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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 address the lack of literature in on-campus active travel, this study aims to investigate the following primary questions:<br/>• What are the modes that students use to travel on campus?<br/>• What are the motivations that underlie the mode choice of students on campus?<br/>My first stage of research involved a series of qualitative investigations. I held one-on-one virtual interviews with students in which I asked them questions about the mode they use and why they feel that their chosen mode works best for them. These interviews served two functions. First, they provided me with insight into the various motivations underlying student mode choice. Second, they provided me with an indication of what explanatory variables should be included in a model of mode choice on campus.<br/>The first half of the research project informed a quantitative survey that was released via the Honors Digest to attract student respondents. Data was gathered on travel behavior as well as relevant explanatory variables.<br/>My analysis involved developing a logit model to predict student mode choice on campus and presenting the model estimation in conjunction with a discussion of student travel motivations based on the qualitative interviews. I use this information to make a recommendation on how campus infrastructure could be modified to better support the needs of the student population.
ContributorsMirtich, Laura Christine (Author) / Salon, Deborah (Thesis director) / Fang, Kevin (Committee member) / School of Public Affairs (Contributor) / School of Life Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
Nucleosomes are the basic repetitive unit of eukaryotic chromatin and are responsible for packing DNA inside the nucleus of the cell. They consist of a complex of eight histone proteins (two copies of four proteins H2A, H2B, H3 and H4) around which 147 base pairs of DNA are wrapped in ~1.67 superhelical turns. Although the nucleosomes are stable protein-DNA complexes, they undergo spontaneous conformational changes that occur in an asynchronous fashion. This conformational dynamics, defined by the "site-exposure" model, involves the DNA unwrapping from the protein core and exposing itself transiently before wrapping back. Physiologically, this allows regulatory proteins to bind to their target DNA sites during cellular processes like replication, DNA repair and transcription. Traditional biochemical assays have stablished the equilibrium constants for the accessibility to various sites along the length of the nucleosomal DNA, from its end to the middle of the dyad axis. Using fluorescence correlation spectroscopy (FCS), we have established the position dependent rewrapping rates for nucleosomes. We have also used Monte Carlo simulation methods to analyze the applicability of FRET fluctuation spectroscopy towards conformational dynamics, specifically motivated by nucleosome dynamics. Another important conformational change that is involved in cellular processes is the disassembly of nucleosome into its constituent particles. The exact pathway adopted by nucleosomes is still not clear. We used dual color fluorescence correlation spectroscopy to study the intermediates during nucleosome disassembly induced by changing ionic strength. Studying the nature of nucleosome conformational change and the kinetics is very important in understanding gene expression. The results from this thesis give a quantitative description to the basic unit of the chromatin.
ContributorsGurunathan, Kaushik (Author) / Levitus, Marcia (Thesis advisor) / Lindsay, Stuart (Committee member) / Woodbury, Neal (Committee member) / Yan, Hao (Committee member) / Arizona State University (Publisher)
Created2011
Description
Surgery as a profession requires significant training to improve both clinical decision making and psychomotor proficiency. In the medical knowledge domain, tools have been developed, validated, and accepted for evaluation of surgeons' competencies. However, assessment of the psychomotor skills still relies on the Halstedian model of apprenticeship, wherein surgeons are observed during residency for judgment of their skills. Although the value of this method of skills assessment cannot be ignored, novel methodologies of objective skills assessment need to be designed, developed, and evaluated that augment the traditional approach. Several sensor-based systems have been developed to measure a user's skill quantitatively, but use of sensors could interfere with skill execution and thus limit the potential for evaluating real-life surgery. However, having a method to judge skills automatically in real-life conditions should be the ultimate goal, since only with such features that a system would be widely adopted. This research proposes a novel video-based approach for observing surgeons' hand and surgical tool movements in minimally invasive surgical training exercises as well as during laparoscopic surgery. Because our system does not require surgeons to wear special sensors, it has the distinct advantage over alternatives of offering skills assessment in both learning and real-life environments. The system automatically detects major skill-measuring features from surgical task videos using a computing system composed of a series of computer vision algorithms and provides on-screen real-time performance feedback for more efficient skill learning. Finally, the machine-learning approach is used to develop an observer-independent composite scoring model through objective and quantitative measurement of surgical skills. To increase effectiveness and usability of the developed system, it is integrated with a cloud-based tool, which automatically assesses surgical videos upload to the cloud.
ContributorsIslam, Gazi (Author) / Li, Baoxin (Thesis advisor) / Liang, Jianming (Thesis advisor) / Dinu, Valentin (Committee member) / Greenes, Robert (Committee member) / Smith, Marshall (Committee member) / Kahol, Kanav (Committee member) / Patel, Vimla L. (Committee member) / Arizona State University (Publisher)
Created2013
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
Healthy mitochondria are essential for cell survival. Described herein is the synthesis of a family of novel aminoquinone antioxidants designed to alleviate oxidative stress and prevent the impairment of cellular function. In addition, a library of bleomycin disaccharide analogues has also been synthesized to better probe the tumor targeting properties of bleomycin. The first study involves the synthesis of a benzoquinone natural product and analogues that closely resemble the redox core of the natural product geldanamycin. The synthesized 5-amino-3-tridecyl-1,4-benzoquinone antioxidants were tested for their ability to protect Friedreich's ataxia (FRDA) lymphocytes from induced oxidative stress. Some of the analogues synthesized conferred cytoprotection in a dose-dependent manner in FRDA lymphocytes at micromolar concentrations. The biological assays suggest that the modification of the 2-hydroxyl and N-(3-carboxypropyl) groups in the natural product can improve its antioxidant activity and significantly enhance its ability to protect mitochondrial function under conditions of oxidative stress. The second project focused on the synthesis of a library of bleomycin disaccharide-dye conjugates and monitored their cellular uptake by fluorescence microscopy. The studies reveal that the position of the carbamoyl group plays an important role in modulating the cellular uptake of the disaccharide. It also led to the discovery of novel disaccharides with improved tumor selectivity.
ContributorsMathilakathu Madathil, Manikandadas (Author) / Hecht, Sidney M. (Thesis advisor) / Rose, Seth (Committee member) / Woodbury, Neal (Committee member) / Arizona State University (Publisher)
Created2013
Description
This dissertation investigates the condition of skeletal muscle insulin resistance using bioinformatics and computational biology approaches. Drawing from several studies and numerous data sources, I have attempted to uncover molecular mechanisms at multiple levels. From the detailed atomistic simulations of a single protein, to datamining approaches applied at the systems biology level, I provide new targets to explore for the research community. Furthermore I present a new online web resource that unifies various bioinformatics databases to enable discovery of relevant features in 3D protein structures.
ContributorsMielke, Clinton (Author) / Mandarino, Lawrence (Committee member) / LaBaer, Joshua (Committee member) / Magee, D. Mitchell (Committee member) / Dinu, Valentin (Committee member) / Willis, Wayne (Committee member) / Arizona State University (Publisher)
Created2013
Description
The living world we inhabit and observe is extraordinarily complex. From the perspective of a person analyzing data about the living world, complexity is most commonly encountered in two forms: 1) in the sheer size of the datasets that must be analyzed and the physical number of mathematical computations necessary to obtain an answer and 2) in the underlying structure of the data, which does not conform to classical normal theory statistical assumptions and includes clustering and unobserved latent constructs. Until recently, the methods and tools necessary to effectively address the complexity of biomedical data were not ordinarily available. The utility of four methods--High Performance Computing, Monte Carlo Simulations, Multi-Level Modeling and Structural Equation Modeling--designed to help make sense of complex biomedical data are presented here.
ContributorsBrown, Justin Reed (Author) / Dinu, Valentin (Thesis advisor) / Johnson, William (Committee member) / Petitti, Diana (Committee member) / Arizona State University (Publisher)
Created2012
Description
Critical care environments are complex in nature. Fluctuating team dynamics and the plethora of technology and equipment create unforeseen demands on clinicians. Such environments become chaotic very quickly due to the chronic exposure to unpredictable clusters of events. In order to cope with this complexity, clinicians tend to develop ad-hoc adaptations to function in an effective manner. It is these adaptations or "deviations" from expected behaviors that provide insight into the processes that shape the overall behavior of the complex system. The research described in this manuscript examines the cognitive basis of clinicians' adaptive mechanisms and presents a methodology for studying the same. Examining interactions in complex systems is difficult due to the disassociation between the nature of the environment and the tools available to analyze underlying processes. In this work, the use of a mixed methodology framework to study trauma critical care, a complex environment, is presented. The hybrid framework supplements existing methods of data collection (qualitative observations) with quantitative methods (use of electronic tags) to capture activities in the complex system. Quantitative models of activities (using Hidden Markov Modeling) and theoretical models of deviations were developed to support this mixed methodology framework. The quantitative activity models developed were tested with a set of fifteen simulated activities that represent workflow in trauma care. A mean recognition rate of 87.5% was obtained in automatically recognizing activities. Theoretical models, on the other hand, were developed using field observations of 30 trauma cases. The analysis of the classification schema (with substantial inter-rater reliability) and 161 deviations identified shows that expertise and role played by the clinician in the trauma team influences the nature of deviations made (p<0.01). The results shows that while expert clinicians deviate to innovate, deviations of novices often result in errors. Experts' flexibility and adaptiveness allow their deviations to generate innovative ideas, in particular when dynamic adjustments are required in complex situations. The findings suggest that while adherence to protocols and standards is important for novice practitioners to reduce medical errors and ensure patient safety, there is strong need for training novices in coping with complex situations as well.
ContributorsVankipuram, Mithra (Author) / Greenes, Robert A (Thesis advisor) / Patel, Vimla L. (Thesis advisor) / Petitti, Diana B. (Committee member) / Dinu, Valentin (Committee member) / Smith, Marshall L. (Committee member) / Arizona State University (Publisher)
Created2012
Description
This work involved the analysis of a public health system, and the design, development and deployment of enterprise informatics architecture, and sustainable community methods to address problems with the current public health system. Specifically, assessment of the Nationally Notifiable Disease Surveillance System (NNDSS) was instrumental in forming the design of the current implementation at the Southern Nevada Health District (SNHD). The result of the system deployment at SNHD was considered as a basis for projecting the practical application and benefits of an enterprise architecture. This approach has resulted in a sustainable platform to enhance the practice of public health by improving the quality and timeliness of data, effectiveness of an investigation, and reporting across the continuum.
ContributorsKriseman, Jeffrey Michael (Author) / Dinu, Valentin (Thesis advisor) / Greenes, Robert (Committee member) / Johnson, William (Committee member) / Arizona State University (Publisher)
Created2012