Eigenvalues and Singular Values of Products of Rectangular Gaussian Random Matrices (The Extended Version)

We consider a product of an arbitrary number of independent rectangular Gaussian random matrices. We derive the mean densities of its eigenvalues and singular values in the thermodynamic limit, eventually verified numerically. These densities are encoded in the form of the so called M-transforms, for which polynomial equations are found. We exploit the methods of planar diagrammatics, enhanced to the non-Hermitian case, and free random variables, respectively; both are described in the appendices. As particular results of these two main equations, we find the singular behavior of the spectral densities near zero. Moreover, we propose a finite-size form of the spectral density of the product close to the border of its eigenvalues' domain. Also, led by the striking similarity between the two main equations, we put forward a conjecture about a simple relationship between the eigenvalues and singular values of any non-Hermitian random matrix whose spectrum exhibits rotational symmetry around zero.Comment: 50 pages, 8 figures, to appear in the Proceedings of the 23rd Marian Smoluchowski Symposium on Statistical Physics: "Random Matrices, Statistical Physics and Information Theory," September 26-30, 2010, Krakow, Polan

Signal and Noise in Correlation Matrix

Using random matrix technique we determine an exact relation between the eigenvalue spectrum of the covariance matrix and of its estimator. This relation can be used in practice to compute eigenvalue invariants of the covariance (correlation) matrix. Results can be applied in various problems where one experimentally estimates correlations in a system with many degrees of freedom, like in statistical physics, lattice measurements of field theory, genetics, quantitative finance and other applications of multivariate statistics.Comment: 17 pages, 3 figures, corrected typos, revtex style changed to elsar

Thermal Stability and Mechanical Properties of 5483 Al Alloy Processed by ECAP

Equal Channel Angular Pressing (ECAP) is one of the methods which allows to obtain ultrafine-grained and nanocrystalline metallic materials. It is well known that microstructure of materials pro-cessed by ECAP in not very stable. There were published many experimental and theoretical evidences of this fact obtained by various methods such as microstructure observations, properties measurement and computer modeling. The aim of presented paper was to investigate the thermal stability of microstructure and mechanical properties of the Al 5483 alloy processed by ECAP. As a result of performed investigations it was concluded that accumulated plastic deformation has no influence on the thermal stability of Al 5483 alloy processed by ECAP. It was also found that properly chosen parameters of ECAP and subsequent annealing allows to produce materials with high strength and plasticity. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3543

A Random Matrix Approach to VARMA Processes

We apply random matrix theory to derive spectral density of large sample covariance matrices generated by multivariate VMA(q), VAR(q) and VARMA(q1,q2) processes. In particular, we consider a limit where the number of random variables N and the number of consecutive time measurements T are large but the ratio N/T is fixed. In this regime the underlying random matrices are asymptotically equivalent to Free Random Variables (FRV). We apply the FRV calculus to calculate the eigenvalue density of the sample covariance for several VARMA-type processes. We explicitly solve the VARMA(1,1) case and demonstrate a perfect agreement between the analytical result and the spectra obtained by Monte Carlo simulations. The proposed method is purely algebraic and can be easily generalized to q1>1 and q2>1.Comment: 16 pages, 6 figures, submitted to New Journal of Physic

Structure and mechanism of human DNA polymerase η

The variant form of the human syndrome xeroderma pigmentosum (XPV) is caused by a deficiency in DNA polymerase eta (Pol eta), a DNA polymerase that enables replication through ultraviolet-induced pyrimidine dimers. Here we report high-resolution crystal structures of human Pol eta at four consecutive steps during DNA synthesis through cis-syn cyclobutane thymine dimers. Pol eta acts like a 'molecular splint' to stabilize damaged DNA in a normal B-form conformation. An enlarged active site accommodates the thymine dimer with excellent stereochemistry for two-metal ion catalysis. Two residues conserved among Pol eta orthologues form specific hydrogen bonds with the lesion and the incoming nucleotide to assist translesion synthesis. On the basis of the structures, eight Pol eta missense mutations causing XPV can be rationalized as undermining the molecular splint or perturbing the active-site alignment. The structures also provide an insight into the role of Pol eta in replicating through D loop and DNA fragile sites

Analysis of the FGF gene family provides insights into aquatic adaptation in cetaceans

Cetacean body structure and physiology exhibit dramatic adaptations to their aquatic environment. Fibroblast growth factors (FGFs) are a family of essential factors that regulate animal development and physiology; however, their role in cetacean evolution is not clearly understood. Here, we sequenced the fin whale genome and analysed FGFs from 8 cetaceans. FGF22, a hair follicle-enriched gene, exhibited pseudogenization, indicating that the function of this gene is no longer necessary in cetaceans that have lost most of their body hair. An evolutionary analysis revealed signatures of positive selection for FGF3 and FGF11, genes related to ear and tooth development and hypoxia, respectively. We found a D203G substitution in cetacean FGF9, which was predicted to affect FGF9 homodimerization, suggesting that this gene plays a role in the acquisition of rigid flippers for efficient manoeuvring. Cetaceans utilize low bone density as a buoyancy control mechanism, but the underlying genes are not known. We found that the expression of FGF23, a gene associated with reduced bone density, is greatly increased in the cetacean liver under hypoxic conditions, thus implicating FGF23 in low bone density in cetaceans. Altogether, our results provide novel insights into the roles of FGFs in cetacean adaptation to the aquatic environment.ope

Analysis of Sample Correlations for Monte Carlo Rendering

Modern physically based rendering techniques critically depend on approximating integrals of high dimensional functions representing radiant light energy. Monte Carlo based integrators are the choice for complex scenes and effects. These integrators work by sampling the integrand at sample point locations. The distribution of these sample points determines convergence rates and noise in the final renderings. The characteristics of such distributions can be uniquely represented in terms of correlations of sampling point locations. Hence, it is essential to study these correlations to understand and adapt sample distributions for low error in integral approximation. In this work, we aim at providing a comprehensive and accessible overview of the techniques developed over the last decades to analyze such correlations, relate them to error in integrators, and understand when and how to use existing sampling algorithms for effective rendering workflows.publishe

Mapping the Hsp90 Genetic Interaction Network in Candida albicans Reveals Environmental Contingency and Rewired Circuitry

The molecular chaperone Hsp90 regulates the folding of diverse signal transducers in all eukaryotes, profoundly affecting cellular circuitry. In fungi, Hsp90 influences development, drug resistance, and evolution. Hsp90 interacts with ∼10% of the proteome in the model yeast Saccharomyces cerevisiae, while only two interactions have been identified in Candida albicans, the leading fungal pathogen of humans. Utilizing a chemical genomic approach, we mapped the C. albicans Hsp90 interaction network under diverse stress conditions. The chaperone network is environmentally contingent, and most of the 226 genetic interactors are important for growth only under specific conditions, suggesting that they operate downstream of Hsp90, as with the MAPK Hog1. Few interactors are important for growth in many environments, and these are poised to operate upstream of Hsp90, as with the protein kinase CK2 and the transcription factor Ahr1. We establish environmental contingency in the first chaperone network of a fungal pathogen, novel effectors upstream and downstream of Hsp90, and network rewiring over evolutionary time