A double-sum Kronecker-type identity

We prove a double-sum analog of an identity known to Kronecker and then express it in terms of functions studied by Appell and Kronecker's student Lerch, in so doing we show that the double-sum analog is of mixed mock modular form. We also give related symmetric generalizations.Comment: Major revisions. Identities (1.10) and (1.11) are ne

An Equivariant Liapunov Stability Test and the Energy-Momentum-Casimir Method

We present an equivariant Liapunov stability criterion for dynamical systems with symmetry. This result yields a simple proof of the energy-momentum-Casimir stability analysis of relative equilibria of equivariant Hamiltonian systems.Comment: 5 page

Machine Learning of User Profiles: Representational Issues

As more information becomes available electronically, tools for finding information of interest to users becomes increasingly important. The goal of the research described here is to build a system for generating comprehensible user profiles that accurately capture user interest with minimum user interaction. The research described here focuses on the importance of a suitable generalization hierarchy and representation for learning profiles which are predictively accurate and comprehensible. In our experiments we evaluated both traditional features based on weighted term vectors as well as subject features corresponding to categories which could be drawn from a thesaurus. Our experiments, conducted in the context of a content-based profiling system for on-line newspapers on the World Wide Web (the IDD News Browser), demonstrate the importance of a generalization hierarchy and the promise of combining natural language processing techniques with machine learning (ML) to address an information retrieval (IR) problem.Comment: 6 page

Two Weight Inequalities for Discrete Positive Operators

We characterize two weight inequalities for general positive dyadic operators. We consider both weak and strong type inequalities, and general (p,q) mapping properties. Special cases include Sawyers Fractional Integral operator results from 1988, and the bilinear embedding inequality of Nazarov-Treil-Volberg from 1999. The method of proof is an extension of Sawyer's argument.Comment: 20 pages, 3 figures. v2 correction of minor typos v3: Correction of typos. v4: Two references adde

Massive quiver matrix models for massive charged particles in AdS

We present a new class of ${\cal N}=4$ supersymmetric quiver matrix models and argue that it describes the stringy low-energy dynamics of internally wrapped D-branes in four-dimensional anti-de Sitter (AdS) flux compactifications. The Lagrangians of these models differ from previously studied quiver matrix models by the presence of mass terms, associated with the AdS gravitational potential, as well as additional terms dictated by supersymmetry. These give rise to dynamical phenomena typically associated with the presence of fluxes, such as fuzzy membranes, internal cyclotron motion and the appearance of confining strings. We also show how these models can be obtained by dimensional reduction of four-dimensional supersymmetric quiver gauge theories on a three-sphere.Comment: 43 pages + appendices, 4 figure