For a group G and X a subset of G, the commuting graph of G on X, denoted by C(G,X), is the graph whose vertex set is X with x, y joined by an edge if x not equal to y and x and y commute. If the elements in X are involutions, then C(G,X) is called a commuting involution graph. This thesis studies C(G,X) when G is either a 4-dimensional projective symplectic group; a 3-dimensional unitary group; 4-dimensional unitary group over a field of characteristic 2; a 2-dimensional projective general linear group; or a 4-dimensional affne orthogonal group, and X a G-conjugacy class of involutions. We determine the diameters and structure of thediscs of these graphs.

Data warehouses were envisioned to facilitate analytical reporting and data visualization by providing a model for the flow of data from operational databases to decision support environments. Decision support environments provide a multidimensional conceptual view of the underlying data warehouse, which is usually stored in relational DBMSs. Typically, there is an impedance mismatch between this conceptual view — shared also by all decision support applications accessing the data warehouse — and the physical model of the data stored in relational DBMSs. This thesis presents a mapping compilation algorithm in the context of the Conceptual Integration Model (CIM) [67] framework. In the CIM framework, the relationships between the conceptual model and the physical model are specified by a set of attribute-to-attribute correspondences. The algorithm compiles these correspondences into a set of mappings that associate each construct in the conceptual model with a query on the physical model. Moreover, the homogeneity and summarizability of data in conceptual models is the key to accurate query answering, a necessity in decision making environments. A data-driven approach to refactor relational models into summarizable schemas and instances is proposed as the solution of this issue. We outline the algorithms and challenges in bridging multidimensional conceptual models and the physical model of data warehouses and discuss experimental results.

Weather data is important for almost everyone today. Thedaily weather report, home thermometers, and a lot of otherthings affect our every day life. In order to develop betterand more efficient equipment, tools and algorithms, thepeople working with this data need to be able to access it inan easily accessible and easy to read format. In thisresearch, methods of visualizing data on mobile platformsare evaluated based on what researchers in the field wants,since their respective fields might want to use very specificvisualizations. The implementability of these visualizationsare then evaluated, based on the implementations madethroughout this paper. The results show that the researchersknow what they want, and that what they want isimplementable on mobile platforms given some limitationscaused by performance.

This research discusses how the design of a tornado forward error correcting channel code (FEC) sends digital data stream profiles to the receiver. The complete design was based on the Tornado channel code, binary phase shift keying (BPSK) modulation on a Gaussian channel (AWGN). The communication link was simulated by using Matlab, which shows the theoretical systems efficiency. Then the data stream was input as data to be simulated communication systems using Matlab. The purpose of this paper is to introduce the audience to a simulation technique that has been successfully used to determine how well a FEC expected to work when transferring digital data streams. The goal is to use this data to show how FEC optimizes a digital data stream to gain a better digital communications systems. The results conclude by making comparisons of different possible styles for the Tornado FEC code.

My research lies in the general area of functional analysis. I am particularly interested in C*-algebras and related dynamical systems. From the very beginning of the theory of operator algebras, in the works of Murray and von Neumann dating from the mid 1930's, dynamical systems and operator algebras have led a symbiotic existence. Murray and von Neumann's work grew from a few esoteric, but clearly original and prescient papers, to a ma jor river of contemporary mathematics. My work lies at the confluence of two important tributaries to this river. On the one hand, the operator algebras that I study are C*-algebras that are built from graphs. On the other, the dynamical systems on which I focus are symbolic dynamical systems of various types. My goal is to use dynamical systems theory to construct new and interesting C*-algebras and to use the algebraic invariants of these algebras to reveal properties of the dynamics. My work has two fairly distinct strands: One deals with C*-algebras built from irreversible dynamical systems. The other deals with group actions on graph C*-algebras and their generalizations.

In this thesis, we are concerned with multi-player games played on finite graphs. They are games in which the players interact trying to fulfil their own objectives which are not necessarily antagonistic to the others’. More particularly, we are interested in the study of dynamics which model the behaviour of the players when they repeatedly update their strategy in order to achieve a better outcome. A dynamics terminates when these updates converge to a state in which the players have no incentive to further update their respective strategies. We define several dynamics characterised by the type of updates made by the players.There are two types of contributions in this thesis. The first one is to draw a general framework to reason about the termination of dynamics in order to show its applicability to particular problems. In this abstract framework, we present several meta-theorems that make the links between games and dynamics explicit. For example, we introduce a notion of game minor that allows to induce simulations between the associated dynamics. The second type of contribution is the application of dynamics to a particular context, characterised by three parameters: the arena of the game, the conditions over the dynamics, and the payoff functions of the players. The first arena we deal with are sequential games (or games played on trees). Among other results, we prove that the acyclicity of the preferences is a necessary and sufficient condition to ensure the termination of dynamics that respect the Subgame Improvement Property (i.e. every update has to improve the payoff in the subgame of the change).Another studied arena is the so called One-player Games. We model BGP (Border Gateway Protocol, which is a standard interdomain routing protocol) into dynamics on graphs. We firstly revisit some classical results of network theory in our context, then we identify a theoretical and relevant framework regarding to the termination of the dynamics. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Philosophiae Doctor - PhD / Understanding the geometries of points in space has been attractive to mathematicians for ages. As a model, twelve years ago, Kurz and Meyer [32] considered point sets in the m-dimensional a ne space Fmq over a nite eld Fq with q = pr elements, p prime, where each squared Euclidean distance of two points is a square in Fq: The latter points are said to be at integral distance in Fmq , and the sets above are called integral point sets.

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archives@tulane.edu / Discrete fracture networks (DFNs) can be modeled with polygonal representations that are useful for geophysical modeling of nuclear waste containment and hydrofrac- turing. Flow and transport calculations are possible, but computationally expensive, limiting the feasibility for model uncertainty quantification. Graphs are used to re- duce model complexity and computation time. We present the formulation of using a graph as a reduced model for DFNs and pose the inversion problem central to this research. We present a novel alternative to Darcy’s law on graphs using the well known Brinkman formulation on the continuum. We apply the Levenberg-Marquardt algorithm to optimize graphs, calibrating them to observed data through the inversion problem. We present the deficiencies in physically motivated graphs, and show how optimized graphs produce better results overall. Our solution finds lumped parameters representing the fracture properties, and is used to reduce the computational time required for particle transport calculations. Breakthrough curves are produced on our obtained solutions, which closely match the high fidelity model. We present examples of creating these reduced models for DFNs with 500 fractures to illustrate the methodology and optimization scheme used to obtain an improved result over a previous formulation. / 1 / Jaime Lopez-Merizalde

Let G and H be graphs. We say G is H-critical, if every proper subgraph of G except G itself is homomorphic to H. This generalizes the widely known concept of k-color-critical graphs, as they are the case H = Kk - 1. In 1963 [T. Gallai, Kritiche Graphen, I., Magyar Tud. Akad. Mat. Kutató Int. Közl. 8 (1963), 373-395], Gallai proved that the vertices of degree k in a Kk-critical graph induce a subgraph whose blocks are either odd cycles or complete graphs. We generalize Gallai's Theorem for every H-critical graph, where H = Kk - 2 + H′, (the join of a complete graph Kk - 2 with any graph H′). This answers one of the two unknown cases of a problem given in [J. Nešetřil, Y. Nigussie, Finite dualities and map-critical graphs on a fixed surface. (Submitted to Journal of Combin. Theory, Series B)]. We also propose an open question, which may be a characterization of all graphs for which Gallai's Theorem holds.