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We consider the problem of statistical inference in a parametric finite Markov chain model and develop a robust estimator of the parameters defining the transition probabilities via minimization of a suitable (empirical) version of the…
Consider a sequence (indexed by n) of Markov chains Z^n in R^d characterized by transition kernels that approximately (in n) depend only on the rescaled state n^{-1} Z^n. Subject to a smoothness condition, such a family can be closely…
Materials with network-like microstructure, including polymers, are the backbone for many natural and human-made materials such as gels, biological tissues, metamaterials, and rubbers. Fracture processes in these networked materials are…
Crack detection, particularly from pavement images, presents a formidable challenge in the domain of computer vision due to several inherent complexities such as intensity inhomogeneity, intricate topologies, low contrast, and noisy…
Surface cracks are a very common indicator of potential structural faults. Their early detection and monitoring is an important factor in structural health monitoring. Left untreated, they can grow in size over time and require expensive…
The prediction of upcoming events in industrial processes has been a long-standing research goal since it enables optimization of manufacturing parameters, planning of equipment maintenance and more importantly prediction and eventually…
The Gene or DNA sequence in every cell does not control genetic properties on its own; Rather, this is done through translation of DNA into protein and subsequent formation of a certain 3D structure. The biological function of a protein is…
The phase field fracture method has emerged as a promising computational tool for modelling a variety of problems including, since recently, hydrogen embrittlement and stress corrosion cracking. In this work, we demonstrate the potential of…
This study introduces a novel approach for learning mixtures of Markov chains, a critical process applicable to various fields, including healthcare and the analysis of web users. Existing research has identified a clear divide in…
Crack-templated networks, metallic frameworks fabricated from crack patterns in sacrificial thin films, can exhibit high optical transmittance, high electric conductivity, and a host of other properties attractive for applications. Despite…
We present a novel algorithm to solve a non-linear system of equations, whose solution can be interpreted as a tight lower bound on the vector of expected hitting times of a Markov chain whose transition probabilities are only partially…
Realistic microscale domains are an essential step towards making modern multiscale simulations more applicable to computational materials engineering. For this purpose, 3D computed tomography scans can be very expensive or technically…
Computational procedures for the stationary probability distribution, the group inverse of the Markovian kernel and the mean first passage times of an irreducible Markov chain, are developed using perturbations. The derivation of these…
This paper studies the estimation of low-rank Markov chains from empirical trajectories. We propose a non-convex estimator based on rank-constrained likelihood maximization. Statistical upper bounds are provided for the Kullback-Leiber…
Detecting and segmenting cracks in infrastructure, such as roads and buildings, is crucial for safety and cost-effective maintenance. In spite of the potential of deep learning, there are challenges in achieving precise results and handling…
This paper is concerned with the estimation of time-varying networks for high-dimensional nonstationary time series. Two types of dynamic behaviors are considered: structural breaks (i.e., abrupt change points) and smooth changes. To…
Identification of cracks is essential to assess the structural integrity of concrete infrastructure. However, robust crack segmentation remains a challenging task for computer vision systems due to the diverse appearance of concrete…
Crack is one of the most common road distresses which may pose road safety hazards. Generally, crack detection is performed by either certified inspectors or structural engineers. This task is, however, time-consuming, subjective and…
Decision trees are commonly used predictive models due to their flexibility and interpretability. This paper is directed at quantifying the uncertainty of decision tree predictions by employing a Bayesian inference approach. This is…
This work presents a novel three-dimensional Crack Element Method (CEM) designed to model transient dynamic crack propagation in quasi-brittle materials efficiently. CEM introduces an advanced element-splitting algorithm that enables…