Related papers: Topological transition in disordered planar matchi…
Recently, the impact of disorder on topological properties has attracted significant attention in photonics, especially the intriguing disorder-induced topological phase transitions in photonic topological Anderson insulators (PTAIs).…
We consider two independent Erd\H{o}s-R\'enyi random graphs, with possibly different parameters, and study two isomorphism problems, a graph embedding problem and a common subgraph problem. Under certain conditions on the graph parameters…
We study the effects of topological (connectivity) disorder on phase transitions. We identify a broad class of random lattices whose disorder fluctuations decay much faster with increasing length scale than those of generic random systems,…
The Abstraction and Reasoning Corpus (ARC) evaluates general reasoning capabilities that are difficult for both machine learning models and combinatorial search methods. We propose a neuro-symbolic approach that combines a transformer for…
The Anderson transition in three dimensions in a randomly varying magnetic flux is investigated in detail by means of the transfer matrix method with high accuracy. Both, systems with and without an additional random scalar potential are…
We discuss the method of conformal mappings applied to perturbative QCD. The approach is based on the Borel-Laplace integral regulated with the principal value prescription and the expansion of the Borel transform in powers of the variable…
We seek the possibility of a disorder driven transition in a tight-binding lattice with a flat band using complexity parameter approach. Our results indicate the existence of a localized to extended states transition with increasing…
The alignment of biological sequences such as DNA, RNA, and proteins, is one of the basic tools that allow to detect evolutionary patterns, as well as functional/structural characterizations between homologous sequences in different…
We establish the connection between a multichannel disordered model --the 1D Dirac equation with $N\times N$ matricial random mass-- and a random matrix model corresponding to a deformation of the Laguerre ensemble. This allows us to derive…
We review connections between phase transitions in high-dimensional combinatorial geometry and phase transitions occurring in modern high-dimensional data analysis and signal processing. In data analysis, such transitions arise as abrupt…
In this paper we study the local behavior of solutions to some free boundary problems. We relate the theory of quasi-conformal maps to the regularity of the solutions to nonlinear thin-obstacle problems; we prove that the contact set is…
introduce {\sc Planar Disjoint Paths Completion}, a completion counterpart of the Disjoint Paths problem, and study its parameterized complexity. The problem can be stated as follows: given a, not necessarily connected, plane graph $G,$ $k$…
We study the diversity of complex spatio-temporal patterns in the behavior of random synchronous asymmetric neural networks (RSANNs). Special attention is given to the impact of disordered threshold values on limit-cycle diversity and…
Exhaustive study of topological semimetal phases of matter in equilibriated electonic systems and myriad extensions has built upon the foundations laid by earlier introduction and study of the Weyl semimetal, with broad applications in…
The attractor dimension at the transition to complete synchronization in a network of chaotic units with time-delayed couplings is investigated. In particular, we determine the Kaplan-Yorke dimension from the spectrum of Lyapunov exponents…
Beyond-planarity focuses on combinatorial properties of classes of non-planar graphs that allow for representations satisfying certain local geometric or topological constraints on their edge crossings. Beside the study of a specific graph…
We study the level-statistics of a disordered system undergoing the Anderson type metal-insulator transition. The disordered Hamiltonian is a sparse random matrix in the site representation and the statistics is obtained by taking an…
A four-fermion model in 2+1 dimensions describing N Dirac fermions interacting via SU(N) invariant N^2-1 four-fermion interactions is solved in the leading order of the 1/N expansion. The 1/N expansion corresponds to 't Hoofts topological…
We study the two-dimensional Ising model on a network with a novel type of quenched topological (connectivity) disorder. We construct random lattices of constant coordination number and perform large scale Monte Carlo simulations in order…
The method of self-consistent expansions is a powerful tool for handling strong coupling problems that might otherwise be beyond the reach of perturbation theory, providing surprisingly accurate approximations even at low order. First…