7,675 research outputs found
General properties of overlap probability distributions in disordered spin systems. Toward Parisi ultrametricity
For a very general class of probability distributions in disordered Ising
spin systems, in the thermodynamical limit, we prove the following property for
overlaps among real replicas. Consider the overlaps among s replicas. Add one
replica s+1. Then, the overlap q(a,s+1) between one of the first s replicas,
let us say a, and the added s+1 is either independent of the former ones, or it
is identical to one of the overlaps q(a,b), with b running among the first s
replicas, excluding a. Each of these cases has equal probability 1/s.Comment: LaTeX2e, 11 pages. Submitted to Journal of Physics A: Mathematical
and General. Also available at
http://rerumnatura.zool.su.se/stefano/ms/ghigu.p
An Extended Variational Principle for the SK Spin-Glass Model
The recent proof by F. Guerra that the Parisi ansatz provides a lower bound
on the free energy of the SK spin-glass model could have been taken as offering
some support to the validity of the purported solution. In this work we present
a broader variational principle, in which the lower bound, as well as the
actual value, are obtained through an optimization procedure for which
ultrametic/hierarchal structures form only a subset of the variational class.
The validity of Parisi's ansatz for the SK model is still in question. The new
variational principle may be of help in critical review of the issue.Comment: 4 pages, Revtex
Aggressive Victims, Passive Victims, and Bullies: Developmental Continuity or Developmental Change?
We evaluated the extent to which aggressive victims show unique developmental pathways that are different from those of passive victims, bullies, and uninvolved children. A total of 1,722 children were followed from 4th grade to 6th grade, and the prevalence and stability of each group were assessed. Aggressive victims became less prevalent and passive victims and bullies became more prevalent with age. Although it was common for aggressive victims and bullies to move from one group to the other across time, there was little overlap with the passive victim group. Stability estimates were higher for the bully and aggressive victim groups than for the passive victim group, and patterns of stability were influenced by peer rejection and exposure to violence
Replica symmetry breaking in mean field spin glasses trough Hamilton-Jacobi technique
During the last years, through the combined effort of the insight, coming
from physical intuition and computer simulation, and the exploitation of
rigorous mathematical methods, the main features of the mean field
Sherrington-Kirkpatrick spin glass model have been firmly established. In
particular, it has been possible to prove the existence and uniqueness of the
infinite volume limit for the free energy, and its Parisi expression, in terms
of a variational principle, involving a functional order parameter. Even the
expected property of ultrametricity, for the infinite volume states, seems to
be near to a complete proof. The main structural feature of this model, and
related models, is the deep phenomenon of spontaneous replica symmetry breaking
(RSB), discovered by Parisi many years ago. By expanding on our previous work,
the aim of this paper is to investigate a general frame, where replica symmetry
breaking is embedded in a kind of mechanical scheme of the Hamilton-Jacobi
type. Here, the analog of the "time" variable is a parameter characterizing the
strength of the interaction, while the "space" variables rule out
quantitatively the broken replica symmetry pattern. Starting from the simple
cases, where annealing is assumed, or replica symmetry, we build up a
progression of dynamical systems, with an increasing number of space variables,
which allow to weaken the effect of the potential in the Hamilton-Jacobi
equation, as the level of symmetry braking is increased. This new machinery
allows to work out mechanically the general K-step RSB solutions, in a
different interpretation with respect to the replica trick, and lightens easily
their properties as existence or uniqueness.Comment: 24 pages, no figure
Interpolating the Sherrington-Kirkpatrick replica trick
The interpolation techniques have become, in the past decades, a powerful
approach to lighten several properties of spin glasses within a simple
mathematical framework. Intrinsically, for their construction, these schemes
were naturally implemented into the cavity field technique, or its variants as
the stochastic stability or the random overlap structures. However the first
and most famous approach to mean field statistical mechanics with quenched
disorder is the replica trick. Among the models where these methods have been
used (namely, dealing with frustration and complexity), probably the best known
is the Sherrington-Kirkpatrick spin glass: In this paper we are pleased to
apply the interpolation scheme to the replica trick framework and test it
directly to the cited paradigmatic model: interestingly this allows to obtain
easily the replica-symmetric control and, synergically with the broken replica
bounds, a description of the full RSB scenario, both coupled with several minor
theorems. Furthermore, by treating the amount of replicas as an
interpolating parameter (far from its original interpretation) this can be
though of as a quenching temperature close to the one introduce in
off-equilibrium approaches and, within this viewpoint, the proof of the
attended commutativity of the zero replica and the infinite volume limits can
be obtained.Comment: This article is dedicated to David Sherrington on the occasion of his
seventieth birthda
The mean field theory of spin glasses: the heuristic replica approach and recent rigorous results
The mathematically correct computation of the spin glasses free energy in the
infinite range limit crowns 25 years of mathematic efforts in solving this
model. The exact solution of the model was found many years ago by using a
heuristic approach; the results coming from the heuristic approach were crucial
in deriving the mathematical results. The mathematical tools used in the
rigorous approach are quite different from those of the heuristic approach. In
this note we will review the heuristic approach to spin glasses in the light of
the rigorous results; we will also discuss some conjectures that may be useful
to derive the solution of the model in an alternative way.Comment: 12 pages, 1 figure; lecture at the Flato Colloquia Day, Thursday 27
November, 200
A Statistical Interpretation of Space and Classical-Quantum duality
By defining a prepotential function for the stationary Schr\"odinger equation
we derive an inversion formula for the space variable as a function of the
wave-function . The resulting equation is a Legendre transform that
relates , the prepotential , and the probability density. We
invert the Schr\"odinger equation to a third-order differential equation for
and observe that the inversion procedure implies a -
duality. This phenomenon is related to a modular symmetry due to the
superposition of the solutions of the Schr\"odinger equation. We propose that
in quantum mechanics the space coordinate can be interpreted as a macroscopic
variable of a statistical system with playing the role of a scaling
parameter. We show that the scaling property of the space coordinate with
respect to is determined by the
``beta-function''. We propose that the quantization of the inversion formula is
a natural way to quantize geometry. The formalism is extended to higher
dimensions and to the Klein-Gordon equation.Comment: 11 pages. Standard Latex. Final version to appear in Physical Review
Letters. Revised and extended version. The formalism is extended to higher
dimensions and to the Klein-Gordon equation. A possible connection with
string theory is considered. The duality is emphasized by a minor
change in the title. The new title is: Duality of and and a
statistical interpretation of space in quantum mechanic
How glassy are neural networks?
In this paper we continue our investigation on the high storage regime of a
neural network with Gaussian patterns. Through an exact mapping between its
partition function and one of a bipartite spin glass (whose parties consist of
Ising and Gaussian spins respectively), we give a complete control of the whole
annealed region. The strategy explored is based on an interpolation between the
bipartite system and two independent spin glasses built respectively by
dichotomic and Gaussian spins: Critical line, behavior of the principal
thermodynamic observables and their fluctuations as well as overlap
fluctuations are obtained and discussed. Then, we move further, extending such
an equivalence beyond the critical line, to explore the broken ergodicity phase
under the assumption of replica symmetry and we show that the quenched free
energy of this (analogical) Hopfield model can be described as a linear
combination of the two quenched spin-glass free energies even in the replica
symmetric framework
Role of α-Tocopherol Acetate on Nasal Respiratory Functions: Mucociliary Clearance and Rhinomanometric Evaluations in Primary Atrophic Rhinitis
Primary atrophic rhinitis is a disease of the nose and of paranasalsinuses characterized by a progressive loss of function of nasal and paranasal mucosa caused by a gradual destruction of ciliary mucosalepithelium with atrophy of serous–mucous glands and loss of bonestructures.The aim of this study was to evaluate the therapeutic effects of topic α-tochopherol acetate (vitamin E) in patients with primary atrophicrhinitis based on subjective and objective data.We analyzed 44 patients with dry nose sensation and endoscopic evidence of atrophic nasal mucosa. We analyzed endoscopic mucosascore, anterior rhinomanometry, and nasal mucociliary clearance before and after 6 months of topic treatment with α-tochopherol acetate. For statistical analysis, we used paired samples t test (95% confidence interval [CI], P <.05) for rhinomanometric and muciliary transit time evaluations and analysis of variance 1-way test (95% CI, P <.05) for endoscopic evaluation. All patients showed an improvement in “dry nose” sensation and inperception of nasal airflow. Rhinomanometric examination showed increase of nasal airflow at follow-up (P <.05); nasal mucociliaryclearance showed a reduction in mean transit time (P <.05); and endoscopic evaluation showed significative improvement of hydration of nasalmucosa and significative decreasing nasal crusts and mucusaccumulation (P <.05). Medical treatment for primary atrophic rhinitis is not clearly documented in the literature; in this research, it was demonstrated that α-ochopherol acetate could be a possible treatment for atrophic rhinitis
The marginally stable Bethe lattice spin glass revisited
Bethe lattice spins glasses are supposed to be marginally stable, i.e. their
equilibrium probability distribution changes discontinuously when we add an
external perturbation. So far the problem of a spin glass on a Bethe lattice
has been studied only using an approximation where marginally stability is not
present, which is wrong in the spin glass phase. Because of some technical
difficulties, attempts at deriving a marginally stable solution have been
confined to some perturbative regimes, high connectivity lattices or
temperature close to the critical temperature. Using the cavity method, we
propose a general non-perturbative approach to the Bethe lattice spin glass
problem using approximations that should be hopeful consistent with marginal
stability.Comment: 23 pages Revised version, hopefully clearer that the first one: six
pages longe
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