Uniform asymptotics of the coefficients of unitary moment polynomials

Keating and Snaith showed that the $2k^{th}$ absolute moment of the characteristic polynomial of a random unitary matrix evaluated on the unit circle is given by a polynomial of degree $k^2$. In this article, uniform asymptotics for the coefficients of that polynomial are derived, and a maximal coefficient is located. Some of the asymptotics are given in explicit form. Numerical data to support these calculations are presented. Some apparent connections between random matrix theory and the Riemann zeta function are discussed.Comment: 31 pages, 1 figure, 2 tables. A few minor misprints fixe

Distribution of parallel vortices studied by spin-polarized neutron reflectivity and magnetization

We present the studies of non-uniformly distributed vortices in Nb/Al multilayers at applied field near parallel to film surface by using spin-polarized neutron reflectivity (SPNR) and DC magnetization measurements. We have observed peaks above the lower critical field, Hc1, in the M-H curves from the multilayers. Previous works with a model calculation of minimizing Gibbs free energy have suggested that the peaks could be ascribed to vortex line transitions for spatial commensuration in a thin film superconductor. In order to directly determine the distribution of vortices, we performed SPNR measurements on the multilayer and found that the distribution and density of vortices are different at ascending and descending fields. At ascending 2000 Oe which is just below the first peak in the M-H curve, SPNR shows that vortices are mostly localized near a middle line of the film meanwhile the vortices are distributed in broader region at the descending 2000 Oe. That is related to the observation of more vortices trapped at the descending field. As the applied field is sightly tilted (< 3.5degree), we observe another peak at a smaller field. The peak position is consistent with the parallel lower critical field (Hc1||). We discuss that the vortices run along the applied field below Hc1|| and rotate parallel to the surface at Hc1||.Comment: 17 pages, 9 figure

A power-law distribution of phase-locking intervals does not imply critical interaction

Neural synchronisation plays a critical role in information processing, storage and transmission. Characterising the pattern of synchronisation is therefore of great interest. It has recently been suggested that the brain displays broadband criticality based on two measures of synchronisation - phase locking intervals and global lability of synchronisation - showing power law statistics at the critical threshold in a classical model of synchronisation. In this paper, we provide evidence that, within the limits of the model selection approach used to ascertain the presence of power law statistics, the pooling of pairwise phase-locking intervals from a non-critically interacting system can produce a distribution that is similarly assessed as being power law. In contrast, the global lability of synchronisation measure is shown to better discriminate critical from non critical interaction.Comment: (v3) Fixed error in Figure 1; (v2) Added references. Minor edits throughout. Clarified relationship between theoretical critical coupling for infinite size system and 'effective' critical coupling system for finite size system. Improved presentation and discussion of results; results unchanged. Revised Figure 1 to include error bars on r and N; results unchanged; (v1) 11 pages, 7 figure

New observations of stratospheric N2O5

The unequivocal detection of N2O5 in the stratosphere was reported by Toon et al. based on measurements of the absorption by the N2O5 bands at 1246 and 1720/cm in solar occulation spectra recorded at sunrise near 47 S latitude by the Atmospheric Trace Molecule Spectroscopy (ATMOS) experiment during the Spacelab 3 (SL3) shuttle mission. Additional measurements and analysis of stratospheric N2O5 derived from the ATMOS/SL3 spectra are reported. The primary results are the detection and measurement of N2O5 absorption at sunset in the lower stratosphere, the inversion of a precise (approximately 10 percent) N2O5 sunrise vertical distribution between 25.5 and 37.5 km altitude, and the identification and measurement of absorption by the N2O5 743/cm band at sunrise. Assuming 4.32 x 10(sup -17) and 4.36 x 10(sup -17)/cm/molecule/sq cm respectively for the integrated intensities of the 1246 and 743/cm bands at stratospheric temperatures, retrieved volume mixing ratios in parts per billion by volume (ppbv) at sunrise (47 S latitude) are 1.32 + or - 0.34 at 37.5 km, 1.53 + or - 0.35 at 35.5 km, 1.63 + or - 0.36 at 33.5 km, 1.60 + or - 0.34 at 31.5 km, 1.43 + or - 0.30 at 29.5 km, 1.15 + or - 0.24 at 27.5 km, and 0.73 + or - 0.15 at 25.5 km. Retrieved VMRs in ppbv at sunset (30 N latitude) are 0.13 + or - 0.05 at 29.5 km, 0.14 + or - 0.05 at 27.5 km, and 0.10 + or - 0.04 at 25.5 km. Quoted error limits (1 sigma) include the error in the assumed band intensities (approximately 20 percent). Within the error limits of the measurements, the inferred mixing ratios at sunrise agree with diurnal photochemical model predictions obtained by two groups using current photochemical data. The measured mixing ratios at sunset are lower than the model predictions with differences of about a factor of 2 at 25 km altitude

Premise Selection and External Provers for HOL4

Learning-assisted automated reasoning has recently gained popularity among the users of Isabelle/HOL, HOL Light, and Mizar. In this paper, we present an add-on to the HOL4 proof assistant and an adaptation of the HOLyHammer system that provides machine learning-based premise selection and automated reasoning also for HOL4. We efficiently record the HOL4 dependencies and extract features from the theorem statements, which form a basis for premise selection. HOLyHammer transforms the HOL4 statements in the various TPTP-ATP proof formats, which are then processed by the ATPs. We discuss the different evaluation settings: ATPs, accessible lemmas, and premise numbers. We measure the performance of HOLyHammer on the HOL4 standard library. The results are combined accordingly and compared with the HOL Light experiments, showing a comparably high quality of predictions. The system directly benefits HOL4 users by automatically finding proofs dependencies that can be reconstructed by Metis

Plasma density measurements using chirped pulse broad-band Raman amplification

Stimulated Raman backscattering is used as a non-destructive method to determine the density of plasma media at localized positions in space and time. By colliding two counter-propagating, ultra-short laser pulses with a spectral bandwidth larger than twice the plasma frequency, amplification occurs at the Stokes wavelengths, which results in regions of gain and loss separated by twice the plasma frequency, from which the plasma density can be deduced. By varying the relative delay between the laser pulses, and therefore the position and timing of the interaction, the spatio-temporal distribution of the plasma density can be mapped out

A Multi Agent Model for the Limit Order Book Dynamics

In the present work we introduce a novel multi-agent model with the aim to reproduce the dynamics of a double auction market at microscopic time scale through a faithful simulation of the matching mechanics in the limit order book. The agents follow a noise decision making process where their actions are related to a stochastic variable, "the market sentiment", which we define as a mixture of public and private information. The model, despite making just few basic assumptions over the trading strategies of the agents, is able to reproduce several empirical features of the high-frequency dynamics of the market microstructure not only related to the price movements but also to the deposition of the orders in the book.Comment: 20 pages, 11 figures, in press European Physical Journal B (EPJB

Molecular dynamic simulation and inhibitor prediction of cysteine synthase structured model as a potential drug target for trichomoniasis

In our presented research, we made an attempt to predict the 3D model for cysteine synthase (A2GMG5-TRIVA) using homology-modeling approaches. To investigate deeper into the predicted structure, we further performed a molecular dynamics simulation for 10 ns and calculated several supporting analysis for structural properties such as RMSF, radius of gyration, and the total energy calculation to support the predicted structured model of cysteine synthase. The present findings led us to conclude that the proposed model is stereochemically stable. The overall PROCHECK G factor for the homology-modeled structure was -0.04. On the basis of the virtual screening for cysteine synthase against the NCI subset II molecule, we present the molecule 1-N, 4-N-bis [3-(1H-benzimidazol-2-yl) phenyl] benzene-1,4-dicarboxamide (ZINC01690699) having the minimum energy score (-13.0 Kcal/Mol) and a log P value of 6 as a potential inhibitory molecule used to inhibit the growth of T. vaginalis infection. © 2013 Satendra Singh et al

Technical and Economic Assessment of Span-Distributed Loading Cargo Aircraft Concepts

A 700,000 kg (1,540,000-lb) aircraft with a cruise Mach number of 0.75 was found to be optimum for the specified mission parameters of a 272 155-kg (600,000-lb) payload, a 5560-km (3000-n.mi.) range, and an annual productivity of 113 billion revenue-ton km (67 billion revenue-ton n. mi.). The optimum 1990 technology level spanloader aircraft exhibited the minimum 15-year life-cycle costs, direct operating costs, and fuel consumption of all candidate versions. Parametric variations of wing sweep angle, thickness ratio, rows of cargo, and cargo density were investigated. The optimum aircraft had two parallel rows of 2.44 x 2.44-m (8 x 8-ft) containerized cargo with a density of 160 kg/cu m (10 lb/ft 3) carried throughout the entire 101-m (331-ft) span of the constant chord, 22-percent thick, supercritical wing. Additional containers or outsized equipment were carried in the 24.4-m (80-ft) long fuselage compartment preceding the wing. Six 284,000-N (64,000-lb) thrust engines were mounted beneath the 0.7-rad (40-deg) swept wing. Flight control was provided by a 36.6-m (120-ft) span canard surface mounted atop the forward fuselage, by rudders on the wingtip verticals and by outboard wing flaperons