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- Member of: ASU Electronic Theses and Dissertations
Description
Nonlinear dispersive equations model nonlinear waves in a wide range of physical and mathematics contexts. They reinforce or dissipate effects of linear dispersion and nonlinear interactions, and thus, may be of a focusing or defocusing nature. The nonlinear Schrödinger equation or NLS is an example of such equations. It appears as a model in hydrodynamics, nonlinear optics, quantum condensates, heat pulses in solids and various other nonlinear instability phenomena. In mathematics, one of the interests is to look at the wave interaction: waves propagation with different speeds and/or different directions produces either small perturbations comparable with linear behavior, or creates solitary waves, or even leads to singular solutions. This dissertation studies the global behavior of finite energy solutions to the $d$-dimensional focusing NLS equation, $i partial _t u+Delta u+ |u|^{p-1}u=0, $ with initial data $u_0in H^1,; x in Rn$; the nonlinearity power $p$ and the dimension $d$ are chosen so that the scaling index $s=frac{d}{2}-frac{2}{p-1}$ is between 0 and 1, thus, the NLS is mass-supercritical $(s>0)$ and energy-subcritical $(s<1).$ For solutions with $ME[u_0]<1$ ($ME[u_0]$ stands for an invariant and conserved quantity in terms of the mass and energy of $u_0$), a sharp threshold for scattering and blowup is given. Namely, if the renormalized gradient $g_u$ of a solution $u$ to NLS is initially less than 1, i.e., $g_u(0)<1,$ then the solution exists globally in time and scatters in $H^1$ (approaches some linear Schr"odinger evolution as $ttopminfty$); if the renormalized gradient $g_u(0)>1,$ then the solution exhibits a blowup behavior, that is, either a finite time blowup occurs, or there is a divergence of $H^1$ norm in infinite time. This work generalizes the results for the 3d cubic NLS obtained in a series of papers by Holmer-Roudenko and Duyckaerts-Holmer-Roudenko with the key ingredients, the concentration compactness and localized variance, developed in the context of the energy-critical NLS and Nonlinear Wave equations by Kenig and Merle. One of the difficulties is fractional powers of nonlinearities which are overcome by considering Besov-Strichartz estimates and various fractional differentiation rules.
ContributorsGuevara, Cristi Darley (Author) / Roudenko, Svetlana (Thesis advisor) / Castillo_Chavez, Carlos (Committee member) / Jones, Donald (Committee member) / Mahalov, Alex (Committee member) / Suslov, Sergei (Committee member) / Arizona State University (Publisher)
Created2011
Description
In an effort to begin validating the large number of discovered candidate biomarkers, proteomics is beginning to shift from shotgun proteomic experiments towards targeted proteomic approaches that provide solutions to automation and economic concerns. Such approaches to validate biomarkers necessitate the mass spectrometric analysis of hundreds to thousands of human samples. As this takes place, a serendipitous opportunity has become evident. By the virtue that as one narrows the focus towards "single" protein targets (instead of entire proteomes) using pan-antibody-based enrichment techniques, a discovery science has emerged, so to speak. This is due to the largely unknown context in which "single" proteins exist in blood (i.e. polymorphisms, transcript variants, and posttranslational modifications) and hence, targeted proteomics has applications for established biomarkers. Furthermore, besides protein heterogeneity accounting for interferences with conventional immunometric platforms, it is becoming evident that this formerly hidden dimension of structural information also contains rich-pathobiological information. Consequently, targeted proteomics studies that aim to ascertain a protein's genuine presentation within disease- stratified populations and serve as a stepping-stone within a biomarker translational pipeline are of clinical interest. Roughly 128 million Americans are pre-diabetic, diabetic, and/or have kidney disease and public and private spending for treating these diseases is in the hundreds of billions of dollars. In an effort to create new solutions for the early detection and management of these conditions, described herein is the design, development, and translation of mass spectrometric immunoassays targeted towards diabetes and kidney disease. Population proteomics experiments were performed for the following clinically relevant proteins: insulin, C-peptide, RANTES, and parathyroid hormone. At least thirty-eight protein isoforms were detected. Besides the numerous disease correlations confronted within the disease-stratified cohorts, certain isoforms also appeared to be causally related to the underlying pathophysiology and/or have therapeutic implications. Technical advancements include multiplexed isoform quantification as well a "dual- extraction" methodology for eliminating non-specific proteins while simultaneously validating isoforms. Industrial efforts towards widespread clinical adoption are also described. Consequently, this work lays a foundation for the translation of mass spectrometric immunoassays into the clinical arena and simultaneously presents the most recent advancements concerning the mass spectrometric immunoassay approach.
ContributorsOran, Paul (Author) / Nelson, Randall (Thesis advisor) / Hayes, Mark (Thesis advisor) / Ros, Alexandra (Committee member) / Williams, Peter (Committee member) / Arizona State University (Publisher)
Created2011
Description
This thesis outlines the development of a vector retrieval technique, based on data assimilation, for a coherent Doppler LIDAR (Light Detection and Ranging). A detailed analysis of the Optimal Interpolation (OI) technique for vector retrieval is presented. Through several modifications to the OI technique, it is shown that the modified technique results in significant improvement in velocity retrieval accuracy. These modifications include changes to innovation covariance portioning, covariance binning, and analysis increment calculation. It is observed that the modified technique is able to make retrievals with better accuracy, preserves local information better, and compares well with tower measurements. In order to study the error of representativeness and vector retrieval error, a lidar simulator was constructed. Using the lidar simulator a thorough sensitivity analysis of the lidar measurement process and vector retrieval is carried out. The error of representativeness as a function of scales of motion and sensitivity of vector retrieval to look angle is quantified. Using the modified OI technique, study of nocturnal flow in Owens' Valley, CA was carried out to identify and understand uncharacteristic events on the night of March 27th 2006. Observations from 1030 UTC to 1230 UTC (0230 hr local time to 0430 hr local time) on March 27 2006 are presented. Lidar observations show complex and uncharacteristic flows such as sudden bursts of westerly cross-valley wind mixing with the dominant up-valley wind. Model results from Coupled Ocean/Atmosphere Mesoscale Prediction System (COAMPS®) and other in-situ instrumentations are used to corroborate and complement these observations. The modified OI technique is used to identify uncharacteristic and extreme flow events at a wind development site. Estimates of turbulence and shear from this technique are compared to tower measurements. A formulation for equivalent wind speed in the presence of variations in wind speed and direction, combined with shear is developed and used to determine wind energy content in presence of turbulence.
ContributorsChoukulkar, Aditya (Author) / Calhoun, Ronald (Thesis advisor) / Mahalov, Alex (Committee member) / Kostelich, Eric (Committee member) / Huang, Huei-Ping (Committee member) / Phelan, Patrick (Committee member) / Arizona State University (Publisher)
Created2013
Description
Signal processing techniques have been used extensively in many engineering problems and in recent years its application has extended to non-traditional research fields such as biological systems. Many of these applications require extraction of a signal or parameter of interest from degraded measurements. One such application is mass spectrometry immunoassay (MSIA) which has been one of the primary methods of biomarker discovery techniques. MSIA analyzes protein molecules as potential biomarkers using time of flight mass spectrometry (TOF-MS). Peak detection in TOF-MS is important for biomarker analysis and many other MS related application. Though many peak detection algorithms exist, most of them are based on heuristics models. One of the ways of detecting signal peaks is by deploying stochastic models of the signal and noise observations. Likelihood ratio test (LRT) detector, based on the Neyman-Pearson (NP) lemma, is an uniformly most powerful test to decision making in the form of a hypothesis test. The primary goal of this dissertation is to develop signal and noise models for the electrospray ionization (ESI) TOF-MS data. A new method is proposed for developing the signal model by employing first principles calculations based on device physics and molecular properties. The noise model is developed by analyzing MS data from careful experiments in the ESI mass spectrometer. A non-flat baseline in MS data is common. The reasons behind the formation of this baseline has not been fully comprehended. A new signal model explaining the presence of baseline is proposed, though detailed experiments are needed to further substantiate the model assumptions. Signal detection schemes based on these signal and noise models are proposed. A maximum likelihood (ML) method is introduced for estimating the signal peak amplitudes. The performance of the detection methods and ML estimation are evaluated with Monte Carlo simulation which shows promising results. An application of these methods is proposed for fractional abundance calculation for biomarker analysis, which is mathematically robust and fundamentally different than the current algorithms. Biomarker panels for type 2 diabetes and cardiovascular disease are analyzed using existing MS analysis algorithms. Finally, a support vector machine based multi-classification algorithm is developed for evaluating the biomarkers' effectiveness in discriminating type 2 diabetes and cardiovascular diseases and is shown to perform better than a linear discriminant analysis based classifier.
ContributorsBuddi, Sai (Author) / Taylor, Thomas (Thesis advisor) / Cochran, Douglas (Thesis advisor) / Nelson, Randall (Committee member) / Duman, Tolga (Committee member) / Arizona State University (Publisher)
Created2012
Description
Cancer claims hundreds of thousands of lives every year in US alone. Finding ways for early detection of cancer onset is crucial for better management and treatment of cancer. Thus, biomarkers especially protein biomarkers, being the functional units which reflect dynamic physiological changes, need to be discovered. Though important, there are only a few approved protein cancer biomarkers till date. To accelerate this process, fast, comprehensive and affordable assays are required which can be applied to large population studies. For this, these assays should be able to comprehensively characterize and explore the molecular diversity of nominally "single" proteins across populations. This information is usually unavailable with commonly used immunoassays such as ELISA (enzyme linked immunosorbent assay) which either ignore protein microheterogeneity, or are confounded by it. To this end, mass spectrometric immuno assays (MSIA) for three different human plasma proteins have been developed. These proteins viz. IGF-1, hemopexin and tetranectin have been found in reported literature to show correlations with many diseases along with several carcinomas. Developed assays were used to extract entire proteins from plasma samples and subsequently analyzed on mass spectrometric platforms. Matrix assisted laser desorption ionization (MALDI) and electrospray ionization (ESI) mass spectrometric techniques where used due to their availability and suitability for the analysis. This resulted in visibility of different structural forms of these proteins showing their structural micro-heterogeneity which is invisible to commonly used immunoassays. These assays are fast, comprehensive and can be applied in large sample studies to analyze proteins for biomarker discovery.
ContributorsRai, Samita (Author) / Nelson, Randall (Thesis advisor) / Hayes, Mark (Thesis advisor) / Borges, Chad (Committee member) / Ros, Alexandra (Committee member) / Arizona State University (Publisher)
Created2012
Description
It is possible in a properly controlled environment, such as industrial metrology, to make significant headway into the non-industrial constraints on image-based position measurement using the techniques of image registration and achieve repeatable feature measurements on the order of 0.3% of a pixel, or about an order of magnitude improvement on conventional real-world performance. These measurements are then used as inputs for a model optimal, model agnostic, smoothing for calibration of a laser scribe and online tracking of velocimeter using video input. Using appropriate smooth interpolation to increase effective sample density can reduce uncertainty and improve estimates. Use of the proper negative offset of the template function has the result of creating a convolution with higher local curvature than either template of target function which allows improved center-finding. Using the Akaike Information Criterion with a smoothing spline function it is possible to perform a model-optimal smooth on scalar measurements without knowing the underlying model and to determine the function describing the uncertainty in that optimal smooth. An example of empiric derivation of the parameters for a rudimentary Kalman Filter from this is then provided, and tested. Using the techniques of Exploratory Data Analysis and the "Formulize" genetic algorithm tool to convert the spline models into more accessible analytic forms resulted in stable, properly generalized, KF with performance and simplicity that exceeds "textbook" implementations thereof. Validation of the measurement includes that, in analytic case, it led to arbitrary precision in measurement of feature; in reasonable test case using the methods proposed, a reasonable and consistent maximum error of around 0.3% the length of a pixel was achieved and in practice using pixels that were 700nm in size feature position was located to within ± 2 nm. Robust applicability is demonstrated by the measurement of indicator position for a King model 2-32-G-042 rotameter.
ContributorsMunroe, Michael R (Author) / Phelan, Patrick (Thesis advisor) / Kostelich, Eric (Committee member) / Mahalov, Alex (Committee member) / Arizona State University (Publisher)
Created2012
Description
Infrastructure systems are facing non-stationary challenges that stem from climate change and the increasingly complex interactions between the social, ecological, and technological systems (SETSs). It is crucial for transportation infrastructures—which enable residents to access opportunities and foster prosperity, quality of life, and social connections—to be resilient under these non-stationary challenges. Vulnerability assessment (VA) examines the potential consequences a system is likely to experience due to exposure to perturbation or stressors and lack of the capacity to adapt. Post-fire debris flow and heat represent particularly challenging problems for infrastructure and users in the arid U.S. West. Post-fire debris flow, which is manifested with heat and drought, produces powerful runoff threatening physical transportation infrastructures. And heat waves have devastating health effects on transportation infrastructure users, including increased mortality rates. VA anticipates the potential consequences of these perturbations and enables infrastructure stakeholders to improve the system's resilience. The current transportation climate VA—which only considers a single direct climate stressor on the infrastructure—falls short of addressing the wildfire and heat challenges. This work proposes advanced transportation climate VA methods to address the complex and multiple climate stressors and the vulnerability of infrastructure users. Two specific regions were chosen to carry out the progressive transportation climate VA: 1) the California transportation networks’ vulnerability to post-fire debris flows, and 2) the transportation infrastructure user’s vulnerability to heat exposure in Phoenix.
ContributorsLi, Rui (Author) / Chester, Mikhail V. (Thesis advisor) / Middel, Ariane (Committee member) / Hondula, David M. (Committee member) / Pendyala, Ram (Committee member) / Arizona State University (Publisher)
Created2022
Description
This work presents a thorough analysis of reconstruction of global wave fields (governed by the inhomogeneous wave equation and the Maxwell vector wave equation) from sensor time series data of the wave field. Three major problems are considered. First, an analysis of circumstances under which wave fields can be fully reconstructed from a network of fixed-location sensors is presented. It is proven that, in many cases, wave fields can be fully reconstructed from a single sensor, but that such reconstructions can be sensitive to small perturbations in sensor placement. Generally, multiple sensors are necessary. The next problem considered is how to obtain a global approximation of an electromagnetic wave field in the presence of an amplifying noisy current density from sensor time series data. This type of noise, described in terms of a cylindrical Wiener process, creates a nonequilibrium system, derived from Maxwell’s equations, where variance increases with time. In this noisy system, longer observation times do not generally provide more accurate estimates of the field coefficients. The mean squared error of the estimates can be decomposed into a sum of the squared bias and the variance. As the observation time $\tau$ increases, the bias decreases as $\mathcal{O}(1/\tau)$ but the variance increases as $\mathcal{O}(\tau)$. The contrasting time scales imply the existence of an ``optimal'' observing time (the bias-variance tradeoff). An iterative algorithm is developed to construct global approximations of the electric field using the optimal observing times. Lastly, the effect of sensor acceleration is considered. When the sensor location is fixed, measurements of wave fields composed of plane waves are almost periodic and so can be written in terms of a standard Fourier basis. When the sensor is accelerating, the resulting time series is no longer almost periodic. This phenomenon is related to the Doppler effect, where a time transformation must be performed to obtain the frequency and amplitude information from the time series data. To obtain frequency and amplitude information from accelerating sensor time series data in a general inhomogeneous medium, a randomized algorithm is presented. The algorithm is analyzed and example wave fields are reconstructed.
ContributorsBarclay, Bryce Matthew (Author) / Mahalov, Alex (Thesis advisor) / Kostelich, Eric J (Thesis advisor) / Moustaoui, Mohamed (Committee member) / Motsch, Sebastien (Committee member) / Platte, Rodrigo (Committee member) / Arizona State University (Publisher)
Created2023
Description
Machine learning (ML) and deep learning (DL) has become an intrinsic part of multiple fields. The ability to solve complex problems makes machine learning a panacea. In the last few years, there has been an explosion of data generation, which has greatly improvised machine learning models. But this comes with a cost of high computation, which invariably increases power usage and cost of the hardware. In this thesis we explore applications of ML techniques, applied to two completely different fields - arts, media and theater and urban climate research using low-cost and low-powered edge devices. The multi-modal chatbot uses different machine learning techniques: natural language processing (NLP) and computer vision (CV) to understand inputs of the user and accordingly perform in the play and interact with the audience. This system is also equipped with other interactive hardware setups like movable LED systems, together they provide an experiential theatrical play tailored to each user. I will discuss how I used edge devices to achieve this AI system which has created a new genre in theatrical play. I will then discuss MaRTiny, which is an AI-based bio-meteorological system that calculates mean radiant temperature (MRT), which is an important parameter for urban climate research. It is also equipped with a vision system that performs different machine learning tasks like pedestrian and shade detection. The entire system costs around $200 which can potentially replace the existing setup worth $20,000. I will further discuss how I overcame the inaccuracies in MRT value caused by the system, using machine learning methods. These projects although belonging to two very different fields, are implemented using edge devices and use similar ML techniques. In this thesis I will detail out different techniques that are shared between these two projects and how they can be used in several other applications using edge devices.
ContributorsKulkarni, Karthik Kashinath (Author) / Jayasuriya, Suren (Thesis advisor) / Middel, Ariane (Thesis advisor) / Yu, Hongbin (Committee member) / Arizona State University (Publisher)
Created2021
Description
Cities globally are experiencing substantial warming due to ongoing urbanization and climate change. However, existing efforts to mitigate urban heat focus mainly on new technologies, exacerbate social injustices, and ignore the need for a sustainability lens that considers environmental, social, and economic perspectives. Heat in urban areas is amplified and urgently needs to be considered as a critical sustainability issue that crosses disciplinary and sectoral (traditional) boundaries. The missing urgency is concerning because urban overheating is a multi-faceted threat to the well-being and performance of individuals as well as the energy efficiency and economy of cities. Urban heat consequences require transformation in ways of thinking by involving the best available knowledge engaging scientists, policymakers, and communities. To do so, effective heat mitigation planning requires a considerable amount of diverse knowledge sources, yet urban planners face multiple barriers to effective heat mitigation, including a lack of usable, policy-relevant science and governance structures. To address these issues, transdisciplinary approaches, such as co-production via partnerships and the creation of usable, policy-relevant science, are necessary to allow for sustainable and equitable heat mitigation that allow cities to work toward multiple Sustainable Development Goals (SDGs) using a systems approach. This dissertation presents three studies that contribute to a sustainability lens on urban heat, improve the holistic and multi-perspective understanding of heat mitigation strategies, provide contextual guidance for reflective pavement as a heat mitigation strategy, and evaluate a multilateral, sustainability-oriented, co-production partnership to foster heat resilience equitably in cities. Results show that science and city practice communicate differently about heat mitigation strategies while both avoid to communicate disservices and trade-offs. Additionally, performance evaluation of heat mitigation strategies for decision-making needs to consider multiple heat metrics, people, and background climate. Lastly, the partnership between science, city practice, and community needs to be evaluated to be accountable and provide a pathway of growth for all partners. The outcomes of this dissertation advance research and awareness of urban heat for science, practice, and community, and provide guidance to improve holistic and sustainable decision-making in cities and partnerships to address SDGs around urban heat.
ContributorsSchneider, Florian Arwed (Author) / Middel, Ariane (Thesis advisor) / Vanos, Jennifer K (Committee member) / Withycombe Keeler, Lauren (Committee member) / Arizona State University (Publisher)
Created2023