Approximation of Rectangular Beta-Laguerre Ensembles and Large Deviations

We investigate the random eigenvalues coming from the beta-Laguerre ensemble with parameter p, which is a generalization of the real, complex and quaternion Wishart matrices of parameter (n,p). In the case that the sample size n is much smaller than the dimension of the population distribution p, a common situation in modern data, we approximate the beta-Laguerre ensemble by a beta-Hermite ensemble which is a generalization of the real, complex and quaternion Wigner matrices. As corollaries, when n is much smaller than p, we show that the largest and smallest eigenvalues of the complex Wishart matrix are asymptotically independent; we obtain the limiting distribution of the condition numbers as a sum of two i.i.d. random variables with a Tracy-Widom distribution, which is much different from the exact square case that n=p by Edelman (1988); we propose a test procedure for a spherical hypothesis test. By the same approximation tool, we obtain the asymptotic distribution of the smallest eigenvalue of the beta-Laguerre ensemble. In the second part of the paper, under the assumption that n is much smaller than p in a certain scale, we prove the large deviation principles for three basic statistics: the largest eigenvalue, the smallest eigenvalue and the empirical distribution of eigenvalues, where the last large deviation is derived by using a non-standard method

Polymer Alloys And Composites Based On Poly (3-Hydroxybutyrate)[RM666.G127 S45 2006 f rb].

Aloi-aloi polimer poli(3-hidroksibutirat) (PHB) dengan poli(ε-kaprolakton) (PCL) dan juga dengan kalsium hidroksiapatit (HAP) kumis bioseramik telah dikaji. Polymer alloys of poly(3-hydroxybutyrate) (PHB) with poly(ε-caprolactone) (PCL) as well as with bioceramic calcium hydroxyapatite (HAP) whiskers were studied

How humans behave and evaluate a social robot in real-environment settings

Behavioral analysis has proven to be an important method to study human-robot interaction in real-life environments providing highly relevant insights for developing new theoretical and practical models of appropriate social robot design. In this paper we describe our approach to study human-robot interaction by combining human behavioral analysis with robot evaluation results. The approach is exemplified by a case study performed with a social robot receptionist in real-life settings. Our preliminary results are encouraging, as many behavior categories could be successfully related to certain evaluation patterns. With our analysis we hope to add a useful contribution to social-robotic design concerning user modeling issues and evaluation predictions

On a Problem of Harary and Schwenk on Graphs with Distinct Eigenvalues

Harary and Schwenk posed the problem forty years ago: Which graphs have distinct adjacency eigenvalues? In this paper, we obtain a necessary and sufficient condition for an Hermitian matrix with simple spectral radius and distinct eigenvalues. As its application, we give an algebraic characterization to the Harary-Schwenk's problem. As an extension of their problem, we also obtain a necessary and sufficient condition for a positive semidefinite matrix with simple least eigenvalue and distinct eigenvalues, which can provide an algebraic characterization to their problem with respect to the (normalized) Laplacian matrix.Comment: 11 page

Group Based Interference Alignment

In the $K$-user single-input single-output (SISO) frequency-selective fading interference channel, it is shown that the maximal achievable multiplexing gain is almost surely $K/2$ by using interference alignment (IA). However, when the signaling dimensions are limited, allocating all the resources to all users simultaneously is not optimal. So, a group based interference alignment (GIA) scheme is proposed, and it is formulated as an unbounded knapsack problem. Optimal and greedy search algorithms are proposed to obtain group patterns. Analysis and numerical results show that the GIA scheme can obtain a higher multiplexing gain when the resources are limited.Comment: 3 pages, 3 figures. resubmitted to IEEE Communications Letter

MIND0/3 Study of the \u27Thermal Rearrangements of Bicyclobutanylidene

It is found that path (i), which is concerted and stereospecific, is favored both thermodynamically and kinetically, in agreement with exp~\u27rimental results. In addition, paths (ii) and (iii) are found to be competitive with each other and both are highly energetic due to steric effects, with activation energy being about 50 kcal/mo!