Statistical eigen-inference from large Wishart matrices

We consider settings where the observations are drawn from a zero-mean multivariate (real or complex) normal distribution with the population covariance matrix having eigenvalues of arbitrary multiplicity. We assume that the eigenvectors of the population covariance matrix are unknown and focus on inferential procedures that are based on the sample eigenvalues alone (i.e., "eigen-inference"). Results found in the literature establish the asymptotic normality of the fluctuation in the trace of powers of the sample covariance matrix. We develop concrete algorithms for analytically computing the limiting quantities and the covariance of the fluctuations. We exploit the asymptotic normality of the trace of powers of the sample covariance matrix to develop eigenvalue-based procedures for testing and estimation. Specifically, we formulate a simple test of hypotheses for the population eigenvalues and a technique for estimating the population eigenvalues in settings where the cumulative distribution function of the (nonrandom) population eigenvalues has a staircase structure. Monte Carlo simulations are used to demonstrate the superiority of the proposed methodologies over classical techniques and the robustness of the proposed techniques in high-dimensional, (relatively) small sample size settings. The improved performance results from the fact that the proposed inference procedures are "global" (in a sense that we describe) and exploit "global" information thereby overcoming the inherent biases that cripple classical inference procedures which are "local" and rely on "local" information.Comment: Published in at http://dx.doi.org/10.1214/07-AOS583 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Free Probability, Sample Covariance Matrices and Stochastic Eigen-Inference

Random matrix theory is now a big subject with applications in many disciplines of science, engineering and finance. This talk is a survey specifically oriented towards the needs and interests of a computationally inclined audience. We include the important mathematics (free probability) that permit the characterization of a large class of random matrices. We discuss how computational software is transforming this theory into practice by highlighting its use in the context of a stochastic eigen-inference application.Singapore-MIT Alliance (SMA

Fire Safety Analysis of a Railway Compartment using Computational Fluid Dynamics

Trains are considered to be the safest on-land transportation means for both passengers and cargo. Train accidents have been mainly disastrous, especially in case of fire, where the consequences are extensive loss of life and goods. The fire would generate smoke and heat which would spread quickly inside the railway compartments. Both heat and smoke are the primary reasons of casualties in a train. This study has been carried out to perform numerical analysis of fire characteristics in a railway compartment using commercial Computational Fluid Dynamics code ANSYS. Non-premixed combustion model has been used to simulate a fire scenario within a railway compartment, while Shear Stress Transport k-ω turbulence model has been used to accurately predict the hot air turbulence parameters within the compartment. The walls of the compartment have been modelled as no-slip stationary adiabatic walls, as is observed in real life conditions. Carbon dioxide concentration (CO2), temperature distribution and air flow velocity within the railway compartment has been monitored. It has been observed that the smoke above the fire source flows to both sides of the compartment. The highest temperature zone is located downstream the fire source, and gradually decreases with the increase in the distance from the fire source. It can be seen that CFD can be used as an effective tool in order to analyse the evolution of fire in railway compartments with reasonable accuracy. The paper also briefly discusses the topical reliability issues

A study on anxiolytic activity and locomotor behavior of Curcuma amada rhizomes using Wistar albino rats

Background: Global burden of disease statistics indicate that 4 of 10 most important causes of disease worldwide are psychiatric in origin. Anxiety affects 1/8th of total population of the world and is a very important area of research interest in psychopharmacology. Medicinal plants and plant products are the oldest tried health-care products. Their importance is growing not only in developing countries but in many developed countries. Curcuma amada Roxb. (CA) commonly known as Mango Ginger is a rhizomatous aromatic herb which is used in this country for culinary purposes and also to treat various diseases. The rhizomes of Curcuma amada was screened for anxiolytic activity and locomotor behavior in Wistar albino rats.Methods: Wistar albino rats were divided into three groups as control (Distilled water with 0.1% CMC), standard (Diazepam - 1mg/kg) and test - Ethanolic Extract of Curcuma amada Rhizome (EECAR-250 mg/kg). They were administered drugs orally for a period of 10 days, and screened for anxiolytic activity using Light dark arena model and Actophotometer for assessing the locomotor behavior on the 10th day. The number of crossings and time spent in light arena for anxiolytic activity, and the number of movements in Actophotometer was noted. Data was analyzed by one way ANOVA followed by Tukey Kramer multiple comparison test using GraphPad InStat software.Results: Curcuma amada (250mg/kg) showed increased time spent in light arena and decreased locomotor behavior which was statistically significant.Conclusions: Curcuma amada possesses significant anxiolytic with CNS depressant activity

Need of luteinizing hormone for early pregnancy in the golden hamster (Mesocricetus auratus)

Administration of LH antiserum to intact pregnant hamsters on any day from Days 6 to 11 of pregnancy resulted in termination of gestation. Following LH antiserum injection, the ovarian weights were markedly reduced

Inelastic Neutron scattering in CeSi_{2-x}Ga_x ferromagnetic Kondo lattice compounds

Inelastic neutron scattering investigation on ferromagnetic Kondo lattice compounds belonging to CeSi_{2-x}Ga_{x}, x = 0.7, 1.0 and 1.3, system is reported. The thermal evolution of the quasielastic response shows that the Kondo interactions dominate over the RKKY interactions with increase in Ga concentration from 0.7 to 1.3. This is related to the increase in k-f hybridization with increasing Ga concentration. The high energy response indicates the ground state to be split by crystal field in all three compounds. Using the experimental results we have calculated the crystal field parameters in all three compounds studied here.Comment: 12 Pages Revtex, 2 eps figures

Evaluation of Effectiveness of Wavelet Based Denoising Schemes Using ANN and SVM for Bearing Condition Classification

The wavelet based denoising has proven its ability to denoise the bearing vibration signals by improving the signal-to-noise ratio (SNR) and reducing the root-mean-square error (RMSE). In this paper seven wavelet based denoising schemes have been evaluated based on the performance of the Artificial Neural Network (ANN) and the Support Vector Machine (SVM), for the bearing condition classification. The work consists of two parts, the first part in which a synthetic signal simulating the defective bearing vibration signal with Gaussian noise was subjected to these denoising schemes. The best scheme based on the SNR and the RMSE was identified. In the second part, the vibration signals collected from a customized Rolling Element Bearing (REB) test rig for four bearing conditions were subjected to these denoising schemes. Several time and frequency domain features were extracted from the denoised signals, out of which a few sensitive features were selected using the Fisher’s Criterion (FC). Extracted features were used to train and test the ANN and the SVM. The best denoising scheme identified, based on the classification performances of the ANN and the SVM, was found to be the same as the one obtained using the synthetic signal