Finite size scaling in crossover among different random matrix ensembles in microscopic lattice models

Using numerical diagonalization we study the crossover among different random matrix ensembles (Poissonian, Gaussian orthogonal ensemble (GOE), Gaussian unitary ensemble (GUE) and Gaussian symplectic ensemble (GSE)) realized in two different microscopic models. The specific diagnostic tool used to study the crossovers is the level spacing distribution. The first model is a one-dimensional lattice model of interacting hard-core bosons (or equivalently spin 1/2 objects) and the other a higher dimensional model of non-interacting particles with disorder and spin-orbit coupling. We find that the perturbation causing the crossover among the different ensembles scales to zero with system size as a power law with an exponent that depends on the ensembles between which the crossover takes place. This exponent is independent of microscopic details of the perturbation. We also find that the crossover from the Poissonian ensemble to the other three is dominated by the Poissonian to GOE crossover which introduces level repulsion while the crossover from GOE to GUE or GOE to GSE associated with symmetry breaking introduces a subdominant contribution. We also conjecture that the exponent is dependent on whether the system contains interactions among the elementary degrees of freedom or not and is independent of the dimensionality of the system.

Orientational relaxation in a random dipolar lattice: Wave-number and frequency dependence

In order to understand the role of translational modes in the orientational relaxation in dense dipolar liquids, we have carried out a computer ''experiment'' where a random dipolar lattice was generated by quenching only the translational motion of the molecules of an equilibrated dipolar liquid. The lattice so generated was orientationally disordered and positionally random. The detailed study of orientational relaxation in this random dipolar lattice revealed interesting differences from those of the corresponding dipolar liquid. In particular, we found that the relaxation of the collective orientational correlation functions at the intermediate wave numbers was markedly slower at the long times for the random lattice than that of the liquid. This verified the important role of the translational modes in this regime, as predicted recently by the molecular theories. The single-particle orientational correlation functions of the random lattice also decayed significantly slowly at long times, compared to those of the dipolar liquid.

Stability of a Random Diffusion with Linear Drift

We consider a Linear system with Markovian switching which is perturbed by Gaussian type noise, If the linear system is mean square stable then we show that under certain conditions the perturbed system is also stable, We also shaw that under certain conditions the linear system with Markovian switching can be stabilized by such noisy perturbation.

Speeding up AdaBoost Classifier with Random Projection

The development of techniques for scaling up classifiers so that they can be applied to problems with large datasets of training examples is one of the objectives of data mining. Recently, AdaBoost has become popular among machine learning community thanks to its promising results across a variety of applications. However, training AdaBoost on large datasets is a major problem, especially when the dimensionality of the data is very high. This paper discusses the effect of high dimensionality on the training process of AdaBoost. Two preprocessing options to reduce dimensionality, namely the principal component analysis and random projection are briefly examined. Random projection subject to a probabilistic length preserving transformation is explored further as a computationally light preprocessing step. The experimental results obtained demonstrate the effectiveness of the proposed training process for handling high dimensional large datasets.

Generation of optimum random pinhole arrays for multiple imaging

Through an analysis using the transfer function of a pinhole camera, the multiple imaging characteristics of photographic diffusers described by Grover and Tremblay [Appl. Opt.21,4500(1982)] is studied. It is found that only one pinhole diameter satisfies the optimum imaging condition for best contrast transfer at any desired spatial frequency. A simple method of generating random pinhole arrays with a controlled pinhole diameter is described. These pinhole arrays are later used to generate high frequency sinusoidal gratings from a coarse grid. The contrast in the final gratings is found to be reasonably high.

A Nonlinear System Under Combined Periodic and Random Excitation

The anharmonic oscillator under combined sinusoidal and white noise excitation is studied using the Gaussian closure approximation. The mean response and the steady-state variance of the system is obtained by the WKBJ approximation and also by the Fokker Planck equation. The multiple steadystate solutions are obtained and their stability analysis is presented. Numerical results are obtained for a particular set of system parameters. The theoretical results are compared with a digital simulation study to bring out the usefulness of the present approximate theory.

Helix-coil stability constants for amino acids in nonaqueous solvents. Studies of random poly(-benzyl-L-glutamate-co-L-alanine) and poly(-benzyl-L-glutamate-co-L-leucine) in a mixed solvent

The host-guest technique has been applied to the determination of the helix-coil stability constants of two naturally occurring amino acids, L-alanine and L-leucine, in a nonaqueous solvent system. Random copolymers containing L-alanine and L-leucine, respectively, as guest residues and -benzyl-L-glutamate as the host residue were synthesized. The polymers were fractionated and characterized for their amino acid content, molecular weight, and helix-coil transition behavior in a dichloroacetic acid (DCA)-1,2-dichloroethane (DCE) mixture. Two types of helix-coil transitions were carried out on the copolymers: solvent-induced transitions in DCA-DCE mixtures at 25°C and thermally induced transitions in a 82:18 (wt %) DCA-DCE mixture. The thermally induced transitions were analyzed by statistical mechanical methods to determine the Zimm-Bragg parameters, and s, of the guest residues. The experimental data indicate that, in the nonaqueous solvent, the L-alanine residue stabilizes the -helical conformation more than the L-leucine residue does. This is in contrast to their behavior in aqueous solution, where the reverse is true. The implications of this finding for the analysis of helical structures in globular proteins are discussed.

Application of various viscosity theories to the viscosity data of methyl methacrylate-acrylonitrile random copolymersstar

Values of Ko, Flory constant related to unperturbed dimensions, are evaluated for methyl methacrylate-acrylonitrile random copolymers using Flory-Fox, Kurata-Stockmayer and Inagaki-Ptitsyn methods and compared with the Ko values obtained by Stockmayer-Fixman method. Ko values are seen to be less in solvents which have large a (Mark-Houwink exponent) values. A correlation between Ko and a is developed to arrive at a more reliable estimate of Ko for this copolymer system.

Non-linear resonance in strings under narrow band random excitation, part I: Planar response and stability

Non-linear planar response of a string to planar narrow band random excitation is investigated in this paper. A response equation for the mean square deflection σ2 is obtained under a single mode approximation by using the equivalent linearization technique. It is shown that the response is triple valued, as in the case of harmonic excitation, if the centre frequency of excitation Ω lies in a certain specified range. The triple valued response occurs only if the excitation bandwidth β is smaller than a critical value βcrit which is a monotonically increasing function of the intensity of excitation. An approximate method of investigating the almost sure asymptotic stability of the solution is presented and regions of instability in the Ω-σ2 plane have been charted. It is shown that planar response can become unstable either due to an unbounded growth of the in-plane component of motion or due to a spontaneous appearance of an out-of-plane component.

Behaviour of methylmethacrylate-acrylonitrile random copolymers in dilute solution

Studies on the dilute solution properties of methylmethacrylate-acrylonitrile random copolymers of three different compositions, 0.236, 0.5 and 0.74 mole fraction (m.f.) of acrylonitrile (AN) designated as MAa, MAb and MAc, respectively, have been made in good solvents and theta solvents. MAa has been studied in benzene (Bz) and ethylacetate (EAc). MAb in acetonitrile (MeCN), dimethyl sulphoxide (DMSO) and a binary solvent mixture of Bz and dimentyl formamide (DMF) in the volume ratio 6.5:1 designated as BM1 and MAc in MeCN, DMSO and Bz + DMF in the volume ratio 1.667:1 designated as BM2. The Mark-Houwink exponent ‘a’ reveals that Bz is a theta solvent for MAa at 20°C. For MAb and MAc, BM1 and BM2, respectively have ‘a’ values of 0.5 at all three temperatures studied (30°, 40° and 50°C). It is not clear whether they represent theta states or preferential adsorption plays a role complicating the behaviour in solution. The values of A2 are very low in MeCN considering that it is a very good solvent for the copolymer, ‘a’ values for MAb and MAc being 0.75 and 0.7, respectively.

Nonstationary Random Critical Seismic Excitations

A method is presented to find nonstationary random seismic excitations with a constraint on mean square value such that the response variance of a given linear system is maximized. It is also possible to incorporate the dominant input frequency into the analysis. The excitation is taken to be the product of a deterministic enveloping function and a zero mean Gaussian stationary random process. The power spectral density function of this process is determined such that the response variance is maximized. Numerical results are presented for a single-degree system and an earth embankment modeled as shear beam.

Distribution of the angle of rotation plane random walks

We study the probability distribution of the angle by which the tangent to the trajectory rotates in the course of a plane random walk. It is shown that the determination of this distribution function can be reduced to an integral equation, which can be rigorously transformed into a differential equation of Hill's type. We derive the asymptotic distribution for very long walks.

A note on the effective medium theory of random resistive-reactive medium

The effective medium theory for a system with randomly distributed point conductivity and polarisability is reformulated, with attention to cross-terms involving the two disorder parameters. The treatment reveals a certain inconsistency of the conventional theory owing to the neglect of the Maxwell-Wagner effect. The results are significant for the critical resistivity and dielectric anomalies of a binary liquid mixture at the phase separation point.

Dilute Solution Properties of Methyl Methacrylate/Acrylonitrile Random Copolymers, 2a)

The Stockmayer-Fixman relation was used to evaluate the short range and long range interaction parameters for methyl methacrylate/acrylonitrile copolymers of 0,566 and 0,657 mole fraction of monomeric units of acrylonitrile in the solvents acetonitrile, 2-butanone, dimethyl formamide, and y-butyrolactone, at different temperatures (30, 45, and 60 “C). The values of KO were found to be lower than those of the parent homopolymers, and their values depend on both solvent and temperature. Even negative Ko-values were obtained, in cases in which the Mark Houwink exponent a is nearly unity. The values of the polymer-solvent interaction parameter, x, , are high and close to 0,5, indicating that these solvents are not good. The values of the excess interaction parameter, xAB, are negative and are not affected by temperature. The large extension of these copolymer chains, as exhibited by a and a;-values, can be understood in terms of unusual short range interactions only. Similar results were obtained for some cellulose derivatives.