We present a theory of scan statistics on hypergraphs and apply the methodology to a time series of email data. This approach is of interest because a hypergraph is better suited to email data than a graph. This is due to the fact that a hypergraph can contain all the recipients of a message in a single hyperedge rather than treating each recipient separately in a graph. The result shows that s...

1. One of the main unsolved problems in the representation theory of the finite Chevalley groups is the determination of the discrete series representations; these are the most basic, but least accessible, representations of such groups. Let me recall that an (ordinary) representation D of a finite Chevalley group G is said to be in the discrete series, or cuspidal, if, for any proper parabolic...

Given a discrete eight-connected curve, it can be represented by discrete eight connected segments. In this paper, we try to determine the minimal number of necessary discrete segments. This problem is known as the min DSS problem. We propose to use a generic curve representation by discrete tangents, called a tangential cover which can be computed in linear-time. We introduce a series of crite...

Here we describe novel Bayesian models for time-frequency analysis of non-stationary audio waveforms. These models are based on the idea of a Gabor regression, in which a time series is represented as a superposition of time-frequency shifted versions of a simple window function. Prior distributions over the corresponding time-frequency coefficients are constructed in a manner which favours bot...

Suppose that G(F) is a real or p-adic group. That is, G is a connected reductive algebraic group over a local field F, which we take to be of characteristic 0. Harmonic analysis on G(F) is built upon the set Htemp(G(F)) of irreducible tempered representations of G(F). These representations include the discrete series for G(F), and consist in general of irreducible constituents of representation...

This article defines and studies a new class of non-stationary random processes constructed from discrete non-decimated wavelets which generalizes the Cramér (Fourier) representation of stationary time series. We define an evolutionary wavelet spectrum (EWS) which quantifies how process power varies locally over time and scale. We show how the EWS may be rigorously estimated by a smoothed wavel...