Superstatistical generalisations of Wishart-Laguerre ensembles of random matrices

Using Beck and Cohen's superstatistics, we introduce in a systematic way a family of generalized Wishart–Laguerre ensembles of random matrices with Dyson index β = 1, 2 and 4. The entries of the data matrix are Gaussian random variables whose variances η fluctuate from one sample to another according to a certain probability density f(η) and a single deformation parameter γ. Three superstatistical classes for f(η) are usually considered: χ2-, inverse χ2- and log-normal distributions. While the first class, already considered by two of the authors, leads to a power-law decay of the spectral density, we here introduce and solve exactly a superposition of Wishart–Laguerre ensembles with inverse χ2-distribution. The corresponding macroscopic spectral density is given by a γ-deformation of the semi-circle and Marčenko–Pastur laws, on a non-compact support with exponential tails. After discussing in detail the validity of Wigner's surmise in the Wishart–Laguerre class, we introduce a generalized γ-dependent surmise with stretched-exponential tails, which well approximates the individual level spacing distribution in the bulk. The analytical results are in excellent agreement with numerical simulations. To illustrate our findings we compare the χ2- and inverse χ2-classes to empirical data from financial covariance matrices

Magnetic neutron star cooling and microphysics

This is the author accepted manuscript. The final version is available from EDP Sciences via the DOI in this record.We study the relative importance of several recent updates of microphysics input to the neutron star cooling theory and the effects brought about by superstrong magnetic fields of magnetars, including the effects of the Landau quantization in their crusts. We use a finite-difference code for simulation of neutron-star thermal evolution on timescales from hours to megayears with an updated microphysics input. The consideration of short timescales ($\lesssim1$ yr) is made possible by a treatment of the heat-blanketing envelope without the quasistationary approximation inherent to its treatment in traditional neutron-star cooling codes. For the strongly magnetized neutron stars, we take into account the effects of Landau quantization on thermodynamic functions and thermal conductivities. We simulate cooling of ordinary neutron stars and magnetars with non-accreted and accreted crusts and compare the results with observations. Suppression of radiative and conductive opacities in strongly quantizing magnetic fields and formation of a condensed radiating surface substantially enhance the photon luminosity at early ages, making the life of magnetars brighter but shorter. These effects together with the effect of strong proton superfluidity, which slows down the cooling of kiloyear-aged neutron stars, can explain thermal luminosities of about a half of magnetars without invoking heating mechanisms. Observed thermal luminosities of other magnetars are still higher than theoretical predictions, which implies heating, but the effects of quantizing magnetic fields and baryon superfluidity help to reduce the discrepancy.The work of A.P. was supported by the Russian Science Foundation (grant 14-12-00316)

Quantifying structure in networks

We investigate exponential families of random graph distributions as a framework for systematic quantification of structure in networks. In this paper we restrict ourselves to undirected unlabeled graphs. For these graphs, the counts of subgraphs with no more than k links are a sufficient statistics for the exponential families of graphs with interactions between at most k links. In this framework we investigate the dependencies between several observables commonly used to quantify structure in networks, such as the degree distribution, cluster and assortativity coefficients.Comment: 17 pages, 3 figure

D-branes with Lorentzian signature in the Nappi-Witten model

Lorentzian signature D-branes of all dimensions for the Nappi-Witten string are constructed. This is done by rewriting the gluing condition $J_+=FJ_-$ for the model chiral currents on the brane as a well posed first order differential problem and by solving it for Lie algebra isometries $F$ other than Lie algebra automorphisms. By construction, these D-branes are not twined conjugacy classes. Metrically degenerate D-branes are also obtained.Comment: 22 page

Opacities and spectra of hydrogen atmospheres of moderately magnetized neutron stars

There is observational evidence that central compact objects (CCOs) in supernova remnants have moderately strong magnetic fields $B\sim10^{11}$ G. Meanwhile, available models of partially ionized hydrogen atmospheres of neutron stars with strong magnetic fields are restricted to $B\gtrsim10^{12}$ G. We extend the equation of state and radiative opacities, presented in previous papers for 10^{12}\mbox{ G}\lesssim B \lesssim 10^{15} G, to weaker fields. An equation of state and radiative opacities for a partially ionized hydrogen plasma are obtained at magnetic fields $B$, temperatures $T$, and densities $\rho$ typical for atmospheres of CCOs and other isolated neutron stars with moderately strong magnetic fields. The first- and second-order thermodynamic functions, monochromatic radiative opacities, and Rosseland mean opacities are calculated and tabulated, taking account of partial ionization, for 3\times10^{10}\mbox{ G}\lesssim B\lesssim 10^{12} G, $10^5$ K $\lesssim T\lesssim 10^7$ K, and a wide range of densities. Atmosphere models and spectra are calculated to verify the applicability of the results and to determine the range of magnetic fields and effective temperatures where the incomplete ionization of the hydrogen plasma is important.The work of AYP on calculation of the opacities and polarizabilities (Sect. 4) has been supported by the Russian Science Foundation (grant 14-12-00316). WCGH appreciates use of computer facilities at KIPAC

Geometry of Information Integration

Information geometry is used to quantify the amount of information integration within multiple terminals of a causal dynamical system. Integrated information quantifies how much information is lost when a system is split into parts and information transmission between the parts is removed. Multiple measures have been proposed as a measure of integrated information. Here, we analyze four of the previously proposed measures and elucidate their relations from a viewpoint of information geometry. Two of them use dually flat manifolds and the other two use curved manifolds to define a split model. We show that there are hierarchical structures among the measures. We provide explicit expressions of these measures

Growth, micro-structuring, spectroscopy, and optical gain in as-deposited Al2O3:ErAl_2O_3:Er waveguides

Deposition and micro-structuring of $Al_2O_3:Er$ layers with low background losses (0.11 dB/cm) and lifetimes up to 7 ms have been optimized for active devices. Net gain of 0.7 dB/cm at 1533 nm has been measured.\ud \u

A cusp model of housing price in Hong Kong

This paper develops a cusp model of housing prices for Hong Kong

Synthetic gene design - The rationale for codon optimization and implications for molecular pharming in plants.

Degeneracy in the genetic code allows multiple codon sequences to encode the same protein. Codon usage bias in genes is the term given to the preferred use of particular synonymous codons. Synonymous codon substitutions had been regarded as "silent" as the primary structure of the protein was not affected; however, it is now accepted that synonymous substitutions can have a significant effect on heterologous protein expression. Codon optimization, the process of altering codons within the gene sequence to improve recombinant protein expression, has become widely practised. Multiple inter-linked factors affecting protein expression need to be taken into consideration when optimizing a gene sequence. Over the years, various computer programmes have been developed to aid in the gene sequence optimization process. However, as the rulebook for altering codon usage to affect protein expression is still not completely understood, it is difficult to predict which strategy, if any, will design the 'optimal' gene sequence. In this review, codon usage bias and factors affecting codon selection will be discussed and the evidence for codon optimization impact will be reviewed for recombinant protein expression using plants as a case study. These developments will be relevant to all recombinant expression systems, however, molecular pharming in plants is an area which has consistently encountered difficulties with low levels of recombinant protein expression, and should benefit from an evidence based rational approach to synthetic gene design