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As a confined thin sheet crumples, it spontaneously segments into flat facets delimited by a network of ridges. Despite the apparent disorder of this process, statistical properties of crumpled sheets exhibit striking reproducibility.…
Sparse sensor arrays have attracted considerable attention in various fields such as radar, array processing, ultrasound imaging and communications. In the context of correlation-based processing, such arrays enable to resolve more…
We study sparse recovery with structured random measurement matrices having independent, identically distributed, and uniformly bounded rows and with a nontrivial covariance structure. This class of matrices arises from random sampling of…
The failure probabilities or the strength distributions of heterogeneous 1D systems with continuous local strength distribution and local load sharing have been studied using a simple, exact, recursive method. The fracture behavior depends…
The variability of temporal (or spatial) fluctuations of any variable is represented in conventional statistical theory by the relative dispersion equal to the standard deviation divided by the mean . The Relative Dispersion decreases with…
We consider sparse digraphs generated by the configuration model with given in-degree and out-degree sequences. We establish that with high probability the cover time is linear up to a poly-logarithmic correction. For a large class of…
We present some new and explicit error bounds for the approximation of distributions. The approximation error is quantified by the maximal density ratio of the distribution $Q$ to be approximated and its proxy $P$. This non-symmetric…
We consider the problem of determining the optimal block (or subsample) size for a spatial subsampling method for spatial processes observed on regular grids. We derive expansions for the mean square error of the subsampling variance…
We study the plastic yielding of disordered media using the perfectly plastic random fuse model. The yield surfaces are shown to be different from those obtained minimizing the sum of the local yield thresholds, i.e. the so-called minimum…
We derive exact statistical properties of a class of recursive fragmentation processes. We show that introducing a fragmentation probability 0<p<1 leads to a purely algebraic size distribution in one dimension, P(x) ~ x^{-2p}. In d…
We create mechanically stable (MS) packings of bidisperse disks using an algorithm in which we successively grow or shrink soft repulsive disks followed by energy minimization until the overlaps are vanishingly small. We focus on small…
In this paper, we demonstrate the construction of generalized Rough Polyhamronic Splines (GRPS) within the Bayesian framework, in particular, for multiscale PDEs with rough coefficients. The optimal coarse basis can be derived automatically…
We consider the propagation of flexural waves across a nearly flat, thin membrane, whose stress-free state is curved. The stress-free configuration is specified by a quenched height field, whose Fourier components are drawn from a Gaussian…
The excess emission seen in spectral energy distributions (SEDs) is commonly used to infer the properties of the emitting circumstellar dust in protoplanetary and debris discs. Most notably, dust size distributions and details of the…
We study the subsampling of the avalanches in the fiber bundle model of fracture. In cases where only a part of the system is observed for the micro-failure events, the recorded avalanche statistics gets distorted compared to the actual…
Many real-world networks of interest are embedded in physical space. We present a new random graph model aiming to reflect the interplay between the geometries of the graph and of the underlying space. The model favors configurations with…
We propose a new wavelet-based method for density estimation when the data are size-biased. More specifically, we consider a power of the density of interest, where this power exceeds 1/2. Warped wavelet bases are employed, where warping is…
We investigate compressive failure of heterogeneous materials on the basis of a continuous progressive damage model. The model explicitely accounts for tensile and shear local damage and reproduces the main features of compressive failure…
We consider a graphene sheet in the vicinity of a substrate, which contains charged impurities. An analytic expression for the probability distribution function of voltage fluctuations due to the charged impurities is derived. The…
Rolling bearings are subject to various faults due to its long-time operation under harsh environment, which will lead to unexpected breakdown of machinery system and cause severe accidents. Deep learning methods recently have gained…