Related papers: Beyond-mean-field fluctuations for the solution of…
The solution-space structure of the 3-Satisfiability Problem (3-SAT) is studied as a function of the control parameter alpha (ratio of number of clauses to the number of variables) using numerical simulations. For this purpose, one has to…
We discuss an analysis of Constraint Satisfaction problems, such as Sphere Packing, K-SAT and Graph Coloring, in terms of an effective energy landscape. Several intriguing geometrical properties of the solution space become in this light…
In microscopic mechanical systems interactions between elastic structures are often mediated by the hydrodynamics of a solvent fluid. At microscopic scales the elastic structures are also subject to thermal fluctuations. Stochastic…
High-dimensional random landscapes underlie phenomena as diverse as glassy physics and optimization in machine learning, and even their simplest toy models already display extraordinarily rich behavior. This thesis aims to deepen our…
Energy landscapes are high-dimensional surfaces representing the dependence of system energy on variable configurations, which determine crucially the system's emergent behavior but are difficult to be analyzed due to their high-dimensional…
We study interactions between Skolem Arithmetic and certain classes of Constraint Satisfaction Problems (CSPs). We revisit results of Glass er et al. in the context of CSPs and settle the major open question from that paper, finding a…
We numerically study a nondisordered lattice spin system with a first order liquid-crystal transition, as a model for supercooled liquids and glasses. Below the melting temperature the system can be kept in the metastable liquid phase, and…
We obtain the non-equilibrium effective action of an inflaton like scalar field --the system-- by tracing over sub Hubble degrees of freedom of "environmental" light scalar fields. The effective action is stochastic leading to effective…
A simple model of a frustrated disordered system is presented. Apart from the (very different) physical interpretation, the model shares many features with that of Sherrington-Kirkpatrick for spin glasses, but, as a consequence of its…
CSP sparsification, introduced by Kogan and Krauthgamer (ITCS 2015), considers the following question: how much can an instance of a constraint satisfaction problem be sparsified (by retaining a reweighted subset of the constraints) while…
The hallmark of highly frustrated systems is the presence of many states close in energy to the ground state. Fluctuations between these states can preclude the emergence of any form of order and lead to the appearance of spin liquids. Even…
We build on a recently proposed method for explaining solutions of constraint satisfaction problems. An explanation here is a sequence of simple inference steps, where the simplicity of an inference step is measured by the number and types…
Using a stochastic algorithm introduced in a previous paper, we study the finite size volume corrections and the fluctuations of the ground state energy in the Sherrington-Kirkpatrick and the Edwards-Anderson models at zero temperature. The…
Spin fluctuation-induced superconductivity in quasi-two dimensional organic compounds, \kappa-BEDT-TTF salts, is investigated within a fluctuation exchange (FLEX) approximation using a half-filled Hubbard model with a right-angled isosceles…
We introduce an efficient message passing scheme for solving Constraint Satisfaction Problems (CSPs), which uses stochastic perturbation of Belief Propagation (BP) and Survey Propagation (SP) messages to bypass decimation and directly…
We formulate a dynamical fluctuation theory for stationary non equilibrium states (SNS) which is tested explicitly in stochastic models of interacting particles. In our theory a crucial role is played by the time reversed dynamics. Within…
Backtracking search algorithms are often used to solve the Constraint Satisfaction Problem (CSP). The efficiency of backtracking search depends greatly on the variable ordering heuristics. Currently, the most commonly used heuristics are…
We introduce a highly structured family of hard satisfiable 3-SAT formulas corresponding to an ordered spin-glass model from statistical physics. This model has provably "glassy" behavior; that is, it has many local optima with large energy…
By concisely representing a joint function of many variables as the combination of small functions, discrete graphical models (GMs) provide a powerful framework to analyze stochastic and deterministic systems of interacting variables. One…
Constraint Satisfaction Problems (CSPs) play a central role in many applications in Artificial Intelligence and Operations Research. In general, solving CSPs is NP-complete. The structure of CSPs is best described by hypergraphs. Therefore,…