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

Influence of socio-cultural factors on child's upbringing in Oshodi/Isolo Local Government Area of Lagos State, Nigeria

This paper investigated the influence of socio-cultural factors on child's upbringing in Oshodi/Isolo Local Government Area of Lagos State, Nigeria. Precisely, 250 parents having children that are 0-12 years were interviewed with the aid of questionnaire schedule. The study tested only two hypotheses. Frequency table, Chi-square and binary logistic regression analysis were employed to analyze the data obtained from the survey. The major findings are: firstly, that the socio-cultural factors identified in this study include; the influence of residential environment, family, culture and social institutions. Secondly, that the socio-cultural factors such as; the influence of family, social institutions and residential environment are significantly related to child's upbringing through authoritarian parenting style.Thus, the paper recommends the following: firstly, that the native culture of every parent should reflect in their choice of authoritarian parenting style. Lastly, the family involvement, social institution and residential environment should form the bedrock in child's upbringing in every Nigerian society

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 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

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

Temperate functional niche availability not resident-invader competition shapes tropicalisation in reef fishes

Temperate reefs are at the forefront of warming-induced community alterations resulting from poleward range shifts. This tropicalisation is exemplified and amplified by tropical species’ invasions of temperate herbivory functions. However, whether other temperate ecosystem functions are similarly invaded by tropical species, and by what drivers, remains unclear. We examine tropicalisation footprints in nine reef fish functional groups using trait-based analyses and biomass of 550 fish species across tropical to temperate gradients in Japan and Australia. We discover that functional niches in transitional communities are asynchronously invaded by tropical species, but with congruent invasion schedules for functional groups across the two hemispheres. These differences in functional group tropicalisation point to habitat availability as a key determinant of multi-species range shifts, as in the majority of functional groups tropical and temperate species share functional niche space in suitable habitat. Competition among species from different thermal guilds played little part in limiting tropicalisation, rather available functional space occupied by temperate species indicates that tropical species can invade. Characterising these drivers of reef tropicalisation is pivotal to understanding, predicting, and managing marine community transformation

On analyticity with respect to the replica number in random energy models I: an exact expression of the moment of the partition function

We provide an exact expression of the moment of the partition function for random energy models of finite system size, generalizing an earlier expression for a grand canonical version of the discrete random energy model presented by the authors in Prog. Theor. Phys. 111, 661 (2004). The expression can be handled both analytically and numerically, which is useful for examining how the analyticity of the moment with respect to the replica numbers, which play the role of powers of the moment, can be broken in the thermodynamic limit. A comparison with a replica method analysis indicates that the analyticity breaking can be regarded as the origin of the one-step replica symmetry breaking. The validity of the expression is also confirmed by numerical methods for finite systems.Comment: 16 pages, 4 figure

The Infrared Imaging Spectrograph (IRIS) for TMT: Instrument Overview

We present an overview of the design of IRIS, an infrared (0.84 - 2.4 micron) integral field spectrograph and imaging camera for the Thirty Meter Telescope (TMT). With extremely low wavefront error (<30 nm) and on-board wavefront sensors, IRIS will take advantage of the high angular resolution of the narrow field infrared adaptive optics system (NFIRAOS) to dissect the sky at the diffraction limit of the 30-meter aperture. With a primary spectral resolution of 4000 and spatial sampling starting at 4 milliarcseconds, the instrument will create an unparalleled ability to explore high redshift galaxies, the Galactic center, star forming regions and virtually any astrophysical object. This paper summarizes the entire design and basic capabilities. Among the design innovations is the combination of lenslet and slicer integral field units, new 4Kx4k detectors, extremely precise atmospheric dispersion correction, infrared wavefront sensors, and a very large vacuum cryogenic system.Comment: Proceedings of the SPIE, 9147-76 (2014

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