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In the free energy landscape picture of glassy systems, the slow dynamics characteristic of these systems is believed to be due to the existence of a complicated free-energy landscape with many local minima. We show here that for a…
We study one-dimensional disordered systems with average non-invertible symmetries, where quenched disorder may locally break part of the symmetry while preserving it upon disorder averaging. A canonical example is the random…
A general formalism is developed to construct a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are therefore internal to the system and not externally specified. For…
A model for studying the ultrametricity of the energy landscape in a disordered heteropolymer is presented. It is treated as a simplified model of a protein molecule in which amino acid residues are modeled as point masses. Pairwise…
This paper advances an analytical incremental contact model for the purely elastic or elastic-perfectly plastic Gaussian rough surfaces. The contact is modelled by the accumulation of identical circular contacts with radius given by the…
Topological phases support edge states that can be robust to material deformations and other perturbations. While well-studied in quantum systems, topological phases have also been observed in stochastic and biochemical systems, yet it…
We consider a paradigmatic solvable model of topological order in two dimensions, Kitaev's honeycomb Hamiltonian, and turn it into a measurement-only dynamics consisting of stochastic measurements of two-qubit bond operators. We find an…
The empirical measure of an interacting particle system is a purely atomic random probability measure. In the limit as the number of particles grows to infinity, we show for McKean-Vlasov systems with common noise that this measure becomes…
For general asymptotically sub-additive potentials (resp. asymptotically additive potentials) on general topological dynamical systems, we establish some variational relations between the topological entropy of the level sets of Lyapunov…
Landscapes evolve toward surfaces with complex networks of channels and ridges in response to climatic and tectonic forcing. Here we analyze variational principles giving rise to minimalist models of landscape evolution as a system of…
Hyperuniform point patterns are characterized by vanishing infinite wavelength density fluctuations and encompass all crystal structures, certain quasi-periodic systems, and special disordered point patterns. This article generalizes the…
Stochastic dynamics on sparse graphs and disordered systems often lead to complex behaviors characterized by heterogeneity in time and spatial scales, slow relaxation, localization, and aging phenomena. The mathematical tools and…
While modern representation learning relies heavily on global error signals, decentralized algorithms driven by local interactions offer a fundamental distributed alternative. However, the macroscopic convergence properties of these…
We study the non-convex optimization landscape for maximum likelihood estimation in the discrete orbit recovery model with Gaussian noise. This model is motivated by applications in molecular microscopy and image processing, where each…
In this paper we study the asymptotic behavior of solutions to systems of strongly coupled integral equations with oscillatory coefficients. The system of equations is motivated by a peridynamic model of the deformation of heterogeneous…
Wrinkling is the phenomenon of out-of-plane deformation patterns in thin walled structures, as a result of a local compressive (internal) loads in combination with a large membrane stiffness and a small but non-zero bending stiffness.…
A class of evolution quasistatic systems which leads, after a suitable time discretization, to recursive nonlinear programs, is considered and optimal control or identification problems governed by such systems are investigated. The…
In a work in 1992, Lyzzaik studies local properties of light harmonic mappings. More precisely, he classifies their critical points and accordingly studies their topological and geometrical behaviours. We will focus our study on smooth…
We prove for an infinite array of globally coupled overdamped anharmonic oscillators subject to additive Gaussian white noise the existence of a well-behaved critical manifold in the parameter space which separates a symmetric phase from a…
The latent space approach to complex networks has revealed fundamental principles and symmetries, enabling geometric methods. However, the conditions under which network topology implies geometricity remain unclear. We provide a…