Related papers: Threshold Saturation in Spatially Coupled Constrai…
The organization of high-dimensional probability spaces is a fundamental problem at the intersection of statistical physics and information theory. Here, we analyze the distributions populating level surfaces of the probability simplex…
This work is motivated by recent progress in information theory and signal processing where the so-called `spatially coupled' design of systems leads to considerably better performance. We address relevant open questions about spatially…
We investigate front propagation and synchronization transitions in dependence on the information transmission delay and coupling strength over scale-free neuronal networks with different average degrees and scaling exponents. As the…
Percolation theory is applied to the phase-transition dynamics of domain pattern formation in segregating binary Bose--Einstein condensates in quasi-two-dimensional systems. Our finite-size-scaling analysis shows that the percolation…
The phase transition patterns displayed by a model of two coupled complex scalar fields are studied at finite temperature and chemical potential. Possible phenomena like symmetry persistence and inverse symmetry breaking at high…
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…
Spectral clustering is a fundamental method for graph partitioning, but its reliance on eigenvector computation limits scalability to massive graphs. Classical sparsification methods preserve spectral properties by sampling edges…
As one of the most important types of (weaker) supervised information in machine learning and pattern recognition, pairwise constraint, which specifies whether a pair of data points occur together, has recently received significant…
Planting a solution into the random RB model, which is a prototype of random constraint satisfaction problem (CSP) with growing domains, can generate very hard satisfiable CSP benchmarks. We study the solution space structure of the planted…
Random instances of Constraint Satisfaction Problems (CSP's) appear to be hard for all known algorithms, when the number of constraints per variable lies in a certain interval. Contributing to the general understanding of the structure of…
We study geometrical properties of the complete set of solutions of the random 3-satisfiability problem. We show that even for moderate system sizes the number of clusters corresponds surprisingly well with the theoretic asymptotic…
Corroborating a prediction from statistical physics, we prove that the Belief Propagation message passing algorithm approximates the partition function of the random $k$-SAT model well for all clause/variable densities and all inverse…
The zero range process is of particular importance as a generic model for domain wall dynamics of one-dimensional systems far from equilibrium. We study this process in one dimension with rates which induce an effective attraction between…
We introduce a new approach to disordered two-dimensional Ising models based on the extension of the combinatorial solution to randomized supercells. Applying it to the site-diluted Ising model on the square lattice, we resolve the full…
Random instances of constraint satisfaction problems such as k-SAT provide challenging benchmarks. If there are m constraints over n variables there is typically a large range of densities r=m/n where solutions are known to exist with…
We use the domination number of a parametrized random digraph family called proportional-edge proximity catch digraphs (PCDs) for testing multivariate spatial point patterns. This digraph family is based on relative positions of data points…
We theoretically study semi-supervised clustering in sparse graphs in the presence of pairwise constraints on the cluster assignments of nodes. We focus on bi-cluster graphs, and study the impact of semi-supervision for varying constraint…
Porous media are often modelled as systems of overlapping obstacles, which leads to the problem of two percolation thresholds in such systems, one for the porous matrix and the other one for the void space. Here we investigate these…
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 present a detailed study of the fidelity, the entanglement entropy, and the entanglement spectrum, for a dimerized chain of spinless fermions---a simplified Su-Schrieffer-Heeger (SSH) model---with open boundary conditions which is a…