the optimal patch region for any given offset between the input and the output texture. The graph cut technique for seam optimization is applicable in two and three dimensions. This graph cut technique of patching into original picture is very much applicable in image processing. We present a new idea to embed text into patching seam using scan pattern with XOR and then placed in the original image. Although this technique is expensive in terms of image area usage but it is a new idea for text embedding and has to be optimized in the sense of original picture usages. We show results for regular, random and the natural images. We also demonstrate how this method can be used interactively. [ABSTRACT FROM AUTHOR]

Traditional relational topic models provide a successful way to discover the hidden topics from a document network. Many theoretical and practical tasks, such as dimensional reduction, document clustering, and link prediction, could benefit from this revealed knowledge. However, existing relational topic models are based on an assumption that the number of hidden topics is known a priori, which is impractical in many real-world applications. Therefore, in order to relax this assumption, we propose a nonparametric relational topic model using stochastic processes instead of fixed-dimensional probability distributions in this paper. Specifically, each document is assigned a Gamma process, which represents the topic interest of this document. Although this method provides an elegant solution, it brings additional challenges when mathematically modeling the inherent network structure of typical document network, i.e., two spatially closer documents tend to have more similar topics. Furthermore, we require that the topics are shared by all the documents. In order to resolve these challenges, we use a subsampling strategy to assign each document a different Gamma process from the global Gamma process, and the subsampling probabilities of documents are assigned with a Markov Random Field constraint that inherits the document network structure. Through the designed posterior inference algorithm, we can discover the hidden topics and its number simultaneously. Experimental results on both synthetic and real-world network datasets demonstrate the capabilities of learning the hidden topics and, more importantly, the number of topics. [ABSTRACT FROM PUBLISHER]

Recently, research on and applications of human fixation detection in video compressed domain have gained increasing attention. However, prediction accuracy and computational complexity still remain a challenge. This paper addresses the problem of compressed domain fixations detection in the videos based on residual discrete cosine transform coefficients norm (RDCN) and Markov random field (MRF). RDCN feature is directly extracted from the compressed video with partial decoding and is normalized. After spatial-temporal filtering, the normalized map [Smoothed RDCN (SRDCN) map] is taken to the MRF model, and the optimal binary label map is obtained. Based on the label map and the center saliency map, saliency enhancement and nonsaliency inhibition are done for the SRDCN map, and the final SRDCN-MRF salient map is obtained. Compared with the similar models, we enhance the available energy functions and introduce an energy function that indicates the positional information of the saliency. The procedure is advantageous for improving prediction accuracy and reducing computational complexity. The validation and comparison are made by several accuracy metrics on two ground truth datasets. Experimental results show that the proposed saliency detection model achieves superior performances over several state-of-the-art compressed-domain and pixel-domain algorithms on evaluation metrics. Computationally, our algorithm reduces 26% more computational complexity with comparison to Similar algorithms. [ABSTRACT FROM AUTHOR]

The Karhunen–Loève expansion and the Fredholm determinant formula are used to derive an asymptotic Rosenblatt-type distribution of a sequence of integrals of quadratic functions of Gaussian stationary random fields ondisplaying long-range dependence. This distribution reduces to the usual Rosenblatt distribution whend= 1. Several properties of this new distribution are obtained. Specifically, its series representation, in terms of independent chi-squared random variables, is established. Its Lévy–Khintchine representation, and membership to the Thorin subclass of self-decomposable distributions are obtained as well. The existence and boundedness of its probability density then follow as a direct consequence. [ABSTRACT FROM PUBLISHER]

Our knowledge of the spatio-temporal variation of river hydrological parameters is surprisingly poor. In situ gauge stations are limited in spatial and temporal coverage, and their number has been decreasing during the past decades. On the other hand, remote sensing techniques have proven their ability to measure different parameters within the Earth system. Satellite imagery, for instance, can provide variations in river area with appropriate temporal sampling. In this study, we develop an automatic algorithm for water body area monitoring based on maximum a posteriori estimation of Markov random fields. The algorithm considers pixel intensity, spatial correlation between neighboring pixels, and temporal behavior of the water body to extract accurate water masks. We solve this optimization problem using the graph cuts technique. We also measure the uncertainty associated with the determined water masks. Our method is applied over three different river reaches of Niger and Congo rivers with different hydrological characteristics. We validate the obtained river area time series by comparing with in situ river discharge and satellite altimetric water level time series. Along the Niger River, we obtain correlation coefficients of 0.85-0.96 for river reaches and 0.65 for the Congo River, which is demonstrably an improvement over other river mask retrieval algorithms. [ABSTRACT FROM AUTHOR]

Since late '80 s Avian metapneumovirus subtype A causes sufficient disease in Europe for commercial companies to have started developing live attenuated vaccines. Here, two of those vaccines were fully consensus sequenced alongside their progenitor field strain (#8544). Sequences comparison shows that the attenuation of field strain #8544 was associated with no common substitutions between the two derived vaccines. This finding suggests that the attenuation of field viruses via serial passage on cell cultures or tissues is the result of a random process, rather than a mechanism aiming to achieve a specific sequence. Furthermore, field vaccination strategies would greatly benefit by the unambiguous vaccine markers identified in this study, enabling a prompt and confident vaccines detection. [ABSTRACT FROM AUTHOR]

• An unsupervised and graph-based image segmentation method is proposed. • It is equipped with a goal-oriented component, favoring subsequent analysis. • It is driven by the intrinsic properties of the data and by the goal to be achieved. • Real applications are examined in the biomedical and remote sensing framework. • Experiments within different domains highlight the method's robustness and adaptation capability. Image segmentation is the process of partitioning a digital image into a set of homogeneous regions (according to some homogeneity criterion) to facilitate a subsequent higher-level analysis. In this context, the present paper proposes an unsupervised and graph-based method of image segmentation, which is driven by an application goal, namely, the generation of image segments associated with a user-defined and application-specific goal. A graph, together with a random grid of source elements, is defined on top of the input image. From each source satisfying a goal-driven predicate, called seed, a propagation algorithm assigns a cost to each pixel on the basis of similarity and topological connectivity, measuring the degree of association with the reference seed. Then, the set of most significant regions is automatically extracted and used to estimate a statistical model for each region. Finally, the segmentation problem is expressed in a Bayesian framework in terms of probabilistic Markov random field (MRF) graphical modeling. An ad hoc energy function is defined based on parametric models, a seed-specific spatial feature, a background-specific potential, and local-contextual information. This energy function is minimized through graph cuts and, more specifically, the alpha-beta swap algorithm, yielding the final goal-driven segmentation based on the maximum a posteriori (MAP) decision rule. The proposed method does not require deep a priori knowledge (e.g., labelled datasets), as it only requires the choice of a goal-driven predicate and a suited parametric model for the data. In the experimental validation with both magnetic resonance (MR) and synthetic aperture radar (SAR) images, the method demonstrates robustness, versatility, and applicability to different domains, thus allowing for further analyses guided by the generated products. [ABSTRACT FROM AUTHOR]

[Display omitted] • A geospatial-temporal solution is developed for predicting failure of buried pipeline. • Spatial dependence and temporal variability of corrosion growth is considered. • An algorithm is developed and demonstrated using a real complex pipe network. Corrosion is a severe threat to the integrity of buried metal pipes due to the interaction of pipe materials with the surrounding soils. A review of the published literature shows that there are serious challenges for engineers to accurately predict failures in the buried pipeline system. In this paper, a network-based geospatial-temporal solution is developed to predict the risk of pipe failures, considering the spatial dependence and temporal variability of corrosion growth. An algorithm is developed integrating theories of reliability, corrosion science, random field, stochastic process, and copula within the framework of Monte Carlo simulation. The application of the developed algorithm is demonstrated using a real complex gas pipeline network. Also, the effect of discrete intervals, temporal variability and corrosion exposure area on probability of pipe failure is investigated. It is found that the failure probability of pipe segments varies spatially and the location of pipe segment with the largest probability of failure varies with time. It is also found that the largest probability of failure of pipe network is less sensitive to the discrete intervals although a fine discretization of the random field will increase the accuracy of simulation. It can be concluded that the proposed method can predict and visualize the location, time and magnitude of risk of a complex pipe network with reasonable accuracy. [ABSTRACT FROM AUTHOR]

This study develops a mesoscale fracture modelling method combining the phase-field regularized cohesive zone model (PF-CZM) and random aggregate models for simulating complicated 3D meso-scale damage and fracture in concrete-like quasi-brittle materials. In this method, the aggregates in the mortar are built using a random generating and packing algorithm, and their surrounding mortar-aggregate interfaces are obtained from an aggregate scaling algorithm. The PF-CZM with cohesive softening laws and an intrinsic length scale is used to model multi-crack initiation and propagation in the mortar and interfaces without remeshing. The method was first validated by a concrete cube under uniaxial tension, with the effects of the mesh size, the length scale, the tensile strength, and the fracture energy investigated in detail. Three concrete beam examples, one under mode-I fracture and two under mixed-mode fracture, were then modelled for further validation and demonstration for practical uses. It is found that the method can effectively simulate 3D stochastic fracture processes and accurately calculate load-carrying capacities with little mesh-dependence. [ABSTRACT FROM AUTHOR]

We study the number of nodal domains of toral Laplace eigenfunctions. Following Nazarov-Sodin's results for random fields and Bourgain's de-randomisation procedure we establish a precise asymptotic result for 'generic' eigenfunctions. Our main results in particular imply an optimal lower bound for the number of nodal domains of generic toral eigenfunctions. [ABSTRACT FROM AUTHOR]

In the recent years, there has been a growing interest in proposing covariance models for multivariate Gaussian random fields. Some of these covariance models are very flexible and can capture both the marginal and the cross-spatial dependence of the components of the associated multivariate Gaussian random field. However, effective estimation methods for these models are somehow unexplored. Maximum likelihood is certainly a useful tool, but it is impractical in all the circumstances where the number of observations is very large. In this work, we consider two possible approaches based on composite likelihood for multivariate covariance model estimation. We illustrate, through simulation experiments, that our methods offer a good balance between statistical efficiency and computational complexity. Asymptotic properties of the proposed estimators are assessed under increasing domain asymptotics. Finally, we apply the method for the analysis of a bivariate dataset on chlorophyll concentration and sea surface temperature in the Chilean coast. [ABSTRACT FROM AUTHOR]

Structural characteristics of random field threshold exceedance sets (e.g., size, connectivity, and boundary regularity) are used in practice for definition of different indicators in spatial and spatio-temporal risk analysis. In this work, point process techniques are applied to study the structural changes derived from random field deformations and blurring transformations, meaningful from both physical and methodological points of view in a variety of contexts. Specifically, based on simulations from a flexible random field model class, features such as aggregation/inhibition of patterns defined by centroids of connected components, as well as by boundary A-exit points, are investigated in relation to the local contraction/dilation effects of deformation and the smoothing properties of blurring. Supplementary materials accompanying this paper appear online. [ABSTRACT FROM AUTHOR]

Max-stable processes are natural models for spatial extremes because they provide suitable asymptotic approximations to the distribution of maxima of random fields. In the recent past, several parametric families of stationary max-stable models have been developed, and fitted to various types of data. However, a recurrent problem is the modeling of non-stationarity. In this paper, we develop non-stationary max-stable dependence structures in which covariates can be easily incorporated. Inference is performed using pairwise likelihoods, and its performance is assessed by an extensive simulation study based on a non-stationary locally isotropic extremal t model. Evidence that unknown parameters are well estimated is provided, and estimation of spatial return level curves is discussed. The methodology is demonstrated with temperature maxima recorded over a complex topography. Models are shown to satisfactorily capture extremal dependence. [ABSTRACT FROM AUTHOR]

We consider the isotropic XY quantum spin chain in a random external field in the z direction, with single site distributions given by i.i.d. random variables times the critical decaying envelope $$j^{-1/2}$$ . Our motivation is the study of many-body localization. We investigate transport properties in terms of polynomial Lieb-Robinson (PLR) bounds. We prove a zero-velocity PLR bound for large disorder strength $$\lambda $$ and for small $$\lambda $$ we show a partial converse, which suggests the existence of a transition to non-trivial transport in the model. [ABSTRACT FROM AUTHOR]

This paper proposes a learning algorithm for the random field models whose energy functions are in the form of linear combinations of rectified filter responses from subsets of wavelets selected from a given over-complete dictionary. The algorithm consists of the following two components. (1) We propose to induce the wavelets into the random field model by a generative version of the epsilon-boosting algorithm. (2) We propose to generate the synthesized images from the random field model using Gibbs sampling on the coefficients (or responses) of the selected wavelets. We show that the proposed learning and sampling algorithms are capable of generating realistic image patterns. We also evaluate our learning method on a dataset of clustering tasks to demonstrate that the models can be learned in an unsupervised setting. The learned models encode the patterns in wavelet sparse coding. Moreover, they can be mapped to the second-layer nodes of a sparsely connected convolutional neural network (CNN). [ABSTRACT FROM AUTHOR]

The analysis of space-time data from complex, real-life phenomena requires the use of flexible and physically motivated covariance functions. In most cases, it is not possible to explicitly solve the equations of motion for the fields or the respective covariance functions. In the statistical literature, covariance functions are often based on mathematical constructions. In this paper, we propose deriving space-time covariance functions by solving 'effective equations of motion', which can be used as statistical representations of systems with diffusive behavior. In particular, we propose to formulate space-time covariance functions based on an equilibrium effective Hamiltonian using the linear response theory. The effective space-time dynamics is then generated by a stochastic perturbation around the equilibrium point of the classical field Hamiltonian leading to an associated Langevin equation. We employ a Hamiltonian which extends the classical Gaussian field theory by including a curvature term and leads to a diffusive Langevin equation. Finally, we derive new forms of space-time covariance functions. [ABSTRACT FROM AUTHOR]

In this paper, we propose an optimized higher order conditional random field (CRF) labeling approach toward automated video object segmentation. Our approach introduces a computerized optimization scheme to fine tune the CRF-associated parameters, and hence make the labeling of segmented regions optimal in formulating the video objects. In comparison with the existing efforts using CRF, our optimized CRF has introduced a number of novel features, which can be highlighted as: 1) higher order CRF labeling is made adaptive to video content changes via a windowed dynamics; 2) fusion of multiple features is automatically optimized via fuzzy modeling of incoming video content and regression of parameters; 3) unary potential of higher order CRF labeling is modulated by the shortest path between neighboring regions to improve the effectiveness of higher order CRF labeling; and 4) making the algorithm affordable for a simpler graph-based video segmentation to reduce the overall computing cost, making the proposed algorithm more efficient without compromising on its performances. [ABSTRACT FROM AUTHOR]

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

In this article, we propose a moving objects detection scheme using Gibbs-Markov random field(GMRF) and Hopfield-type neural network (HTNN) in expectation maximization (EM) framework for video sequences captured by static camera. In the considered technique, the background model is built by considering a running Gaussian average over few past frames. The change vector analysis (CVA) scheme is followed on the considered target frame and the constructed reference frame to generate a difference image. The moving objects in target frame are detected by segmenting the difference image into two classes: changed and unchanged, where the changed class represents moving object regions and the unchanged class the background regions. For segmentation, we have modeled the CVA generated difference image with GMRF and the segmentation problem is solved using the maximum a posteriori probability (MAP) estimation principle. The MAP estimator is found to be exponential in nature; and thus a modified HTNN is exploited for estimating the MAP. The parameters of the GMRF model are estimated using EM algorithm. Experiments are carried out on three video sequences. Results of the proposed change detection scheme are compared with those of the codebook-based background subtraction and GMRF model with graph-cut schemes. It is found that the proposed technique provides better results. [ABSTRACT FROM AUTHOR]

This paper describes the use of a clustering approach based on hidden Markov random field to extract potential homogeneous segments from a large length right-of-way of a pipeline structure with heterogeneous soil properties. This approach extends the conventional finite mixture model so that the spatial correlation of external corrosion sites can be taken into consideration. An algorithm is established for classifying corrosion defects using soil properties from an in-situ survey and location information from in-line inspection reports. The categorized corrosion defects reveal the hidden patterns of corrosion degradation in different segments along a pipeline structure. Stochastic simulation is employed to test this clustering approach. An example involving a 110-km pipeline interval is employed to illustrate the implementation of the clustering approach. The results indicate that the process of external corrosion propagation in a buried pipeline is position-dependent and is highly related to the soil environment. In addition, the results show that this phenomenon can be interpreted by segmentation using the proposed clustering method. A clustering-based inspection strategy is discussed as a way to apply the present approach. [ABSTRACT FROM AUTHOR]

This paper studies the problem of detecting unknown objects within indoor environments in an active and natural manner. The visual saliency scheme utilizing both color and depth cues is proposed to arouse the interests of the machine system for detecting unknown objects at salient positions in a 3D scene. The 3D points at the salient positions are selected as seed points for generating object hypotheses using the 3D shape. We perform multi-class labeling on a Markov random field (MRF) over the voxels of the 3D scene, combining cues from object hypotheses and 3D shape. The results from MRF are further refined by merging the labeled objects, which are spatially connected and have high correlation between color histograms. Quantitative and qualitative evaluations on two benchmark RGB-D datasets illustrate the advantages of the proposed method. The experiments of object detection and manipulation performed on a mobile manipulator validate its effectiveness and practicability in robotic applications. [ABSTRACT FROM AUTHOR]

The conditional random field (CRF) model is suitable for the image segmentation because this model relaxes the assumption of conditional independence of the observed data and models the data-dependent label interaction in the image modeling. However, this model has a limited ability to capture the global and local image information from the perspective of multiresolution analysis. Moreover, for synthetic aperture radar (SAR) image segmentation, SAR scattering statistics that are essential to SAR image processing are not considered in the CRF model. In this paper, we propose a hierarchical CRF (HIECRF) model for SAR image segmentation. The HIECRF model belongs to the discriminative models according to the semantic structure. While inheriting the advantages of the CRF model, the HIECRF model achieves the integration of the image features and SAR scattering statistics and captures the contextual structure information in the spatial and scale spaces. Moreover, we derive a hierarchical inference algorithm for the HIECRF model in virtue of the mean-field approximation (MFA) to provide the maximization of the posterior marginal (MPM) estimate of the HIECRF model. Then, by the bottom-up and the top-down recursions in the hierarchical inference procedure, the HIECRF model effectively exploits the global and local image information, including the contextual structures, the image features, and the scattering statistics, to achieve the MPM segmentation. The effectiveness of the HIECRF model is demonstrated by the application to the semisupervised segmentation of the simulated images and the real SAR images. [ABSTRACT FROM PUBLISHER]

For improving the accuracy of stereo matching and maintaining discontinuity of object edge and continuity of non-edge area in the matching result, a stereo matching method based on guided filter and mean shift is proposed in this paper. Matching cost function based on Markov random field (MRF) and guided filter are established, and the initial disparity value of each pixel is calculated by minimizing the corresponding matching cost function. Mean shift algorithm is used to segment the stereo images into independent areas, and improve the final disparity map. Results of the proposed method are tested on the international standard Middlebury stereo benchmark and compared with other methods. Comparative results show high accuracy of the proposed algorithm and its superiority to some prevailing algorithms. [ABSTRACT FROM AUTHOR]

Age at first marriage, after controlling for socio-economic and demographic variables, varies across regions and districts. A geo-additive hazard model allows for measuring spatial effects. The nonlinear and baseline effects are modeled by Bayesian penalized splines; spatial components are treated as correlated random effects following a Markov random field. Application is based on data from 1999, 2003, and 2008 Nigeria Demographic and Health Surveys. Age at first marriage is positively associated with education and urbanization and depends on religion. It presents a north-south divide. [ABSTRACT FROM AUTHOR]