Related papers: Triplets of local minima in a high-dimensional ran…
We use Kac-Rice method to analyze statistical features of an "optimization landscape" of the loss function in a random version of the Oblique Procrustes Problem, one of the simplest optimization problems of the least-square type on a…
In this work we describe the rank-reduced variant of the equation-of-motion coupled cluster theory with complete inclusion of single, double, and triple excitations. The advantage of the proposed formalism in comparison with the canonical…
Individual cationic site--energies are explicitly determined from molecular dynamics simulations of alkali silicate glasses, and the properties and relevance of this local energetics to ion transport are studied. The absence of relaxations…
A cluster of three spins coupled by single-axis anisotropic exchange exhibits classical behaviors ranging from regular motion at low and high energies, to chaotic motion at intermediate energies. A change of variable, taking advantage of…
We analyze the energy barriers that allow escapes from a given local minimum in a mean-field model of glasses. We perform this study by using the Kac-Rice method and computing the typical number of critical points of the energy function at…
Motivated by the recently observed phenomenon of topology trivialization of potential energy landscapes (PELs) for several statistical mechanics models, we perform a numerical study of the finite size $2$-spin spherical model using both…
We study quantum spin systems in the 1D, 2D square and 3D cubic lattices with nearest-neighbour XY exchange. We use the coupled-cluster method (CCM) to calculate the ground-state energy, the T=0 sublattice magnetisation and the excited…
Neural network models have been used to construct energy landscapes for modeling biological phenomena, in which the minima of the landscape correspond to memory patterns stored by the network. Here, we show that dynamic properties of those…
The configuration model generates random graphs with any given degree distribution, and thus serves as a null model for scale-free networks with power-law degrees and unbounded degree fluctuations. For this setting, we study the local…
We use non-perturbative linked-cluster expansions to determine the ground-state energy per site of the spin-one Heisenberg model on the kagome lattice. To this end, a parameter is introduced allowing to interpolate between a fully…
In order to study the activated dynamics of mean-field glasses, which takes place on times of order exp(N), where N is the system size, we introduce a new model, the Correlated Random Energy Model (CREM), that allows for a smooth…
We present a method to obtain the average and the typical value of the number of critical points of the empirical risk landscape for generalized linear estimation problems and variants. This represents a substantial extension of previous…
For a system consisting of active soft spheres in three dimensions, we study the transition from a fluid where overlaps between particles can only occur for a short time after a collision to a state where clusters of overlapping particles…
We review recent results on the potential energy landscape (PES) of model liquids. The role of saddle-points in the PES in connecting dynamics to statics is investigated, confirming that a change between minima-dominated and…
Cyclic transitions between active and passive states are central to many natural and synthetic systems, ranging from light-driven active particles to animal migrations. Here, we investigate a minimal model of self-propelled Brownian…
The parametric motion of energy levels for non-interacting electrons at the Anderson localization critical point is studied by computing the energy level-curvatures for a quasiperiodic ring with twisted boundary conditions. We find a…
We analyze statistical features of the ``optimization landscape'' in a random version of one of the simplest constrained optimization problems of the least-square type: finding the best approximation for the solution of an overcomplete…
We revisit the globally coupled map lattice (GCML). We show that in the so called turbulent regime various periodic cluster attractor states are formed even though the coupling between the maps are very small relative to the non-linearity…
The nuclear landscape has been investigated within the triaxial relativistic Hartree-Bogoliubov theory with the PC-PK1 density functional, and the beyond-mean-field dynamical correlation energies are taken into account by a microscopically…
The properties of higher-index saddle points have been invoked in recent theories of the dynamics of supercooled liquids. Here we examine in detail a mapping of configurations to saddle points using minimization of $|\nabla E|^2$, which has…