There has been in the past and still is controversy over the genesis of the third heart sound (S3). Recent studies, strongly suggest that S3 is a manifestation of a sudden intrinsic limitation in the expansion of the left ventricle. The thesis has aimed to explore that hypothesis further using combined echocardiographic and spectral analysis techniques. Spectral analysis was carried out via conventional fast fourier transform methods and the maximum entropy method. The efficacy of these techniques, in relation to clinical and scientific application, was explored further. Briefly discussed was the application of autoregressive-moving average (ARMA) modelling for spectral analysis of S3, in relation to further work. Following is a brief synopsis of the thesis: CHAPTER 1 This gives an historical and general introduction to heart sound analysis. Discussed briefly is the physiology of the heart and heart sounds and the diagnostic implications of S3 analysis. CHAPTER 2 Here is discussed the instrumentation system used and phonocardiographic and echocardiographic data aquisition. Data preprocessing and storage is also covered. CHAPTER 3 In this chapter the application of a FFT method and correlation of resultant spectral parameters with echocardiographic parameters is reported. CHAPTER 4 The theoretical development of the maximum entropy technique (based on published papers and expanded) is discussed here. Numerical experiments with the method and associated problems are also discussed. CHAPTER 5 The MEM is applied to the spectral analysis of S3 and compared with the FFT method. Correlation analysis of MEM derived spectral parameters with echocardiograhic data is performed. CHAPTER 6 Here ARMA modelling and application to further work is discussed. An ARMA model from the maxixum entropy coefficients is derived. The application of this model to the deconvolution of the chest wall transfer function is discussed as an approach for further work. / Thesis (M.Sc.)--School of Mathematical Sciences, 1989.

The dissertation focuses on the application of entropy theory in hydrologic analysis and simulation, namely, rainfall analysis, streamflow simulation and drought analysis. The extreme value distribution has been employed for modeling extreme rainfall values. Based on the analysis of changes in the frequency distribution of annual rainfall maxima in Texas with the changes in duration, climate zone and distance from the sea, an entropy-based distribution is proposed as an alternative distribution for modeling extreme rainfall values. The performance of the entropy based distribution is validated by comparing with the commonly used generalized extreme value (GEV) distribution based on synthetic and observed data and is shown to be preferable for extreme rainfall values with high skewness. An entropy based method is proposed for single-site monthly streamflow simulation. An entropy-copula method is also proposed to simplify the entropy based method and preserve the inter-annual dependence of monthly streamflow. Both methods are shown to preserve statistics, such as mean, standard deviation, skenwess and lag-one correlation, well for monthly streamflow in the Colorado River basin. The entropy and entropy-copula methods are also extended for multi-site annual streamflow simulation at four stations in the Colorado River basin. Simulation results show that both methods preserve the mean, standard deviation and skewness equally well but differ in preserving the dependence structure (e.g., Pearson linear correlation). An entropy based method is proposed for constructing the joint distribution of drought variables with different marginal distributions and is applied for drought analysis based on monthly streamflow of Brazos River at Waco, Texas. Coupling the entropy theory and copula theory, an entropy-copula method is also proposed for constructing the joint distribution for drought analysis, which is illustrated with a case study based on the Parmer drought severity index (PDSI) data in Climate Division 5 in Texas.

The knowledge of the three-dimensional structures of proteins and polypeptides is essential to understand their functions. The work shown in this thesis has two objectives. The first one is to develop a new analytical method based on maximum entropy (ME) theory to analyze NMR experimental data such as NOEs and J-couplings in order to reconstitute φ,ψ Ramachandran plots of flexible biomolecules. Two model systems have been used, the flexible polypeptide motilin and the disaccharide α-D-Mannosep-(1-2)-α-D-Mannosep-O-Me (M2M). The experimental data was defined as constraints that were combined with prior information (priors) which were the φ,ψ distributions obtained from either a coil library, the Protein DataBank or Molecular Dynamics Simulations. ME theory was utilized to formulate φ,ψ distributions (posteriors) that are least committed to the priors and in full agreement with the experimental data. Reparamerization of the Karplus relation was necessary to obtain realistic distributions for the M2M. Clear structural propensities were found in motilin with a nascent α-helix in the central part (residues Y7-E17), a left handed 31 helix in the C-terminus (R18-G21) and an extended conformation in the N-terminus. The contribution of each residue to the thermodynamic entropy (segmental entropy) was calculated from the posteriors and compared favorably to the segmental entropies estimated from 15N-relaxation data. For M2M the dominating conformation of the glycosidic linkage was found to be at φH=-40° ψH=33°, which is governed by the exo-anomeric effect. Another minor conformation with a negative ψH angle was discovered in M2M. The ratio between both populations is about 3:1. The second part of the thesis is a structural study of a DNA-binding protein, the C repressor of the P2 bacteriophage (P2 C). P2 C represses the lytic genes of the P2 bacteriophage, thereby directing the P2 lifecycle toward the lysogenic lifemode. The crystal and solution structures of P2 C have been solved by X-ray crystallography and NMR, respectively. Both structures revealed a homodimeric protein with five rigid α-helices made up by residues 5-66 and a β-strand conformation in residues 69-76 in each monomer. 15N-relaxation data showed that the C-terminus (residues 85-99) is highly flexible and fully unstructured. A model representing the P2 C-DNA complex was built based on the structure and available biochemical data. In the model, P2 C binds DNA cooperatively and two homodimeric P2 C molecules are close enough to interact and bind one direct DNA repeat each. / At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 4: In press. Paper 5: Manuscript.

PRICAI 2008: Trends in Artificial Intelligence 10th Pacific Rim International Conference on Artificial Intelligence, Hanoi, Vietnam, December 15-19, 2008. Proceedings

Spray models are increasingly becoming the principal tools in the design and development of gas turbine combustors. Spray modeling requires a knowledge of the liquid atomization process, and the sizes and velocities of subsequently formed droplets as initial conditions. In order to have a better understanding of the liquid atomization process,the breakup characteristics of plane liquid sheets in co-flowing gas streams are investigated by means of linear and nonlinear hydrodynamic instability analyses. The liquid sheet breakup process is studied for initial sinuous and varicose modes of disturbance. It is observed that the sheet breakup occurs at half-wavelength intervals for an initial sinuous disturbance and at full-wavelength intervals for an initial varicose disturbance. It is also found that under certain operating conditions, the breakup process is dictated by the initial varicose disturbance compare to its sinuous counterpart. Further, the breakup process is studied for the combined mode and it is found that the sheet breakup occurs at half- or full-wavelength intervals depending on the proportion of the individual sinuous and varicose disturbances. In general, the breakup length decreases with the increase in the Weber number, gas-to-liquid velocity and density ratios. A predictive model of the initial droplet size and velocity distributions for the subsequently formed spray is also formulated here. The present model incorporates the deterministic aspect of spray formation by calculating the breakup length and the mass-mean diameter and the stochastic aspect by statistical means through the maximum entropy principle based on Bayesian entropy. The two sub-models are coupled together by the various source terms signifying the liquid-gas interaction and a prior distribution based on instability analysis, which provides information regarding the unstable wave elements on the two liquid-gas interfaces. Experimental investigation of the breakup characteristics of the liquid sheet is performed by a high speed CCD camera and the measurement of the initial droplet size and distributions is conducted by phase-Doppler interferometry. Good agreement of the theoretical breakup length with the experiment is obtained for a planar, an annular and a gas turbine nozzle. The predicted initial droplet size and velocity distributions show reasonably satisfactory agreement with experimental data for all the three types of nozzles. Hence this spray model can be utilized to predict the initial droplet size and velocity distributions in sprays, which can then be implemented as a front-end subroutine to the existing computer codes.

Moment Problems with Applications to Value-At-Risk and Portfolio Management By Ruilin Tian May 2008 Committee Chair: Dr. Samuel H. Cox Major Department: Risk Management and Insurance My dissertation provides new applications of moment theory and optimization to financial and insurance risk management. In the investment and managerial areas, one often needs to determine some measure of risk, especially the risk of extreme events. However, complete information of the underlying outcomes is usually unavailable; instead one has access to partial information such as the mean, variance, mode, or range. In Chapters 2 and 3, we find the semiparametric upper and lower bounds for the value-at-risk (VaR) with incomplete information, that is, moments of the underlying distribution. When a single variable is concerned, bounds on VaR are computed to obtain a 100% confidence interval. When the sample financial data have a global maximum, we show that unimodal assumption tightens the optimal bounds. Next we further analyze a function of two correlated random variables. Specifically, we find bounds on the probability of two joint extreme events. When three or more variables are involved, the multivariate problem can sometimes be converted to a single variable problem. In all cases, we use the physical measure rather than the commonly used equivalent pricing probability measure. In addition to solving these problems using the traditional approach based on the geometry of a moment problem, a more efficient method is proposed to solve a general class of moment bounds via semidefinite programming. In the last part of the thesis, we apply optimization techniques to improve financial portfolio risk management. Instead of considering VaR, we work with a coherent risk measure, the conditional VaR (CVaR). As an extension of Krokhmal et al. (2002), we impose CVaR-related functions to the portfolio selection problem. The CVaR approach sets a β-level CVaR as the objective function and maximizes the worst case on the tail of the distribution. The CVaR-like constraints approach adds a set of CVaR-like constraints to the traditional Markowitz problem, reshaping the portfolio distribution. Both methods greatly increase the skewness of portfolios, although the CVaR approach may lose control of the variance. This capability of increasing skewness is very attractive to the investors who may prefer higher probability of obtaining higher returns. We compare the CVaR-related approaches to some other popular portfolio optimization methods. Our numerical analysis provides empirical support for the superiority of the CVaR-like constraints approach in terms of portfolio efficiency.

Spray models are increasingly becoming the principal tools in the design and development of gas turbine combustors. Spray modeling requires a knowledge of the liquid atomization process, and the sizes and velocities of subsequently formed droplets as initial conditions. In order to have a better understanding of the liquid atomization process,the breakup characteristics of plane liquid sheets in co-flowing gas streams are investigated by means of linear and nonlinear hydrodynamic instability analyses. The liquid sheet breakup process is studied for initial sinuous and varicose modes of disturbance. It is observed that the sheet breakup occurs at half-wavelength intervals for an initial sinuous disturbance and at full-wavelength intervals for an initial varicose disturbance. It is also found that under certain operating conditions, the breakup process is dictated by the initial varicose disturbance compare to its sinuous counterpart. Further, the breakup process is studied for the combined mode and it is found that the sheet breakup occurs at half- or full-wavelength intervals depending on the proportion of the individual sinuous and varicose disturbances. In general, the breakup length decreases with the increase in the Weber number, gas-to-liquid velocity and density ratios. A predictive model of the initial droplet size and velocity distributions for the subsequently formed spray is also formulated here. The present model incorporates the deterministic aspect of spray formation by calculating the breakup length and the mass-mean diameter and the stochastic aspect by statistical means through the maximum entropy principle based on Bayesian entropy. The two sub-models are coupled together by the various source terms signifying the liquid-gas interaction and a prior distribution based on instability analysis, which provides information regarding the unstable wave elements on the two liquid-gas interfaces. Experimental investigation of the breakup characteristics of the liquid sheet is performed by a high speed CCD camera and the measurement of the initial droplet size and distributions is conducted by phase-Doppler interferometry. Good agreement of the theoretical breakup length with the experiment is obtained for a planar, an annular and a gas turbine nozzle. The predicted initial droplet size and velocity distributions show reasonably satisfactory agreement with experimental data for all the three types of nozzles. Hence this spray model can be utilized to predict the initial droplet size and velocity distributions in sprays, which can then be implemented as a front-end subroutine to the existing computer codes.

We investigate the applicability of the method of maximum entropy regularization (MER) including convergence and convergence rates of regularized solutions to the specific inverse problem (SIP) of calibrating a purely time-dependent volatility function. In this context, we extend the results of [16] and [17] in some details. Due to the explicit structure of the forward operator based on a generalized Black-Scholes formula the ill-posedness character of the nonlinear inverse problem (SIP) can be verified. Numerical case studies illustrate the chances and limitations of (MER) versus Tikhonov regularization (TR) for smooth solutions and solutions with a sharp peak.

Thesis (Ph. D.)--University of Missouri-Columbia, 1999. / Typescript. Vita. Includes bibliographical references (leaves 114-121). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 1999. / Typescript. Vita. Includes bibliographical references (leaves 114-121). Also available on the Internet.