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#SMT, or model counting for logical theories, is a well-known hard problem that generalizes such tasks as counting the number of satisfying assignments to a Boolean formula and computing the volume of a polytope. In the realm of…
Mean-field models of glasses that present a random first order transition exhibit highly non-trivial fluctuations. Building on previous studies that focused on the critical scaling regime, we here obtain a fully quantitative framework for…
The study of the properties of glass-forming liquids is difficult for many reasons. Analytic solutions of mean field models are usually available only for systems embedded in a space with an unphysically high number of spatial dimensions;…
In certain mean field models for spin glasses there occurs a one step replica symmetry breaking pattern. As an example of general $1/N$-corrections in such systems, the fluctuations in the internal energy are calculated. For this specific…
Systems of globally coupled logistic maps (GCLM) can display complex collective behaviour characterized by the formation of synchronous clusters. In the dynamical clustering regime, such systems possess a large number of coexisting…
The glass transition is considered within two toys models, a mean field spin glass and a directed polymer in a correlated random potential. In the spin glass model there occurs a dynamical transition, where the system condenses in a state…
The dynamical behavior of a kind of models with hierarchically constrained dynamics is investigated. The models exhibit many properties resembling real structural glasses. In particular, we focus on the study of time-dependent temperature…
Phase transitions in spin glass type systems and, more recently, in related computational problems have gained broad interest in disparate arenas. In the current work, we focus on the "community detection" problem when cast in terms of a…
A new method for solving systems of linear algebraic equations of a special type arising in solving problems of image reconstruction has been proposed. This method, due to a certain symmetry of the matrix and the choice of the voxel…
Moment closure methods are widely used to analyze mathematical models. They are specifically geared toward derivation of approximations of moments of stochastic models, and of similar quantities in other models. The methods possess several…
We survey a number of moment hierarchies and test their performances in computing one-dimensional shock structures. It is found that for high Mach numbers, the moment hierarchies are either computationally expensive or hard to converge,…
We use the method of Maximum (relative) Entropy to process information in the form of observed data and moment constraints. The generic "canonical" form of the posterior distribution for the problem of simultaneous updating with data and…
A new approach to solving random matrix models directly in the large $N$ limit is developed. First, a set of numerical values for some low-pt correlation functions is guessed. The large $N$ loop equations are then used to generate values of…
We provide an overview of the different types of computational techniques developed over the years to study supercooled liquids, glassy materials and the physics of the glass transition. We organise these numerical strategies into four…
Melt supercooling leads to glass formation. Liquid-to-liquid phase transitions are observed depending on thermal paths. Viscosity, density and surface tension thermal dependences measured at heating and subsequent cooling show hysteresis…
Spin glasses are quintessential examples of complex matter. Although much about their order remains uncertain, abstract models of them inform, e.g., the classification of combinatorial optimization problems, the magnetic ordering in metals…
Moment closure methods appear in myriad scientific disciplines in the modelling of complex systems. The goal is to achieve a closed form of a large, usually even infinite, set of coupled differential (or difference) equations. Each equation…
Liquids relax extremely slowly upon approaching the glass state. One explanation is that an entropy crisis, due to the rarefaction of available states, makes it increasingly arduous to reach equilibrium in that regime. Validating this…
We provide a multiplicity result for solutions of time-independent Gross-Pitaevskii equations on closed Riemannian manifolds. Such solutions arise as (possibly non-minimizing) critical points of the Ginzburg-Landau energy having prescribed…
We construct a class of matrix models, where supersymmetry (SUSY) is spontaneously broken at the matrix size $N$ infinite. The models are obtained by dimensional reduction of matrix-valued SUSY quantum mechanics. The potential of the models…