Universal Cubic Eigenvalue Repulsion for Random Normal Matrices

Random matrix models consisting of normal matrices, defined by the sole constraint $[N^{\dag},N]=0$, will be explored. It is shown that cubic eigenvalue repulsion in the complex plane is universal with respect to the probability distribution of matrices. The density of eigenvalues, all correlation functions, and level spacing statistics are calculated. Normal matrix models offer more probability distributions amenable to analytical analysis than complex matrix models where only a model wth a Gaussian distribution are solvable. The statistics of numerically generated eigenvalues from gaussian distributed normal matrices are compared to the analytical results obtained and agreement is seen.Comment: 15 pages, 2 eps figures. to appar in Physical Review

Microsecond folding dynamics of the F13W G29A mutant of the B domain of staphylococcal protein A by laser-induced temperature jump

The small size (58 residues) and simple structure of the B domain of staphylococcal protein A (BdpA) have led to this domain being a paradigm for theoretical studies of folding. Experimental studies of the folding of BdpA have been limited by the rapidity of its folding kinetics. We report the folding kinetics of a fluorescent mutant of BdpA (G29A F13W), named F13W*, using nanosecond laser-induced temperature jump experiments. Automation of the apparatus has permitted large data sets to be acquired that provide excellent signal-to-noise ratio over a wide range of experimental conditions. By measuring the temperature and denaturant dependence of equilibrium and kinetic data for F13W*, we show that thermodynamic modeling of multidimensional equilibrium and kinetic surfaces is a robust method that allows reliable extrapolation of rate constants to regions of the folding landscape not directly accessible experimentally. The results reveal that F13W* is the fastest-folding protein of its size studied to date, with a maximum folding rate constant at 0 M guanidinium chloride and 45°C of 249,000 (s-1). Assuming the single-exponential kinetics represent barrier-limited folding, these data limit the value for the preexponential factor for folding of this protein to at least ≈2 x 10(6) s(-1)

Almost-Hermitian Random Matrices: Crossover from Wigner-Dyson to Ginibre eigenvalue statistics

By using the method of orthogonal polynomials we analyze the statistical properties of complex eigenvalues of random matrices describing a crossover from Hermitian matrices characterized by the Wigner- Dyson statistics of real eigenvalues to strongly non-Hermitian ones whose complex eigenvalues were studied by Ginibre. Two-point statistical measures (as e.g. spectral form factor, number variance and small distance behavior of the nearest neighbor distance distribution $p(s)$) are studied in more detail. In particular, we found that the latter function may exhibit unusual behavior $p(s)\propto s^{5/2}$ for some parameter values.Comment: 4 pages, RevTE

Critical statistics for non-Hermitian matrices

We introduce a generalized ensemble of nonhermitian matrices interpolating between the Gaussian Unitary Ensemble, the Ginibre ensemble and the Poisson ensemble. The joint eigenvalue distribution of this model is obtained by means of an extension of the Itzykson-Zuber formula to general complex matrices. Its correlation functions are studied both in the case of weak nonhermiticity and in the case of strong nonhermiticity. In the weak nonhermiticity limit we show that the spectral correlations in the bulk of the spectrum display critical statistics: the asymptotic linear behavior of the number variance is already approached for energy differences of the order of the eigenvalue spacing. To lowest order, its slope does not depend on the degree of nonhermiticity. Close the edge, the spectral correlations are similar to the Hermitian case. In the strong nonhermiticity limit the crossover behavior from the Ginibre ensemble to the Poisson ensemble first appears close to the surface of the spectrum. Our model may be relevant for the description of the spectral correlations of an open disordered system close to an Anderson transition.Comment: 25 pages, 6 figure

Integrated use of residues from olive mill and winery for lipase production by solid state fermentation with Aspergillus sp

Two phase olive mill waste (TPOMW) is presently the major waste produced by the olive mill industry. This waste has potential to be used as substrate for solid state fermentation (SSF) despite of its high concentration of phenolic compounds and low nitrogen content. In this work, it is demonstrated that mixtures of TPOMW with winery wastes support the production of lipase by Aspergillus spp. By agar plate screening, Aspergillus niger MUM 03.58, Aspergillus ibericus MUM 03.49 and Aspergillus uvarum MUM 08.01 were chosen for lipase production by SSF. Plackett-Burman experimental design was employed to evaluate the effect of substrate composition and time on lipase production. The highest amounts of lipase were produced by A. ibericus on a mixture of TPOMW, urea and exhausted grape mark (EGM). Urea was found to be the most influent factor for the lipase production. Further optimization of lipase production by A. ibericus using a full factorial design (32) conducted to optimal conditions of substrate composition (0.073 g urea/g and 25% of EGM) achieving 18.67 U/g of lipolytic activity.Jose Manuel Salgado is grateful for Postdoctoral fellowship (EX-2010-0402) of Education Ministry of Spanish Government. Luis Abrunhosa was supported by the grant SFRH/BPD/43922/2008 from Fundacao para a Ciencia e Tecnologia-FCT, Portugal. Authors thank Fundacao para a Ciencia e a Tecnologia (FCT) for financial support through the project FCT Pest-OE/EQB/LA0023/2011

Extended superconformal symmetry and Calogero-Marchioro model

We show that the two dimensional Calogero-Marchioro Model (CMM) without the harmonic confinement can naturally be embedded into an extended SU(1,1|2) superconformal Hamiltonian. We study the quantum evolution of the superconformal Hamiltonian in terms of suitable compact operators of the N=2 extended de Sitter superalgebra with central charge and discuss the pattern of supersymmetry breaking. We also study the arbitrary D dimensional CMM having dynamical OSp(2|2) supersymmetry and point out the relevance of this model in the context of the low energy effective action of the dimensionally reduced Yang-Mills theory.Comment: 18 pages, RevTeX, No figures; Added clarifications & discussions, Change in format, version to appear in Journal of Physics A : Mathematical & General; Corrected typo