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 $\alpha$. 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

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 $L$-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

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