This tutorial paper discusses the known representations based on Binary Decision Diagrams (BDDs) for various types of discrete objects: incompletely specified functions, sets, finite state machines, binary and multi-valued relations, etc. While presenting the known material, the emphasis is on those aspects of implicit representations that are important to achieve speed-up in computation. The n...

Recurrent neural networks are appropriate tools for modeling time-varying systems (e.g. nancial markets, physical dynamical systems, speech recognition, etc.). They can be used to recognize pattern sequences (e.g. speech recognition) or they can be used for forecasting future patterns (e.g. nancial markets). These applications are generally not well-suited for addressing fundamental issues of r...

This paper deals with the Markov properties of a new class of graphical time series models which focus on the dynamic interrelationships between the components of multivariate time series. The modelling approach is based on the concept of strong Granger-causality and thus can also be applied to nonlinear models. The constraints defining the models are encoded by mixed graphs in which each compo...

A discrete alternative to scale space filtering is presented. The new method provides for fast solutions to problems of spatial containment, filtering and matching, without using arbitrary parameters and smoothing of the input. The discrete space-scale representation is a hierarchical perceptual organization that has concrete applications in computer vision research. Examples of actual implemen...

For a Weyl group W , we investigate simple closed formulas (valid on elliptic conjugacy classes) for the character of the representation of W in the homology of a Springer fiber. We also give a formula (valid again on elliptic conjugacy classes) of the W -character of an irreducible discrete series representation with real central character of a graded affine Hecke algebra with arbitrary parame...

Coherent continuation π2 of a representation π1 of a semisimple Lie algebra arises by tensoring π1 with a finite dimensional representation F and projecting it to the eigenspace of a particular infinitesimal character. Some relations exist between the spaces of harmonic spinors (involving Kostant’s cubic Dirac operator and the usual Dirac operator) with coefficients in the three modules. For th...

Let G be a connected linear semisimple Lie group having a Holomorphic Discrete Series representation π. Let H be a connected reductive subgroupof G so that the global symmetric space attached to H is a real form of the Hermitian symmetric space associated to G. Fix a maximal compact subgroup K of G so that H ∩ K is a maximal compact subgroup for H. Let τ be the lowest K−type for π and let τ? de...

In this paper we summarize and give examples of a generalization of the coorbit space theory initiated in the 1980’s by H.G. Feichtinger and K.H. Gröchenig. Coorbit theory has been a powerful tool in characterizing Banach spaces of distributions with the use of integrable representations of locally compact groups. Examples are a wavelet characterization of the Besov spaces and a characterizatio...

Abstract. Let G be a connected, semisimple Lie group with finite center and let K be a maximal compact subgroup. We investigate a method to compute multiplicities of K-types in the discrete series using a rational expression for a generating function obtained from Blattner’s formula. This expression involves a product with a character of an irreducible finite dimensional representation of K and...

In commonly used approaches for the discrete-time bulk service queue, the stationary queue length distribution follows from the roots inside or outside the unit circle of a characteristic equation. We present analytic representations of these roots in the form of sample values of periodic functions with analytically given Fourier series coefficients, making these approaches more transparent and...