Retrieval Properties of Hopfield and Correlated Attractors in an Associative Memory Model

We examine a previouly introduced attractor neural network model that explains the persistent activities of neurons in the anterior ventral temporal cortex of the brain. In this model, the coexistence of several attractors including correlated attractors was reported in the cases of finite and infinite loading. In this paper, by means of a statistical mechanical method, we study the statics and dynamics of the model in both finite and extensive loading, mainly focusing on the retrieval properties of the Hopfield and correlated attractors. In the extensive loading case, we derive the evolution equations by the dynamical replica theory. We found several characteristic temporal behaviours, both in the finite and extensive loading cases. The theoretical results were confirmed by numerical simulations.Comment: 12 pages, 7 figure

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

Thermodynamics of impurity-enhanced vacancy formation in metals

Hydrogen induced vacancy formation in metals and metal alloys has been of great interest during the past couple of decades. The main reason for this phenomenon, often referred to as the superabundant vacancy formation, is the lowering of vacancy formation energy due to the trapping of hydrogen. By means of thermodynamics, we study the equilibrium vacancy formation in fcc metals (Pd, Ni, Co, and Fe) in correlation with the H amounts. The results of this study are compared and found to be in good agreement with experiments. For the accurate description of the total energy of the metal-hydrogen system, we take into account the binding energies of each trapped impurity, the vibrational entropy of defects, and the thermodynamics of divacancy formation. We demonstrate the effect of vacancy formation energy, the hydrogen binding, and the divacancy binding energy on the total equilibrium vacancy concentration. We show that the divacancy fraction gives the major contribution to the total vacancy fraction at high H fractions and cannot be neglected when studying superabundant vacancies. Our results lead to a novel conclusion that at high hydrogen fractions, superabundant vacancy formation takes place regardless of the binding energy between vacancies and hydrogen. We also propose the reason of superabundant vacancy formation mainly in the fcc phase. The equations obtained within this work can be used for any metal-impurity system, if the impurity occupies an interstitial site in the lattice. Published by AIP Publishing.Peer reviewe

Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators

We show that a wide class of uncoupled limit cycle oscillators can be in-phase synchronized by common weak additive noise. An expression of the Lyapunov exponent is analytically derived to study the stability of the noise-driven synchronizing state. The result shows that such a synchronization can be achieved in a broad class of oscillators with little constraint on their intrinsic property. On the other hand, the leaky integrate-and-fire neuron oscillators do not belong to this class, generating intermittent phase slips according to a power low distribution of their intervals.Comment: 10 pages, 3 figure

Strong Spherical Asymptotics for Rotor-Router Aggregation and the Divisible Sandpile

The rotor-router model is a deterministic analogue of random walk. It can be used to define a deterministic growth model analogous to internal DLA. We prove that the asymptotic shape of this model is a Euclidean ball, in a sense which is stronger than our earlier work. For the shape consisting of $n=\omega_d r^d$ sites, where $\omega_d$ is the volume of the unit ball in $\R^d$, we show that the inradius of the set of occupied sites is at least $r-O(\log r)$, while the outradius is at most $r+O(r^\alpha)$ for any $\alpha > 1-1/d$. For a related model, the divisible sandpile, we show that the domain of occupied sites is a Euclidean ball with error in the radius a constant independent of the total mass. For the classical abelian sandpile model in two dimensions, with $n=\pi r^2$ particles, we show that the inradius is at least $r/\sqrt{3}$, and the outradius is at most $(r+o(r))/\sqrt{2}$. This improves on bounds of Le Borgne and Rossin. Similar bounds apply in higher dimensions.Comment: [v3] Added Theorem 4.1, which generalizes Theorem 1.4 for the abelian sandpile. [v4] Added references and improved exposition in sections 2 and 4. [v5] Final version, to appear in Potential Analysi

Depth-dependent ordering, two-length-scale phenomena and crossover behavior in a crystal featuring a skin-layer with defects

Structural defects in a crystal are responsible for the "two length-scale" behavior, in which a sharp central peak is superimposed over a broad peak in critical diffuse X-ray scattering. We have previously measured the scaling behavior of the central peak by scattering from a near-surface region of a V2H crystal, which has a first-order transition in the bulk. As the temperature is lowered toward the critical temperature, a crossover in critical behavior is seen, with the temperature range nearest to the critical point being characterized by mean field exponents. Near the transition, a small two-phase coexistence region is observed. The values of transition and crossover temperatures decay with depth. An explanation of these experimental results is here proposed by means of a theory in which edge dislocations in the near-surface region occur in walls oriented in the two directions normal to the surface. The strain caused by the dislocation lines causes the ordering in the crystal to occur as growth of roughly cylindrically shaped regions. After the regions have reached a certain size, the crossover in the critical behavior occurs, and mean field behavior prevails. At a still lower temperature, the rest of the material between the cylindrical regions orders via a weak first-order transition.Comment: 12 pages, 8 figure

First principles simulations of liquid Fe-S under Earth's core conditions

First principles electronic structure calculations, based upon density functional theory within the generalized gradient approximation and ultra-soft Vanderbilt pseudopotentials, have been used to simulate a liquid alloy of iron and sulfur at Earth's core conditions. We have used a sulfur concentration of $\approx 12$wt, in line with the maximum recent estimates of the sulfur abundance in the Earth's outer core. The analysis of the structural, dynamical and electronic structure properties has been used to report on the effect of the sulfur impurities on the behavior of the liquid. Although pure sulfur is known to form chains in the liquid phase, we have not found any tendency towards polymerization in our liquid simulation. Rather, a net S-S repulsion is evident, and we propose an explanation for this effect in terms of the electronic structure. The inspection of the dynamical properties of the system suggests that the sulfur impurities have a negligible effect on the viscosity of Earth's liquid core.Comment: 24 pages (including 8 figures

Associative memory storing an extensive number of patterns based on a network of oscillators with distributed natural frequencies in the presence of external white noise

We study associative memory based on temporal coding in which successful retrieval is realized as an entrainment in a network of simple phase oscillators with distributed natural frequencies under the influence of white noise. The memory patterns are assumed to be given by uniformly distributed random numbers on $[0,2\pi)$ so that the patterns encode the phase differences of the oscillators. To derive the macroscopic order parameter equations for the network with an extensive number of stored patterns, we introduce the effective transfer function by assuming the fixed-point equation of the form of the TAP equation, which describes the time-averaged output as a function of the effective time-averaged local field. Properties of the networks associated with synchronization phenomena for a discrete symmetric natural frequency distribution with three frequency components are studied based on the order parameter equations, and are shown to be in good agreement with the results of numerical simulations. Two types of retrieval states are found to occur with respect to the degree of synchronization, when the size of the width of the natural frequency distribution is changed.Comment: published in Phys. Rev.

IQGAP1 Is Involved in Post-Ischemic Neovascularization by Regulating Angiogenesis and Macrophage Infiltration

Neovascularization is an important repair mechanism in response to ischemic injury and is dependent on inflammation, angiogenesis and reactive oxygen species (ROS). IQGAP1, an actin-binding scaffold protein, is a key regulator for actin cytoskeleton and motility. We previously demonstrated that IQGAP1 mediates vascular endothelial growth factor (VEGF)-induced ROS production and migration of cultured endothelial cells (ECs); however, its role in post-ischemic neovascularization is unknown.Ischemia was induced by left femoral artery ligation, which resulted in increased IQGAP1 expression in Mac3(+) macrophages and CD31(+) capillary-like ECs in ischemic legs. Mice lacking IQGAP1 exhibited a significant reduction in the post-ischemic neovascularization as evaluated by laser Doppler blood flow, capillary density and α-actin positive arterioles. Furthermore, IQGAP1(-/-) mice showed a decrease in macrophage infiltration and ROS production in ischemic muscles, leading to impaired muscle regeneration and increased necrosis and fibrosis. The numbers of bone marrow (BM)-derived cells in the peripheral blood were not affected in these knockout mice. BM transplantation revealed that IQGAP1 expressed in both BM-derived cells and tissue resident cells, such as ECs, is required for post-ischemic neovascularization. Moreover, thioglycollate-induced peritoneal macrophage recruitment and ROS production were inhibited in IQGAP1(-/-) mice. In vitro, IQGAP1(-/-) BM-derived macrophages showed inhibition of migration and adhesion capacity, which may explain the defective macrophage recruitment into the ischemic tissue in IQGAP1(-/-) mice.IQGAP1 plays a key role in post-ischemic neovascularization by regulating, not only, ECs-mediated angiogenesis but also macrophage infiltration as well as ROS production. Thus, IQGAP1 is a potential therapeutic target for inflammation- and angiogenesis-dependent ischemic cardiovascular diseases

A broad distribution of the alternative oxidase in microsporidian parasites

Microsporidia are a group of obligate intracellular parasitic eukaryotes that were considered to be amitochondriate until the recent discovery of highly reduced mitochondrial organelles called mitosomes. Analysis of the complete genome of Encephalitozoon cuniculi revealed a highly reduced set of proteins in the organelle, mostly related to the assembly of ironsulphur clusters. Oxidative phosphorylation and the Krebs cycle proteins were absent, in keeping with the notion that the microsporidia and their mitosomes are anaerobic, as is the case for other mitosome bearing eukaryotes, such as Giardia. Here we provide evidence opening the possibility that mitosomes in a number of microsporidian lineages are not completely anaerobic. Specifically, we have identified and characterized a gene encoding the alternative oxidase (AOX), a typically mitochondrial terminal oxidase in eukaryotes, in the genomes of several distantly related microsporidian species, even though this gene is absent from the complete genome of E. cuniculi. In order to confirm that these genes encode functional proteins, AOX genes from both A. locustae and T. hominis were over-expressed in E. coli and AOX activity measured spectrophotometrically using ubiquinol-1 (UQ-1) as substrate. Both A. locustae and T. hominis AOX proteins reduced UQ-1 in a cyanide and antimycin-resistant manner that was sensitive to ascofuranone, a potent inhibitor of the trypanosomal AOX. The physiological role of AOX microsporidia may be to reoxidise reducing equivalents produced by glycolysis, in a manner comparable to that observed in trypanosome