Novel Statistical Methodologies in Analysis of Position Emission Tomography Data: Applications in Segmentation, Normalization, and Trajectory Modeling

Position emission tomography (PET) is a powerful functional imaging modality with wide uses in fields such as oncology, cardiology, and neurology. Motivated by imaging datasets from a psoriasis clinical trial and a cohort of Alzheimer\u27s disease (AD) patients, several interesting methodological challenges were identified in various steps of quantitative analysis of PET data. In Chapter 1, we consider a classification scenario of bivariate thresholding of a predictor using an upper and lower cutpoints, as motivated by an image segmentation problem of the skin. We introduce a generalization of ROC analysis and the concept of the parameter path in ROC space of a classifier. Using this framework, we define the optimal ROC (OROC) to identify and assess performance of optimal classifiers, and describe a novel nonparametric estimation of OROC which simultaneous estimates the parameter path of the optimal classifier. In simulations, we compare its performance to alternative methods of OROC estimation. In Chapter 2, we develop a novel method to normalize PET images as an essential preprocessing step for quantitative analysis. We propose a method based on application of functional data analysis to image intensity distribution functions, assuming that that individual image density functions are variations from a template density. By modeling the warping functions using a modified function-on-scalar regression, the variations in density functions due to nuisance parameters are estimated and subsequently removed for normalization. Application to our motivating data indicate persistence of residual variations in standardized image densities. In Chapter 3, we propose a nonlinear mixed effects framework to model amyloid-beta (Aβ), an important biomarker in AD. We incorporate the hypothesized functional form of Aβ trajectory by assuming a common trajectory model for all subjects with variations in the location parameter, and a mixture distribution for the random effects of the location parameter address our empirical findings that some subjects may not accumulate Aβ. Using a Bayesian hierarchical model, group differences are specified into the trajectory parameters. We show in simulation studies that the model closely estimates the true parameters under various scenarios, and accurately estimates group differences in the age of onset

Bias Momentum Sizing for Hovering Dual-Spin Platforms

An atmospheric flight vehicle in hover is typically controlled by varying its thrust vector. Achieving both levitation and attitude control with the propulsion system places considerable demands on it for agility and precision, particularly if the vehicle is statically unstable, or nearly so. These demands can be relaxed by introducing an appropriately sized angular momentum bias aligned with the vehicle's yaw axis, thus providing an additional margin of attitude stability about the roll and pitch axes. This paper describes a methodical approach for trading off angular momentum bias level needed with desired levels of vehicle response due to the design disturbance environment given a vehicle's physical parameters. It also describes several simplifications that provide a more physical and intuitive understanding of dual-spin dynamics for hovering atmospheric vehicles. This approach also mitigates the need for control torques and inadvertent actuator saturation difficulties in trying to stabilize a vehicle via control torques produced by unsteady aerodynamics, thrust vectoring, and unsteady throttling. Simulation results, based on a subscale laboratory test flying platform, demonstrate significant improvements in the attitude control robustness of the vehicle with respect to both wind disturbances and off-center of gravity payload changes during flight

Cohomology of quantum groups: An analog of Kostant's Theorem

We prove the analog of Kostant's Theorem on Lie algebra cohomology in the context of quantum groups. We prove that Kostant's cohomology formula holds for quantum groups at a generic parameter $q$, recovering an earlier result of Malikov in the case where the underlying semisimple Lie algebra $\mathfrak{g} = \mathfrak{sl}(n)$. We also show that Kostant's formula holds when $q$ is specialized to an $\ell$-th root of unity for odd $\ell \ge h-1$ (where $h$ is the Coxeter number of $\mathfrak{g}$) when the highest weight of the coefficient module lies in the lowest alcove. This can be regarded as an extension of results of Friedlander-Parshall and Polo-Tilouine on the cohomology of Lie algebras of reductive algebraic groups in prime characteristic.Comment: 12 page

Effect of psoriasis severity on hypertension control: a population-based study in the United Kingdom.

IMPORTANCE: Hypertension is prevalent among patients with psoriasis. The effect of psoriasis and its severity on hypertension control is unknown. OBJECTIVE: To determine the association between uncontrolled blood pressure and psoriasis, both overall and according to objectively measured psoriasis severity, among patients with diagnosed hypertension. DESIGN, SETTING, AND PARTICIPANTS: Population-based cross-sectional study nested in a prospective cohort drawn from The Health Improvement Network (THIN), an electronic medical records database broadly representative of the general population in the United Kingdom. The study population included a random sample of patients with psoriasis (n = 1322) between the ages of 25 and 64 years in THIN who were included in the Incident Health Outcomes and Psoriasis Events prospective cohort and their age- and practice-matched controls without psoriasis (n = 11,977). All included patients had a diagnosis of hypertension; their psoriasis diagnosis was confirmed and disease severity was classified by their general practitioners. MAIN OUTCOMES AND MEASURES: Uncontrolled hypertension was defined as a systolic blood pressure of 140 mm Hg or higher or a diastolic blood pressure of 90 mm Hg or higher based on the blood pressure recorded closest in time to the assessment of psoriasis severity. RESULTS: There was a significant positive dose-response relationship between uncontrolled hypertension and psoriasis severity as objectively determined by the affected body surface area in both unadjusted and adjusted analyses that controlled for age, sex, body mass index, smoking and alcohol use status, presence of comorbid conditions, and current use of antihypertensive medications and nonsteroidal anti-inflammatory drugs (adjusted odds ratio [aOR], 0.97; 95% CI, 0.82-1.14 for mild psoriasis; aOR, 1.20; 95% CI, 0.99-1.45 for moderate psoriasis; and aOR, 1.48; 95% CI, 1.08-2.04 for severe psoriasis; P = .01 for trend). The likelihood of uncontrolled hypertension among psoriasis overall was also increased, although not statistically significantly so (aOR, 1.10; 95% CI, 0.98-1.24). CONCLUSIONS AND RELEVANCE: Among patients with hypertension, psoriasis was associated with a greater likelihood of uncontrolled hypertension in a dose-dependent manner, with the greatest likelihood observed among those with moderate to severe psoriasis defined by 3% or more of the body surface area affected. Our data suggest a need for more effective blood pressure management, particularly among patients with more severe psoriasis

Nociceptive interneurons control modular motor pathways to promote escape behavior in Drosophila.

Rapid and efficient escape behaviors in response to noxious sensory stimuli are essential for protection and survival. Yet, how noxious stimuli are transformed to coordinated escape behaviors remains poorly understood. In Drosophila larvae, noxious stimuli trigger sequential body bending and corkscrew-like rolling behavior. We identified a population of interneurons in the nerve cord of Drosophila, termed Down-and-Back (DnB) neurons, that are activated by noxious heat, promote nociceptive behavior, and are required for robust escape responses to noxious stimuli. Electron microscopic circuit reconstruction shows that DnBs are targets of nociceptive and mechanosensory neurons, are directly presynaptic to pre-motor circuits, and link indirectly to Goro rolling command-like neurons. DnB activation promotes activity in Goro neurons, and coincident inactivation of Goro neurons prevents the rolling sequence but leaves intact body bending motor responses. Thus, activity from nociceptors to DnB interneurons coordinates modular elements of nociceptive escape behavior

Nociceptive interneurons control modular motor pathways to promote escape behavior in Drosophila

Rapid and efficient escape behaviors in response to noxious sensory stimuli are essential for protection and survival. Yet, how noxious stimuli are transformed to coordinated escape behaviors remains poorly understood. In Drosophila larvae, noxious stimuli trigger sequential body bending and corkscrew-like rolling behavior. We identified a population of interneurons in the nerve cord of Drosophila, termed Down-and-Back (DnB) neurons, that are activated by noxious heat, promote nociceptive behavior, and are required for robust escape responses to noxious stimuli. Electron microscopic circuit reconstruction shows that DnBs are targets of nociceptive and mechanosensory neurons, are directly presynaptic to pre-motor circuits, and link indirectly to Goro rolling command-like neurons. DnB activation promotes activity in Goro neurons, and coincident inactivation of Goro neurons prevents the rolling sequence but leaves intact body bending motor responses. Thus, activity from nociceptors to DnB interneurons coordinates modular elements of nociceptive escape behavior