5,435 research outputs found
Retrieving information from a noisy "knowledge network"
We address the problem of retrieving information from a noisy version of the
``knowledge networks'' introduced by Maslov and Zhang. We map this problem onto
a disordered statistical mechanics model, which opens the door to many
analytical and numerical approaches. We give the replica symmetric solution,
compare with numerical simulations, and finally discuss an application to real
datas from the United States Senate.Comment: 10 pages, 4 figures. Writing of the last section improved; version
accepted in JSTA
From Large Scale Rearrangements to Mode Coupling Phenomenology
We consider the equilibrium dynamics of Ising spin models with multi-spin
interactions on sparse random graphs (Bethe lattices). Such models undergo a
mean field glass transition upon increasing the graph connectivity or lowering
the temperature. Focusing on the low temperature limit, we identify the large
scale rearrangements responsible for the dynamical slowing-down near the
transition. We are able to characterize exactly the dynamics near criticality
by analyzing the statistical properties of such rearrangements. Our approach
can be generalized to a large variety of glassy models on sparse random graphs,
ranging from satisfiability to kinetically constrained models.Comment: 4 pages, 4 figures, minor corrections, accepted versio
Basic properties of nonsmooth Hormander's vector fields and Poincare's inequality
We consider a family of vector fields defined in some bounded domain of R^p,
and we assume that they satisfy Hormander's rank condition of some step r, and
that their coefficients have r-1 continuous derivatives. We extend to this
nonsmooth context some results which are well-known for smooth Hormander's
vector fields, namely: some basic properties of the distance induced by the
vector fields, the doubling condition, Chow's connectivity theorem, and, under
the stronger assumption that the coefficients belong to C^{r-1,1}, Poincare's
inequality. By known results, these facts also imply a Sobolev embedding. All
these tools allow to draw some consequences about second order differential
operators modeled on these nonsmooth Hormander's vector fields.Comment: 60 pages, LaTeX; Section 6 added and Section 7 (6 in the previous
version) changed. Some references adde
The Bethe approximation for solving the inverse Ising problem: a comparison with other inference methods
The inverse Ising problem consists in inferring the coupling constants of an
Ising model given the correlation matrix. The fastest methods for solving this
problem are based on mean-field approximations, but which one performs better
in the general case is still not completely clear. In the first part of this
work, I summarize the formulas for several mean- field approximations and I
derive new analytical expressions for the Bethe approximation, which allow to
solve the inverse Ising problem without running the Susceptibility Propagation
algorithm (thus avoiding the lack of convergence). In the second part, I
compare the accuracy of different mean field approximations on several models
(diluted ferromagnets and spin glasses) defined on random graphs and regular
lattices, showing which one is in general more effective. A simple improvement
over these approximations is proposed. Also a fundamental limitation is found
in using methods based on TAP and Bethe approximations in presence of an
external field.Comment: v3: strongly revised version with new methods and results, 25 pages,
21 figure
Glassy phases in Random Heteropolymers with correlated sequences
We develop a new analytic approach for the study of lattice heteropolymers,
and apply it to copolymers with correlated Markovian sequences. According to
our analysis, heteropolymers present three different dense phases depending
upon the temperature, the nature of the monomer interactions, and the sequence
correlations: (i) a liquid phase, (ii) a ``soft glass'' phase, and (iii) a
``frozen glass'' phase. The presence of the new intermediate ``soft glass''
phase is predicted for instance in the case of polyampholytes with sequences
that favor the alternation of monomers.
Our approach is based on the cavity method, a refined Bethe Peierls
approximation adapted to frustrated systems. It amounts to a mean field
treatment in which the nearest neighbor correlations, which are crucial in the
dense phases of heteropolymers, are handled exactly. This approach is powerful
and versatile, it can be improved systematically and generalized to other
polymeric systems
On Spin-Glass Complexity
We study the quenched complexity in spin-glass mean-field models satisfying
the Becchi-Rouet-Stora-Tyutin supersymmetry. The outcome of such study,
consistent with recent numerical results, allows, in principle, to conjecture
the absence of any supersymmetric contribution to the complexity in the
Sherrington-Kirkpatrick model. The same analysis can be applied to any model
with a Full Replica Symmetry Breaking phase, e.g. the Ising -spin model
below the Gardner temperature. The existence of different solutions, breaking
the supersymmetry, is also discussed.Comment: 4 pages, 2 figures; Text changed in some parts, typos corrected,
Refs. [17],[21] and [22] added, two Refs. remove
Comparison of the Effects of Browning-Inducing Capsaicin on Two Murine Adipocyte Models
The increasing prevalence of obesity and its associated comorbidities has gained attention in developing effective treatments and strategies that promote energy expenditure and the conversion of fat from a white to a brite phenotype. Capsaicin, bioactive component of chili peppers and a transient receptor potential channel vanilloid 1 (TRPV1) agonist, has been known to stimulate the process of thermogenesis. In this study, the effects of capsaicin were assessed on two murine cellular models by quantifying the dynamic of lipid droplets (LDs) and the expression of genes involved in adipocyte browning. Present findings demonstrated that treatment with norepinephrine or capsaicin combined with norepinephrine on 3T3-L1 cells and X9 cells significantly promoted the reduction of LDs area surface and size. The transcription of browning related genes such as uncoupling protein 1 (Ucp1), T-box transcription factor 1 (Tbx1), PR domain containing 16 (Prdm16), peroxisome proliferator-activated receptor g coactivator 1a (Ppargc1a) and cell death- inducing DNA fragmentation factor A-like effector A (Cidea) was up-regulated by chronic capsaicin treatment on differentiated 3T3-L1 cells. Instead, X9 cells were significantly responsive only to the treatment with norepinephrine, used as positive control
Instability of one-step replica-symmetry-broken phase in satisfiability problems
We reconsider the one-step replica-symmetry-breaking (1RSB) solutions of two
random combinatorial problems: k-XORSAT and k-SAT. We present a general method
for establishing the stability of these solutions with respect to further steps
of replica-symmetry breaking. Our approach extends the ideas of [A.Montanari
and F. Ricci-Tersenghi, Eur.Phys.J. B 33, 339 (2003)] to more general
combinatorial problems.
It turns out that 1RSB is always unstable at sufficiently small clauses
density alpha or high energy. In particular, the recent 1RSB solution to 3-SAT
is unstable at zero energy for alpha< alpha_m, with alpha_m\approx 4.153. On
the other hand, the SAT-UNSAT phase transition seems to be correctly described
within 1RSB.Comment: 26 pages, 7 eps figure
Replicated Bethe Free Energy: A Variational Principle behind Survey Propagation
A scheme to provide various mean-field-type approximation algorithms is
presented by employing the Bethe free energy formalism to a family of
replicated systems in conjunction with analytical continuation with respect to
the number of replicas. In the scheme, survey propagation (SP), which is an
efficient algorithm developed recently for analyzing the microscopic properties
of glassy states for a fixed sample of disordered systems, can be reproduced by
assuming the simplest replica symmetry on stationary points of the replicated
Bethe free energy. Belief propagation and generalized SP can also be offered in
the identical framework under assumptions of the highest and broken replica
symmetries, respectively.Comment: appeared in Journal of the Physical Society of Japan 74, 2133-2136
(2005
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