140 research outputs found
Multi-surface coding simulations of the restricted solid-on-solid model in four dimensions
We study the Restricted Solid on Solid (RSOS) model for surface growth in
spatial dimension d=4 by means of a multi-surface coding technique that allows
to analyze samples to analyze samples of size up to in the steady state
regime. For such large systems we are able to achieve a controlled asymptotic
regime where the typical scale of the fluctuations are larger than the lattice
spacing used in the simulations. A careful finite-size scaling analysis of the
critical exponents clearly indicate that d=4 is not the upper critical
dimension of the model.Comment: 6 pages, 3 pdf figures, changed title and minor changes in the
abstract, added some references. This is the published versio
Numerical estimate of the Kardar Parisi Zhang universality class in (2 + 1) dimensions
We study the Restricted Solid on Solid model for surface growth in spatial
dimension by means of a multi-surface coding technique that allows to
produce a large number of samples of samples in the stationary regime in a
reasonable computational time. Thanks to: (i) a careful finite-size scaling
analysis of the critical exponents, (ii) the accurate estimate of the first
three moments of the height fluctuations, we can quantify the wandering
exponent with unprecedented precision: . This figure is
incompatible with the long-standing conjecture due to Kim and Koesterlitz that
hypothesized .Comment: 4 pages, 4 figure
Threshold values, stability analysis and high-q asymptotics for the coloring problem on random graphs
We consider the problem of coloring Erdos-Renyi and regular random graphs of
finite connectivity using q colors. It has been studied so far using the cavity
approach within the so-called one-step replica symmetry breaking (1RSB) ansatz.
We derive a general criterion for the validity of this ansatz and, applying it
to the ground state, we provide evidence that the 1RSB solution gives exact
threshold values c_q for the q-COL/UNCOL phase transition. We also study the
asymptotic thresholds for q >> 1 finding c_q = 2qlog(q)-log(q)-1+o(1) in
perfect agreement with rigorous mathematical bounds, as well as the nature of
excited states, and give a global phase diagram of the problem.Comment: 23 pages, 10 figures. Replaced with accepted versio
Estimating the size of the solution space of metabolic networks
In this work we propose a novel algorithmic strategy that allows for an
efficient characterization of the whole set of stable fluxes compatible with
the metabolic constraints. The algorithm, based on the well-known Bethe
approximation, allows the computation in polynomial time of the volume of a non
full-dimensional convex polytope in high dimensions. The result of our
algorithm match closely the prediction of Monte Carlo based estimations of the
flux distributions of the Red Blood Cell metabolic network but in incomparably
shorter time. We also analyze the statistical properties of the average fluxes
of the reactions in the E-Coli metabolic network and finally to test the effect
of gene knock-outs on the size of the solution space of the E-Coli central
metabolism.Comment: 8 pages, 7 pdf figure
Statistical mechanics of sparse generalization and model selection
One of the crucial tasks in many inference problems is the extraction of
sparse information out of a given number of high-dimensional measurements. In
machine learning, this is frequently achieved using, as a penality term, the
norm of the model parameters, with for efficient dilution. Here
we propose a statistical-mechanics analysis of the problem in the setting of
perceptron memorization and generalization. Using a replica approach, we are
able to evaluate the relative performance of naive dilution (obtained by
learning without dilution, following by applying a threshold to the model
parameters), dilution (which is frequently used in convex optimization)
and dilution (which is optimal but computationally hard to implement).
Whereas both diluted approaches clearly outperform the naive approach, we
find a small region where works almost perfectly and strongly outperforms
the simpler to implement dilution.Comment: 18 pages, 9 eps figure
An analytic approximation of the feasible space of metabolic networks
Assuming a steady-state condition within a cell, metabolic fluxes satisfy an
under-determined linear system of stoichiometric equations. Characterizing the
space of fluxes that satisfy such equations along with given bounds (and
possibly additional relevant constraints) is considered of utmost importance
for the understanding of cellular metabolism. Extreme values for each
individual flux can be computed with Linear Programming (as Flux Balance
Analysis), and their marginal distributions can be approximately computed with
Monte-Carlo sampling. Here we present an approximate analytic method for the
latter task based on Expectation Propagation equations that does not involve
sampling and can achieve much better predictions than other existing analytic
methods. The method is iterative, and its computation time is dominated by one
matrix inversion per iteration. With respect to sampling, we show through
extensive simulation that it has some advantages including computation time,
and the ability to efficiently fix empirically estimated distributions of
fluxes
Propagation of external regulation and asynchronous dynamics in random Boolean networks
Boolean Networks and their dynamics are of great interest as abstract
modeling schemes in various disciplines, ranging from biology to computer
science. Whereas parallel update schemes have been studied extensively in past
years, the level of understanding of asynchronous updates schemes is still very
poor. In this paper we study the propagation of external information given by
regulatory input variables into a random Boolean network. We compute both
analytically and numerically the time evolution and the asymptotic behavior of
this propagation of external regulation (PER). In particular, this allows us to
identify variables which are completely determined by this external
information. All those variables in the network which are not directly fixed by
PER form a core which contains in particular all non-trivial feedback loops. We
design a message-passing approach allowing to characterize the statistical
properties of these cores in dependence of the Boolean network and the external
condition. At the end we establish a link between PER dynamics and the full
random asynchronous dynamics of a Boolean network.Comment: 19 pages, 14 figures, to appear in Chao
Stability of the replica symmetric solution in diluted perceptron learning
We study the role played by the dilution in the average behavior of a
perceptron model with continuous coupling with the replica method. We analyze
the stability of the replica symmetric solution as a function of the dilution
field for the generalization and memorization problems. Thanks to a Gardner
like stability analysis we show that at any fixed ratio between the
number of patterns M and the dimension N of the perceptron (),
there exists a critical dilution field above which the replica symmetric
ansatz becomes unstable.Comment: Stability of the solution in arXiv:0907.3241, 13 pages, (some typos
corrected
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