Related papers: Cavity Method: Message Passing from a Physics Pers…
Relativistic Coulomb systems are studied in velocity space, prompted by the fact that the study of Newtonian Kepler/Coulomb systems in velocity space provides a method much simpler (and more elegant) than the familiar analytic solutions in…
In this note we explain the use of the cavity method directly at zero temperature, in the case of the spin glass on a Bethe lattice. The computation is done explicitly in the formalism equivalent to 'one step replica symmetry breaking'; we…
A variational approach to finite connectivity spin-glass-like models is developed and applied to describe the structure of optimal solutions in random satisfiability problems. Our variational scheme accurately reproduces the known replica…
The interpolation method is a powerful tool for rigorous analysis of mean-field spin glass models, both with and without dilution. In this study, we show that the interpolation method can be applied to Ising spin glass models in one…
After reviewing the basics of the cavity method in classical systems, we show how its quantum version, with some appropriate approximation scheme, can be used to study a system of spins with random ferromagnetic interactions and a random…
We study the low temperature properties of p-spin glass models with finite connectivity and of some optimization problems. Using a one-step functional replica symmetry breaking Ansatz we can solve exactly the saddle-point equations for…
In this paper we analyze the structure of the UNSAT-phase of the overconstrained 3-SAT model by studying the low temperature phase of the associated disordered spin model. We derive the $\infty$ Replica Symmetry Broken equations for a…
C-dismantling (CD) problem aims at finding the minimum vertex set D of a graph G(V,E) after removing which the remaining graph will break into connected components with the size not larger than C. In this paper, we introduce a spin-glass…
A common problem in teaching Physics in secondary school is due to the gap in terms of difficulty between the physical concepts and the mathematical tools which are necessary to study them quantitatively. Advanced statistical estimators are…
This paper proposes a simple self-supervised approach for learning a representation for visual correspondence from raw video. We cast correspondence as prediction of links in a space-time graph constructed from video. In this graph, the…
The last few years have seen the development of a promising theoretical framework for statistics of the cosmic large-scale structure -- the theory of large deviations (LDT) for modelling weak-lensing one-point statistics in the mildly…
We present the first iterative spectral algorithm to find near-optimal solutions for a random quadratic objective over the discrete hypercube, resolving a conjecture of Subag [Subag, Communications on Pure and Applied Mathematics, 74(5),…
Knowledge representation is an important, long-history topic in AI, and there have been a large amount of work for knowledge graph embedding which projects symbolic entities and relations into low-dimensional, real-valued vector space.…
This thesis is divided in two parts. The first presents an overview of known results in statistical mechanics of disordered systems and its approach to random combinatorial optimization problems. The second part is a discussion of two…
Many important theories in modern physics can be stated using differential geometry. Symplectic geometry is the natural framework to deal with autonomous Hamiltonian mechanics. This admits several generalizations for nonautonomous systems,…
We introduce a self-calibration method that can be applied to the intrinsic ellipticity--intrinsic ellipticity (II) and gravitational shear -- intrinsic ellipticity (GI) types of intrinsic alignment of galaxies. The method combines previous…
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…
Using a graph approach to quantum systems, we prove that descriptions of 3-dim Kochen-Specker (KS) setups as well as descriptions of 3-dim spin systems by means of Greechie lattices that we find in the literature are wrong. Correct lattices…
Using Monte Carlo simulations, we study in detail the overlap distribution for individual samples for several spin-glass models including the infinite-range Sherrington-Kirkpatrick model, short-range Edwards-Anderson models in three and…
We propose a method for calculating the Franz-Parisi potential for spin glass models on sparse random graphs using the replica method under the replica symmetric ansatz. The resulting self-consistent equations have the solution with the…