Related papers: Criticality and Heterogeneity in the Solution Spac…
Using elementary rigorous methods we prove the existence of a clustered phase in the random $K$-SAT problem, for $K\geq 8$. In this phase the solutions are grouped into clusters which are far away from each other. The results are in…
We develop a real space renormalisation group analysis of disordered models of glasses, in particular of the spin models at the origin of the Random First Order Transition theory. We find three fixed points respectively associated to the…
For several models of random constraint satisfaction problems, it was conjectured by physicists and later proved that a sharp satisfiability transition occurs. For random $k$-SAT and related models it happens at clause density $\alpha$…
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…
The solution space of many classical optimization problems breaks up into clusters which are extensively distant from one another in the Hamming metric. Here, we show that an analogous quantum clustering phenomenon takes place in the ground…
We analyze critical points that can be induced in glassy systems by the presence of constraints. These critical points are predicted by the Mean Field Thermodynamic approach and they are precursors of the standard glass transition in…
Satisfiability is considered the canonical NP-complete problem and is used as a starting point for hardness reductions in theory, while in practice heuristic SAT solving algorithms can solve large-scale industrial SAT instances very…
Many complex systems satisfy a set of constraints on their degrees of freedom, and at the same time, they are able to work and adapt to different conditions. Here, we describe the emergence of this ability in a simplified model in which the…
The aim of this review paper is to give a panoramic of the impact of spin glass theory and statistical physics in the study of the K-sat problem. The introduction of spin glass theory in the study of the random K-sat problem has indeed left…
We determine under which conditions certain natural models of random constraint satisfaction problems have sharp thresholds of satisfiability. These models include graph and hypergraph homomorphism, the $(d,k,t)$-model, and binary…
We show that the dynamics of a laser driven Rydberg gas in the limit of strong dephasing is described by a master equation with manifest kinetic constraints. The equilibrium state of the system is uncorrelated but the constraints in the…
We introduce a simple model of a growing system with $m$ competing communities. The model corresponds to the phenomenon of defeats suffered by social groups living in isolation. A nonequilibrium phase transition is observed when at critical…
This work investigates a model describing the interaction of two species in habiting separate but adjacent areas. These populations are governed by a system of equations that account for spatial variations in growth rates and the effects of…
One of the general mechanisms that give rise to the slow cooperative relaxation characteristic of classical glasses is the presence of kinetic constraints in the dynamics. Here we show that dynamical constraints can similarly lead to slow…
Many difficult computational problems involve the simultaneous satisfaction of multiple constraints which are individually easy to satisfy. Such problems occur in diffractive imaging, protein folding, constrained optimization (e.g., spin…
Transient chaos is an ubiquitous phenomenon characterizing the dynamics of phase space trajectories evolving towards a steady state attractor in physical systems as diverse as fluids, chemical reactions and condensed matter systems. Here we…
There is mounting empirical evidence that many communities of living organisms display key features which closely resemble those of physical systems at criticality. We here introduce a minimal model framework for the dynamics of a community…
In this paper we revisit and extend the mapping between two apparently different classes of models. The first class contains the prototypical models described --at the mean-field level-- by the Random First Order Transition (RFOT) theory of…
Only recently the essential role of the percolation critical point has been considered on the dynamical properties of connected regions of aligned spins (domains) after a sudden temperature quench. In equilibrium, it is possible to resolve…
In this paper we initiate the study of the heterogeneous capacitated $k$-center problem: given a metric space $X = (F \cup C, d)$, and a collection of capacities. The goal is to open each capacity at a unique facility location in $F$, and…