Two methods of evaluating matrix elements of a function in a polynomial basis are considered: the expansion method, where the function is expanded in the basis and the integrals are evaluated analytically, and the numerical method, where the integration is performed directly using numerical quadrature. A reduced grid is proposed for the latter which makes use of the symmetry of the basis. Compa...

Trust has been used to replace or complement ratingbased similarity in recommender systems, to improve the accuracy of rating prediction. However, people trusting each other may not always share similar preferences. In this paper, we try to fill in this gap by decomposing the original single-aspect trust information into four general trust aspects, i.e. benevolence, integrity, competence, and p...

The present understanding of nonperturbative ground states in the fractional quantum Hall effect is based on effective theories of the Jain “composite fermion” excitations. We review the approach based on matrix variables, i.e. D0 branes, originally introduced by Susskind and Polychronakos. We show that the Maxwell-Chern-Simons matrix gauge theory provides a matrix generalization of the quantum...

We present effective and efficient matrix-free preconditioning techniques for the augmented immersed interface method (AIIM). AIIM has been developed recently and is shown to be very effective for interface problems and problems on irregular domains. GMRES is often used to solve for the augmented variable(s) associated with a Schur complement A in AIIM that is defined along the interface or the...

in the present paper, we introduce the sequence space [{l_p}(e,delta) = left{ x = (x_n)_{n = 1}^infty : sum_{n = 1}^infty left|  sum_{j in {e_n}} x_j - sum_{j in e_{n + 1}} x_jright| ^p < infty right},] where $e=(e_n)$ is a partition of finite subsets of the positive integers and $pge 1$. we investigate its topological properties and inclusion relations. moreover, we consider the problem of fin...

We study the low-energy effective action of the IIB matrix model in the derivative interpretation, where the diffeomorphism invariance is manifest and arbitrary manifolds are described by matrices. We show that it is expressed as a sum of terms, each of which is factorized into a product of diffeomorphism invariant action functionals: S = ∑

Recent developments in the theory of weak decays of heavy flavours are reviewed. Applications to exclusive semileptonic B decays, the semileptonic branching ratio and charm counting, beauty lifetimes, and hadronic B decays are discussed. Invited talk presented at the International Europhysics Conference on High Energy Physics Jerusalem, Israel, 19–26 August 1997 CERN-TH/98-2 January 1998 19: He...

We study matrix models related to SO/Sp gauge theories with flavors. We give the effective superpotentials for gauge theories with arbitrary tree level superpotential up to first instanton level. For quartic tree level superpotential we obtained exact one-cut solution. We also derive Seiberg-Witten curve for these gauge theories from matrix model argument.

Traditional approaches to the study of fragmented landscapes invoke an island-ocean model and assume that the nonhabitat matrix surrounding remnant patches is uniform. Patch isolation, a crucial parameter to the predictions of island biogeography and metapopulation theories, is measured by distance alone. To test whether the type of interpatch matrix can contribute significantly to patch isolat...

We study the relation between the effective Lagrangian in Matrix Theory and eleven dimensional supergravity. In particular, we provide a relationship between supergravity operators and the corresponding terms in the post-Newtonian approximation of Matrix Theory.