Fast matrix computations for pair-wise and column-wise commute times and Katz scores

We first explore methods for approximating the commute time and Katz score between a pair of nodes. These methods are based on the approach of matrices, moments, and quadrature developed in the numerical linear algebra community. They rely on the Lanczos process and provide upper and lower bounds on an estimate of the pair-wise scores. We also explore methods to approximate the commute times and Katz scores from a node to all other nodes in the graph. Here, our approach for the commute times is based on a variation of the conjugate gradient algorithm, and it provides an estimate of all the diagonals of the inverse of a matrix. Our technique for the Katz scores is based on exploiting an empirical localization property of the Katz matrix. We adopt algorithms used for personalized PageRank computing to these Katz scores and theoretically show that this approach is convergent. We evaluate these methods on 17 real world graphs ranging in size from 1000 to 1,000,000 nodes. Our results show that our pair-wise commute time method and column-wise Katz algorithm both have attractive theoretical properties and empirical performance.Comment: 35 pages, journal version of http://dx.doi.org/10.1007/978-3-642-18009-5_13 which has been submitted for publication. Please see http://www.cs.purdue.edu/homes/dgleich/publications/2011/codes/fast-katz/ for supplemental code

Editor\u27s Introduction (Review Symposium on \u3ci\u3eConverging Divergences: Worldwide Changes in Employment Systems\u3c/i\u3e)

[Excerpt] During the past two decades there have been significant changes in employment systems across industrialized countries. Converging Divergences: Worldwide Changes in Employment Systems, by Harry C. Katz and Owen Darbishire, examines changes since 1980 in employment practices in seven industrialized countries—the United States, the United Kingdom, Australia, Germany, Japan, Sweden, and Italy—with a focus on the automotive and telecommunications industries. Katz and Darbishire find that variations in employment patterns within these countries have been increasing over the past two decades. The increase in variation is not simply a result of a decline in union strength in some sectors of the economy; variation has increased within both union and nonunion sectors. Despite this within-country divergence, Katz and Darbishire find that employment systems across countries are converging toward four common patterns of work practices: a low-wage employment pattern; the human resource management (HRM) employment pattern; a Japanese-oriented employment pattern; and a joint team-based employment pattern. Significant differences in national employment-related institutions have resulted in some variation across countries in how these work patterns are implemented. Still, Katz and Darbishire find that there are many commonalities in the employment systems of the seven countries and in the processes through which these commonalities have developed

On the faithfulness of parabolic cohomology as a Hecke module over a finite field

In this article we prove conditions under which a certain parabolic group cohomology space over a finite field F is a faithful module for the Hecke algebra of Katz modular forms over an algebraic closure of F. These results can e.g. be used to compute Katz modular forms of weight one with methods of linear algebra over F. This is essentially Chapter 3 of my thesis.Comment: 26 pages; small corrections and change

On the ℓ\ell-adic Fourier transform and the determinant of the middle convolution

We study the relation of the middle convolution to the $\ell$-adic Fourier transformation in the \'etale context. Using Katz' work and Laumon's theory of local Fourier transformations we obtain a detailed description of the local monodromy and the determinant of Katz' middle convolution functor \MC_\chi in the tame case. The theory of local $\epsilon$-constants then implies that the property of an \'etale sheaf of having an at most quadratic determinant is often preserved under \MC_\chi if $\chi$ is quadratic

Einstein-Katz action, variational principle, Noether charges and the thermodynamics of AdS-black holes

In this paper we describe 4-dimensional gravity coupled to scalar and Maxwell fields by the Einstein-Katz action, that is, the covariant version of the "Gamma-Gamma $-$ Gamma-Gamma" part of the Hilbert action supplemented by the divergence of a generalized "Katz vector". We consider static solutions of Einstein's equations, parametrized by some integration constants, which describe an ensemble of asymptotically AdS black holes. Instead of the usual Dirichlet boundary conditions, which aim at singling out a specific solution within the ensemble, we impose that the variation of the action vanishes on shell for the broadest possible class of solutions. We will see that, when a long-range scalar "hair" is present, only sub-families of the solutions can obey that criterion. The Katz-Bicak-Lynden-Bell ("KBL") superpotential built on this (generalized) vector will then give straightforwardly the Noether charges associated with the spacetime symmetries (that is, in the static case, the mass). Computing the action on shell, we will see next that the solutions which obey the imposed variational principle, and with Noether charges given by the KBL superpotential, satisfy the Gibbs relation, the Katz vectors playing the role of "counterterms". Finally, we show on the specific example of dyonic black holes that the sub-class selected by our variational principle satisfies the first law of thermodynamics when their mass is defined by the KBL superpotential.Comment: Accepted for publication by JHE

The Katz-Francis scale of attitude toward Judaism : internal consistency reliability and construct validity among female undergraduate students in Israel

The Katz-Francis Scale of Attitude toward Judaism was developed to extend to the Jewish community a growing body of international research concerned to map the correlates, antecedents, and consequences of individual differences in attitude toward religion as assessed by the Francis Scale of Attitude toward Christianity. The internal consistency reliability and construct validity of the Katz-Francis Scale of Attitude toward Judaism were supported by data provided by 284 Hebrew-speaking female undergraduate students attending Bar-Ilan University. This instrument is commended for application in further research

Being Both: Embracing Two Religions in One Interfaith Family

Being Both: Embracing Two Religions in One Interfaith Family Susan Katz Miller Boston: Beacon Press, 201