Physical Sciences and Mathematics Commons^™

Limitations And Extensions Of The Wolf-Phc Algorithm, Philip R. Cook

Theses and Dissertations

Policy Hill Climbing (PHC) is a reinforcement learning algorithm that extends Q-learning to learn probabilistic policies for multi-agent games. WoLF-PHC extends PHC with the "win or learn fast" principle. A proof that PHC will diverge in self-play when playing Shapley's game is given, and WoLF-PHC is shown empirically to diverge as well. Various WoLF-PHC based modifications were created, evaluated, and compared in an attempt to obtain convergence to the single shot Nash equilibrium when playing Shapley's game in self-play without using more information than WoLF-PHC uses. Partial Commitment WoLF-PHC (PCWoLF-PHC), which performs best on Shapley's game, is tested on other …

Discrete Algorithms For Analysis Of Genotype Data, Dumitru Brinza

Computer Science Dissertations

Accessibility of high-throughput genotyping technology makes possible genome-wide association studies for common complex diseases. When dealing with common diseases, it is necessary to search and analyze multiple independent causes resulted from interactions of multiple genes scattered over the entire genome. The optimization formulations for searching disease-associated risk/resistant factors and predicting disease susceptibility for given case-control study have been introduced. Several discrete methods for disease association search exploiting greedy strategy and topological properties of case-control studies have been developed. New disease susceptibility prediction methods based on the developed search methods have been validated on datasets from case-control studies for several common …

Modular Exponentiation Via The Explicit Chinese Remainder Theorem, Daniel J. Bernstein, Jonathan P. Sorenson

Scholarship and Professional Work - LAS

In this paper we consider the problem of computing xe mod m for large integers x, e, and m. This is the bottleneck in Rabin’s algorithm for testing primality, the Diffie-Hellman algorithm for exchanging cryptographic keys, and many other common algorithms.

Algorithm Refinement For Fluctuating Hydrodynamics, Alejandro Garcia, S. Williams, J. B. Bell

Faculty Publications

This paper introduces an adaptive mesh and algorithm refinement method for fluctuating hydrodynamics. This particle-continuum hybrid simulates the dynamics of a compressible fluid with thermal fluctuations. The particle algorithm is direct simulation Monte Carlo (DSMC), a molecular-level scheme based on the Boltzmann equation. The continuum algorithm is based on the Landau–Lifshitz Navier–Stokes (LLNS) equations, which incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. It uses a recently developed solver for the LLNS equations based on third-order Runge–Kutta. We present numerical tests of systems in and out of equilibrium, including time-dependent systems, and demonstrate dynamic adaptive refinement by the …

Algorithm Refinement For Fluctuating Hydrodynamics, Alejandro Garcia, Sarah Williams, John B. Bell

Alejandro Garcia

This paper introduces an adaptive mesh and algorithm refinement method for fluctuating hydrodynamics. This particle-continuum hybrid simulates the dynamics of a compressible fluid with thermal fluctuations. The particle algorithm is direct simulation Monte Carlo (DSMC), a molecular-level scheme based on the Boltzmann equation. The continuum algorithm is based on the Landau–Lifshitz Navier–Stokes (LLNS) equations, which incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. It uses a recently developed solver for the LLNS equations based on third-order Runge–Kutta. We present numerical tests of systems in and out of equilibrium, including time-dependent systems, and demonstrate dynamic adaptive refinement by the …

Frequency Distribution Of Pyroxene Types And A Method To Separate The Composition Of Multiple Pyroxenes In A Sample, Jimmy Allen Davis

Electronic Theses and Dissertations

Determining mafic mineral composition of asteroid bodies is a topic reviewed by M.J. Gaffey et al. (2002). The iterative procedure discussed can be implemented as an algorithm, and such efforts revealed weaknesses that are examined in this work. We seek to illustrate the limits of this method and graphically determine its predictions. There are boundaries in the formulae given where the equations break down. In ranges where mafic mixtures are predicted, a method is illustrated that allows a decoupling of these mixtures into the constituents.

Validation And Data Characteristics Of Methane And Nitrous Oxide Profiles Observed By Mipas And Processed With Version 4.61 Algorithm, S Payan, C Camy-Peyret, H Oelhaf, G Wetzel, G Maucher, Nicholas B. Jones, S Wood, M De Maziere, T Blumenstock, P Duchatelet, D Smale, G Bianchini, G Redaelli, F Mencaraglia, M Pirre, N Huret, C Piccolo, U Cortesi, C Keim, N Glatthor, S Mikuteit, G P. Stiller, C Vigouroux, A Engel, M C. Volk, J Kuttippurath, H Kuellmann, P Raspollini, M Mahieu, V Payne, A Bracher, K Grunow, P Jeseck, Y Te, K Pfeilsticker, A Butz, Justus Notholt, Voltaire A. Velazco

Faculty of Science - Papers (Archive)

The ENVISAT validation programme for the atmospheric instruments MIPAS, SCIAMACHY and GOMOS is based on a number of balloon-bone, aircraft and ground-based correlative measurements. In particular the activities of validation scientists were coordinated by ESA within the ENVISAT Stratospheric Aircraft and Balloon Campaign of ESABC. As part of a series of similar papers on other species [this issue] and in parallel to the contribution of the individual validation teams, the present paper provides a synthesis of comparisons performed between MIPAS CH4 and N2O profiles produced by the current ESA operational software (Instrument Processing Facility version 4.61 or IPF v4.61) and …

Probabilistic Methods, Joseph Kwaku Asafu-Adjei

Theses and Dissertations

The Probabilistic Method was primarily used in Combinatorics and pioneered by Erdös Pai, better known to Westerners as Paul Erdos in the 1950s. The probabilistic method is a powerful tool for solving many problems in discrete mathematics, combinatorics and also in graph .theory. It is also very useful to solve problems in number theory, combinatorial geometry, linear algebra and real analysis. More recently, it has been applied in the development of efficient algorithms and in the study of various computational problems.Broadly, the probabilistic method is somewhat opposite of the extremal graph theory. Instead of considering how a graph can behave …

Integer Programming With Groebner Basis, Isabella Brooke Ginn

Theses and Dissertations

Integer Programming problems are difficult to solve. The goal is to find an optimal solution that minimizes cost. With the help of Groebner based algorithms the optimal solution can be found if it exists. The application of the Groebner based algorithm and how it works is the topic of research. The Algorithms are The Conti-Traverso Algorithm and the Original Conti-Traverso Algorithm. Examples are given as well as proofs that correspond to the algorithms. The latter algorithm is more efficient as well as user friendly. The algorithms are not necessarily the best way to solve and integer programming problem, but they …

High Performance Text Document Clustering, Yanjun Li

Browse all Theses and Dissertations

Data mining, also known as knowledge discovery in database (KDD), is the process to discover interesting unknown knowledge from a large amount of data. Text mining is to apply data mining techniques to extract interesting and nontrivial information and knowledge from unstructured text. Text clustering is one of important techniques of text mining, which is the unsupervised classification of similar documents into different groups.

This research focuses on improving the performance of text clustering. We investigated the text clustering algorithms in four aspects: document representation, documents closeness measurement, high dimension reduction and parallelization. We propose a group of high performance …

Two Number-Theoretic Problems That Illustrate The Power And Limitations Of Randomness, Andrew Shallue

Scholarship

This thesis contains work on two problems in algorithmic number theory. The first problem is to give an algorithm that constructs a rational point on an elliptic curve over a finite field. A fast and easy randomized algorithm has existed for some time. We prove that in the case where the finite field has characteristic 2, there is a deterministic algorithm with the same asymptotic running time as the existing randomized algorithm.

Two Number-Theoretic Problems That Illustrate The Power And Limitations Of Randomness, Andrew Shallue

Andrew Shallue

This thesis contains work on two problems in algorithmic number theory. The first problem is to give an algorithm that constructs a rational point on an elliptic curve over a finite field. A fast and easy randomized algorithm has existed for some time. We prove that in the case where the finite field has characteristic 2, there is a deterministic algorithm with the same asymptotic running time as the existing randomized algorithm.