This dissertation focuses on several issues pertaining to three-state progressive stochastic processes. Casting survival data within a three-state framework is an effective way to incorporate intermediate events into an analysis. These events can yield valuable insights into treatment interventions and the natural history of a process, especially when the right censoring is heavy. Exploiting the uni-directional nature of these processes allows for more effective modelling of the types of incomplete data commonly encountered in practice, as well as time-dependent explanatory variables and different time scales. In Chapter 2, we extend the model developed by Frydman (1995) by incorporating explanatory variables and by permitting interval censoring for the time to the terminal event. The resulting model is quite general and combines features of the models proposed by Frydman (1995) and Kim <i>et al</i>. (1993). The decomposition theorem of Gu (1996) is used to show that all of the estimating equations arising from Frydman's log likelihood function are self-consistent. An AIDS data set analyzed by these authors is used to illustrate our regression approach. Estimating the standard errors of our regression model parameters, by adopting a piecewise constant approach for the baseline intensity parameters, is the focus of Chapter 3. We also develop data-driven algorithms which select changepoints for the intervals of support, based on the Akaike and Schwarz Information Criteria. A sensitivity study is conducted to evaluate these algorithms. The AIDS example is considered here once more; standard errors are estimated for several piecewise constant regression models selected by the model criteria. Our results indicate that for both the example and the sensitivity study, the resulting estimated standard errors of certain model parameters can be quite large. Chapter 4 evaluates the goodness-of-link function for the transition intensity between states 2 and 3 in the regression model we introduced in chapter 2. By embedding this hazard function in a one-parameter family of hazard functions, we can assess its dependence on the specific parametric form adopted. In a simulation study, the goodness-of-link parameter is estimated and its impact on the regression parameters is assessed. The logistic specification of the hazard function from state 2 to state 3 is appropriate for the discrete, parametric-based data sets considered, as well as for the AIDS data. We also investigate the uniqueness and consistency of the maximum likelihood estimates based on our regression model for these AIDS data. In Chapter 5 we consider the possible efficiency gains realized in estimating the survivor function when an intermediate auxiliary variable is incorporated into a time-to-event analysis. Both Markov and hybrid time scale frameworks are adopted in the resulting progressive three-state model. We consider three cases for the amount of information available about the auxiliary variable: the observation is completely unknown, known exactly, or known to be within an interval of time. In the Markov framework, our results suggest that observing subjects at just two time points provides as much information about the survivor function as knowing the exact time of the intermediate event. There was generally a greater loss of efficiency in the hybrid time setting. The final chapter identifies some directions for future research.

There have been reports on the use of Ultrasound (US) for monitoring fracture repair and for measuring muscle volume. Change in muscle mass is a useful bio-marker for monitoring the use and disuse of muscle, and the affects of age, disease and injury. The main modality for imaging bone is X-ray and for muscle volume Magnetic Resonance (MR). Previous studies have shown US to have advantages over X-ray and MR. US can image all stages of the fracture repair process and can detect signs of healing 4-6 weeks before X-ray allowing earlier detection of possible complications. Compared to MR, US is less resource intensive, easier to access and also has fewer exclusion criteria for patients. Despite these advantages, the limited field of view that US can provide results in high operator dependency for scan interpretation and also for length and volume measurements. Three-dimensional Ultrasound (3D US) has been developed to overcome these limitations and has been used to provide extended field of view images of the foetus and the heart and to obtain accurate volume measurements for organs. In this thesis it is hypothesized that 3D US can provide a more comprehensive method of imaging fracture repair than X-ray and is also a viable alternative to MR for determining muscle volumes in vivo. Initially, an electromagnetically (EM) tracked 3D US system was evaluated for clinical use using phantom-based experiments. It was found that the presence of metal objects in or near the EM field caused distortion and resulted in errors in the volume measurements of phantoms of up to ±20%. An optically tracked system was also evaluated and it was found that length measurements of a phantom could be made to within ±1.3%. Fracture repair was monitored in five patients with lower limb fractures. Signs of healing were visible earlier on 3D US with a notable, although variable, lag between callus development on X-ray compared to 3D US. 3D US provided a clearer view of callus formation and the changes in density of the callus as it matured. Additional information gained by applying image processing methods to the 3D US data was used to develop a measure of callus density and to identify the frequency dependent appearance of the callus. Volume measurements of the rectus femoris quadricep muscle were obtained using 3DUS from eleven healthy volunteers and were validated against volume measurements derived using MR. The mean difference between muscle volume measurements obtained using 3D US and MR was 0.53 cm3 with a standard deviation of 1.09 cm3 and 95% confidence intervals of 0.20 - 1.27 cm3 In conclusion, 3D US demonstrates great potential as a tool for imaging components of the musculoskeletal system and as means of measuring callus density.

<p>Fibronectin (FN) is a large extracellular matrix (ECM) protein that is made up of</p><p>type I (FNI), type II (FNII), & type III (FNIII) domains. It assembles into an insoluble</p><p>supra-­‐‑molecular structure: the fibrillar FN matrix. FN fibrillogenesis is a cell‐‑mediated process, which is initiated when FN binds to integrins on the cell surface. The FN matrix plays an important role in cell migration, proliferation, signaling & adhesion. Despite decades of research, the FN matrix is one of the least understood supra-­‐‑molecular protein assemblies. There have been several attempts to elucidate the exact mechanism of matrix assembly resulting in significant progress in the field but it is still unclear as to what are FN-­‐‑FN interactions, the nature of these interactions and the domains of FN that</p><p>are in contact with each other. FN matrix fibrils are elastic in nature. Two models have been proposed to explain the elasticity of the fibrils. The first model: the ‘domain unfolding’ model postulates that the unraveling of FNIII domains under tension explains fibril elasticity.</p><p>The second model relies on the conformational change of FN from compact to extended to explain fibril elasticity. FN contain 15 FNIII domains, each a 7-­‐‑strand beta sandwich. Earlier work from our lab used the technique of labeling a buried Cys to study the ‘domain unfolding’ model. They used mutant FNs containing a buried Cys in a single FNIII domain and found that 6 of the 15 FNIII domains label in matrix fibrils. Domain unfolding due to tension, matrix associated conformational changes or spontaneous folding and unfolding are all possible explanation for labeling of the buried Cys. The present study also uses the technique of labeling a buried Cys to address whether it is spontaneous folding and unfolding that labels FNIII domains in cell culture. We used thiol reactive DTNB to measure the kinetics of labeling of buried Cys in eleven FN III domains over a wide range of urea concentrations (0-­‐‑9M). The kinetics data were globally fit using Mathematica. The results are equivalent to those of H-­‐‑D exchange, and</p><p>provide a comprehensive analysis of stability and unfolding/folding kinetics of each</p><p>domain. For two of the six domains spontaneous folding and unfolding is possibly the reason for labeling in cell culture. For the rest of the four domains it is probably matrix associated conformational changes or tension induced unfolding.</p><p>A long-­‐‑standing debate in the protein-­‐‑folding field is whether unfolding rate</p><p>constants or folding rate constants correlate to the stability of a protein. FNIII domains all have the same ß sandwich structure but very different stabilities and amino acid sequences. Our study analyzed the kinetics of unfolding and folding and stabilities of eleven FNIII domains and our results show that folding rate constants for FNIII domains are relatively similar and the unfolding rates vary widely and correlate to stability. FN forms a fibrillar matrix and the FN-­‐‑FN interactions during matrix fibril formation are not known. FNI 1-­‐‑9 or the N-­‐‑ terminal region is indispensible for matrix formation and its major binding partner has been shown to be FNIII 2. Earlier work from our lab, using FRET analysis showed that the interaction of FNI 1-­‐‑9 with a destabilized FNIII 2 (missing the G strand, FNIII 2ΔG) reduces the FRET efficiency. This efficiency is restored in the presence of FUD (bacterial adhesion from S. pyogenes) that has been known to interact with FNI 1-­‐‑9 via a tandem ß zipper. In the present study we</p><p>use FRET analysis and a series of deletion mutants of FNIII 2ΔG to study the shortest fragment of FNIII 2ΔG that is required to bind FNI 1-­‐‑9. Our results presented here are qualitative and show that FNIII 2ΔC’EFG is the shortest fragment required to bind FNI 1-­‐‑9. Deletion of one more strand abolishes the interaction with FNI 1-­‐‑9.</p> / Dissertation

Approved for public release, distribution unlimited / With the unveiling of ForceNet, the Navy's architectural framework for how naval warfare is to be conducted in the information age, much of the technological focus has been placed on Web technology. One of the most promising technologies is Web services. Web services provide for a standard way to move and share data more reliably, securely, and quickly. The capabilities imbedded in Extensible Markup Language (XML) and Simple Object Access Protocol (SOAP) can merge previously disparate systems into one integrated environment. Already proven successful in the administrative realm, wide-area networks such as the Secure Internet Protocol Network (SIPRNET) have become secure and reliable enough to pass data between systems and units to support tactical operations. The Modeling, Virtual Environments and Simulation (MOVES) Institute at the Naval Postgraduate School is currently working to extend these precepts into the modeling and simulation world under the Extensible Modeling and Simulation Framework (XMSF) project. By leveraging existing Web service technology, warfighters at the "tip of the spear" can have access to previously unrealized amounts of tactically-relevant data, analysis, and planning tools. The goal of this thesis is to apply the XMSF and Extensible 3D (X3D) graphics to the field of sonar visualization. Undersea warfare is a complex operation that requires a continuous and detailed analysis of the acoustic environment. Tactical sensor employment without a firm understanding of the complete undersea picture can lead to fatal consequences. The Navy has spent significant resources to develop training systems and tactical decision aids in an effort to integrate training, rehearsal and execution. Unfortunately, many of the high-resolution analysis tools that can provide high-resolution sonar prediction results are not easily accessible to the fleet. By taking advantage of Web services and XMSF technology, warfighters will need only access to the network to be able to pull real-time environmental analysis data from large databases, remotely run sonar prediction models on supercomputers, and view detailed three-dimensional (3D) virtual worlds that visualize the undersea picture.

A fairly general method for studying electromagnetic induction in cases where any lateral variations in conductivity are confined to the near-surface region is developed using the thin-sheet technique. The significant feature is that extended anomalies, subject only to the restriction that well-defined two-dimensional problems are approached at infinity, can be handled. The approximate boundary condition is that gradients parallel to the coordinate axes vanish at infinity. / Graduate

The problem and purpose of this paper is to develop Lane's Integral in two-space, and then to expand these concepts into three-space and n-space. Lane's Integral can be used by both mathematicians and statisticians as one of the tools in the calculation of certain probabilities and expectations. The method of presentation is straightforward with the basic concepts of integration theory and Stieltjes Integral assumed.

The problem encountered in this study was threefold: 1. To analyze the field of engineering models used in design studies and identify and define the way in which they are applied to product development. 2. To determine the degree and extent of skills and knowledge necessary for constructing engineering models. 3. To compare the skills and knowledge associated with model building to course content offered in industrial arts.

The aim of this study is to seek to determine the philosophic grounds which prompt this painter in particular to incorporate both two- and three-dimensional space within each painting.

Ryanodine receptors (RyR) are intracellular channels that are intricately involved in Ca2+ release. These channels large membrane proteins~2.26MDa in size. In this multi-goal project firstly we successfully studied the gating mechanics of the RyR1 in the presence of Mg2+. We used single particle reconstruction and image processing techniques to obtain the 3D structure of the RyR1 with Mg2+. The 3D structure in the presence of Mg2+ and an ATP analog is the closest representation of human physiological conditions. The open and closed state structures of RyR1 are known. However, the physiologically closed state has not been studied before. Understanding this structure will help in the understanding of protein interactions. Our second goal was the validation of this 3D structure under different levels of noise. Validation under different noise levels analyzed the problem of noise bias is present in the field of cryo-EM and single particle reconstruction in select cases.

Approved for public release; distribution is unlimited. / Inverse Synthetic Aperture Radar (ISAR) provides full range detection and classification of sea and air based targets through two-dimensional range-Doppler imaging. The Naval Postgraduate School has developed a custom integrated circuit that can simulate false ISAR images in order to fool enemy ISAR platforms. To validate specific hardware choices within this design, this thesis explores the effect on image quality of an overflow occurring within the final 16-bit summation adder of this circuit. Three solutions to the problem of overflows are presented and analyzed. The logical extension of ISAR development, that of three-dimensional target imaging, is next presented through the discussion of 3D monopulse radar, 3D interferometric ISAR, and a 3D, three receiver ISAR. The relative strengths of each approach are compared, along with both MATLAB and X3D software models created for one specific 3D ISAR implementation. Through the superposition of 2D ISAR images it is shown how 3D ISAR images may be created. Moreover, emphasis is placed on using this knowledge to both enhance current 2D ISAR techniques and to modify the false-target chip to handle 3D ISAR return signals. The thesis concludes with a study of Non-Uniform Rational B-Splines, through which the X3D software model was created. / Ensign, United States Naval Reserve