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

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

The infrared imaging spectrograph (IRIS) for TMT: status report for IRIS imager

The current status of IRIS imager at NAOJ is reported. IRIS (Infrared Imaging Spectrograph) is a first light instrument of TMT (Thirty Meter Telescope). IRIS has just passed the preliminary design review and moved forward to the final design phase. In this paper, optical and mechanical design of IRIS imager and prototyping activities conducted during the preliminary design phase are summarized

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

Sample preparation procedure for the determination of polycyclic aromatic hydrocarbons in petroleum vacuum residue and bitumen

This paper describes a novel method of sample preparation for the determination of trace concentrations of polycyclic aromatic hydrocarbons (PAHs) in high-boiling petroleum products. Limits of quantitation of the investigated PAHs in materials of this type range from tens of nanograms per kilogram to <20 μg/kg. The studies revealed that in order to separate most of interferences from the analytes without a significant loss of PAHs, it is necessary to use size exclusion chromatography as the first step of sample preparation, followed by adsorption using normal-phase liquid chromatography. The use of orthogonal separation procedure described in the paper allows the isolation of only a group of unsubstituted and substituted aromatic hydrocarbons with a specific range of molar mass. The lower the required limit of quantitation of PAHs, the larger is the scale of preparative liquid chromatography in both steps of sample preparation needed. The use of internal standard allows quantitative results to be corrected for the degree of recovery of PAHs during the sample preparation step. Final determination can be carried out using HPLC-FLD, GC-MS, or HPLC-UV–VIS/DAD. The last technique provides a degree of identification through the acquired UV–VIS spectra

Complex Random Energy Model: Zeros and Fluctuations

The partition function of the random energy model at inverse temperature $\beta$ is a sum of random exponentials $Z_N(\beta)=\sum_{k=1}^N \exp(\beta \sqrt{n} X_k)$, where $X_1,X_2,...$ are independent real standard normal random variables (= random energies), and $n=\log N$. We study the large $N$ limit of the partition function viewed as an analytic function of the complex variable $\beta$. We identify the asymptotic structure of complex zeros of the partition function confirming and extending predictions made in the theoretical physics literature. We prove limit theorems for the random partition function at complex $\beta$, both on the logarithmic scale and on the level of limiting distributions. Our results cover also the case of the sums of independent identically distributed random exponentials with any given correlations between the real and imaginary parts of the random exponent.Comment: 31 pages, 1 figur