Distribution of partition function zeros of the ±J\pm J model on the Bethe lattice

The distribution of partition function zeros is studied for the $\pm J$ model of spin glasses on the Bethe lattice. We find a relation between the distribution of complex cavity fields and the density of zeros, which enables us to obtain the density of zeros for the infinite system size by using the cavity method. The phase boundaries thus derived from the location of the zeros are consistent with the results of direct analytical calculations. This is the first example in which the spin glass transition is related to the distribution of zeros directly in the thermodynamical limit. We clarify how the spin glass transition is characterized by the zeros of the partition function. It is also shown that in the spin glass phase a continuous distribution of singularities touches the axes of real field and temperature.Comment: 23 pages, 12 figure

Statistical mechanical analysis of a hierarchical random code ensemble in signal processing

We study a random code ensemble with a hierarchical structure, which is closely related to the generalized random energy model with discrete energy values. Based on this correspondence, we analyze the hierarchical random code ensemble by using the replica method in two situations: lossy data compression and channel coding. For both the situations, the exponents of large deviation analysis characterizing the performance of the ensemble, the distortion rate of lossy data compression and the error exponent of channel coding in Gallager's formalism, are accessible by a generating function of the generalized random energy model. We discuss that the transitions of those exponents observed in the preceding work can be interpreted as phase transitions with respect to the replica number. We also show that the replica symmetry breaking plays an essential role in these transitions.Comment: 24 pages, 4 figure

Solution space heterogeneity of the random K-satisfiability problem: Theory and simulations

The random K-satisfiability (K-SAT) problem is an important problem for studying typical-case complexity of NP-complete combinatorial satisfaction; it is also a representative model of finite-connectivity spin-glasses. In this paper we review our recent efforts on the solution space fine structures of the random K-SAT problem. A heterogeneity transition is predicted to occur in the solution space as the constraint density alpha reaches a critical value alpha_cm. This transition marks the emergency of exponentially many solution communities in the solution space. After the heterogeneity transition the solution space is still ergodic until alpha reaches a larger threshold value alpha_d, at which the solution communities disconnect from each other to become different solution clusters (ergodicity-breaking). The existence of solution communities in the solution space is confirmed by numerical simulations of solution space random walking, and the effect of solution space heterogeneity on a stochastic local search algorithm SEQSAT, which performs a random walk of single-spin flips, is investigated. The relevance of this work to glassy dynamics studies is briefly mentioned.Comment: 11 pages, 4 figures. Final version as will appear in Journal of Physics: Conference Series (Proceedings of the International Workshop on Statistical-Mechanical Informatics, March 7-10, 2010, Kyoto, Japan

Replica analysis of partition-function zeros in spin-glass models

We study the partition-function zeros in mean-field spin-glass models. We show that the replica method is useful to find the locations of zeros in a complex parameter plane. For the random energy model, we obtain the phase diagram in the plane and find that there are two types of distribution of zeros: two-dimensional distribution within a phase and one-dimensional one on a phase boundary. Phases with a two-dimensional distribution are characterized by a novel order parameter defined in the present replica analysis. We also discuss possible patterns of distributions by studying several systems.Comment: 23 pages, 12 figures; minor change

Statistical Mechanics of Dictionary Learning

Finding a basis matrix (dictionary) by which objective signals are represented sparsely is of major relevance in various scientific and technological fields. We consider a problem to learn a dictionary from a set of training signals. We employ techniques of statistical mechanics of disordered systems to evaluate the size of the training set necessary to typically succeed in the dictionary learning. The results indicate that the necessary size is much smaller than previously estimated, which theoretically supports and/or encourages the use of dictionary learning in practical situations.Comment: 6 pages, 4 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

Physcomitrella patens Has Kinase-LRR R Gene Homologs and Interacting Proteins

Peer reviewe

The Hyper Suprime-Cam SSP Survey: Overview and Survey Design

Hyper Suprime-Cam (HSC) is a wide-field imaging camera on the prime focus of the 8.2m Subaru telescope on the summit of Maunakea in Hawaii. A team of scientists from Japan, Taiwan and Princeton University is using HSC to carry out a 300-night multi-band imaging survey of the high-latitude sky. The survey includes three layers: the Wide layer will cover 1400 deg$^2$ in five broad bands ($grizy$), with a $5\,\sigma$ point-source depth of $r \approx 26$. The Deep layer covers a total of 26~deg$^2$ in four fields, going roughly a magnitude fainter, while the UltraDeep layer goes almost a magnitude fainter still in two pointings of HSC (a total of 3.5 deg$^2$). Here we describe the instrument, the science goals of the survey, and the survey strategy and data processing. This paper serves as an introduction to a special issue of the Publications of the Astronomical Society of Japan, which includes a large number of technical and scientific papers describing results from the early phases of this survey.Comment: 14 pages, 7 figures, 5 tables. Corrected for a typo in the coordinates of HSC-Wide spring equatorial field in Table