Pattern reconstruction and sequence processing in feed-forward layered neural networks near saturation

The dynamics and the stationary states for the competition between pattern reconstruction and asymmetric sequence processing are studied here in an exactly solvable feed-forward layered neural network model of binary units and patterns near saturation. Earlier work by Coolen and Sherrington on a parallel dynamics far from saturation is extended here to account for finite stochastic noise due to a Hebbian and a sequential learning rule. Phase diagrams are obtained with stationary states and quasi-periodic non-stationary solutions. The relevant dependence of these diagrams and of the quasi-periodic solutions on the stochastic noise and on initial inputs for the overlaps is explicitly discussed.Comment: 9 pages, 7 figure

Instability of frozen-in states in synchronous Hebbian neural networks

The full dynamics of a synchronous recurrent neural network model with Ising binary units and a Hebbian learning rule with a finite self-interaction is studied in order to determine the stability to synaptic and stochastic noise of frozen-in states that appear in the absence of both kinds of noise. Both, the numerical simulation procedure of Eissfeller and Opper and a new alternative procedure that allows to follow the dynamics over larger time scales have been used in this work. It is shown that synaptic noise destabilizes the frozen-in states and yields either retrieval or paramagnetic states for not too large stochastic noise. The indications are that the same results may follow in the absence of synaptic noise, for low stochastic noise.Comment: 14 pages and 4 figures; accepted for publication in J. Phys. A: Math. Ge

Some tests on the grinding of cement clinker with a Hardinge Conical Ball Mill

The Hardinge Conical Mill is the invention of Mr. H.W. Hardinge and has been fully patented by him. It has been used successfully in the grinding of ores, limestone, phosphate rock, feldspar and talc. The purpose of the tests in this thesis was to determine the worth and adaptability of the Conical Mill for the preliminary grinding of cement clinker and to determine the relative merits of this type of grinder as compared to the roll type of grinder. The tests herein were performed under the direction of the writer assisted personally and through correspondence by Mr. H.W. Hardinge of the Hardinge Conical Mill Co. While conclusive results have not been determined, the main results have been attained and further testing will be in the nature of adjusting and designing suitable screening and feeding devices --Scope of Thesis, Page 2

Period-two cycles in a feed-forward layered neural network model with symmetric sequence processing

The effects of dominant sequential interactions are investigated in an exactly solvable feed-forward layered neural network model of binary units and patterns near saturation in which the interaction consists of a Hebbian part and a symmetric sequential term. Phase diagrams of stationary states are obtained and a new phase of cyclic correlated states of period two is found for a weak Hebbian term, independently of the number of condensed patterns $c$.Comment: 8 pages and 5 figure

Why Are There So Many Cichlid Species? On the Interplay of Speciation and Adaptive Radiation

The explosive speciation of cichlid fishes in the African great lakes has intrigued biologists for many decades. Interest was revitalized in 1996 after the publication in Science of geological data [1] indicating that the youngest lake, Lake Victoria, must have been completely dry during the most recent Ice perhaps as recently as 12,400 years ago. This implies that the approximately 500 haplochromine cichlid species must have evolved within this extremely short timespan from a single ancestral species [2]. But even with lower estimates of species number and higher estimates of the age of the species flock, the haplochromine cichlids still present one of the most dramatic examples of speciation and diversification in vertebrates

Symmetric sequence processing in a recurrent neural network model with a synchronous dynamics

The synchronous dynamics and the stationary states of a recurrent attractor neural network model with competing synapses between symmetric sequence processing and Hebbian pattern reconstruction is studied in this work allowing for the presence of a self-interaction for each unit. Phase diagrams of stationary states are obtained exhibiting phases of retrieval, symmetric and period-two cyclic states as well as correlated and frozen-in states, in the absence of noise. The frozen-in states are destabilised by synaptic noise and well separated regions of correlated and cyclic states are obtained. Excitatory or inhibitory self-interactions yield enlarged phases of fixed-point or cyclic behaviour.Comment: Accepted for publication in Journal of Physics A: Mathematical and Theoretica

Hox Genes, Digit Identities and the Theropod/Bird Transition

Vargas and Fallon (2005) propose that Hox gene expression patterns indicate that the most anterior digit in bird wings is homologous to digit 1 rather than to digit 2 in other amniotes. This interpretation is based on the presence of Hoxd13 expression in combination with the absence of Hoxd12 expression in the second digit condensation from which this digit develops (the first condensation is transiently present). This is a pattern that is similar to that in the developing digit 1 of the chicken foot and the mouse hand and foot. They have tested this new hypothesis by analysing Hoxd12 and Hoxd13 expression patterns in two polydactylous chicken mutants, Silkie and talpid2. They conclude that the data supports the notion that the most anterior remaining digit of the bird wing is homologous to digit 1 in other amniotes either in a standard phylogenetic sense, or alternatively in a (limited) developmental sense in agreement with the Frameshift Hypothesis of Wagner and Gautier (1997, i.e. that the developmental pathway is homologous to the one that leads to a digit 1 identity in other amniotes, albeit that it occurs in the second instead of the first digit condensation). We argue that the Hoxd12 and Hoxd13 expression patterns found for these and other limb mutants do not allow distinguishing between the hypothesis of Vargas and Fallon (2005) and the alternative one, i.e. the most anterior digit in bird wings is homologous to digit 2 in other amniotes, in a phylogenetic, or developmental sense. Therefore, at the moment the data on limb mutants does not present a challenge to the hypothesis, based on other developmental data (Holmgren 55, Hinchliffe 484, Burke and Feduccia 497, Kundrat et al. 2002, Larsson and Wagner 2002, Feduccia and Nowicki 2002), that the digits of bird wings are homologous to digits 2,3,4 in amniotes. We recommend further testing of the hypothesis by comparing Hoxd expression patterns in different taxa

Aliquoting structure for centrifugal microfluidics based on a new pneumatic valve

We present a new microvalve that can be monolithically integrated in centrifugally driven lab-on-a-chip systems. In contrast to existing operation principles that use hydrophobic patches, geometrically defined capillary stops or siphons, here we present a pneumatic principle. It needs neither additional local coatings nor expensive micro sized geometries. The valve is controlled by the spinning frequency and can be switched to be open when the centrifugal pressure overcomes the pneumatic pressure inside an unvented reaction cavity. We designed and characterized valves ranging in centrifugal burst pressure from 6700 Pa to 2100 Pa. Based on this valving principle we present a new structure for aliquoting of liquids. We experimentally demonstrated this by splitting 105 muL volumes into 16 aliquots with a volume CV of 3 %

Conservation of the Segmented Germband Stage: Robustness or Pleiotropy?

Gene expression patterns of the segment polarity genes in the extended and segmented germband stage are remarkably conserved among insects. To explain the conservation of these stages, two hypotheses have been proposed. One hypothesis states that the conservation reflects a high interactivity between modules, so that mutations would have several pleiotropic effects in other parts of the body, resulting in stabilizing selection against mutational variation. The other hypothesis states that the conservation is caused by robustness of the segment polarity network against mutational changes. When evaluating the empirical evidence for these hypotheses, we found strong support for pleiotropy and little evidence supporting robustness of the segment polarity network. This points to a key role for stabilizing selection in the conservation of these stages. Finally, we discuss the implications for robustness of organizers and long-term conservation in general