Thermodynamic properties of extremely diluted symmetric Q-Ising neural networks

Using the replica-symmetric mean-field theory approach the thermodynamic and retrieval properties of extremely diluted {\it symmetric} $Q$-Ising neural networks are studied. In particular, capacity-gain parameter and capacity-temperature phase diagrams are derived for $Q=3, 4$ and $Q=\infty$. The zero-temperature results are compared with those obtained from a study of the dynamics of the model. Furthermore, the de Almeida-Thouless line is determined. Where appropriate, the difference with other $Q$-Ising architectures is outlined.Comment: 16 pages Latex including 6 eps-figures. Corrections, also in most of the figures have been mad

Amanita wadulawitu (Basidiomycota), a new species from Western Australia, and an expanded description of A. kalamundae

A new species of Amanita Pers. is documented from Western Australia. Amanita wadulawitu L.E.McGurk, E.M.Davison & E.L.J.Watkin is described from the Perth IBRA subregion. Amanita kalamundae O.K.Mill. is redescribed to include additional collections, drawing attention to the presence of clamp connections in the lamellae and at the base of basidia. A BLASTn search has shown that there are no exact matches of the nuclear ribosomal internal transcribed spacer (ITS) region of either species in GenBank

Correlated patterns in non-monotonic graded-response perceptrons

The optimal capacity of graded-response perceptrons storing biased and spatially correlated patterns with non-monotonic input-output relations is studied. It is shown that only the structure of the output patterns is important for the overall performance of the perceptrons.Comment: 4 pages, 4 figure

Neotypification and redescription of Amanita preissii (Basidiomycota), and reconsideration of the status of A. griseibrunnea

Amanita preissii (Fr.) Sacc. is redescribed. Re-examination of collections of A. griseibrunnea O.K.Mill. show that they do not differ significantly from A. preissii and the two species are combined. This species is common in the Perth IBRA subregion. Sequence data from the nuclear ribosomal internal transcribed spacer (ITS) region, 28S nuclear ribosomal large subunit rRNA (28S) region, RNA polymerase II (RPB2) region, β-tubulin region and translation elongation factor 1-α (EF1-α) region have been deposited in GenBank

The Little-Hopfield model on a Random Graph

We study the Hopfield model on a random graph in scaling regimes where the average number of connections per neuron is a finite number and where the spin dynamics is governed by a synchronous execution of the microscopic update rule (Little-Hopfield model).We solve this model within replica symmetry and by using bifurcation analysis we prove that the spin-glass/paramagnetic and the retrieval/paramagnetictransition lines of our phase diagram are identical to those of sequential dynamics.The first-order retrieval/spin-glass transition line follows by direct evaluation of our observables using population dynamics. Within the accuracy of numerical precision and for sufficiently small values of the connectivity parameter we find that this line coincides with the corresponding sequential one. Comparison with simulation experiments shows excellent agreement.Comment: 14 pages, 4 figure

Multi-Choice Minority Game

The generalization of the problem of adaptive competition, known as the minority game, to the case of $K$ possible choices for each player is addressed, and applied to a system of interacting perceptrons with input and output units of the type of $K$-states Potts-spins. An optimal solution of this minority game as well as the dynamic evolution of the adaptive strategies of the players are solved analytically for a general $K$ and compared with numerical simulations.Comment: 5 pages, 2 figures, reorganized and clarifie

Draft Genome Sequence of the Iron-Oxidizing, Acidophilic, and Halotolerant “Thiobacillus prosperus” Type Strain DSM 5130

“Thiobacillus prosperus” is a halotolerant mesophilic acidophile that gains energy through iron and sulfur oxidation. Its physiology is poorly understood. Here, we describe the principal genomic features of the type strain of T. prosperus, DSM 5130. This is the first public genome sequence of an acidophilic halotolerant bacterium

A Hebbian approach to complex network generation

Through a redefinition of patterns in an Hopfield-like model, we introduce and develop an approach to model discrete systems made up of many, interacting components with inner degrees of freedom. Our approach clarifies the intrinsic connection between the kind of interactions among components and the emergent topology describing the system itself; also, it allows to effectively address the statistical mechanics on the resulting networks. Indeed, a wide class of analytically treatable, weighted random graphs with a tunable level of correlation can be recovered and controlled. We especially focus on the case of imitative couplings among components endowed with similar patterns (i.e. attributes), which, as we show, naturally and without any a-priori assumption, gives rise to small-world effects. We also solve the thermodynamics (at a replica symmetric level) by extending the double stochastic stability technique: free energy, self consistency relations and fluctuation analysis for a picture of criticality are obtained

Retrieval behavior and thermodynamic properties of symmetrically diluted Q-Ising neural networks

The retrieval behavior and thermodynamic properties of symmetrically diluted Q-Ising neural networks are derived and studied in replica-symmetric mean-field theory generalizing earlier works on either the fully connected or the symmetrical extremely diluted network. Capacity-gain parameter phase diagrams are obtained for the Q=3, Q=4 and $Q=\infty$ state networks with uniformly distributed patterns of low activity in order to search for the effects of a gradual dilution of the synapses. It is shown that enlarged regions of continuous changeover into a region of optimal performance are obtained for finite stochastic noise and small but finite connectivity. The de Almeida-Thouless lines of stability are obtained for arbitrary connectivity, and the resulting phase diagrams are used to draw conclusions on the behavior of symmetrically diluted networks with other pattern distributions of either high or low activity.Comment: 21 pages, revte