Related papers: Subminimal Paths on a Stochastic Graph
In this work we discuss a short range version of the $p$-spin model. The model is provided with a parameter that allows to control the crossover with the mean field behaviour. We detect a discrepancy between the perturbative approach and…
An important but little-studied property of spin glasses is the stability of their ground states to changes in one or a finite number of couplings. It was shown in earlier work that, if multiple ground states are assumed to exist, then…
The proximal stochastic gradient method (PSGD) is one of the state-of-the-art approaches for stochastic composite-type problems. In contrast to its deterministic counterpart, PSGD has been found to have difficulties with the correct…
We consider optimization problems for complex systems in which the cost function has a multivalleyed landscape. We introduce a new class of dynamical algorithms which, using a suitable annealing procedure coupled with a balanced…
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…
We present a methodology for generating Ising Hamiltonians of tunable complexity and with a priori known ground states based on a decomposition of the model graph into edge-disjoint subgraphs. The idea is illustrated with a spin-glass model…
We develop a mean-field theory for random quantum spin systems using the spin coherent state path integral representation. After the model is reduced to the mean field one-body Hamiltonian, the integral is analyzed with the aid of several…
Quenched disorder effects on frustrated systems are explored by considering random fluctuations on the antiferromagnetic (AF) interactions between spins on the checkerboard lattice. The replica framework is adopted within a cluster…
In this paper we consider a recently developed distributed optimization algorithm based on gradient tracking. We propose a system theory framework to analyze its structural properties on a preliminary, quadratic optimization set-up.…
In order to study certain questions concerning the distribution of the overlap in Sherrington--Kirkpatrick type models, such as the chaos and ultrametricity problems, it seems natural to study the free energy of multiple systems with…
Quantum many-body systems with kinetic constraints exhibit intriguing relaxation dynamics. Recent experimental progress in the field of cold atomic gases offers a handle for probing collective behavior of such systems, in particular for…
We study the dynamics of bond-disordered Ising spin systems on random graphs with finite connectivity, using generating functional analysis. Rather than disorder-averaged correlation and response functions (as for fully connected systems),…
Kinetically constrained spin models are known to exhibit dynamical behavior mimicking that of glass forming systems. They are often understood as coarse-grained models of glass formers, in terms of some "mobility" field. The identity of…
Sparse Knowledge Graphs (KGs) are commonly encountered in real-world applications, where knowledge is often incomplete or limited. Sparse KG reasoning, the task of inferring missing knowledge over sparse KGs, is inherently challenging due…
We discuss a phase transition in spin glass models which have been rarely considered in the past, namely the phase transition that may take place when two real replicas are forced to be at a larger distance (i.e. at a smaller overlap) than…
We study the quenched disordered magnetic system, which is obtained from the 2D SO(3) quantum Heisenberg model, on a square lattice, with nearest neighbors interaction, by taking a Gaussian random distribution of couplings centered in an…
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…
Consider the Euclidean traveling salesman problem with $n$ random points on the plane. Suppose that one of the points is shifted to a new random location. This gives us a new optimal path. Consider such shifts for each of the $n$ points. Do…
Since the discovery of spin glasses in dilute magnetic systems, their study has been largely focused on understanding randomness and defects as the driving mechanism. The same paradigm has also been applied to explain glassy states found in…
In this document, some novel theoretical and computational techniques for constrained approximation of data-driven systems, are presented. The motivation for the development of these techniques came from structure-preserving matrix…