In this pa�, we suggest marry ing Dempster-Shafer (DS) theory w1th Knowledge Representation (KR). Born out of this marr iage is the defmition of "Dempster-Shafer Belief Bases", abstract data types representing uncertain knowledge that use DS theory for representing strength of belief about our knowledge, and the linguistic structures of an arbitrary KR system for representing the knowledge itse...

We introduce the basic concepts of Gröbner basis theory and its relations to polytope theory. This will cover very basic parts of [1], the basic chapters from [3] and the first chapters from [11]. In particular, we will define the Gröbner fan, which will play a major role in some of the research problems we will pose later. In this lecture we relate triangulations to Gröbner bases and Hilbert-s...

This article studies the expressive power of finite automata recognizing sets of real numbers encoded in positional notation. We consider Muller automata as well as the restricted class of weak deterministic automata, used as symbolic set representations in actual applications. In previous work, it has been established that the sets of numbers that are recognizable by weak deterministic automat...

We investigate various kinds of bases in infinite dimensional Banach spaces. In particular, we consider the complexity of Hamel bases in separable and non-separable Banach spaces and show that in a separable Banach space a Hamel basis cannot be analytic, whereas there are non-separable Hilbert spaces which have a discrete and closed Hamel basis. Further we investigate the existence of certain c...

We construct Markov chain algorithms for sampling from discrete exponential families conditional on a sufticient statistic. Examples include contingency tables, logistic regression, and spectral analysis of permutation data. The algorithms involve computations in polynomial rings using Grobner bases. 1. Introduction. This paper describes new algorithms for sampling from the conditional distribu...

G-Frames in Hilbert spaces are a redundant set of operators which yield a representation for each vector in the space. In this paper we investigate the connection between g-frames, g-orthonormal bases and g-Riesz bases. We show that a family of bounded operators is a g-Bessel sequences if and only if the Gram matrix associated to its denes a bounded operator.

We review the matrix bases for a family of noncommutative ? products based on a Weyl map. These products include the Moyal product, as well as the Wick–Voros products and other translation invariant ones. We also review the derivation of Lie algebra type star products, with adapted matrix bases. We discuss the uses of these matrix bases for field theory, fuzzy spaces and emergent gravity.

Bases of atomic-like functions provide a natural, physically motivated description of electronic states, and Gaussian-type orbitals are the most widely used basis functions in molecular simulations. This paper aims at developing a systematic analysis of numerical approximations based on linear combinations of some Gaussian-type orbitals. We give a priori error estimates for Hermite-type Gaussia...

We consider the problem of determining Gröbner bases of binomial ideals associated with linear error correcting codes. Computation of Gröbner bases of linear codes have become a topic of interest to many researchers in coding theory because of its several applications in decoding and error corrections. In this paper, Gröbner bases of linear codes associated to Grassmann varieties and Schubert v...

In this paper we construct a mathematical model for DNA replication based on Shannon's mathematical theory for communication. We treat DNA replication as a communication channel. We show that the mean replication rate is maximal with four nucleotide bases under the primary assumption that the pairing time of the G-C bases is between 1.65 and 3 times the pairing time of the A-T bases.