2,572 research outputs found
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 -user single-input single-output (SISO) frequency-selective fading
interference channel, it is shown that the maximal achievable multiplexing gain
is almost surely 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!
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