Related papers: Spin Glass Concepts in Computer Science, Statistic…
Despite the extreme simplicity in their definition, spin glasses disclose a wide variety of non-trivial behaviors that are not yet fully understood. In this thesis we try to shed light on some of them, focusing on one hand on the search of…
A sketch of the chapter appearing under the same heading in the book ``New Optimization Algorithms in Physics'' (A.K. Hartmann and H. Rieger, Eds.) is given. After a general introduction to spin glasses, important aspects of heuristic…
To identify emerging microscopic structures in low temperature spin glasses, we study self-sustained clusters (SSC) in spin models defined on sparse random graphs. A message-passing algorithm is developed to determine the probability of…
The problem of statistical inference in its various forms has been the subject of decades-long extensive research. Most of the effort has been focused on characterizing the behavior as a function of the number of available samples, with far…
Measuring, characterizing and modelling the slow dynamics of glassy soft matter is a great challenge, with an impact that ranges from industrial applications to fundamental issues in modern statistical physics, such as the glass transition…
This paper is divided into two parts. The first part concerns several standard scenarios for how short-range spin glasses might behave at low temperature. Earlier theorems of the authors are reviewed, and some new results presented,…
Tensor models play an increasingly prominent role in many fields, notably in machine learning. In several applications, such as community detection, topic modeling and Gaussian mixture learning, one must estimate a low-rank signal from a…
In these notes the main theoretical concepts and techniques in the field of mean-field spin-glasses are reviewed in a compact and pedagogical way, for the benefit of the graduate and undergraduate student. One particular spin-glass model is…
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…
Replica symmetry breaking postulates that near optima of spin glass Hamiltonians have an ultrametric structure. Namely, near optima can be associated to leaves of a tree, and the Euclidean distance between them corresponds to the distance…
The physics of glasses can be studied from many viewpoints, from material scientists interested in the development of new materials to statistical physicists inventing new theoretical tools to deal with disordered systems. In these lectures…
This work presents a statistical mechanics characterization of neural networks, motivated by the replica symmetry breaking (RSB) phenomenon in spin glasses. A Hopfield-type spin glass model is constructed from a given feedforward neural…
We discuss the utility of analytical and numerical investigation of spin models, in particular spin glasses, on ordinary ``thin'' random graphs (in effect Feynman diagrams) using methods borrowed from the ``fat'' graphs of two dimensional…
Dilute magnetic nanoparticle systems exhibit slow dynamics [1] due to a broad distribution of relaxation times that can be traced to a correspondingly broad distribution of particle sizes [1]. However, at higher concentrations interparticle…
This paper deals with the scenario approach to robust optimization. This relies on a random sampling of the possibly infinite number of constraints induced by uncertainties in the parameters of an optimization problem. Solving the resulting…
This paper revisits the principle of uniform convergence in statistical learning, discusses how it acts as the foundation behind machine learning, and attempts to gain a better understanding of the essential problem that current deep…
In this work we study numerically a short range p-spin glass model in three dimensions. The behaviour of the model appears to be remarkably different from mean field predictions. In fact it shares some features typical of models with full…
The local minima (inherent structures) of a system and their associated transition links give rise to a network. Here we consider the topological and distance properties of such a network in the context of spin glasses. We use steepest…
We consider the Hamiltonians of mean-field spin glasses, which are certain random functions $H_N$ defined on high-dimensional cubes or spheres in $\mathbb R^N$. The asymptotic maximum values of these functions were famously obtained by…
We discuss replica symmetry breaking (RSB) in spin glasses. We update work in this area, from both the analytical and numerical points of view. We give particular attention to the difficulties stressed by Newman and Stein concerning the…