Random Matrices with Correlated Elements: A Model for Disorder with Interactions

The complicated interactions in presence of disorder lead to a correlated randomization of states. The Hamiltonian as a result behaves like a multi-parametric random matrix with correlated elements. We show that the eigenvalue correlations of these matrices can be described by the single parametric Brownian ensembles. The analogy helps us to reveal many important features of the level-statistics in interacting systems e.g. a critical point behavior different from that of non-interacting systems, the possibility of extended states even in one dimension and a universal formulation of level correlations.Comment: 19 Pages, No Figures, Major Changes to Explain the Mathematical Detail

The Extent of Autism Knowledge of Novice Alternatively Certified Special Education Teachers in Texas

An increase in the prevalence rate of autism is not necessarily matched by a concurrent increase in the rate of highly qualified special education teachers, resulting in chronic teacher shortages in this area. Alternative certification (AC) is used as a mechanism to alleviate the demand for highly qualified special education teachers. However, AC routes have often left novice teachers underprepared for teaching students with autism, more specifically in the implementation of evidence-based practices necessary for instructional effectiveness. The purpose of the study was to assess the knowledge of novice AC teachers in the area of autism intervention and to determine the extent to which demographic, educational and professional factors predict the variance in knowledge scores. Data were collected through an electronic survey instrument disseminated to all novice (i.e., first-and second-year) alternatively certified special education teachers in the state of Texas. Results indicated that AC teachers were not adequately knowledgeable about autism and the largest predictor of autism knowledge was hours engaged in self-directed learning. Implications for improving the quality of AC programs in Texas are discussed

Computational Investigation of Furnace Wall for Silica Ramming Mass with FDM

Furnaces are useful for melting different materials for casting process. In this research paper, we had done advanced heat transfer analysis of induction furnace wall made of silica ramming mass using explicit finite difference method. We have divided actual geometry of furnace refractory wall into 14 elements and 24 nodes. We have derived explicit finite difference equations for all 24 nodes. We have calculated temperature distribution and thermal stress distribution for all different nodes with respect to time. We have plotted graphs for maximum temperature v/s time and maximum stress v/s time. We found that results indicate the effect of thermal fatigue in the induction furnace wall for silica ramming mass. The analysis is very helpful in understanding how thermal fatigue failure of refractory wall happens

Towards a common thread in Complexity: an accuracy-based approach

The complexity of a system, in general, makes it difficult to determine some or almost all matrix elements of its operators. The lack of accuracy acts as a source of randomness for the matrix elements which are also subjected to an external potential due to existing system conditions. The fluctuation of accuracy due to varying system-conditions leads to a diffusion of the matrix elements. We show that, for the single well potentials, the diffusion can be described by a common mathematical formulation where system information enters through a single parameter. This further leads to a characterization of physical properties by an infinite range of single parametric universality classes

Thermodynamics of protein folding: a random matrix formulation

The process of protein folding from an unfolded state to a biologically active, folded conformation is governed by many parameters e.g the sequence of amino acids, intermolecular interactions, the solvent, temperature and chaperon molecules. Our study, based on random matrix modeling of the interactions, shows however that the evolution of the statistical measures e.g Gibbs free energy, heat capacity, entropy is single parametric. The information can explain the selection of specific folding pathways from an infinite number of possible ways as well as other folding characteristics observed in computer simulation studies.Comment: 21 Pages, no figure

Multi-Channel Transport in Disordered Medium under Generic Scattering Conditions

Our study of the evolution of transmission eigenvalues, due to changes in various physical parameters in a disordered region of arbitrary dimensions, results in a generalization of the celebrated DMPK equation. The evolution is shown to be governed by a single complexity parameter which implies a deep level of universality of transport phenomena through a wide range of disordered regions. We also find that the interaction among eigenvalues is of many body type that has important consequences for the statistical behavior of transport properties.Comment: 19 Pages, No Figure

Universal Level dynamics of Complex Systems

. We study the evolution of the distribution of eigenvalues of a $N\times N$ matrix subject to a random perturbation drawn from (i) a generalized Gaussian ensemble (ii) a non-Gaussian ensemble with a measure variable under the change of basis. It turns out that, in the case (i), a redefinition of the parameter governing the evolution leads to a Fokker-Planck equation similar to the one obtained when the perturbation is taken from a standard Gaussian ensemble (with invariant measure). This equivalence can therefore help us to obtain the correlations for various physically-significant cases modeled by generalized Gaussian ensembles by using the already known correlations for standard Gaussian ensembles. For large $N$-values, our results for both cases (i) and (ii) are similar to those obtained for Wigner-Dyson gas as well as for the perturbation taken from a standard Gaussian ensemble. This seems to suggest the independence of evolution, in thermodynamic limit, from the nature of perturbation involved as well as the initial conditions and therefore universality of dynamics of the eigenvalues of complex systems.Comment: 11 Pages, Latex Fil

Higher Order Correlations in Quantum Chaotic Spectra

The statistical properties of the quantum chaotic spectra have been studied, so far, only up to the second order correlation effects. The numerical as well as the analytical evidence that random matrix theory can successfully model the spectral fluctuatations of these systems is available only up to this order. For a complete understanding of spectral properties it is highly desirable to study the higher order spectral correlations. This will also inform us about the limitations of random matrix theory in modelling the properties of quantum chaotic systems. Our main purpose in this paper is to carry out this study by a semiclassical calculation for the quantum maps; however results are also valid for time-independent systems.Comment: Revtex, Four figures (Postscript files), Phys. Rev E (in press

A Survey of Word Reordering Model in Statistical Machine Translation

Machine translation is the process of translating one natural language in to another natural language by computers. In statistical machine translation word reordering is a big challenge between distant language pair. It is important factor for its quality and efficiency. Word reordering is major challenge For Indian languages who have big structural difference like English and Hindi language. This paper present description about statistical machine translation, reordering model and reordering types

Toward semiclassical theory of quantum level correlations of generic chaotic systems

In the present work we study the two-point correlation function $R(\epsilon)$ of the quantum mechanical spectrum of a classically chaotic system. Recently this quantity has been computed for chaotic and for disordered systems using periodic orbit theory and field theory. In this work we present an independent derivation, which is based on periodic orbit theory. The main ingredient in our approach is the use of the spectral zeta function and its autocorrelation function $C(\epsilon)$. The relation between $R(\epsilon)$ and $C(\epsilon)$ is constructed by making use of a probabilistic reasoning similar to that which has been used for the derivation of Hardy -- Littlewood conjecture. We then convert the symmetry properties of the function $C(\epsilon)$ into relations between the so-called diagonal and the off-diagonal parts of $R(\epsilon)$. Our results are valid for generic systems with broken time reversal symmetry, and with non-commensurable periods of the periodic orbits.Comment: 15 pages(twocolumn format), LaTeX, EPSF, (figures included