相关论文: Clusters of solutions and replica symmetry breakin…
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…
A method is introduced for studying large deviations in the context of statistical physics of disordered systems. The approach, based on an extension of the cavity method to atypical realizations of the quenched disorder, allows us to…
In order to study the resonance spectra of chaotic cavities subject to some damping (which can be due to absorption or partial reflection at the boundaries), we use a model of damped quantum maps. In the high-frequency limit, the…
Since the early 2000s physicists have developed an ingenious but non-rigorous formalism called the cavity method to put forward precise conjectures on phase transitions in random problems [Mezard, Parisi, Zecchina: Science 2002]. The cavity…
This paper investigates the model degrees of freedom in k-means clustering. An extension of Stein's lemma provides an expression for the effective degrees of freedom in the k-means model. Approximating the degrees of freedom in practice…
We present efficient counting and sampling algorithms for random $k$-SAT when the clause density satisfies $\alpha \le \frac{2^k}{\mathrm{poly}(k)}.$ In particular, the exponential term $2^k$ matches the satisfiability threshold…
We start with a rather detailed, general discussion of recent results of the replica approach to statistical mechanics of a single classical particle placed in a random $N (\gg 1)$-dimensional Gaussian landscape and confined by a…
The spectral density of various ensembles of sparse symmetric random matrices is analyzed using the cavity method. We consider two cases: matrices whose associated graphs are locally tree-like, and sparse covariance matrices. We derive a…
The $k$-center problem is a canonical and long-studied facility location and clustering problem with many applications in both its symmetric and asymmetric forms. Both versions of the problem have tight approximation factors on worst case…
Causal effects are often characterized with population summaries. These might provide an incomplete picture when there are heterogeneous treatment effects across subgroups. Since the subgroup structure is typically unknown, it is more…
During the past decade, phase-transition phenomena in the random 3-satisfiability (3-SAT) problem has been intensively studied by statistical physics methods. In this work, we study the random 3-SAT problem by the mean-field first-step…
In a standard cluster analysis, such as k-means, in addition to clusters locations and distances between them, it's important to know if they are connected or well separated from each other. The main focus of this paper is discovering the…
We introduce two simplicial clustering approaches for compositional data, that are adaptations of the $K$--means and of the Gaussian mixture models algorithms, by employing the $\alpha$--transformation. By utilizing clustering validation…
The cavity approach is used to address the physical properties of random solids in equilibrium. Particular attention is paid to the fraction of localized particles and the distribution of localization lengths characterizing their thermal…
Random constraint satisfaction problems (CSP) have been studied extensively using statistical physics techniques. They provide a benchmark to study average case scenarios instead of the worst case one. The interplay between statistical…
Spin-glass theory is one of the leading paradigms of complex physics and describes condensed matter, neural networks and biological systems, ultracold atoms, random photonics, and many other research fields. According to this theory,…
Clustering is one of the most fundamental tools in data science and machine learning, and k-means clustering is one of the most common such methods. There is a variety of approximate algorithms for the k-means problem, but computing the…
Bayesian models offer great flexibility for clustering applications---Bayesian nonparametrics can be used for modeling infinite mixtures, and hierarchical Bayesian models can be utilized for sharing clusters across multiple data sets. For…
We introduce a version of the cavity method for diluted mean-field spin models that allows the computation of thermodynamic quantities similar to the Franz-Parisi quenched potential in sparse random graph models. This method is developed in…
Replica symmetry breaking (RSB) underlies the complex organization of disordered systems, yet quantitative validation beyond $N \sim 100$ spins has remained computationally challenging. We use quantum annealing to access ground states of…