Matching Items (109)
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
The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system, with a projective Hilbert space regarded as the phase space. This thesis extends the theory by including some aspects of the symplectic topology of the quantum phase space. It is shown that the quantum mechanical uncertainty principle is a special case of an inequality from J-holomorphic map theory, that is, J-holomorphic curves minimize the difference between the quantum covariance matrix determinant and a symplectic area. An immediate consequence is that a minimal determinant is a topological invariant, within a fixed homology class of the curve. Various choices of quantum operators are studied with reference to the implications of the J-holomorphic condition. The mean curvature vector field and Maslov class are calculated for a lagrangian torus of an integrable quantum system. The mean curvature one-form is simply related to the canonical connection which determines the geometric phases and polarization linear response. Adiabatic deformations of a quantum system are analyzed in terms of vector bundle classifying maps and related to the mean curvature flow of quantum states. The dielectric response function for a periodic solid is calculated to be the curvature of a connection on a vector bundle.
ContributorsSanborn, Barbara (Author) / Suslov, Sergei K (Thesis advisor) / Suslov, Sergei (Committee member) / Spielberg, John (Committee member) / Quigg, John (Committee member) / Menéndez, Jose (Committee member) / Jones, Donald (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 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
This dissertation is intended to tie together a body of work which utilizes a variety of methods to study applied mathematical models involving heterogeneity often omitted with classical modeling techniques. I posit three cogent classifications of heterogeneity: physiological, behavioral, and local (specifically connectivity in this work). I consider physiological heterogeneity using the method of transport equations to study heterogeneous susceptibility to diseases in open populations (those with births and deaths). I then present three separate models of behavioral heterogeneity. An SIS/SAS model of gonorrhea transmission in a population of highly active men-who-have-sex-with-men (MSM) is presented to study the impact of safe behavior (prevention and self-awareness) on the prevalence of this endemic disease. Behavior is modeled in this examples via static parameters describing consistent condom use and frequency of STD testing. In an example of behavioral heterogeneity, in the absence of underlying dynamics, I present a generalization to ``test theory without an answer key" (also known as cultural consensus modeling or CCM). CCM is commonly used to study the distribution of cultural knowledge within a population. The generalized framework presented allows for selecting the best model among various extensions of CCM: multiple subcultures, estimating the degree to which individuals guess yes, and making competence homogenous in the population. This permits model selection based on the principle of information criteria. The third behaviorally heterogeneous model studies adaptive behavioral response based on epidemiological-economic theory within an $SIR$ epidemic setting. Theorems used to analyze the stability of such models with a generalized, non-linear incidence structure are adapted and applied to the case of standard incidence and adaptive incidence. As an example of study in spatial heterogeneity I provide an explicit solution to a generalization of the continuous time approximation of the Albert-Barabasi scale-free network algorithm. The solution is found by recursively solving the differential equations via integrating factors, identifying a pattern for the coefficients and then proving this observed pattern is consistent using induction. An application to disease dynamics on such evolving structures is then studied.
ContributorsMorin, Benjamin (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Hiebeler, David (Thesis advisor) / Hruschka, Daniel (Committee member) / Suslov, Sergei (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
Description
Immunosignaturing is a technology that allows the humoral immune response to be observed through the binding of antibodies to random sequence peptides. The immunosignaturing microarray is based on complex mixtures of antibodies binding to arrays of random sequence peptides in a multiplexed fashion. There are computational and statistical challenges to the analysis of immunosignaturing data. The overall aim of my dissertation is to develop novel computational and statistical methods for immunosignaturing data to access its potential for diagnostics and drug discovery. Firstly, I discovered that a classification algorithm Naive Bayes which leverages the biological independence of the probes on our array in such a way as to gather more information outperforms other classification algorithms due to speed and accuracy. Secondly, using this classifier, I then tested the specificity and sensitivity of immunosignaturing platform for its ability to resolve four different diseases (pancreatic cancer, pancreatitis, type 2 diabetes and panIN) that target the same organ (pancreas). These diseases were separated with >90% specificity from controls and from each other. Thirdly, I observed that the immunosignature of type 2 diabetes and cardiovascular complications are unique, consistent, and reproducible and can be separated by 100% accuracy from controls. But when these two complications arise in the same person, the resultant immunosignature is quite different in that of individuals with only one disease. I developed a method to trace back from informative random peptides in disease signatures to the potential antigen(s). Hence, I built a decipher system to trace random peptides in type 1 diabetes immunosignature to known antigens. Immunosignaturing, unlike the ELISA, has the ability to not only detect the presence of response but also absence of response during a disease. I observed, not only higher but also lower peptides intensities can be mapped to antigens in type 1 diabetes. To study immunosignaturing potential for population diagnostics, I studied effect of age, gender and geographical location on immunosignaturing data. For its potential to be a health monitoring technology, I proposed a single metric Coefficient of Variation that has shown potential to change significantly when a person enters a disease state.
ContributorsKukreja, Muskan (Author) / Johnston, Stephen Albert (Thesis advisor) / Stafford, Phillip (Committee member) / Dinu, Valentin (Committee member) / Arizona State University (Publisher)
Created2012
Description
DNA methylation, a subset of epigenetics, has been found to be a significant marker associated with variations in gene expression and activity across the entire human genome. As of now, however, there is little to no information about how DNA methylation varies between different tissues inside a singular person's body. By using research data from a preliminary study of lean and obese clinical subjects, this study attempts to put together a profile of the differences in DNA methylation that can be observed between two particular body tissues from this subject group: blood and skeletal muscle. This study allows us to start describing the changes that occur at the epigenetic level that influence how differently these two tissues operate, along with seeing how these tissues change between individuals of different weight classes, especially in the context of the development of symptoms of Type 2 Diabetes.
ContributorsRappazzo, Micah Gabriel (Author) / Coletta, Dawn (Thesis director) / Katsanos, Christos (Committee member) / Dinu, Valentin (Committee member) / Barrett, The Honors College (Contributor) / Harrington Bioengineering Program (Contributor) / Department of Psychology (Contributor)
Created2013-12