This work addresses the advanced probabilistic modeling of the stochastic nature of microgrinding in the machining of high-aspect ratio, ceramic micro-features. The heightened sensitivity of such high-fidelity workpieces to excessive grit cutting force drives a need for improved stochastic modeling. Statistical propagation is used to generate a comprehensive analytic probabilistic model for static wheel topography. Numerical simulation and measurement of microgrinding wheels show the model accurately predicts the stochastic nature of the topography when exact wheel specifications are known. Investigation into the statistical scale affects associated microgrinding wheels shows that the decreasing number of abrasives in the wheel increases the relative statistical variability in the wheel topography although variability in the wheel concentration number dominates the source of variance. An in situ microgrinding wheel measurement technique is developed to aid in the calibration of the process model to improve on the inaccuracy caused by wheel specification error. A probabilistic model is generated for straight traverse and infeed microgrinding dynamic wheel topography. Infeed microgrinding was shown to provide a method of measuring individual grit cutting forces with constant undeformed chip thickness within the grind zone. Measurements of the dynamic wheel topography in infeed microgrinding verified the accuracy of the probabilistic model.

A phenomenon as complex as protein folding requires a complex model to approximate it. This thesis presents a bottom-up approach for building complex probabilistic models of protein secondary structure by incorporating the multiple information sources which we call experts. Expert opinions are represented by probability distributions over the set of possible structures. Bayesian treatment of a group of experts results in a consensus opinion that combines the experts' probability distributions using the operators of normalized product, quotient and exponentiation. The expression of this consensus opinion simplifiesto a product of the expert opinions with two assumptions: (1) balanced training of experts, i. e. , uniform prior probability over all structures, and (2) conditional independence between expert opinions,given the structure. This research also studies how Markov chains and hidden Markov models may be used to represent expert opinion. Closure properties areproven, and construction algorithms are given for product of hidden Markov models, and product, quotient and exponentiation of Markovchains. Algorithms for extracting single-structure predictions from these models are also given. Current product-of-experts approaches in machine learning are top-down modeling strategies that assume expert independence, and require simultaneous training of all experts. This research describes a bottom-up modeling strategy that can incorporate conditionally dependent experts, and assumes separately trained experts.

In this thesis, we present enhancements of hidden Markov models for the problem of finding genes in DNA sequences. Genes are the parts of DNA that serve as a template for synthesis of proteins. Thus, gene finding is a crucial step in the analysis of DNA sequencing data. <br /><br /> Hidden Markov models are a key tool used in gene finding. Yhis thesis presents three methods for extending the capabilities of hidden Markov models to better capture the statistical properties of DNA sequences. In all three, we encounter limiting factors that lead to trade-offs between the model accuracy and those limiting factors. <br /><br /> First, we build better models for recognizing biological signals in DNA sequences. Our new models capture non-adjacent dependencies within these signals. In this case, the main limiting factor is the amount of training data: more training data allows more complex models. Second, we design methods for better representation of length distributions in hidden Markov models, where we balance the accuracy of the representation against the running time needed to find genes in novel sequences. Finally, we show that creating hidden Markov models with complex topologies may be detrimental to the prediction accuracy, unless we use more complex prediction algorithms. However, such algorithms require longer running time, and in many cases the prediction problem is NP-hard. For gene finding this means that incorporating some of the prior biological knowledge into the model would require impractical running times. However, we also demonstrate that our methods can be used for solving other biological problems, where input sequences are short. <br /><br /> As a model example to evaluate our methods, we built a gene finder ExonHunter that outperforms programs commonly used in genome projects.

In this thesis, we present enhancements of hidden Markov models for the problem of finding genes in DNA sequences. Genes are the parts of DNA that serve as a template for synthesis of proteins. Thus, gene finding is a crucial step in the analysis of DNA sequencing data. <br /><br /> Hidden Markov models are a key tool used in gene finding. Yhis thesis presents three methods for extending the capabilities of hidden Markov models to better capture the statistical properties of DNA sequences. In all three, we encounter limiting factors that lead to trade-offs between the model accuracy and those limiting factors. <br /><br /> First, we build better models for recognizing biological signals in DNA sequences. Our new models capture non-adjacent dependencies within these signals. In this case, the main limiting factor is the amount of training data: more training data allows more complex models. Second, we design methods for better representation of length distributions in hidden Markov models, where we balance the accuracy of the representation against the running time needed to find genes in novel sequences. Finally, we show that creating hidden Markov models with complex topologies may be detrimental to the prediction accuracy, unless we use more complex prediction algorithms. However, such algorithms require longer running time, and in many cases the prediction problem is NP-hard. For gene finding this means that incorporating some of the prior biological knowledge into the model would require impractical running times. However, we also demonstrate that our methods can be used for solving other biological problems, where input sequences are short. <br /><br /> As a model example to evaluate our methods, we built a gene finder ExonHunter that outperforms programs commonly used in genome projects.

A phenomenon as complex as protein folding requires a complex model to approximate it. This thesis presents a bottom-up approach for building complex probabilistic models of protein secondary structure by incorporating the multiple information sources which we call experts. Expert opinions are represented by probability distributions over the set of possible structures. Bayesian treatment of a group of experts results in a consensus opinion that combines the experts' probability distributions using the operators of normalized product, quotient and exponentiation. The expression of this consensus opinion simplifiesto a product of the expert opinions with two assumptions: (1) balanced training of experts, i. e. , uniform prior probability over all structures, and (2) conditional independence between expert opinions,given the structure. This research also studies how Markov chains and hidden Markov models may be used to represent expert opinion. Closure properties areproven, and construction algorithms are given for product of hidden Markov models, and product, quotient and exponentiation of Markovchains. Algorithms for extracting single-structure predictions from these models are also given. Current product-of-experts approaches in machine learning are top-down modeling strategies that assume expert independence, and require simultaneous training of all experts. This research describes a bottom-up modeling strategy that can incorporate conditionally dependent experts, and assumes separately trained experts.

The most common mode of levee failure, breach due to overtopping, is generally considered as a function of a complex set of contributing factors. The goal of this research is to enhance the state of the art and practice for performing levee overtopping risk assessment. For this purpose, a dataset of levee overtopping event records within the portfolio of levee systems maintained by the U.S. Army Corps of Engineers (USACE) is presented. The dataset is utilized with logistic regression analysis to develop a probabilistic model to calculate system response probabilities and assess risk related to levee overtopping. The presented dataset can be used for identifying key factors controlling overtopping behavior, validation of model results, and providing new insight into the phenomenon of levee overtopping. The proposed model offers a practical yet robust tool for levee risk analysis and can be readily employed by engineers and other stakeholders.

A high degree of variability is commonly encountered in biomechanical investigations of the shoulder. Researchers have hypothesized that the variation between individuals explains why only certain workers are injured when performing the same tasks as other individuals. One source for the variability is inter-individual differences in shoulder musculoskeletal geometry. The purpose of this thesis was to use computational modeling to assess the functional roles of the scapulohumeral muscles, compare model-predicted data to the reviewed literature, and quantify the sensitivity of these functional roles to changes in muscle geometry. Muscle moment arms, lines of action, stability ratios, and forces were quantified throughout arm elevation in the scapular plane using a widely investigated upper extremity model. Monte Carlo simulations were performed to iteratively adjust muscle attachment locations in order to reflect potential inter-individual differences in muscle geometry. Model-predicted muscle moment arms agreed well qualitatively with the reviewed literature; however, several muscle lines of action were inconsistent between the model and previous data collected in cadavers available in the literature. Sensitivity of muscle functional roles to attachment changes was muscle-specific, and depended upon the elevation angle as well as outcome measure. Regressions were developed to identify which attachment locations at the clavicle, scapula, and humerus caused the greatest change in muscle functional roles. In general, muscle moment arms were most sensitive to changes of the muscle attachment closest to the joint centre (humeral attachment for rotator cuff muscles; scapular attachment for deltoids). Lines of action were most affected by perturbations in scapular attachment location. Overall, these findings indicate that inter-individual musculoskeletal geometry differences can substantially alter muscle functional roles, which are expected to require altered muscle activity and kinematic coordination patterns between people. These variations in musculoskeletal geometry may differentially affect risk of work-related shoulder musculoskeletal disorders among individuals. / Thesis / Master of Science (MSc)

Microarrays emerged in the 1990s as a consequence of the efforts to speed up the process of drug discovery. They revolutionized molecular biological research by enabling monitoring of thousands of genes together. Typical microarray experiments measure the expression levels of a large numberof genes on very few tissue samples. The resulting sparsity of data presents major challenges to statistical methods used to perform any kind of analysis on this data. This research posits that phenotypic classification and prediction serve as good objective functions for both optimization and evaluation of microarray data analysis methods. This is because classification measures whatis needed for diagnostics and provides quantitative performance measures such as leave-one-out (LOO) or held-out prediction accuracy and confidence. Under the classification framework, various microarray data normalization procedures are evaluated using a class label hypothesis testing framework and also employing Support Vector Machines (SVM) and linear discriminant based classifiers. A novel normalization technique based on minimizing the squared correlation coefficients between expression levels of gene pairs is proposed and evaluated along with the other methods. Our results suggest that most normalization methods helped classification on the datasets considered except the rank method, most likely due to its quantization effects.Another contribution of this research is in developing machine learning methods for incorporating an independent source of information, in the form of gene annotations, to analyze microarray data. Recently, genes of many organisms have been annotated with terms from a limited vocabulary called Gene Ontologies (GO), describing the genes' roles in various biological processes, molecular functions and their locations within the cell. Novel probabilistic generative models are proposed for clustering genes using both their expression levels and GO tags. These models are similar in essence to the ones used for multimodal data, such as images and words, with learning and inference done in a Bayesian framework. The multimodal generative models are used for phenotypic class prediction. More specifically, the problems of phenotype prediction for static gene expression data and state prediction for time-course data are emphasized. Using GO tags for organisms whose genes have been studied more comprehensively leads to an improvement in prediction. Our methods also have the potential to provide a way to assess the quality of available GO tags for the genes of various model organisms.

In my thesis I focuse on the lottery theme. I describe its historical development and contemporary situacion. The main part of mine thesis is focused on the "Sportka" and "Eurojackpot" lotteries. For these two lotteries, I do probabilistic modeling, which primary aims on the probabiliti of winning. I have created also a worklist on the topic lottery and win, which is divided for studenst of secondary school and for students of elementery school too. Furthermore in this thesis is lottery "Účtenkovka" described too and instructions how to win in lottery.

<p>The intent of the work discussed in this dissertation is to apply the engineering methods of theory/modeling, numerics/computation, and experimentation to a diverse assemblage of projects. Several projects are discussed: probabilistic modeling of decompression sickness, comparative hydrodynamics of cetacean flippers, optimization of CT/MRI protocols, evaluation of modified catheters, rudder cavitation, and modeling of mass transfer in amphibian cone outer segments. </p><p>The first project discussed is the probabilistic modeling of decompression sickness (DCS). This project involved developing a system for evaluating the success of decompression models in predicting DCS probability from empirical data. Model parameters were estimated using maximum likelihood techniques, and exact integrals of risk functions and tissue kinetics transition times were derived. Agreement with previously published results was excellent including maximum likelihood values within one log-likelihood unit of previous results and improvements by re-optimization, mean predicted DCS incidents within 1.4% of observed DCS, and time of DCS occurrence prediction. Alternative optimization and homogeneous parallel processing techniques yielded faster model optimization times. The next portion of this project involved investigating the nature and utility of marginal decompression sickness (DCS) events in fitting probabilistic decompression models to experimental dive trial data. Three null models were developed and compared to a known decompression model that was optimized on dive trial data containing only marginal DCS and no-DCS events. It was found that although marginal DCS events are related to exposure to decompression, empirical dive data containing marginal and full DCS outcomes are not combinable under a single DCS model; therefore, marginal DCS should be counted as no-DCS events when optimizing probabilistic DCS models with binomial likelihood functions. The final portion of this project involved the exploration of a multinomial DCS model. Two separate models based on the exponential-exponential/linear-exponential framework were developed: a trinomial model, which is able to predict the probabilities of mild, serious and no-DCS simultaneously, and a tetranomial model, which is able to predict the probabilities of mild, serious, marginal and no-DCS simultaneously. The trinomial DCS model was found to be qualitatively better than the tetranomial model, for reasons found earlier concerning the utility of marginal DCS events in DCS modeling. </p><p>The next project discussed is comparative hydrodynamics of cetacean flippers. Cetacean flippers may be viewed as being analogous to modern engineered hydrofoils, which have hydrodynamic properties such as lift coefficient, drag coefficient and associated efficiency. The hydrodynamics of cetacean flippers have not previously been rigorously examined and thus their performance properties are unknown. By conducting water tunnel testing using scale models of cetacean flippers derived via computed tomography (CT) scans, as well as computational fluid dynamic (CFD) simulations, a baseline work is presented to describe the hydrodynamic properties of several cetacean flippers. It was found that flippers of similar planform shape had similar hydrodynamic performance properties. Furthermore, one group of flippers of planform shape similar to modern swept wings was found to have lift coefficients that increased with angle of attack nonlinearly, which was caused by the onset of vortex-dominated lift. Drag coefficient versus angle of attack curves were found to be less dependent on planform shape. Larger cetacean flippers were found to have degraded performance at a Re of 250,000 compared to flippers of smaller odontocetes, while performance of larger and smaller cetacean flippers was similar at a swim speed of 2 m/s. Idealization of the planforms of cetacean flippers was found to capture the relevant hydrodynamic effects of the real flippers, although unintended consequences such as the lift curve slope changing from linear to nonlinear were sometimes observed. A numerical study of an idealized model of the humpback whale flipper showed that the leading-edge tubercles delay stall compared to a baseline (no tubercle) flipper because larger portions of the flow remaining attached at higher angles of attack. </p><p>The third project discussed is optimization of CT/MRI protocols. In order to optimize contrast material administration protocols for Computed Tomography (CT) and Magnetic Resonance Imaging (MRI), a custom-built physiologic flow phantom was constructed to model flow in the human body. This flow phantom was used to evaluate the effect of varying volumes, rates, and types of contrast material, use of a saline chase, and cardiac output on aortic enhancement characteristics. For CT, reducing the volume of contrast material decreased duration peak enhancement and reduced the maximum value of peak enhancement. Increasing the rate of contrast media administration increased peak enhancement and decreased duration of peak enhancement. Use of a saline chase resulted in an increase in peak enhancement. Peak aortic enhancement increased when reduced cardiac output was simulated. For MRI, when the same volume of contrast material was injected at the same rate, the type of contrast material used has a significant effect on the greatest peak signal intensity and duration peak signal intensity. A higher injection rate of saline chaser is more advantageous than a larger volume of saline chaser to increase the peak aortic signal intensity using low contrast material doses. Furthermore, for higher volumes of contrast material, the effect of increasing the volume of saline chaser makes almost no difference while increasing the rate of injection makes a significant difference. When a saline chaser with a high injection rate is used, the dose of the contrast material may be reduced by 25-50% and more than 86% of the non-reduced dose peak aortic enhancement will be attained.</p><p>The next project discussed is evaluation of modified angiocatheters. In this study, a standard peripheral end hole angiocatheter was compared to those modified with side holes or side slits by using experimental techniques to qualitatively compare the contrast material exit jets, and by using numeric techniques to provide flow visualization and quantitative comparisons. A Schlieren imaging system was used to visualize the angiocatheter exit jet fluid dynamics at two different flow rates, and a commercial computational fluid dynamics (CFD) package was used to calculate numeric results for various catheter orientations and vessel diameters. Experimental images showed that modifying standard peripheral intravenous angiocatheters with side holes or side slits qualitatively changed the overall flow field and caused the exiting jet to become less well-defined. Numeric calculations showed that the addition of side holes or slits resulted in a 9-30% reduction of the velocity of contrast material exiting the end hole of the angiocatheter. With the catheter tip directed obliquely to the wall, the maximum wall shear stress was always highest for the unmodified catheter and always lowest for the 4 side slit catheter. Modified angiocatheters may have the potential to reduce extravasation events in patients by reducing vessel wall shear stress. </p><p>The next project discussed involves studying the effect of leading-edge tubercles on cavitation characteristics for marine rudders. Three different rudders were constructed and tested in a water tunnel: baseline, 3-tubercle leading edge, and 5-tubercle leading edge. In the linear (non-stall) regime, tubercled rudders performed equally to the smooth rudder. Hydrodynamic stall occurred at smaller angles of attack for the tubercled rudders than for the smooth rudder. When stall did occur, it was more gradual for the tubercled rudders, whereas the smooth rudder demonstrated a more dramatic loss of lift. At lower Re, the tubercled rudders also maintained a higher value of lift post-stall than the smooth rudder. Cavitation onset for the tubercled rudders occurred at lower angles of attack and higher values of cavitation number than for the smooth rudder, but cavities on the tubercled rudders were localized in the slots as opposed to the smooth rudder where the cavity spread across the entire leading edge. </p><p>In the final project discussed, modeling of mass transfer in amphibian cone outer segments, a detailed derivation of a simplified (continuum, one-dimensional) mathematical model for the radio-labeled opsin density profile in the amphibian cone outer segment is presented. This model relies on only one free parameter, which was the mass transfer coefficient between the plasmalemma and disc region. The descriptive equations were nondimensionalized, and scale analysis showed that advective effects could be neglected as a first approximation for early times so that a simplified system could be obtained. Through numeric computation the solution behavior was found to have three distinct stages. The first stage was marked by diffusion in the plasmalemma and no mass transfer in the disc region. The second stage first involved the plasmalemma reaching a metastable state whereas the disc region density increased, then involved both the plasmalemma and disc regions increasing in density with their distributions being qualitatively the same. The final stage involved a slow relaxation to the steady-state solution.</p> / Dissertation