Related papers: Discontinuous BBP transitions
We study a spectral initialization method that serves a key role in recent work on estimating signals in nonconvex settings. Previous analysis of this method focuses on the phase retrieval problem and provides only performance bounds. In…
Transition points mark qualitative changes in the macroscopic properties of large complex systems. Explosive transitions, exhibiting properties of both continuous and discontinuous phase transitions, have recently been uncovered in network…
The multigap superconductivity modulated by quantum confinement effects in a superlattice of quantum wells is presented. Our theoretical BCS approach captures the low-energy physics of a shape resonance in the superconducting gaps when the…
The Binder cumulant (BC) has been widely used for locating the phase transition point accurately in systems with thermal noise. In systems with quenched disorder, the BC may show subtle finite-size effects due to large sample-to-sample…
High-dimensional feature spaces in particle physics events pose a fundamental challenge to density-estimation-based weakly supervised anomaly detection, whose fidelity degrades rapidly with an increasing number of dimensions. We propose a…
We propose an unsupervised real-time dense depth completion from a sparse depth map guided by a single image. Our method generates a smooth depth map while preserving discontinuity between different objects. Our key idea is a Binary…
Baryon Acoustic Oscillation (BAO) surveys will be a leading method for addressing the dark energy challenge in the next decade. We explore in detail the effect of allowing for small amplitude admixtures of general isocurvature perturbations…
Solid materials that deviate from the harmonic crystal paradigm exhibit characteristic anomalies in the specific heat and vibrational density of states (VDOS) with respect to Debye's theory predictions. The boson peak (BP), a low-frequency…
In the field of signal processing, phase transition phenomena have recently attracted great attention. Donoho's work established the signal recovery threshold using indicators such as restricted isotropy (RIP) and incoherence and proved…
The shift of energy levels owing to broadband electromagnetic vacuum fluctuations, the Lamb shift, has been pivotal in the development of quantum electrodynamics and in understanding atomic spectra. Currently, small energy shifts in…
Diffusive dynamics in presence of deep energy minima and weak nongradient forces can be coarse-grained into a mesoscopic jump process over the various basins of attraction. Combining standard weak-noise results with a path integral…
There is a growing interest in the estimation of the number of unseen features, mostly driven by biological applications. A recent work brought out a peculiar property of the popular completely random measures (CRMs) as prior models in…
Suppose that local characteristics of several independent compound Poisson and Wiener processes change suddenly and simultaneously at some unobservable disorder time. The problem is to detect the disorder time as quickly as possible after…
In this paper we introduce a novel approach for an important problem of break detection. Specifically, we are interested in detection of an abrupt change in the covariance structure of a high-dimensional random process -- a problem, which…
The scaling limit where both the size of the training set $P$ and the width $N$ of a deep neural network grow at the same rate, the so-called proportional-width regime, has been intensely studied for shallow, single-hidden-layer networks.…
The evolution from BCS to BEC superconductivity in the s-wave and d-wave channels is analyzed at zero temperature for a two-dimensional superconductor. Spectroscopic quantities for s-wave and d-wave systems present fundamental differences…
In this paper, we consider the singular values and singular vectors of low rank perturbations of large rectangular random matrices, in the regime the matrix is "long": we allow the number of rows (columns) to grow polynomially in the number…
Current deep neural networks are highly overparameterized (up to billions of connection weights) and nonlinear. Yet they can fit data almost perfectly through variants of gradient descent algorithms and achieve unexpected levels of…
We consider the high energy physics unfolding problem where the goal is to estimate the spectrum of elementary particles given observations distorted by the limited resolution of a particle detector. This important statistical inverse…
Since the discovery a half century ago that 1/r^2-type long-range interactions in the one-dimensional Ising model change the phase transition type, long-range interactions in diverse systems have received considerable attention. Recently,…