The path-integral analysis of an associative memory model storing an infinite number of finite limit cycles

It is shown that an exact solution of the transient dynamics of an associative memory model storing an infinite number of limit cycles with l finite steps by means of the path-integral analysis. Assuming the Maxwell construction ansatz, we have succeeded in deriving the stationary state equations of the order parameters from the macroscopic recursive equations with respect to the finite-step sequence processing model which has retarded self-interactions. We have also derived the stationary state equations by means of the signal-to-noise analysis (SCSNA). The signal-to-noise analysis must assume that crosstalk noise of an input to spins obeys a Gaussian distribution. On the other hand, the path-integral method does not require such a Gaussian approximation of crosstalk noise. We have found that both the signal-to-noise analysis and the path-integral analysis give the completely same result with respect to the stationary state in the case where the dynamics is deterministic, when we assume the Maxwell construction ansatz. We have shown the dependence of storage capacity (alpha_c) on the number of patterns per one limit cycle (l). Storage capacity monotonously increases with the number of steps, and converges to alpha_c=0.269 at l ~= 10. The original properties of the finite-step sequence processing model appear as long as the number of steps of the limit cycle has order l=O(1).Comment: 24 pages, 3 figure

Linear Complexity Lossy Compressor for Binary Redundant Memoryless Sources

A lossy compression algorithm for binary redundant memoryless sources is presented. The proposed scheme is based on sparse graph codes. By introducing a nonlinear function, redundant memoryless sequences can be compressed. We propose a linear complexity compressor based on the extended belief propagation, into which an inertia term is heuristically introduced, and show that it has near-optimal performance for moderate block lengths.Comment: 4 pages, 1 figur

Coupling Unifications in Gauge-Higgs Unified Orbifold Models

Supersymmetric gauge theories, in higher dimensions compactified in an orbifold, give a natural framework to unify the gauge bosons, Higgs fields and even the matter fields in a single multiplet of the unifying gauge symmetry. The extra dimensions and the supersymmetry are the two key ingredients for such an unification. In this work, we investigate various scenarios for the unification of the three gauge couplings, and the Yukawa couplings in the Minimal Supersymmetric Standard Model (MSSM), as well as the trilinear Higgs couplings \lambda and \kappa of the Non-Minimal Supersymmetric Standard Model (NMSSM). We present an SU(8) model in six dimensions with N=2 supersymmetry, compactified in a T^2/Z_6 orbifold which unifies the three gauge couplings with \lambda and \kappa of NMSSM. Then, we present an SU(9) model in 6D, which, in addition, includes partial unification of Yukawa couplings, either for the up-type (top quark and Dirac tau-neutrino) or down-type (bottom quark and tau lepton). We also study the phenomenological implications of these various unification scenarios using the appropriate renormalization group equations, and show that such unification works very well with the measured low energy values of the couplings. The predicted upper bounds for the lightest neutral Higgs boson mass in our model is higher than those in MSSM, but lower that those in the general NMSSM (where the couplings \lambda and \kappa are arbitrary). Some of the predictions of our models can be tested in the upcoming Large Hadron Collider.Comment: 29 pages, 4 figure

Synapse efficiency diverges due to synaptic pruning following over-growth

In the development of the brain, it is known that synapses are pruned following over-growth. This pruning following over-growth seems to be a universal phenomenon that occurs in almost all areas -- visual cortex, motor area, association area, and so on. It has been shown numerically that the synapse efficiency is increased by systematic deletion. We discuss the synapse efficiency to evaluate the effect of pruning following over-growth, and analytically show that the synapse efficiency diverges as O(log c) at the limit where connecting rate c is extremely small. Under a fixed synapse number criterion, the optimal connecting rate, which maximize memory performance, exists.Comment: 15 pages, 16 figure

Dynamical replica theoretic analysis of CDMA detection dynamics

We investigate the detection dynamics of the Gibbs sampler for code-division multiple access (CDMA) multiuser detection. Our approach is based upon dynamical replica theory which allows an analytic approximation to the dynamics. We use this tool to investigate the basins of attraction when phase coexistence occurs and examine its efficacy via comparison with Monte Carlo simulations.Comment: 18 pages, 2 figure

Error correcting code using tree-like multilayer perceptron

An error correcting code using a tree-like multilayer perceptron is proposed. An original message \mbi{s}^0 is encoded into a codeword \boldmath{y}_0 using a tree-like committee machine (committee tree) or a tree-like parity machine (parity tree). Based on these architectures, several schemes featuring monotonic or non-monotonic units are introduced. The codeword \mbi{y}_0 is then transmitted via a Binary Asymmetric Channel (BAC) where it is corrupted by noise. The analytical performance of these schemes is investigated using the replica method of statistical mechanics. Under some specific conditions, some of the proposed schemes are shown to saturate the Shannon bound at the infinite codeword length limit. The influence of the monotonicity of the units on the performance is also discussed.Comment: 23 pages, 3 figures, Content has been extended and revise

From Wave Geometry to Fake Supergravity

The `Wave Geometry' equation of the pre-WWII Hiroshima program is also the key equation of the current `fake supergravity' program. I review the status of (fake) supersymmetric domain walls and (fake) pseudo-supersymmetric cosmologies. An extension of the domain-wall/cosmology correspondence to a triple correspondence with instantons shows that `pseudo-supersymmetry' has another interpretation as Euclidean supersymmetry.Comment: 14 pages. Minor Revisions to original. To appear in proceedings of the 5th International Symposium on Quantum Theory and Symmetries (QTS5), Vallodolid, July 2007. in version

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

Temperature dependent Eu 3d-4f X-ray Absorption and Resonant Photoemission Study of the Valence Transition in EuNi2(Si0.2Ge0.8)2EuNi_2(Si_{0.2}Ge_{0.8})_2

We study the mixed valence transition ($T$$_{v}$ $\sim$80 K) in EuNi$_{2}$(Si$_{0.2}$Ge$_{0.8}$)$_{2}$ using Eu 3$d-4f$ X-ray absorption spectroscopy (XAS) and resonant photoemission spectroscopy (RESPES). The Eu$^{2+}$ and Eu$^{3+}$ main peaks show a giant resonance and the spectral features match very well with atomic multiplet calculations. The spectra show dramatic temperature ($T$)-dependent changes over large energies ($\sim$10 eV) in RESPES and XAS. The observed non-integral mean valencies of $\sim$2.35 $\pm$ 0.03 ($T$ = 120 K) and $\sim$2.70 $\pm$ 0.03 ($T$ = 40 K) indicate homogeneous mixed valence above and below $T$$_{v}$. The redistribution between Eu$^{2+}$$4f^7$+$[spd]^0$ and Eu$^{3+}$$4f^6$+$[spd]^1$ states is attributed to a hybridization change coupled to a Kondo-like volume collapse.Comment: 4 pages, 3 figure