289 research outputs found
Distribution of partition function zeros of the model on the Bethe lattice
The distribution of partition function zeros is studied for the 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
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 in five broad
bands (), with a point-source depth of . The
Deep layer covers a total of 26~deg 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). 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
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