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Numerical path integration of stochastic systems
Title
Numerical path integration of stochastic systems.
Creator
Yu, Jinshou., Florida Atlantic University, Lin, Y. K., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description
The present dissertation is focused on the numerical method of path integration for stochastic systems. The existing procedures of numerical path integration are re-examined. A comparison study is made of the results obtained using various interpolation schemes. The amounts of computation time and relative accuracies of the existing procedures are tested with different mesh sizes and different time step sizes. A new numerical procedure based on Gauss-Legendre integration formula is proposed,...
Show moreThe present dissertation is focused on the numerical method of path integration for stochastic systems. The existing procedures of numerical path integration are re-examined. A comparison study is made of the results obtained using various interpolation schemes. The amounts of computation time and relative accuracies of the existing procedures are tested with different mesh sizes and different time step sizes. A new numerical procedure based on Gauss-Legendre integration formula is proposed, which requires no explicit numerical interpolation. The probability evolution is represented in terms of the transition probabilities among Gauss points in various sub-intervals. Each transition probability is assumed to be Gaussian, and it can be obtained from the moment equations. Gaussian closure is used to truncate the moment equations in the case of a nonlinear system. The computation parameters of the new procedure, such as size of time-step and number of sub-intervals, can be determined in a systematic manner. The approximate Gaussianity of the transition probability obtained from the moment equations is first tested by comparing it with the simulation results, from which a proper time-step size is selected. The standard deviation of the transition probability in each direction of the state space can then be obtained from the moment equations, and is used to determine the size of the sub-intervals in that direction. The new numerical path integration procedure is applied to several one-dimensional and two-dimensional stochastic systems, for which the responses are homogeneous Markov processes. It is shown that the new procedure is not only accurate and efficient, but also numerically stable and highly adaptable. The new procedure is also applied to a nonlinear stochastic system subjected to both sinusoidal and random excitations. The system response in this case is a non-homogeneous Markov process. The algorithm is adapted for this case, so that re-computation of the transition probability density at every time step can be avoided.
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Date Issued
1997
PURL
http://purl.flvc.org/fcla/dt/12506
Subject Headings
Stochastic systems, Numerical integration, Markov processes
Format
Document (PDF)
Gapless alignment revisited
Title
Gapless alignment revisited.
Creator
Raley, Elizabeth Anne, Florida Atlantic University, Yu, Yi-Kuo
Abstract/Description
The purpose of sequence alignment is to detect mutual similarity, characterized by the so-called "alignment score", between sequences compared. To quantitatively assess the confidence level of an alignment result requires the knowledge of alignment score statistics under a certain null model and is the central issue in sequence alignment. In this thesis, the score statistics of Markov null model were revisited and the score statistics of non-Markov null model were investigated for two state...
Show moreThe purpose of sequence alignment is to detect mutual similarity, characterized by the so-called "alignment score", between sequences compared. To quantitatively assess the confidence level of an alignment result requires the knowledge of alignment score statistics under a certain null model and is the central issue in sequence alignment. In this thesis, the score statistics of Markov null model were revisited and the score statistics of non-Markov null model were investigated for two state-of-the-art algorithms, namely, the gapless Smith-Waterman and Hybrid algorithms. These two algorithms were further used to find highly related signals in unrelated sequences and in weakly related sequences corresponding, respectively, to Markov null model and non-Markov null model. The confidence levels of these models were also studied. Since the sequence similarity we are interested in comes from evolutionary history, we also investigated the relationship between sequence alignment, the tool to find similarity, and evolution. The average evolution distance between the daughter sequences was found and compared with their expected values, for individual trees and as an average over many trees.
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Date Issued
2001
PURL
http://purl.flvc.org/fcla/dt/12856
Subject Headings
Bioinformatics, Amino acid sequence--Databases, Markov processes
Format
Document (PDF)
Web log analysis: Experimental studies
Title
Web log analysis: Experimental studies.
Creator
Yang, Zhijian., Florida Atlantic University, Zhong, Shi, Pandya, Abhijit S., College of Engineering and Computer Science, Department of Computer and Electrical Engineering and Computer Science
Abstract/Description
With rapid growth of the World Wide Web, web performance becomes increasingly important for modern businesses, especially for e-commerce. As we all know, web server logs contain potentially useful empirical data to improve web server performance. In this thesis, we discuss some topics related to the analysis of a website's server logs for enhancing server performance, which will benefit some applications in business. Markov chain models are used and allow us to dynamically model page...
Show moreWith rapid growth of the World Wide Web, web performance becomes increasingly important for modern businesses, especially for e-commerce. As we all know, web server logs contain potentially useful empirical data to improve web server performance. In this thesis, we discuss some topics related to the analysis of a website's server logs for enhancing server performance, which will benefit some applications in business. Markov chain models are used and allow us to dynamically model page sequences extracted from server logs. My experimental studies contain three major parts. First, I present a workload characterization study of the website used for my research. Second, Markov chain models are constructed for both page request and page-visiting sequence prediction. Finally, I carefully evaluate the constructed models using an independent test data set, which is from server logs on a different day. The research results demonstrate the effectiveness of Markov chain models for characterizing page-visiting sequences.
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Date Issued
2005
PURL
http://purl.flvc.org/fcla/dt/13202
Subject Headings
Markov processes, Operations research, Business enterprises--Computer networks, Electronic commerce--Data processing
Format
Document (PDF)
Biological Computation: the development of a genomic analysis pipeline to identify cellular genes modulated by the transcription / splicing factor srsf1
Title
Biological Computation: the development of a genomic analysis pipeline to identify cellular genes modulated by the transcription / splicing factor srsf1.
Creator
Clark, Evan, Asghar, Waseem, Florida Atlantic University, College of Engineering and Computer Science, Department of Computer and Electrical Engineering and Computer Science
Abstract/Description
SRSF1 is a widely expressed mammalian protein with multiple functions in the regulation of gene expression through processes including transcription, mRNA splicing, and translation. Although much is known of SRSF1 role in alternative splicing of specific genes little is known about its functions as a transcription factor and its global effect on cellular gene expression. We utilized a RNA sequencing (RNA-¬‐Seq) approach to determine the impact of SRSF1 in on cellular gene expression and...
Show moreSRSF1 is a widely expressed mammalian protein with multiple functions in the regulation of gene expression through processes including transcription, mRNA splicing, and translation. Although much is known of SRSF1 role in alternative splicing of specific genes little is known about its functions as a transcription factor and its global effect on cellular gene expression. We utilized a RNA sequencing (RNA-¬‐Seq) approach to determine the impact of SRSF1 in on cellular gene expression and analyzed both the short term (12 hours) and long term (48 hours) effects of SRSF1 expression in a human cell line. Furthermore, we analyzed and compared the effect of the expression of a naturally occurring deletion mutant of SRSF1 (RRM12) to the full-¬‐length protein. Our analysis reveals that shortly after SRSF1 is over-¬‐expressed the transcription of several histone coding genes is down-¬‐regulated, allowing for a more relaxed chromatin state and efficient transcription by RNA Polymerase II. This effect is reversed at 48 hours. At the same time key genes for the immune pathways are activated, more notably Tumor Necrosis Factor-¬‐Alpha (TNF-¬‐α), suggesting a role for SRSF1 in T cell functions.
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Date Issued
2017
PURL
http://purl.flvc.org/fau/fd/FA00004858, http://purl.flvc.org/fau/fd/FA00004858
Subject Headings
Gene expression., Computational biology., Markov processes., Bioinformatics., Genetic engineering., Molecular biology.
Format
Document (PDF)
Frequency Line Tracking in Spectrograms Using Hidden Markov Models
Title
Frequency Line Tracking in Spectrograms Using Hidden Markov Models.
Creator
Gunes, Tuncay, Erdol, Nurgun, Florida Atlantic University
Abstract/Description
One of the limiting factors restricting aircraft landings at maJor airports is the minimum spacing requirements due to vortex wake avoidance. If it can be shown that the separation requirements are too conservative, then it may be possible to increase the rate of landings on a given runway. During August/September 2003, NASA and the (United States Department of Transportation) USDOT sponsored a wake acoustics test at the Denver International Airport. The central instrument of the test was a...
Show moreOne of the limiting factors restricting aircraft landings at maJor airports is the minimum spacing requirements due to vortex wake avoidance. If it can be shown that the separation requirements are too conservative, then it may be possible to increase the rate of landings on a given runway. During August/September 2003, NASA and the (United States Department of Transportation) USDOT sponsored a wake acoustics test at the Denver International Airport. The central instrument of the test was a large microphone phased array. Different types of aircrafts were recorded during landing and the acoustic data obtained was stored. From acoustic data the spectrograms were generated using the technique of AutoRegressive (AR) spectral estimation from multitaper autocorrelation estimates. Several sources of sound that are recorded in the audio files can be observed in the spectrograms. Some these signals, such as the noise generated from the aircraft engine can be identified easily because of their strength and the Doppler shift they undergo. In contrast to this, the wake vortex signal is weaker and does not exhibit a Doppler shift because it's stationary in space. Therefore it may not be identified easily because of the existence of stronger signals. The motive in our research is to develop methods to determine these strong signals that appear as spectral lines in the spectrogram. In the future, the results obtained in this work can be used to eliminate these strong signals from the spectrogram thus allowing us to see and identify wake vortex signal which is more important to us.
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Date Issued
2006
PURL
http://purl.flvc.org/fau/fd/FA00012525
Subject Headings
Markov processes, Economics--Mathematical models, Wave structure function--Analysis, Adaptive control systems, Spectrum analysis
Format
Document (PDF)
Hurst analysis applied to the study of single calcium-activated potassium channel kinetics
Title
Hurst analysis applied to the study of single calcium-activated potassium channel kinetics.
Creator
Liebovitch, Larry S., Figueiroa, Josed N., Nogueira, Romildo A., Varanda, Wamberto A.
Date Issued
2000-10-07
PURL
http://purl.flvc.org/FAU/165249
Subject Headings
Ion channels-Mathematical models, Memory, Chemical kinetics, Calcium channels, Fractals, Markov processes, Leydig cells, Molecular biology--Statistical methods
Format
Document (PDF)
Fractal ion-channel behavior generates fractal firing patterns in neuronal models
Title
Fractal ion-channel behavior generates fractal firing patterns in neuronal models.
Creator
Liebovitch, Larry S., Lowen, Steven B., White, John A.
Date Issued
1999-05
PURL
http://purl.flvc.org/fau/165477
Subject Headings
Biophysics--Research, Fractals, Neural networks (Neurobiology)--Mathematical models, Neurons--Mathematical models, Markov processes--Mathematical models, Ion channels--Mathematical models
Format
Document (PDF)