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Physical Sciences and Mathematics

Louisiana State University

Theses/Dissertations

Algorithms

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Practical Considerations And Applications For Autonomous Robot Swarms, Rory Alan Hector Apr 2022

Practical Considerations And Applications For Autonomous Robot Swarms, Rory Alan Hector

LSU Doctoral Dissertations

In recent years, the study of autonomous entities such as unmanned vehicles has begun to revolutionize both military and civilian devices. One important research focus of autonomous entities has been coordination problems for autonomous robot swarms. Traditionally, robot models are used for algorithms that account for the minimum specifications needed to operate the swarm. However, these theoretical models also gloss over important practical details. Some of these details, such as time, have been considered before (as epochs of execution). In this dissertation, we examine these details in the context of several problems and introduce new performance measures to capture practical …


Algorithms Related To Triangle Groups, Bao The Pham Jul 2021

Algorithms Related To Triangle Groups, Bao The Pham

LSU Doctoral Dissertations

Given a finite index subgroup of $\PSL_2(\Z)$, one can talk about the different properties of this subgroup. These properties have been studied extensively in an attempt to classify these subgroups. Tim Hsu created an algorithm to determine whether a subgroup is a congruence subgroup by using permutations \cite{hsu}. Lang, Lim, and Tan also created an algorithm to determine if a subgroup is a congruence subgroup by using Farey Symbols \cite{llt}. Sebbar classified torsion-free congruence subgroups of genus 0 \cite{sebbar}. Pauli and Cummins computed and tabulated all congruence subgroups of genus less than 24 \cite{ps}. However, there are still some problems …


Oblivious Buy-At-Bulk Network Design Algorithms, Srivathsan Srinivasagopalan Jan 2011

Oblivious Buy-At-Bulk Network Design Algorithms, Srivathsan Srinivasagopalan

LSU Doctoral Dissertations

Large-scale networks such as the Internet has emerged as arguably the most complex distributed communication network system. The mere size of such networks and all the various applications that run on it brings a large variety of challenging problems. Similar problems lie in any network - transportation, logistics, oil/gas pipeline etc where efficient paths are needed to route the flow of demands. This dissertation studies the computation of efficient paths from the demand sources to their respective destination(s). We consider the buy-at-bulk network design problem in which we wish to compute efficient paths for carrying demands from a set of …


Chemical Analysis Of Polymer Blends Via Synchrotron X-Ray Tomography, Heath Alan Barnett Jan 2008

Chemical Analysis Of Polymer Blends Via Synchrotron X-Ray Tomography, Heath Alan Barnett

LSU Doctoral Dissertations

Material properties of industrial polymer blends are of great importance. X-ray tomography has been used to obtain spatial chemical information about various polymer blends. The spatial images are acquired with synchrotron X-ray tomography because of its rapidity, good spatial resolution, large field-of-view, and elemental sensitivity. The spatial absorption data acquired from X-ray tomography experiments is converted to spatial chemical information via a linear least squares fit of multi-spectral X-ray absorption data. A fiberglass-reinforced polymer blend with a new-generation flame retardant is studied with multi-energy synchrotron X-ray tomography to assess the blend homogeneity. Relative to other composite materials, this sample is …