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

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

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

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

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

(1R,2R,3S,6aS,7R,8R,9S,12aS)-1,2,3,7,8,9-Hexahydroxy­perhydro­dipyrido[1,2-a:1′,2′-d]pyrazine-6,12-dione

The crystal structure of the title compound, C12H18N2O8, exists as O—H⋯O hydrogen-bonded layers of mol­ecules running parallel to the ab plane. Each mol­ecule is a donor and acceptor for six hydrogen bonds. The absolute stereochemistry was determined by the use of d-glucuronolactone as the starting material

Statistical Mechanical Development of a Sparse Bayesian Classifier

The demand for extracting rules from high dimensional real world data is increasing in various fields. However, the possible redundancy of such data sometimes makes it difficult to obtain a good generalization ability for novel samples. To resolve this problem, we provide a scheme that reduces the effective dimensions of data by pruning redundant components for bicategorical classification based on the Bayesian framework. First, the potential of the proposed method is confirmed in ideal situations using the replica method. Unfortunately, performing the scheme exactly is computationally difficult. So, we next develop a tractable approximation algorithm, which turns out to offer nearly optimal performance in ideal cases when the system size is large. Finally, the efficacy of the developed classifier is experimentally examined for a real world problem of colon cancer classification, which shows that the developed method can be practically useful.Comment: 13 pages, 6 figure

Slowly evolving geometry in recurrent neural networks I: extreme dilution regime

We study extremely diluted spin models of neural networks in which the connectivity evolves in time, although adiabatically slowly compared to the neurons, according to stochastic equations which on average aim to reduce frustration. The (fast) neurons and (slow) connectivity variables equilibrate separately, but at different temperatures. Our model is exactly solvable in equilibrium. We obtain phase diagrams upon making the condensed ansatz (i.e. recall of one pattern). These show that, as the connectivity temperature is lowered, the volume of the retrieval phase diverges and the fraction of mis-aligned spins is reduced. Still one always retains a region in the retrieval phase where recall states other than the one corresponding to the `condensed' pattern are locally stable, so the associative memory character of our model is preserved.Comment: 18 pages, 6 figure

Generalizing with perceptrons in case of structured phase- and pattern-spaces

We investigate the influence of different kinds of structure on the learning behaviour of a perceptron performing a classification task defined by a teacher rule. The underlying pattern distribution is permitted to have spatial correlations. The prior distribution for the teacher coupling vectors itself is assumed to be nonuniform. Thus classification tasks of quite different difficulty are included. As learning algorithms we discuss Hebbian learning, Gibbs learning, and Bayesian learning with different priors, using methods from statistics and the replica formalism. We find that the Hebb rule is quite sensitive to the structure of the actual learning problem, failing asymptotically in most cases. Contrarily, the behaviour of the more sophisticated methods of Gibbs and Bayes learning is influenced by the spatial correlations only in an intermediate regime of $\alpha$, where $\alpha$ specifies the size of the training set. Concerning the Bayesian case we show, how enhanced prior knowledge improves the performance.Comment: LaTeX, 32 pages with eps-figs, accepted by J Phys

Near-Infrared Spectroscopy of Molecular Filaments in the Reflection Nebula NGC 7023

We present near-infrared spectroscopy of fluorescent molecular hydrogen (H_2) emission from molecular filaments in the reflection nebula NGC 7023. We derive the relative column densities of H_2 rotational-vibrational states from the measured line emission and compare these results with several model photodissociation regions covering a range of densities, incident UV-fields, and excitation mechanisms. Our best-fit models for one filament suggest, but do not require, either a combination of different densities, suggesting clumps of 10^6 cm^{-3} in a 10^4 - 10^5 cm^{-3} filament, or a combination of fluorescent excitation and thermally-excited gas, perhaps due to a shock from a bipolar outflow. We derive densities and UV fields for these molecular filaments that are in agreement with previous determinations.Comment: ApJ accepted, 26 pages including 5 embedded figures, uses AASTEX. Also available at http://www-astronomy.mps.ohio-state.edu/~martini/pubs.htm