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ANALYSIS OF KOLMOGOROV'S SUPERPOSITION THEOREM AND ITS IMPLEMENTATION IN APPLICATIONS WITH LOW AND HIGH DIMENSIONAL DATA.
Title
ANALYSIS OF KOLMOGOROV'S SUPERPOSITION THEOREM AND ITS IMPLEMENTATION IN APPLICATIONS WITH LOW AND HIGH DIMENSIONAL DATA.
Creator
Bryant, Donald, Li, Xin, University of Central Florida
Abstract / Description
In this dissertation, we analyze Kolmogorov's superposition theorem for high dimensions. Our main goal is to explore and demonstrate the feasibility of an accurate implementation of Kolmogorov's theorem. First, based on Lorentz's ideas, we provide a thorough discussion on the proof and its numerical implementation of the theorem in dimension two. We present computational experiments which prove the feasibility of the theorem in applications of low dimensions (namely, dimensions...
Show moreIn this dissertation, we analyze Kolmogorov's superposition theorem for high dimensions. Our main goal is to explore and demonstrate the feasibility of an accurate implementation of Kolmogorov's theorem. First, based on Lorentz's ideas, we provide a thorough discussion on the proof and its numerical implementation of the theorem in dimension two. We present computational experiments which prove the feasibility of the theorem in applications of low dimensions (namely, dimensions two and three). Next, we present high dimensional extensions with complete and detailed proofs and provide the implementation that aims at applications with high dimensionality. The amalgamation of these ideas is evidenced by applications in image (two dimensional) and video (three dimensional) representations, the content based image retrieval, video retrieval, de-noising and in-painting, and Bayesian prior estimation of high dimensional data from the fields of computer vision and image processing.
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Date Issued
2008
Identifier
CFE0002236, ucf:47909
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0002236
A Framework for Measuring the Value-Added of Knowledge Processes with Analysis of Process Interactions and Dynamics
Title
A Framework for Measuring the Value-Added of Knowledge Processes with Analysis of Process Interactions and Dynamics.
Creator
Cintron, Jose, Rabelo, Luis, Elshennawy, Ahmad, Thompson, William, Ajayi, Richard, University of Central Florida
Abstract / Description
The most known and widely used methods use cash flows and tangible assets to measure the impact of investments in the organization's outputs. But in the last decade many newer organizations whose outputs are heavily dependent on information technology utilize knowledge as their main asset. These organizations' market values lie on the knowledge of its employees and their technological capabilities. In the current technology-based business landscape the value added by assets utilized for...
Show moreThe most known and widely used methods use cash flows and tangible assets to measure the impact of investments in the organization's outputs. But in the last decade many newer organizations whose outputs are heavily dependent on information technology utilize knowledge as their main asset. These organizations' market values lie on the knowledge of its employees and their technological capabilities. In the current technology-based business landscape the value added by assets utilized for generation of outputs cannot be appropriately measured and managed without considering the role that intangible assets and knowledge play in executing processes. The analysis of processes for comparison and decision making based on intangible value added can be accomplished using the knowledge required to execute processes. The measurement of value added by knowledge can provide a more realistic framework for analysis of processes where traditional cost methods are not appropriate, enabling managers to better allocate and control knowledge-based processes. Further consideration of interactions and complexity between proposed process alternatives can yield answers about where and when investments can improve value-added while dynamically providing higher returns on investment.
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Date Issued
2013
Identifier
CFE0004983, ucf:49585
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0004983
Effect of Nonclassical Optical Turbulence on a Propagating Laser Beam
Title
Effect of Nonclassical Optical Turbulence on a Propagating Laser Beam.
Creator
Beason, Melissa, Phillips, Ronald, Atia, George, Richardson, Martin, Andrews, Larry, Shivamoggi, Bhimsen, University of Central Florida
Abstract / Description
Theory developed for the propagation of a laser beam through optical turbulence generally assumes that the turbulence is both homogeneous and isotropic and that the associated spectrum follows the classical Kolmogorov spectral power law of . If the atmosphere deviates from these assumptions, beam statistics such as mean intensity, correlation, and scintillation index could vary significantly from mathematical predictions. This work considers the effect of nonclassical turbulence on a...
Show moreTheory developed for the propagation of a laser beam through optical turbulence generally assumes that the turbulence is both homogeneous and isotropic and that the associated spectrum follows the classical Kolmogorov spectral power law of . If the atmosphere deviates from these assumptions, beam statistics such as mean intensity, correlation, and scintillation index could vary significantly from mathematical predictions. This work considers the effect of nonclassical turbulence on a propagated beam. Namely, anisotropy of the turbulence and a power law that deviates from . A mathematical model is developed for the scintillation index of a Gaussian beam propagated through nonclassical turbulence and theory is extended for the covariance function of intensity of a plane wave propagated through nonclassical turbulence. Multiple experiments over a concrete runway and a grass range verify the presence of turbulence which varies between isotropy and anisotropy. Data is taken throughout the day and the evolution of optical turbulence is considered. Also, irradiance fluctuation data taken in May 2018 over a concrete runway and July 2018 over a grass range indicate an additional beam shaping effect. A simplistic mathematical model was formulated which reproduced the measured behavior of contours of equal mean intensity and scintillation index.?
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Date Issued
2018
Identifier
CFE0007310, ucf:52646
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0007310