172 research outputs found
Glass models on Bethe lattices
We consider ``lattice glass models'' in which each site can be occupied by at
most one particle, and any particle may have at most l occupied nearest
neighbors. Using the cavity method for locally tree-like lattices, we derive
the phase diagram, with a particular focus on the vitreous phase and the
highest packing limit. We also study the energy landscape via the
configurational entropy, and discuss different equilibrium glassy phases.
Finally, we show that a kinetic freezing, depending on the particular dynamical
rules chosen for the model, can prevent the equilibrium glass transitions.Comment: 24 pages, 11 figures; minor corrections + enlarged introduction and
conclusio
Quiet Planting in the Locked Constraint Satisfaction Problems
We study the planted ensemble of locked constraint satisfaction problems. We
describe the connection between the random and planted ensembles. The use of
the cavity method is combined with arguments from reconstruction on trees and
first and second moment considerations; in particular the connection with the
reconstruction on trees appears to be crucial. Our main result is the location
of the hard region in the planted ensemble. In a part of that hard region
instances have with high probability a single satisfying assignment.Comment: 21 pages, revised versio
Amorphous-amorphous transition and the two-step replica symmetry breaking phase
The nature of polyamorphism and amorphous-to-amorphous transition is
investigated by means of an exactly solvable model with quenched disorder, the
spherical s+p multi-spin interaction model. The analysis is carried out in the
framework of Replica Symmetry Breaking theory and leads to the identification
of low temperature glass phases of different kinds. Besides the usual
`one-step' solution, known to reproduce all basic properties of structural
glasses, also a physically consistent `two-step' solution arises. More
complicated phases are found as well, as temperature is further decreased,
expressing a complex variety of metastable states structures for amorphous
systems.Comment: 8 pages, 7 figures, longer version, new references adde
Assessment of subseasonal-to-seasonal (S2S) ensemble extreme precipitation forecast skill over Europe
Heavy precipitation can lead to floods and landslides, resulting in widespread damage and significant casualties. Some of its impacts can be mitigated if reliable forecasts and warnings are available. Of particular interest is the subseasonal-to-seasonal (S2S) prediction timescale. The S2S prediction timescale has received increasing attention in the research community because of its importance for many sectors. However, very few forecast skill assessments of precipitation extremes in S2S forecast data have been conducted. The goal of this article is to assess the forecast skill of rare events, here extreme precipitation, in S2S forecasts, using a metric specifically designed for extremes. We verify extreme precipitation events over Europe in the S2S forecast model from the European Centre for Medium-Range Weather Forecasts. The verification is conducted against ERA5 reanalysis precipitation. Extreme precipitation is defined as daily precipitation accumulations exceeding the seasonal 95th percentile. In addition to the classical Brier score, we use a binary loss index to assess skill. The binary loss index is tailored to assess the skill of rare events. We analyze daily events that are locally and spatially aggregated, as well as 7 d extreme-event counts. Results consistently show a higher skill in winter compared to summer. The regions showing the highest skill are Norway, Portugal and the south of the Alps. Skill increases when aggregating the extremes spatially or temporally. The verification methodology can be adapted and applied to other variables, e.g., temperature extremes or river discharge.</p
Statistical Mechanics of the Hyper Vertex Cover Problem
We introduce and study a new optimization problem called Hyper Vertex Cover.
This problem is a generalization of the standard vertex cover to hypergraphs:
one seeks a configuration of particles with minimal density such that every
hyperedge of the hypergraph contains at least one particle. It can also be used
in important practical tasks, such as the Group Testing procedures where one
wants to detect defective items in a large group by pool testing. Using a
Statistical Mechanics approach based on the cavity method, we study the phase
diagram of the HVC problem, in the case of random regualr hypergraphs.
Depending on the values of the variables and tests degrees different situations
can occur: The HVC problem can be either in a replica symmetric phase, or in a
one-step replica symmetry breaking one. In these two cases, we give explicit
results on the minimal density of particles, and the structure of the phase
space. These problems are thus in some sense simpler than the original vertex
cover problem, where the need for a full replica symmetry breaking has
prevented the derivation of exact results so far. Finally, we show that
decimation procedures based on the belief propagation and the survey
propagation algorithms provide very efficient strategies to solve large
individual instances of the hyper vertex cover problem.Comment: Submitted to PR
Cusps and shocks in the renormalized potential of glassy random manifolds: How Functional Renormalization Group and Replica Symmetry Breaking fit together
We compute the Functional Renormalization Group (FRG) disorder- correlator
function R(v) for d-dimensional elastic manifolds pinned by a random potential
in the limit of infinite embedding space dimension N. It measures the
equilibrium response of the manifold in a quadratic potential well as the
center of the well is varied from 0 to v. We find two distinct scaling regimes:
(i) a "single shock" regime, v^2 ~ 1/L^d where L^d is the system volume and
(ii) a "thermodynamic" regime, v^2 ~ N. In regime (i) all the equivalent
replica symmetry breaking (RSB) saddle points within the Gaussian variational
approximation contribute, while in regime (ii) the effect of RSB enters only
through a single anomaly. When the RSB is continuous (e.g., for short-range
disorder, in dimension 2 <= d <= 4), we prove that regime (ii) yields the
large-N FRG function obtained previously. In that case, the disorder correlator
exhibits a cusp in both regimes, though with different amplitudes and of
different physical origin. When the RSB solution is 1-step and non- marginal
(e.g., d < 2 for SR disorder), the correlator R(v) in regime (ii) is
considerably reduced, and exhibits no cusp. Solutions of the FRG flow
corresponding to non-equilibrium states are discussed as well. In all cases the
regime (i) exhibits a cusp non-analyticity at T=0, whose form and thermal
rounding at finite T is obtained exactly and interpreted in terms of shocks.
The results are compared with previous work, and consequences for manifolds at
finite N, as well as extensions to spin glasses and related models are
discussed.Comment: v2: Note added in proo
The cavity method for large deviations
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 compute exponentially small probabilities (rate functions) over different
classes of random graphs. It is illustrated with two combinatorial optimization
problems, the vertex-cover and coloring problems, for which the presence of
replica symmetry breaking phases is taken into account. Applications include
the analysis of models on adaptive graph structures.Comment: 18 pages, 7 figure
Statistical mechanics of error exponents for error-correcting codes
Error exponents characterize the exponential decay, when increasing message
length, of the probability of error of many error-correcting codes. To tackle
the long standing problem of computing them exactly, we introduce a general,
thermodynamic, formalism that we illustrate with maximum-likelihood decoding of
low-density parity-check (LDPC) codes on the binary erasure channel (BEC) and
the binary symmetric channel (BSC). In this formalism, we apply the cavity
method for large deviations to derive expressions for both the average and
typical error exponents, which differ by the procedure used to select the codes
from specified ensembles. When decreasing the noise intensity, we find that two
phase transitions take place, at two different levels: a glass to ferromagnetic
transition in the space of codewords, and a paramagnetic to glass transition in
the space of codes.Comment: 32 pages, 13 figure
Message passing for vertex covers
Constructing a minimal vertex cover of a graph can be seen as a prototype for
a combinatorial optimization problem under hard constraints. In this paper, we
develop and analyze message passing techniques, namely warning and survey
propagation, which serve as efficient heuristic algorithms for solving these
computational hard problems. We show also, how previously obtained results on
the typical-case behavior of vertex covers of random graphs can be recovered
starting from the message passing equations, and how they can be extended.Comment: 25 pages, 9 figures - version accepted for publication in PR
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