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Articles 1 - 6 of 6
Full-Text Articles in Physical Sciences and Mathematics
Nonparametric Bayesian Deep Learning For Scientific Data Analysis, Devanshu Agrawal
Nonparametric Bayesian Deep Learning For Scientific Data Analysis, Devanshu Agrawal
Doctoral Dissertations
Deep learning (DL) has emerged as the leading paradigm for predictive modeling in a variety of domains, especially those involving large volumes of high-dimensional spatio-temporal data such as images and text. With the rise of big data in scientific and engineering problems, there is now considerable interest in the research and development of DL for scientific applications. The scientific domain, however, poses unique challenges for DL, including special emphasis on interpretability and robustness. In particular, a priority of the Department of Energy (DOE) is the research and development of probabilistic ML methods that are robust to overfitting and offer reliable …
Dynamic Neuromechanical Sets For Locomotion, Aravind Sundararajan
Dynamic Neuromechanical Sets For Locomotion, Aravind Sundararajan
Doctoral Dissertations
Most biological systems employ multiple redundant actuators, which is a complicated problem of controls and analysis. Unless assumptions about how the brain and body work together, and assumptions about how the body prioritizes tasks are applied, it is not possible to find the actuator controls. The purpose of this research is to develop computational tools for the analysis of arbitrary musculoskeletal models that employ redundant actuators. Instead of relying primarily on optimization frameworks and numerical methods or task prioritization schemes used typically in biomechanics to find a singular solution for actuator controls, tools for feasible sets analysis are instead developed …
Analysis Of The Continuity Of The Value Function Of An Optimal Stopping Problem, Samuel Morris Nehls
Analysis Of The Continuity Of The Value Function Of An Optimal Stopping Problem, Samuel Morris Nehls
Theses and Dissertations
In order to study model uncertainty of an optimal stopping problem of a stochastic process with a given state dependent drift rate and volatility, we analyze the effects of perturbing the parameters of the problem. This is accomplished by translating the original problem into a semi-infinite linear program and its dual. We then approximate this dual linear program by a countably constrained sub-linear program as well as an infinite sequence of finitely constrained linear programs. We find that in this framework the value function will be lower semi-continuous with respect to the parameters. If in addition we restrict ourselves to …
Combinatorial And Asymptotic Statistical Properties Of Partitions And Unimodal Sequences, Walter Mcfarland Bridges
Combinatorial And Asymptotic Statistical Properties Of Partitions And Unimodal Sequences, Walter Mcfarland Bridges
LSU Doctoral Dissertations
Our main results are asymptotic zero-one laws satisfied by the diagrams of unimodal sequences of positive integers. These diagrams consist of columns of squares in the plane; the upper boundary is called the shape. For various types of unimodal sequences, we show that, as the number of squares tends to infinity, 100% of shapes are near a certain curve---that is, there is a single limit shape. Similar phenomena have been well-studied for integer partitions, but several technical difficulties arise in the extension of such asymptotic statistical laws to unimodal sequences. We develop a widely applicable method for obtaining these limit …
Using Modern Portfolio Theory To Analyze Virgil's Aeneid (Or Any Other Poem), David Patterson
Using Modern Portfolio Theory To Analyze Virgil's Aeneid (Or Any Other Poem), David Patterson
Master's Theses
This paper demonstrates that it is possible to use mathematics to study literature as it has been used to study the social sciences. By focusing on mathematically defining economic and literary terms, it can be shown that the underlying mathematical structure behind key concepts in economics and literature are analogous. This opens the possibility of applying economic models in literature. Specifically, it is demonstrated that the economic mathematical model of modern portfolio theory can answer long standing questions around the Roman epic Aeneid by Virgil. The poet died before completing his poem. The relative completeness of the books of the …
Measuring And Modeling Information Flow On Social Networks, Tyson Charles Pond
Measuring And Modeling Information Flow On Social Networks, Tyson Charles Pond
Graduate College Dissertations and Theses
With the rise of social media, researchers have become increasingly interested in understanding how individuals inform, influence, and interact with others in their social network and how the network mediates the flow of information. Previous research on information flow has primarily used models of contagion to study the adoption of a technology, propagation of purchase recommendations, or virality of online activity. Social (or "complex") contagions spread differently than biological ("simple") contagions. A limitation when researchers validate contagion models is that they neglect much of the massive amounts of data now available through online social networks. Here we model a recently …