Related papers: Localization properties of the sparse Barrat-M\'ez…
Recently, it has been observed that when representations are learnt in a way that encourages sparsity, improved performance is obtained on classification tasks. These methods involve combinations of activation functions, sampling steps and…
The convolutional sparse model has recently gained increasing attention in the signal and image processing communities, and several methods have been proposed for solving the pursuit problem emerging from it -- in particular its convex…
This paper addresses the problem of bearing-based network localization, which aims to localize all the nodes in a static network given the locations of a subset of nodes termed anchors and inter-node bearings measured in a common reference…
We elaborate on a geometric characterization of the electromagnetic properties of matter. A fundamental complex quantity, z_{L}, is introduced to study the localization properties of extended quantum systems. z_L, which allows us to…
In the presence of quasiperiodic potentials, the celebrated Kitaev chain presents an intriguing phase diagram with ergodic, localized and and multifractal states. In this work, we generalize these results by studying the localization…
We elucidate the different mechanisms of wave localisation in disordered finite systems of subwavelength resonators, where the disorder is in the spatial arrangement of the resonators. To do so, we employ the capacitance matrix formalism…
The prevalence of sparsity in interacting many-body systems motivates an investigation into the spectral statistics of sparse random matrices with on-site disorder. We numerically demonstrate that the Anderson transition can be identified…
Dynamic processes of interacting units on a network are out of equilibrium in general. In the case of a directed tree, the dynamic cavity method provides an efficient tool that characterises the dynamic trajectory of the process for the…
In this work, we consider multitask learning problems where clusters of nodes are interested in estimating their own parameter vector. Cooperation among clusters is beneficial when the optimal models of adjacent clusters have a good number…
Results of large-scale numerical simulations are reported on the Anderson localization in a two-dimensional square lattice tight-binding model with random flux. Localization lengths, fluctuations of the conductance, and the density of…
The spectral properties of the adjacency matrix, in particular its largest eigenvalue and the associated principal eigenvector, dominate many structural and dynamical properties of complex networks. Here we focus on the localization…
This article proposes diffusion LMS strategies for distributed estimation over adaptive networks that are able to exploit sparsity in the underlying system model. The approach relies on convex regularization, common in compressive sensing,…
ATMs enable the public to perform financial transactions. Banks try to strategically position their ATMs in order to maximize transactions and revenue. In this paper, we introduce a model which provides a score to an ATM location, which…
We review the problem of how to compute the spectral density of sparse symmetric random matrices, i.e. weighted adjacency matrices of undirected graphs. Starting from the Edwards-Jones formula, we illustrate the milestones of this line of…
We construct a quasiperiodic lattice model in curved spacetime to explore the crossover concerning both condensed matter and curved spacetime physics. We study the related Anderson localization and find that the model has a clear boundary…
For Anderson tight-binding models in dimension $d$ with random on-site energies $\epsilon_{\vec r}$ and critical long-ranged hoppings decaying typically as $V^{typ}(r) \sim V/r^d$, we show that the strong multifractality regime…
Recent works have shown an interest in investigating the frequentist asymptotic properties of Bayesian procedures for high-dimensional linear models under sparsity constraints. However, there exists a gap in the literature regarding…
Rosenzweig-Porter (RP) model has garnered much attention in the last decade, as it is a simple analytically tractable model showing both ergodic--nonergodic extended and Anderson localization transitions. Thus, it is a good toy model to…
This paper introduces a novel approach to learning sparsity-promoting regularizers for solving linear inverse problems. We develop a bilevel optimization framework to select an optimal synthesis operator, denoted as $B$, which regularizes…
The complex eigenvalues of Markov generators govern oscillatory properties of relaxation, autocorrelation, and linear response. Here we show that these eigenvalues are localized by nonequilibrium cycles of the generator, thus revealing a…