397 research outputs found
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
Eigenvalues and Singular Values of Products of Rectangular Gaussian Random Matrices
We derive exact analytic expressions for the distributions of eigenvalues and
singular values for the product of an arbitrary number of independent
rectangular Gaussian random matrices in the limit of large matrix dimensions.
We show that they both have power-law behavior at zero and determine the
corresponding powers. We also propose a heuristic form of finite size
corrections to these expressions which very well approximates the distributions
for matrices of finite dimensions.Comment: 13 pages, 3 figure
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
Impacts of soil management practices on crop productivity, on indicators for climate change mitigation, and on the chemical, physical and biological quality of soil
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
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