345 research outputs found
Boosting search by rare events
Randomized search algorithms for hard combinatorial problems exhibit a large
variability of performances. We study the different types of rare events which
occur in such out-of-equilibrium stochastic processes and we show how they
cooperate in determining the final distribution of running times. As a
byproduct of our analysis we show how search algorithms are optimized by random
restarts.Comment: 4 pages, 3 eps figures. References update
A Causal Algebra for Liouville Exponentials
A causal Poisson bracket algebra for Liouville exponentials on a cylinder is
derived using an exchange algebra for free fields describing the in and out
asymptotics. The causal algebra involves an even number of space-time points
with a minimum of four. A quantum realisation of the algebra is obtained which
preserves causality and the local form of non-equal time brackets.Comment: 10 page
Exponentially hard problems are sometimes polynomial, a large deviation analysis of search algorithms for the random Satisfiability problem, and its application to stop-and-restart resolutions
A large deviation analysis of the solving complexity of random
3-Satisfiability instances slightly below threshold is presented. While finding
a solution for such instances demands an exponential effort with high
probability, we show that an exponentially small fraction of resolutions
require a computation scaling linearly in the size of the instance only. This
exponentially small probability of easy resolutions is analytically calculated,
and the corresponding exponent shown to be smaller (in absolute value) than the
growth exponent of the typical resolution time. Our study therefore gives some
theoretical basis to heuristic stop-and-restart solving procedures, and
suggests a natural cut-off (the size of the instance) for the restart.Comment: Revtex file, 4 figure
Coloring random graphs
We study the graph coloring problem over random graphs of finite average
connectivity . Given a number of available colors, we find that graphs
with low connectivity admit almost always a proper coloring whereas graphs with
high connectivity are uncolorable. Depending on , we find the precise value
of the critical average connectivity . Moreover, we show that below
there exist a clustering phase in which ground states
spontaneously divide into an exponential number of clusters and where the
proliferation of metastable states is responsible for the onset of complexity
in local search algorithms.Comment: 4 pages, 1 figure, version to app. in PR
A hard-sphere model on generalized Bethe lattices: Statics
We analyze the phase diagram of a model of hard spheres of chemical radius
one, which is defined over a generalized Bethe lattice containing short loops.
We find a liquid, two different crystalline, a glassy and an unusual
crystalline glassy phase. Special attention is also paid to the close-packing
limit in the glassy phase. All analytical results are cross-checked by
numerical Monte-Carlo simulations.Comment: 24 pages, revised versio
Diagonalization of replicated transfer matrices for disordered Ising spin systems
We present an alternative procedure for solving the eigenvalue problem of
replicated transfer matrices describing disordered spin systems with (random)
1D nearest neighbor bonds and/or random fields, possibly in combination with
(random) long range bonds. Our method is based on transforming the original
eigenvalue problem for a matrix (where ) into an
eigenvalue problem for integral operators. We first develop our formalism for
the Ising chain with random bonds and fields, where we recover known results.
We then apply our methods to models of spins which interact simultaneously via
a one-dimensional ring and via more complex long-range connectivity structures,
e.g. dimensional neural networks and `small world' magnets.
Numerical simulations confirm our predictions satisfactorily.Comment: 24 pages, LaTex, IOP macro
Causal Poisson Brackets of the SL(2,R) WZNW Model and its Coset Theories
From the basic chiral and anti-chiral Poisson bracket algebra of the SL(2,R)
WZNW model, non-equal time Poisson brackets are derived. Through Hamiltonian
reduction we deduce the corresponding brackets for its coset theories.Comment: 7 pages, LaTeX, no figure
Zero temperature solutions of the Edwards-Anderson model in random Husimi Lattices
We solve the Edwards-Anderson model (EA) in different Husimi lattices. We
show that, at T=0, the structure of the solution space depends on the parity of
the loop sizes. Husimi lattices with odd loop sizes have always a trivial
paramagnetic solution stable under 1RSB perturbations while, in Husimi lattices
with even loop sizes, this solution is absent. The range of stability under
1RSB perturbations of this and other RS solutions is computed analytically
(when possible) or numerically. We compute the free-energy, the complexity and
the ground state energy of different Husimi lattices at the level of the 1RSB
approximation. We also show, when the fraction of ferromagnetic couplings
increases, the existence, first, of a discontinuous transition from a
paramagnetic to a spin glass phase and latter of a continuous transition from a
spin glass to a ferromagnetic phase.Comment: 20 pages, 10 figures (v3: Corrected analysis of transitions. Appendix
proof fixed
Leukotriene receptor expression in esophageal squamous cell cancer and non-transformed esophageal epithelium: a matched case control study
Study questionnaire. (DOC 21 kb
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