Abstract. This paper is an exposition of some classic results in graph theory and their applications. A proof of Tutte’s theorem is given, which is then used to derive Hall’s marriage theorem for bipartite graphs. Some compelling applications of Hall’s theorem are provided as well. In the final section we present a detailed proof of Menger’s theorem and demonstrate its power by deriving König’s...

We consider two questions in string “phenomenology.” First, are there any generic string predictions? Second, are there any general lessons which string theory suggests for thinking about low energy models, particularly in the framework of supersymmetry? Among the topics we consider are the squark and slepton spectrum, flavor symmetries, discrete symmetries including CP , and Peccei-Quinn symme...

2.1 Basic notions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Complex measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Riesz representation theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.4 Lebesgue-Radon-Nikodym theorem . . . . . . . . . . . . . . . . . . . ...

We review two subjects in the theoretical study of jet production at the Tevatron collider: the uncertainties in the determination of the partonic densities inside the proton and the uncertainties in the calculation of higher-order corrections to the QCD matrix

This monograph provides a brief introduction on approximate inference and goes in depth for a selected list of related topics. Many of the presented materials are adapted from my published papers, my research notes during PhD, and my (draft) PhD thesis. I expect to keep updating this list of topics to include new techniques.

Learning and using language requires retrieving concepts from memory in response to an ongoing stream of information. The human memory system solves this problem by using the gist of a sentence, conversation, or document to predict related concepts and disambiguate words. Two approaches to representing gist have dominated research on semantic representation: semantic networks and semantic space...

In this paper we evaluate a potential curriculum to be used in upcoming semesters of CMSC430 (Compilers). We present the major material covered in chronological order, and the corresponding assignments. Each of the following sections begins with a general overview of the material covered. A subsection is devoted to teaching methods or other sticking points in the material that may require speci...

The symmetry of a graph is measured by its automorphism group: the set of permutations of the vertices so that all edges and non-edges are preserved. There are natural questions which arise when considering the automorphism group and there are several interesting results in this area that are not well-known. This talk presents some of these results and maybe even proves one or two. First, we wi...

Percolation is the study of connectedness in a randomly-chosen subset of an infinite graph. Following Grimmett[4], we set up percolation on a square lattice. We establish the existence of a critical edge-density, prove several results about the behavior of percolation systems above and below this critical density, and use these results to find the critical density of percolation on the two-dime...

An important part of dialogue management in a dialogue system is topic management: The system has to keep track of topic aspects (current topic, context, obligations, : : : ) in order to be able to resolve ambiguities and to respond in a cooperative and sensible way. In the schisma project, we are developing a system that takes part in a conversation about theater performances and is able to ma...