252 research outputs found
Replica symmetric evaluation of the information transfer in a two-layer network in presence of continuous+discrete stimuli
In a previous report we have evaluated analytically the mutual information
between the firing rates of N independent units and a set of multi-dimensional
continuous+discrete stimuli, for a finite population size and in the limit of
large noise. Here, we extend the analysis to the case of two interconnected
populations, where input units activate output ones via gaussian weights and a
threshold linear transfer function. We evaluate the information carried by a
population of M output units, again about continuous+discrete correlates. The
mutual information is evaluated solving saddle point equations under the
assumption of replica symmetry, a method which, by taking into account only the
term linear in N of the input information, is equivalent to assuming the noise
to be large. Within this limitation, we analyze the dependence of the
information on the ratio M/N, on the selectivity of the input units and on the
level of the output noise. We show analytically, and confirm numerically, that
in the limit of a linear transfer function and of a small ratio between output
and input noise, the output information approaches asymptotically the
information carried in input. Finally, we show that the information loss in
output does not depend much on the structure of the stimulus, whether purely
continuous, purely discrete or mixed, but only on the position of the threshold
nonlinearity, and on the ratio between input and output noise.Comment: 19 pages, 4 figure
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 . 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 . An
analysis of this solution shows that the system must have a phase transition at
some finite value of . 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
On bi-integrable natural Hamiltonian systems on the Riemannian manifolds
We introduce the concept of natural Poisson bivectors, which generalizes the
Benenti approach to construction of natural integrable systems on the
Riemannian manifolds and allows us to consider almost the whole known zoo of
integrable systems in framework of bi-hamiltonian geometry.Comment: 24 pages, LaTeX with AMSfonts (some new references were added
Children’s Moral Emotion Attribution in the Happy Victimizer Task: The Role of Response Format
Previous research in the happy victimizer tradition indicated that preschool and early elementary-school children attribute positive emotions to the violator of a moral norm, whereas older children attribute negative moral emotions. Cognitive and motivational processes have been suggested as underlying this developmental shift. The current research investigated whether making the happy victimizer task less cognitively demanding, by providing children with alternative response formats, would increase children’s attribution of moral emotions and moral motivation. In Study 1, 93 4- to 7-year-old British children responded to the happy victimizer questions either in a normal condition (where they spontaneously pointed with a finger), a wait condition (where they had to wait before giving their answers), or an arrow condition (where they had to point with a paper arrow). In Study 2, 40 Spanish 4-year-old children responded in the happy victimizer task either in a normal or a wait condition. In both studies, participants’ attribution of moral emotions and moral motivation was significantly higher in the conditions with alternative response formats (wait, arrow) than in the normal condition. The role of cognitive abilities for emotion attribution in the happy victimizer task is discussed
One invariant measure and different Poisson brackets for two nonholonomic systems
We discuss the nonholonomic Chaplygin and the Borisov-Mamaev-Fedorov systems,
for which symplectic forms are different deformations of the square root from
the corresponding invariant volume form. In both cases second Poisson bivectors
are determined by -tensors with non-zero torsion on the configurational
space, in contrast with the well known Eisenhart-Benenti and Turiel
constructions.Comment: 18 pages, LaTeX with AMSfont
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Measuring Unethical Consumer Behavior Across Four Countries
The huge amounts spent on store security and crime prevention worldwide, not only costs international businesses, but also amounts to a hidden tax on those law-binding consumers who bear higher prices. Most previous research has focused on shoplifting and ignored many other ways in which consumers cheat businesses. Using a hybrid of both qualitative research and survey approaches in four countries, an index of 37 activities was developed to examine consumers’ unethical activities across UK, US, France, and Austria. The findings indicate that around three quarters of consumers in all four countries can be classified as heavy offenders for these minor cheats. The paper argues that government agencies, marketers, and retailers should adopt more pro-active preventative approaches, rather than reactive loss limitation measures to combat unethical behavior
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