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Articles 1 - 8 of 8
Full-Text Articles in Other Applied Mathematics
Reinforcement Learning: Low Discrepancy Action Selection For Continuous States And Actions, Jedidiah Lindborg
Reinforcement Learning: Low Discrepancy Action Selection For Continuous States And Actions, Jedidiah Lindborg
Electronic Theses and Dissertations
In reinforcement learning the process of selecting an action during the exploration or exploitation stage is difficult to optimize. The purpose of this thesis is to create an action selection process for an agent by employing a low discrepancy action selection (LDAS) method. This should allow the agent to quickly determine the utility of its actions by prioritizing actions that are dissimilar to ones that it has already picked. In this way the learning process should be faster for the agent and result in more optimal policies.
Zeta Function Regularization And Its Relationship To Number Theory, Stephen Wang
Zeta Function Regularization And Its Relationship To Number Theory, Stephen Wang
Electronic Theses and Dissertations
While the "path integral" formulation of quantum mechanics is both highly intuitive and far reaching, the path integrals themselves often fail to converge in the usual sense. Richard Feynman developed regularization as a solution, such that regularized path integrals could be calculated and analyzed within a strictly physics context. Over the past 50 years, mathematicians and physicists have retroactively introduced schemes for achieving mathematical rigor in the study and application of regularized path integrals. One such scheme was introduced in 2007 by the mathematicians Klaus Kirsten and Paul Loya. In this thesis, we reproduce the Kirsten and Loya approach to …
Analysis On Sharp And Smooth Interface, Elizabeth V. Hawkins
Analysis On Sharp And Smooth Interface, Elizabeth V. Hawkins
Electronic Theses and Dissertations
In biology, minimizing a free energy functional gives an equilibrium shape that is the most stable in nature. The formulation of these functionals can vary in many ways, in particular they can have either a smooth or sharp interface. Minimizing a functional can be done through variational calculus or can be proved to exist using various analysis techniques. The functionals investigated here have a smooth and sharp interface and are analyzed using analysis and variational calculus respectively. From the former we find the condition for extremum and its second variation. The second variation is commonly used to analyze stability of …
Reduced Dataset Neural Network Model For Manuscript Character Recognition, Mohammad Anwarul Islam
Reduced Dataset Neural Network Model For Manuscript Character Recognition, Mohammad Anwarul Islam
Electronic Theses and Dissertations
The automatic character recognition task has been of practical interest for a long time. Nowadays, there are well-established technologies and software to perform character recognition accurately from scanned documents. Although handwritten character recognition from the manuscript image is challenging, the advancement of modern machine learning techniques makes it astonishingly manageable. The problem of accurately recognizing handwritten character remains of high practical interest since a large number of manuscripts are currently not digitized, and hence inaccessible to the public. We create our repository of the datasets by cropping each letter image manually from the manuscript images. The availability of datasets is …
Developments In Multivariate Post Quantum Cryptography., Jeremy Robert Vates
Developments In Multivariate Post Quantum Cryptography., Jeremy Robert Vates
Electronic Theses and Dissertations
Ever since Shor's algorithm was introduced in 1994, cryptographers have been working to develop cryptosystems that can resist known quantum computer attacks. This push for quantum attack resistant schemes is known as post quantum cryptography. Specifically, my contributions to post quantum cryptography has been to the family of schemes known as Multivariate Public Key Cryptography (MPKC), which is a very attractive candidate for digital signature standardization in the post quantum collective for a wide variety of applications. In this document I will be providing all necessary background to fully understand MPKC and post quantum cryptography as a whole. Then, I …
Optimal Supply Delivery Under Military Specific Constraints, Talena Fletcher
Optimal Supply Delivery Under Military Specific Constraints, Talena Fletcher
Electronic Theses and Dissertations
Through-out military history, the need to safely and effectively allocate resources to various military operations was a task of extreme importance. Satisfying the needs of multiple consumers by optimally pairing with appropriate suppliers falls into the category of vehicle routing problems (VRP), which has been intensively studied over the years. In general, finding the optimal solution to VRP is known to be NP-hard. The proposed solutions rely on mathematical programming and the size of the problems that can be optimally solved is typically limited. In military settings, balancing the needs of multiple consumers with the current operational environment has always …
Extending Difference Of Votes Rules On Three Voting Models., Sarah Schulz King
Extending Difference Of Votes Rules On Three Voting Models., Sarah Schulz King
Electronic Theses and Dissertations
In a voting situation where there are only two competing alternatives, simple majority rule outputs the alternatives with the most votes or declares a tie if both alternatives receive the same number of votes. For any non-negative integer k, the difference of votes rule Mk outputs the alternative that beats the competing alternative by more than k votes. Llamazares (2006) gives a characterization of the difference of votes rules in terms of five axioms. In this thesis, we extend Llamazares' result by completely describing the class of voting rules that satisfy only two out of his five axioms. …
Structure Vs. Properties Using Chemical Graph Theory, Tabitha N. Williford
Structure Vs. Properties Using Chemical Graph Theory, Tabitha N. Williford
Electronic Theses and Dissertations
Chemical graph theory began as a way for mathematicians to bring together the areas of the Physical Sciences and Mathematics. Through its use, mathematicians are able to model chemical systems, predict their properties as well as structure-property relationships. In this dissertation, we consider two questions involving chemical graph theory and its applications. We first look at tree-like polyphenyl systems, which form an important family of compounds in Chemistry, particularly in Material Science. The importance can be seen in LEDs, transmitters, and electronics. In recent years, many extremal results regarding such systems under specific constraints have been reported. More specifically are …