Related papers: Percolation under Noise: Detecting Explosive Perco…
We prove that the Poisson Boolean model, also known as the Gilbert disc model, is noise sensitive at criticality. This is the first such result for a Continuum Percolation model, and the first for which the critical probability p_c \ne 1/2.…
Understanding how network structure constrains and enables information processing is a central problem in the statistical mechanics of interacting systems. Here we study random networks across the structural percolation transition and…
High-temperature superconductor $Bi_{2}Sr_{2}CaCu_{2}O_{8}+x$ has been investigated by the high-resolution electron microscope (HREM) and the photodensitometric technique in order to resolve the sub-atomic shifts in the modulated structure.…
The evolution of the usual Erd\H{o}s-R\'{e}nyi random graph model on n vertices can be described as follows: At time 0 start with the empty graph, with n vertices and no edges. Now at each time k, choose 2 vertices uniformly at random and…
The problem of learning tree-structured Gaussian graphical models from independent and identically distributed (i.i.d.) samples is considered. The influence of the tree structure and the parameters of the Gaussian distribution on the…
Can there be a `Litmus test' for determining the nature of transition in models of percolation? In this paper we argue that the answer is in the affirmative. All one needs to do is to measure the `growth exponent' $\chi$ of the largest…
Pathological brain lesions exhibit diverse appearance in brain images, in terms of intensity, texture, shape, size, and location. Comprehensive sets of data and annotations are difficult to acquire. Therefore, unsupervised anomaly detection…
We study structure learning for linear Gaussian SEMs in the presence of latent confounding. Existing continuous methods excel when errors are independent, while deconfounding-first pipelines rely on pervasive factor structure or…
Microscopic current fluctuations are inseparable from conductance. We give an integral account of both quantized conductance and nonequilibrium thermal noise in one-dimensional ballistic wires. Our high-current noise theory opens a very…
Generative modeling is typically framed as learning mapping rules, but from an observer's perspective without access to these rules, the task becomes disentangling the geometric support from the probability distribution. We propose that…
With the space-borne missions CoRoT and Kepler, a large amount of asteroseismic data is now available. So-called global oscillation parameters are inferred to characterize the large sets of stars, to perform ensemble asteroseismology, and…
The notion of neural collapse refers to several emergent phenomena that have been empirically observed across various canonical classification problems. During the terminal phase of training a deep neural network, the feature embedding of…
A noise-based non-parametric technique for detecting nebulous objects, for example, irregular or clumpy galaxies, and their structure in noise is introduced. "Noise-based" and "non-parametric" imply that this technique imposes negligible…
We study percolation problems of overlapping objects where the underlying geometry is such that in D-dimensions, a subset of the directions has a lattice structure, while the remaining directions have a continuum structure. The resulting…
We study one-shot detection under isotropic multivariate Cauchy noise using finite constellations, with emphasis on the geometric mechanisms governing symbol-level reliability. Under isotropic Cauchy noise, the maximum-likelihood rule…
We investigate the correspondence between classical noise and quantum environments. Although it has been known that the classical noise can be mapped to the quantum environments only for pure dephasing and infinite-temperature dissipation…
Exponential random graph models (ERGMs) are flexible probability models allowing edge dependency. However, it is known that, to a first-order approximation, many ERGMs behave like Erd\"os-R\'enyi random graphs, where edges are independent.…
The recently developed information-theoretic approach to crystallographic symmetry classifications and quantifications in two dimensions (2D) from digital transmission electron and scanning probe microscope images is adapted for the…
The purpose of this paper is to prove ergodicity and provide asymptotic formulae for probabilities of threshold crossing related to smooth approximations of three fundamental nonlinear mechanical models: (a) an elasto-plastic oscillator,…
We study noise sensitivity of properties of the largest components $({\cal C}_j)_{j\geq 1}$ of the random graph ${\cal G}(n,p)$ in its critical window $p=(1+\lambda n^{-1/3})/n$. For instance, is the property "$|{\cal C}_1|$ exceeds its…