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

Modification of the Unitarity Relation for sin2beta-Vub in Supersymmetric Models

Recently, a more than 2sigma discrepancy has been observed between the well measured inclusive value of Vub and the predicted value of Vub from the unitarity triangle fit using the world average value of sin2beta. We attempt to resolve this tension in the context of grand unified SO(10) and SU(5) models where the neutrino mixing matrix is responsible for flavor changing neutral current at the weak scale and the models with non-proportional A-terms (can be realized simply in the context of intersecting D-brane models) and investigate the interplay between the constraints arising from B_{s,d}-\bar B_{s,d} mixings, epsilon_K, Br(tau -> mu gamma), Br(mu -> e gamma) and a fit of this new discrepancy. We also show that the ongoing measurement of the phase of Bs mixing will be able to identify the grand unified model. The measurement of Br(tau -> e gamma) will also be able to test these scenarios, especially the models with non-proportional A-terms.Comment: 20 pages, 4 figures. Minor corrections, references adde

Correlation between direct dark matter detection and Br(B_s -> mu mu) with a large phase of B_s - anti-B_s mixing

We combine the analyses for flavor changing neutral current processes and dark matter solutions in minimal-type supersymmetric grand unified theory (GUT) models, SO(10) and SU(5), with a large B_s - anti-B_s mixing phase and large tan beta. For large tan beta, the double penguin diagram dominates the SUSY contribution to the B_s - anti-B_s mixing amplitude. Also, the Br(B_s -> mu mu) constraint becomes important as it grows as tan^6 beta, although it can still be suppressed by large pseudoscalar Higgs mass m_A. We investigate the correlation between B_s -> mu mu and the dark matter direct detection cross-section through their dependence on m_A. In the minimal-type of SU(5) with type I seesaw, the large mixing in neutrino Dirac couplings results in large lepton flavor violating decay process tau to mu gamma, which in turn sets upper bound on m_A. In the SO(10) case, the large mixing can be chosen to be in the Majorana couplings instead, and the constraint from Br(tau -> mu gamma) can be avoided. The heavy Higgs funnel region turns out to be an interesting possibility in both cases and the direct dark matter detection should be possible in the near future in these scenarios.Comment: 19 pages, 8 figure

More anomaly-free models of six-dimensional gauged supergravity

We construct a huge number of anomaly-free models of six-dimensional N = (1,0) gauged supergravity. The gauge groups are products of U(1) and SU(2), and every hyperino is charged under some of the gauge groups. It is also found that the potential may have flat directions when the R-symmetry is diagonally gauged together with another gauge group. In an appendix, we determine the contribution to the global SU(2) anomaly from symplectic Majorana Weyl fermions in six dimensions.Comment: 20 pages, v3: published versio

Statistical mechanics of lossy compression using multilayer perceptrons

Statistical mechanics is applied to lossy compression using multilayer perceptrons for unbiased Boolean messages. We utilize a tree-like committee machine (committee tree) and tree-like parity machine (parity tree) whose transfer functions are monotonic. For compression using committee tree, a lower bound of achievable distortion becomes small as the number of hidden units K increases. However, it cannot reach the Shannon bound even where K -> infty. For a compression using a parity tree with K >= 2 hidden units, the rate distortion function, which is known as the theoretical limit for compression, is derived where the code length becomes infinity.Comment: 12 pages, 5 figure

Suppressing Proton Decay in the Minimal SO(10) Model

We show that in a class of minimal supersymmetric SO(10) models which have been found to be quite successful in predicting neutrino mixings, all proton decay modes can be suppressed by a particular choice of Yukawa textures. This suppression works for contributions from both left and right operators for nucleon decay and for arbitrary \tan\beta. The required texture not only fits all lepton and quark masses as well as CKM parameters but it also predicts neutrino mixing parameter U_e3 and Dirac CP phase \sin|\delta_MNS| to be 0.07-0.09 and 0.3-0.7 respectively. We also discuss the relation between the GUT symmetry breaking parameters for the origin of these textures.Comment: 7 pages, 2 figure

Parallel dynamics of continuous Hopfield model revisited

We have applied the generating functional analysis (GFA) to the continuous Hopfield model. We have also confirmed that the GFA predictions in some typical cases exhibit good consistency with computer simulation results. When a retarded self-interaction term is omitted, the GFA result becomes identical to that obtained using the statistical neurodynamics as well as the case of the sequential binary Hopfield model.Comment: 4 pages, 2 figure

Belief Propagation for Error Correcting Codes and Lossy Compression Using Multilayer Perceptrons

The belief propagation (BP) based algorithm is investigated as a potential decoder for both of error correcting codes and lossy compression, which are based on non-monotonic tree-like multilayer perceptron encoders. We discuss that whether the BP can give practical algorithms or not in these schemes. The BP implementations in those kind of fully connected networks unfortunately shows strong limitation, while the theoretical results seems a bit promising. Instead, it reveals it might have a rich and complex structure of the solution space via the BP-based algorithms.Comment: 18 pages, 18 figure

Preface to special issue (Fast reaction - slow diffusion scenarios: PDE approximations and free boundaries)

This issue is focussed on the modeling, analysis and simulation of fast reaction-slow transport scenarios as well as corresponding fast-reaction limits. Within this framework, internal sharp and thin reaction layers form and travel through the spatial domain often producing unexpected effects. Such situations appear in a variety of significant applications; for example flame propagation in combustion, segregation and aggregation of biological individuals, chemical attack on reactive porous materials (such as concrete or natural stone), dissolution and precipitation reactions in minerals, tumor growth, grain boundary motion, and temperature-induced phase transitions in shape-memory alloys represent typical cases in which the fast process is localized within a a priori unknown internal active layer