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Articles 1 - 3 of 3
Full-Text Articles in Dynamic Systems
Learning Problems Related To Stochastic Differential Equations, Jinpu Zhou
Learning Problems Related To Stochastic Differential Equations, Jinpu Zhou
LSU Doctoral Dissertations
Stochastic differential equations (SDEs) are essential for modeling systems influenced by both deterministic dynamics and random fluctuations, with applications in a wide variety of disciplines. This thesis develops a Bayesian framework for nonparametric learning in SDEs, addressing key challenges in inference, particularly when dealing with complex systems and incomplete data. The thesis begins by establishing a theoretical foundation in optimization over Hilbert spaces, including a generalized representer theorem to address infinite-dimensional optimization problems encountered in nonparametric inference. Building on this, we introduce a Bayesian framework with shrinkage priors to learn drift functions from high-frequency data. Bayesian approach incorporates low-cost sparse …
Characterizing The Northern Hemisphere Circumpolar Vortex Through Space And Time, Nazla Bushra
Characterizing The Northern Hemisphere Circumpolar Vortex Through Space And Time, Nazla Bushra
LSU Doctoral Dissertations
This hemispheric-scale, steering atmospheric circulation represented by the circumpolar vortices (CPVs) are the middle- and upper-tropospheric wind belts circumnavigating the poles. Variability in the CPV area, shape, and position are important topics in geoenvironmental sciences because of the many links to environmental features. However, a means of characterizing the CPV has remained elusive. The goal of this research is to (i) identify the Northern Hemisphere CPV (NHCPV) and its morphometric characteristics, (ii) understand the daily characteristics of NHCPV area and circularity over time, (iii) identify and analyze spatiotemporal variability in the NHCPV’s centroid, and (iv) analyze how CPV features relate …
Finding Music In Chaos: Designing And Composing With Virtual Instruments Inspired By Chaotic Equations, Landon P. Viator
Finding Music In Chaos: Designing And Composing With Virtual Instruments Inspired By Chaotic Equations, Landon P. Viator
LSU Doctoral Dissertations
Using chaos theory to design novel audio synthesis engines has been explored little in computer music. This could be because of the difficulty of obtaining harmonic tones or the likelihood of chaos-based synthesis engines to explode, which then requires re-instantiating of the engine to proceed with sound production. This process is not desirable when composing because of the time wasted fixing the synthesis engine instead of the composer being able to focus completely on the creative aspects of composition. One way to remedy these issues is to connect chaotic equations to individual parts of the synthesis engine instead of relying …