Cross-Correlation in cricket data and RMT

We analyze cross-correlation between runs scored over a time interval in cricket matches of different teams using methods of random matrix theory (RMT). We obtain an ensemble of cross-correlation matrices $C$ from runs scored by eight cricket playing nations for (i) test cricket from 1877 -2014 (ii)one-day internationals from 1971 -2014 and (iii) seven teams participating in the Indian Premier league T20 format (2008-2014) respectively. We find that a majority of the eigenvalues of C fall within the bounds of random matrices having joint probability distribution $P(x_1...,x_n)=C_{N \beta} \, \prod_{j<k}w(x_j)| x_j-x_k |^\beta$ where $w(x)=x^{N\beta a}\exp(-N\beta b x)$ and $\beta$ is the Dyson parameter. The corresponding level density gives Marchenko-Pastur (MP) distribution while fluctuations of every participating team agrees with the universal behavior of Gaussian Unitary Ensemble (GUE). We analyze the components of the deviating eigenvalues and find that the largest eigenvalue corresponds to an influence common to all matches played during these periods.Comment: 12 pages, 6 figure

Bulk asymptotics of skew-orthogonal polynomials for quartic double well potential and universality in the matrix model

We derive bulk asymptotics of skew-orthogonal polynomials (sop) \pi^{\bt}_{m}, $\beta=1$, 4, defined w.r.t. the weight $\exp(-2NV(x))$, $V (x)=gx^4/4+tx^2/2$, $g>0$ and $t<0$. We assume that as $m,N \to\infty$ there exists an $\epsilon > 0$, such that $\epsilon\leq (m/N)\leq \lambda_{\rm cr}-\epsilon$, where $\lambda_{\rm cr}$ is the critical value which separates sop with two cuts from those with one cut. Simultaneously we derive asymptotics for the recursive coefficients of skew-orthogonal polynomials. The proof is based on obtaining a finite term recursion relation between sop and orthogonal polynomials (op) and using asymptotic results of op derived in \cite{bleher}. Finally, we apply these asymptotic results of sop and their recursion coefficients in the generalized Christoffel-Darboux formula (GCD) \cite{ghosh3} to obtain level densities and sine-kernels in the bulk of the spectrum for orthogonal and symplectic ensembles of random matrices.Comment: 6 page

Variations in the SDN Loop of Class A Beta-Lactamases: A Study of the Molecular Mechanism of BlaC (Mycobacterium tuberculosis) to Alter the Stability and Catalytic Activity Towards Antibiotic Resistance of MBIs

The emergence of multidrug-resistant (MDR) and extensively drug-resistant (XDR) tuberculosis calls for an immediate search for novel treatment strategies. Recently, BlaC, the principal beta-lactamase of Mycobacterium tuberculosis, was recognized as a potential therapeutic target. BlaC belongs to Ambler class A, which is generally susceptible to the beta-lactamase inhibitors currently used in clinics: tazobactam, sulbactam, and clavulanate. Alterations at Ser130 in conserved SDN loop confer resistance to mechanism-based inhibitors (MBIs) commonly observed in various clinical isolates. The absence of clinical evidence of S130G conversion in M. tuberculosis draws our attention to build laboratory mutants of S130G and S130A of BlaC. The study involving steady state, inhibition kinetics, and fluorescence microscopy shows the emergence of resistance against MBIs to the mutants expressing S130G and S130A. To understand the molecular reasoning behind the unavailability of such mutation in real life, we have used circular dichroism (CD) spectroscopy, differential scanning calorimetry (DSC), molecular dynamics (MD) simulation, and stability-based enzyme activity to compare the stability and dynamic behaviors of native and S130G/A mutant form of BlaC. A significant decrease in melting temperature (BlaC T M 60°C, S130A T M 50°C, and S130G T M 45°C), kinetic instability at higher temperature, and comparative dynamic instability correlate the fact that resistance to beta-lactam/beta-lactamase inhibitor combinations will likely not arise from the structural alteration of BlaC, therefore establishing confidence that this therapeutic modality can be potentially applied as a part of a successful treatment regimen against M. tuberculosis

Skew-orthogonal polynomials and random matrix theory

Orthogonal polynomials satisfy a three-term recursion relation irrespective of the weight function with respect to which they are defined. This gives a simple formula for the kernel function, known in the literature as the Christoffel-Darboux sum. The availability of asymptotic results of orthogonal polynomials and the simple structure of the Christoffel-Darboux sum make the study of unitary ensembles of random matrices relatively straightforward. In this book, the author develops the theory of skew-orthogonal polynomials and obtains recursion relations which, unlike orthogonal polynomials, depend on weight functions. After deriving reduced expressions, called the generalized Christoffel-Darboux formulas (GCD), he obtains universal correlation functions and non-universal level densities for a wide class of random matrix ensembles using the GCD. The author also shows that once questions about higher order effects are considered (questions that are relevant in different branches of physics and mathematics) the use of the GCD promises to be efficient

Study of gasification behavior for a biorefinery lignin waste in a fluidized bed gasification reactor

Sustainable energy supply and waste management are two of the major challenges of the present time. The proper utilization of the vast resource of renewable biomass is necessary for a sustainable civilization toward the net-zero emission target. To achieve this goal, biomass conversion technologies can contribute with their great potential. Gasification of biomass is such a process that produces product gas that can be utilized for power generation or as a raw material for secondary fuel production. Lignin, an available source of biomass, is the second most prevalent natural polymer. It has the potential to be employed effectively in biofuel production. Experiments on the gasification of lignin in a bubbling fluidized bed reactor were carried out in a pilot-scale reactor at the University of South-Eastern Norway (USN), Porsgrunn. A simulation model based on the Computational Particle Fluid Dynamics (CPFD) method was developed using the commercial software Barracuda VR and the results were compared to the experimental data. The average volume percentage of carbon monoxide, hydrogen, methane and nitrogen were found to be around 15.55%, 13.32%, 4.33% and 51.23% respectively in the experiment for the equivalence ratio (ER) 0.165. The data for the gas compositions were also analyzed at the ER of 0.215 and 0.264. The simulation results agree well with most of the experimental results. The oxygen concentration during the experiment was around 1% which showed some degree of air contamination of the gas samples. Product gas yield (GY), lower heating value (LHV), carbon conversion efficiency (CCE), cold gas efficiency (CGE), and energy rate were calculated to analyze the gasifier performance. Lignin pellets showed acceptable results, with an average carbon conversion of around 38%