1,180 research outputs found
Generation of unpredictable time series by a Neural Network
A perceptron that learns the opposite of its own output is used to generate a
time series. We analyse properties of the weight vector and the generated
sequence, like the cycle length and the probability distribution of generated
sequences. A remarkable suppression of the autocorrelation function is
explained, and connections to the Bernasconi model are discussed. If a
continuous transfer function is used, the system displays chaotic and
intermittent behaviour, with the product of the learning rate and amplification
as a control parameter.Comment: 11 pages, 14 figures; slightly expanded and clarified, mistakes
corrected; accepted for publication in PR
Cluster Dynamics for Randomly Frustrated Systems with Finite Connectivity
In simulations of some infinite range spin glass systems with finite
connectivity, it is found that for any resonable computational time, the
saturatedenergy per spin that is achieved by a cluster algorithm is lowered in
comparison to that achieved by Metropolis dynamics.The gap between the average
energies obtained from these two dynamics is robust with respect to variations
of the annealing schedule. For some probability distribution of the
interactions the ground state energy is calculated analytically within the
replica symmetry assumptionand is found to be saturated by a cluster algorithm.Comment: Revtex, 4 pages with 3 figure
EP-1622: Delineation of the CTV-breast performed by RTTs and radiation oncologists: a comparative study
The influence of red blood cell deformability on hematocrit profiles and platelet margination
Metastable configurations of spin models on random graphs
One-flip stable configurations of an Ising-model on a random graph with
fluctuating connectivity are examined. In order to perform the quenched average
of the number of stable configurations we introduce a global order-parameter
function with two arguments. The analytical results are compared with numerical
simulations.Comment: 11 pages Revtex, minor changes, to appear in Phys. Rev.
Statistical mechanics of the random K-SAT model
The Random K-Satisfiability Problem, consisting in verifying the existence of
an assignment of N Boolean variables that satisfy a set of M=alpha N random
logical clauses containing K variables each, is studied using the replica
symmetric framework of diluted disordered systems. We present an exact
iterative scheme for the replica symmetric functional order parameter together
for the different cases of interest K=2, K>= 3 and K>>1. The calculation of the
number of solutions, which allowed us [Phys. Rev. Lett. 76, 3881 (1996)] to
predict a first order jump at the threshold where the Boolean expressions
become unsatisfiable with probability one, is thoroughly displayed. In the case
K=2, the (rigorously known) critical value (alpha=1) of the number of clauses
per Boolean variable is recovered while for K>=3 we show that the system
exhibits a replica symmetry breaking transition. The annealed approximation is
proven to be exact for large K.Comment: 34 pages + 1 table + 8 fig., submitted to Phys. Rev. E, new section
added and references update
Survey propagation for the cascading Sourlas code
We investigate how insights from statistical physics, namely survey
propagation, can improve decoding of a particular class of sparse error
correcting codes. We show that a recently proposed algorithm, time averaged
belief propagation, is in fact intimately linked to a specific survey
propagation for which Parisi's replica symmetry breaking parameter is set to
zero, and that the latter is always superior to belief propagation in the high
connectivity limit. We briefly look at further improvements available by going
to the second level of replica symmetry breaking.Comment: 14 pages, 5 figure
Statistical properties of genealogical trees
We analyse the statistical properties of genealogical trees in a neutral
model of a closed population with sexual reproduction and non-overlapping
generations. By reconstructing the genealogy of an individual from the
population evolution, we measure the distribution of ancestors appearing more
than once in a given tree. After a transient time, the probability of
repetition follows, up to a rescaling, a stationary distribution which we
calculate both numerically and analytically. This distribution exhibits a
universal shape with a non-trivial power law which can be understood by an
exact, though simple, renormalization calculation. Some real data on human
genealogy illustrate the problem, which is relevant to the study of the real
degree of diversity in closed interbreeding communities.Comment: Accepted for publication in Phys. Rev. Let
Numerical Results for Ground States of Mean-Field Spin Glasses at low Connectivities
An extensive list of results for the ground state properties of spin glasses
on random graphs is presented. These results provide a timely benchmark for
currently developing theoretical techniques based on replica symmetry breaking
that are being tested on mean-field models at low connectivity. Comparison with
existing replica results for such models verifies the strength of those
techniques. Yet, we find that spin glasses on fixed-connectivity graphs (Bethe
lattices) exhibit a richer phenomenology than has been anticipated by theory.
Our data prove to be sufficiently accurate to speculate about some exact
results.Comment: 4 pages, RevTex4, 5 ps-figures included, related papers available at
http://www.physics.emory.edu/faculty/boettcher
Cluster expansions in dilute systems: applications to satisfiability problems and spin glasses
We develop a systematic cluster expansion for dilute systems in the highly
dilute phase. We first apply it to the calculation of the entropy of the
K-satisfiability problem in the satisfiable phase. We derive a series expansion
in the control parameter, the average connectivity, that is identical to the
one obtained by using the replica approach with a replica symmetric ({\sc rs})
{\it Ansatz}, when the order parameter is calculated via a perturbative
expansion in the control parameter. As a second application we compute the
free-energy of the Viana-Bray model in the paramagnetic phase. The cluster
expansion allows one to compute finite-size corrections in a simple manner and
these are particularly important in optimization problems. Importantly enough,
these calculations prove the exactness of the {\sc rs} {\it Ansatz} below the
percolation threshold and might require its revision between this and the
easy-to-hard transition.Comment: 21 pages, 7 figs, to appear in Phys. Rev.
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