2,771 research outputs found

### A perturbative approach to non-linearities in the information carried by a two layer neural network

We evaluate the mutual information between the input and the output of a two
layer network in the case of a noisy and non-linear analogue channel. In the
case where the non-linearity is small with respect to the variability in the
noise, we derive an exact expression for the contribution to the mutual
information given by the non-linear term in first order of perturbation theory.
Finally we show how the calculation can be simplified by means of a
diagrammatic expansion. Our results suggest that the use of perturbation
theories applied to neural systems might give an insight on the contribution of
non-linearities to the information transmission and in general to the neuronal
dynamics.Comment: Accepted as a preprint of ICTP, Triest

### Stability of the replica symmetric solution for the information conveyed by by a neural network

The information that a pattern of firing in the output layer of a feedforward
network of threshold-linear neurons conveys about the network's inputs is
considered. A replica-symmetric solution is found to be stable for all but
small amounts of noise. The region of instability depends on the contribution
of the threshold and the sparseness: for distributed pattern distributions, the
unstable region extends to higher noise variances than for very sparse
distributions, for which it is almost nonexistant.Comment: 19 pages, LaTeX, 5 figures. Also available at
http://www.mrc-bbc.ox.ac.uk/~schultz/papers.html . Submitted to Phys. Rev. E
Minor change

### Effective Free Energy for Individual Dynamics

Physics and economics are two disciplines that share the common challenge of
linking microscopic and macroscopic behaviors. However, while physics is based
on collective dynamics, economics is based on individual choices. This
conceptual difference is one of the main obstacles one has to overcome in order
to characterize analytically economic models. In this paper, we build both on
statistical mechanics and the game theory notion of Potential Function to
introduce a rigorous generalization of the physicist's free energy, which
includes individual dynamics. Our approach paves the way to analytical
treatments of a wide range of socio-economic models and might bring new
insights into them. As first examples, we derive solutions for a congestion
model and a residential segregation model.Comment: 8 pages, 2 figures, presented at the ECCS'10 conferenc

### Multifractal Properties of Price Fluctuations of Stocks and Commodities

We analyze daily prices of 29 commodities and 2449 stocks, each over a period
of $\approx 15$ years. We find that the price fluctuations for commodities have
a significantly broader multifractal spectrum than for stocks. We also propose
that multifractal properties of both stocks and commodities can be attributed
mainly to the broad probability distribution of price fluctuations and
secondarily to their temporal organization. Furthermore, we propose that, for
commodities, stronger higher order correlations in price fluctuations result in
broader multifractal spectra.Comment: Published in Euro Physics Letters (14 pages, 5 figures

### Synchronization interfaces and overlapping communities in complex networks

We show that a complex network of phase oscillators may display interfaces
between domains (clusters) of synchronized oscillations. The emergence and
dynamics of these interfaces are studied in the general framework of
interacting phase oscillators composed of either dynamical domains (influenced
by different forcing processes), or structural domains (modular networks). The
obtained results allow to give a functional definition of overlapping
structures in modular networks, and suggest a practical method to identify
them. As a result, our algorithm could detect information on both single
overlapping nodes and overlapping clusters.Comment: 5 pages, 4 figure

### Precision radial velocities of double-lined spectroscopic binaries with an iodine absorption cell

A spectroscopic technique employing an iodine absorption cell (I_2) to
superimpose a reference spectrum onto a stellar spectrum is currently the most
widely adopted approach to obtain precision radial velocities of solar-type
stars. It has been used to detect ~80 extrasolar planets out of ~130 know. Yet
in its original version, it only allows us to measure precise radial velocities
of single stars. In this paper, we present a novel method employing an I_2
absorption cell that enables us to accurately determine radial velocities of
both components of double-lined binaries. Our preliminary results based on the
data from the Keck I telescope and HIRES spectrograph demonstrate that 20-30
m/s radial velocity precision can be routinely obtained for "early" type
binaries (F3-F8). For later type binaries, the precision reaches ~10 m/s. We
discuss applications of the technique to stellar astronomy and searches for
extrasolar planets in binary systems. In particular, we combine the
interferometric data collected with the Palomar Testbed Interferometer with our
preliminary precision velocities of the spectroscopic double-lined binary HD
4676 to demonstrate that with such a combination one can routinely obtain
masses of the binary components accurate at least at the level of 1.0%.Comment: Accepted for publication in The Astrophysical Journa

### The mutual information of a stochastic binary channel: validity of the Replica Symmetry Ansatz

We calculate the mutual information (MI) of a two-layered neural network with
noiseless, continuous inputs and binary, stochastic outputs under several
assumptions on the synaptic efficiencies. The interesting regime corresponds to
the limit where the number of both input and output units is large but their
ratio is kept fixed at a value $\alpha$. We first present a solution for the MI
using the replica technique with a replica symmetric (RS) ansatz. Then we find
an exact solution for this quantity valid in a neighborhood of $\alpha = 0$. An
analysis of this solution shows that the system must have a phase transition at
some finite value of $\alpha$. This transition shows a singularity in the third
derivative of the MI. As the RS solution turns out to be infinitely
differentiable, it could be regarded as a smooth approximation to the MI. This
is checked numerically in the validity domain of the exact solution.Comment: Latex, 29 pages, 2 Encapsulated Post Script figures. To appear in
Journal of Physics

### Modelling the individual and collective dynamics of the propensity to offend

We introduce a general framework for modelling the dynamics of the propensity to offend in a population of (possibly interacting) agents. We consider that each agent has an honesty index which parameterizes his probability of abiding by the law. This probability also depends on a composite parameter associated to the attractiveness of the crime outcome and of the crime setting (the context which makes a crime more or less likely to occur, such as the presence or not of a guardian). Within this framework we explore some consequences of the working hypothesis that punishment has a deterrent effect, assuming that, after a criminal act, an agent's honesty index may increase if he is caught and decrease otherwise. We provide both analytical and numerical results. We show that in the space of parameters characterizing the probability of punishment, there are two phases: one corresponding to a population with a low crime rate and the other to a population with a large crime rate. We speculate on the possible existence of a self-organized state in which, due to the society reaction against crime activities, the population dynamics would be stabilized on the critical line, leading to a wide distribution of propensities to offend in the population. In view of empirical works on the causes of the recent evolution of crime rates in developed countries, we discuss how changes of socio-economic conditions may affect the model parameters, and hence the crime rate in the population. We suggest possible extensions of the model that will allow us to take into account more realistic features.Fil: Nadal, J. P.. Centre National de la Recherche Scientifique; Francia. École des Hautes Études en Sciences Sociales; Francia. Université Pierre et Marie Curie; FranciaFil: Gordon, M. B.. Université de Grenoble I; FranciaFil: Iglesias, J. R.. Universidade Federal do Rio Grande do Sul; BrasilFil: Semeshenko, Viktoriya. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Económicas. Departamento de Economía; Argentin

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