Bump formation in a binary attractor neural network

This paper investigates the conditions for the formation of local bumps in the activity of binary attractor neural networks with spatially dependent connectivity. We show that these formations are observed when asymmetry between the activity during the retrieval and learning is imposed. Analytical approximation for the order parameters is derived. The corresponding phase diagram shows a relatively large and stable region, where this effect is observed, although the critical storage and the information capacities drastically decrease inside that region. We demonstrate that the stability of the network, when starting from the bump formation, is larger than the stability when starting even from the whole pattern. Finally, we show a very good agreement between the analytical results and the simulations performed for different topologies of the network.Comment: about 14 page

Shannon Meets Carnot: Generalized Second Thermodynamic Law

The classical thermodynamic laws fail to capture the behavior of systems with energy Hamiltonian which is an explicit function of the temperature. Such Hamiltonian arises, for example, in modeling information processing systems, like communication channels, as thermal systems. Here we generalize the second thermodynamic law to encompass systems with temperature-dependent energy levels, $dQ=TdS+dT$, where $$ denotes averaging over the Boltzmann distribution and reveal a new definition to the basic notion of temperature. This generalization enables to express, for instance, the mutual information of the Gaussian channel as a consequence of the fundamental laws of nature - the laws of thermodynamics

Polynomial evaluation over finite fields: new algorithms and complexity bounds

An efficient evaluation method is described for polynomials in finite fields. Its complexity is shown to be lower than that of standard techniques when the degree of the polynomial is large enough. Applications to the syndrome computation in the decoding of Reed-Solomon codes are highlighted.Comment: accepted for publication in Applicable Algebra in Engineering, Communication and Computing. The final publication will be available at springerlink.com. DOI: 10.1007/s00200-011-0160-

Thresholds in layered neural networks with variable activity

The inclusion of a threshold in the dynamics of layered neural networks with variable activity is studied at arbitrary temperature. In particular, the effects on the retrieval quality of a self-controlled threshold obtained by forcing the neural activity to stay equal to the activity of the stored paterns during the whole retrieval process, are compared with those of a threshold chosen externally for every loading and every temperature through optimisation of the mutual information content of the network. Numerical results, mostly concerning low activity networks are discussed.Comment: 15 pages, Latex2e, 6 eps 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

Provisional Assessment of Candidate High-Temperature Thermal Conductivity Reference Materials in the EMRP “Thermo” Project

This article describes the provisional assessment of a short list of four candidate high-temperature thermal conductivity reference materials in a European research project, “Thermo.” These four candidate materials are low-density calcium silicate, amorphous silica, high-density calcium silicate, and exfoliated vermiculite. Based on initial tests on material composition and microstructure changes, dimensional stability, mechanical stability, chemical stability and uniformity, the best two candidate materials that would be considered for further detailed characterization in the next stage are low-density calcium silicate and high-density calcium silicate. These two materials are dimensionally, mechanically, and chemically stable, which are more robust and easier to handle than others. However, the specimens need to be selected to meet the requirement for material uniformity in terms of density, i.e., density variation within 2%

An iterative algorithm for parametrization of shortest length shift registers over finite rings

The construction of shortest feedback shift registers for a finite sequence S_1,...,S_N is considered over the finite ring Z_{p^r}. A novel algorithm is presented that yields a parametrization of all shortest feedback shift registers for the sequence of numbers S_1,...,S_N, thus solving an open problem in the literature. The algorithm iteratively processes each number, starting with S_1, and constructs at each step a particular type of minimal Gr\"obner basis. The construction involves a simple update rule at each step which leads to computational efficiency. It is shown that the algorithm simultaneously computes a similar parametrization for the reciprocal sequence S_N,...,S_1.Comment: Submitte

New approaches to coding information using inverse scattering transform

Remarkable mathematical properties of the integrable nonlinear Schrödinger equation (NLSE) can offer advanced solutions for the mitigation of nonlinear signal distortions in optical fiber links. Fundamental optical soliton, continuous, and discrete eigenvalues of the nonlinear spectrum have already been considered for the transmission of information in fiber-optic channels. Here, we propose to apply signal modulation to the kernel of the Gelfand-Levitan-Marchenko equations that offers the advantage of a relatively simple decoder design. First, we describe an approach based on exploiting the general N-soliton solution of the NLSE for simultaneous coding of N symbols involving 4×N coding parameters. As a specific elegant subclass of the general schemes, we introduce a soliton orthogonal frequency division multiplexing (SOFDM) method. This method is based on the choice of identical imaginary parts of the N-soliton solution eigenvalues, corresponding to equidistant soliton frequencies, making it similar to the conventional OFDM scheme, thus, allowing for the use of the efficient fast Fourier transform algorithm to recover the data. Then, we demonstrate how to use this new approach to control signal parameters in the case of the continuous spectrum

The role of duality in optimization problems involving entropy functionals with applications to information theory

We consider infinite-dimensional optimization problems involving entropy-type functionals in the objective function as well as as in the constraints. A duality theory is developed for such problems and applied to the reliability rate function problem in information theory.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45233/1/10957_2004_Article_BF00939682.pd