Related papers: Critical Behavior and Universality Classes for an …
In topological insulators and topological superconductors, the discrete jump of the topological invariant upon tuning a certain system parameter defines a topological phase transition. A unified framework is employed to address the quantum…
A recently proposed curvature renormalization group scheme for topological phase transitions defines a generic `curvature function' as a function of the parameters of the theory and shows that topological phase transitions are signalled by…
Many non-equilibrium systems display dynamic phase transitions from active to absorbing states, where fluctuations cease entirely. Based on a field theory representation of the master equation, the critical behavior can be analyzed by means…
In (online) learning theory the concepts of sparsity, variance and curvature are well-understood and are routinely used to obtain refined regret and generalization bounds. In this paper we further our understanding of these concepts in the…
Kinetically constrained models (KCM) are reversible interacting particle systems on $\mathbb{Z}^d$ with continuous-time constrained Glauber dynamics. They are a natural non-monotone stochastic version of the family of cellular automata with…
In machine learning, statistics, econometrics and statistical physics, cross-validation (CV) is used asa standard approach in quantifying the generalisation performance of a statistical model. A directapplication of CV in time-series leads…
Classic supervised learning involves algorithms trained on $n$ labeled examples to produce a hypothesis $h \in \mathcal{H}$ aimed at performing well on unseen examples. Meta-learning extends this by training across $n$ tasks, with $m$…
We numerically investigate the stability of universal properties at continuous phase transitions against perturbations of the Markov Chain Monte Carlo algorithm used to simulate the system. We consider the three dimensional XY model as test…
We conducted an extensive computational experiment, lasting multiple CPU-years, to optimally select parameters for two important classes of algorithms for finding sparse solutions of underdetermined systems of linear equations. We make the…
We consider a sparse linear regression model Y=X\beta^{*}+W where X has a Gaussian entries, W is the noise vector with mean zero Gaussian entries, and \beta^{*} is a binary vector with support size (sparsity) k. Using a novel conditional…
Quantum phase transitions also occur in non-Hermitian systems. In this work we show that density functional theory, for the first time, uncovers universal behaviors for phase transitions in non-Hermitian many-body systems. To be specific,…
We consider stability and uniqueness in real phase retrieval problems over general input sets. Specifically, we assume the data consists of noisy quadratic measurements of an unknown input x in R^n that lies in a general set T and study…
In this paper we investigate the universality and scaling properties of the well-known quantities in classical statistical mechanics near the quantum phase transition point. We show that transverse susceptibility and derivatives of…
We analyze from the renormalization group perspective a universality class of reaction-diffusion systems with absorbing states. It describes models where the vacuum state is not accessible, as the set of reactions $2 A \to A$ together with…
We investigate the signal reconstruction performance of sparse linear regression in the presence of noise when piecewise continuous nonconvex penalties are used. Among such penalties, we focus on the SCAD penalty. The contributions of this…
The phase retrieval problem asks to recover a natural signal $y_0 \in \mathbb{R}^n$ from $m$ quadratic observations, where $m$ is to be minimized. As is common in many imaging problems, natural signals are considered sparse with respect to…
We study the critical behavior of a generalized icosahedral model on the simple cubic lattice. The field variable of the icosahedral model might take one of twelve vectors of unit length, which are given by the normalized vertices of the…
We provide theoretical analysis of the statistical and computational properties of penalized $M$-estimators that can be formulated as the solution to a possibly nonconvex optimization problem. Many important estimators fall in this…
Quantum corrections to transport through a chaotic ballistic cavity are known to be universal. The universality not only applies to the magnitude of quantum corrections, but also to their dependence on external parameters, such as the Fermi…
We consider a random sparse graph with bounded average degree, in which a subset of vertices has higher connectivity than the background. In particular, the average degree inside this subset of vertices is larger than outside (but still…