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- Genre: Doctoral Dissertation
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
Surface plasmon resonance (SPR) has emerged as a popular technique for elucidating subtle signals from biological events in a label-free, high throughput environment. The efficacy of conventional SPR sensors, whose signals are mass-sensitive, diminishes rapidly with the size of the observed target molecules. The following work advances the current SPR sensor paradigm for the purpose of small molecule detection. The detection limits of two orthogonal components of SPR measurement are targeted: speed and sensitivity. In the context of this report, speed refers to the dynamic range of measured kinetic rate constants, while sensitivity refers to the target molecule mass limitation of conventional SPR measurement. A simple device for high-speed microfluidic delivery of liquid samples to a sensor surface is presented to address the temporal limitations of conventional SPR measurement. The time scale of buffer/sample switching is on the order of milliseconds, thereby minimizing the opportunity for sample plug dispersion. The high rates of mass transport to and from the central microfluidic sensing region allow for SPR-based kinetic analysis of binding events with dissociation rate constants (kd) up to 130 s-1. The required sample volume is only 1 μL, allowing for minimal sample consumption during high-speed kinetic binding measurement. Charge-based detection of small molecules is demonstrated by plasmonic-based electrochemical impedance microscopy (P-EIM). The dependence of surface plasmon resonance (SPR) on surface charge density is used to detect small molecules (60-120 Da) printed on a dextran-modified sensor surface. The SPR response to an applied ac potential is a function of the surface charge density. This optical signal is comprised of a dc and an ac component, and is measured with high spatial resolution. The amplitude and phase of local surface impedance is provided by the ac component. The phase signal of the small molecules is a function of their charge status, which is manipulated by the pH of a solution. This technique is used to detect and distinguish small molecules based on their charge status, thereby circumventing the mass limitation (~100 Da) of conventional SPR measurement.
ContributorsMacGriff, Christopher Assiff (Author) / Tao, Nongjian (Thesis advisor) / Wang, Shaopeng (Committee member) / LaBaer, Joshua (Committee member) / Chae, Junseok (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
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
A general continuum model for simulating the flow of ions in the salt baths that surround and fill excitable neurons is developed and presented. The ion densities and electric potential are computed using the drift-diffusion equations. In addition, a detailed model is given for handling the electrical dynamics on interior membrane boundaries, including a model for ion channels in the membranes that facilitate the transfer of ions in and out of cells. The model is applied to the triad synapse found in the outer plexiform layer of the retina in most species. Experimental evidence suggests the existence of a negative feedback pathway between horizontal cells and cone photoreceptors that modulates the flow of calcium ions into the synaptic terminals of cones. However, the underlying mechanism for this feedback is controversial and there are currently three competing hypotheses: the ephaptic hypothesis, the pH hypothesis and the GABA hypothesis. The goal of this work is to test some features of the ephaptic hypothesis using detailed simulations that employ rigorous numerical methods. The model is first applied in a simple rectangular geometry to demonstrate the effects of feedback for different extracellular gap widths. The model is then applied to a more complex and realistic geometry to demonstrate the existence of strictly electrical feedback, as predicted by the ephaptic hypothesis. Lastly, the effects of electrical feedback in regards to the behavior of the bipolar cell membrane potential is explored. Figures for the ion densities and electric potential are presented to verify key features of the model. The computed steady state IV curves for several cases are presented, which can be compared to experimental data. The results provide convincing evidence in favor of the ephaptic hypothesis since the existence of feedback that is strictly electrical in nature is shown, without any dependence on pH effects or chemical transmitters.
ContributorsJones, Jeremiah (Author) / Gardner, Carl (Committee member) / Baer, Steven (Committee member) / Crook, Sharon (Committee member) / Kostelich, Eric (Committee member) / Ringhofer, Christian (Committee member) / Arizona State University (Publisher)
Created2013
Description
Glioblastoma (GBM), the most common and aggressive primary brain tumor affecting adults, is characterized by an aberrant yet druggable epigenetic landscape. The Histone Deacetylases (HDACs), a major family of epigenetic regulators, favor transcriptional repression by mediating chromatin compaction and are frequently overexpressed in human cancers, including GBM. Hence, over the last decade there has been considerable interest in using HDAC inhibitors (HDACi) for the treatment of malignant primary brain tumors. However, to date most HDACi tested in clinical trials have failed to provide significant therapeutic benefit to patients with GBM. This is because current HDACi have poor or unknown pharmacokinetic profiles, lack selectivity towards the different HDAC isoforms, and have narrow therapeutic windows. Isoform selectivity for HDACi is important given that broad inhibition of all HDACs results in widespread toxicity across different organs. Moreover, the functional roles of individual HDAC isoforms in GBM are still not well understood. Here, I demonstrate that HDAC1 expression increases with brain tumor grade and is correlated with decreased survival in GBM. I find that HDAC1 is the essential HDAC isoform in glioma stem cells and its loss is not compensated for by its paralogue HDAC2 or other members of the HDAC family. Loss of HDAC1 alone has profound effects on the glioma stem cell phenotype in a p53-dependent manner and leads to significant suppression of tumor growth in vivo. While no HDAC isoform-selective inhibitors are currently available, the second-generation HDACi quisinostat harbors high specificity for HDAC1. I show that quisinostat exhibits potent growth inhibition in multiple patient-derived glioma stem cells. Using a pharmacokinetics- and pharmacodynamics-driven approach, I demonstrate that quisinostat is a brain-penetrant molecule that reduces tumor burden in flank and orthotopic models of GBM and significantly extends survival both alone and in combination with radiotherapy. The work presented in this thesis thereby unveils the non-redundant functions of HDAC1 in therapy- resistant glioma stem cells and identifies a brain-penetrant HDACi with higher selectivity towards HDAC1 as a potent radiosensitizer in preclinical models of GBM. Together, these results provide a rationale for developing quisinostat as a potential adjuvant therapy for the treatment of GBM.
ContributorsLo Cascio, Costanza (Author) / LaBaer, Joshua (Thesis advisor) / Mehta, Shwetal (Committee member) / Mirzadeh, Zaman (Committee member) / Mangone, Marco (Committee member) / Paek, Andrew (Committee member) / Arizona State University (Publisher)
Created2022
Description
Transient Receptor Potential Vanilloid-1 (TRPV1) is an integral membrane polymodal cation channel involved in various essential biological functions, including thermosensing, thermoregulation, and nociception. Discrete TRPV1 activation modes such as ligand, heat, and proton have been challenging to disentangle. However, dissecting the polymodal nature of TRPV1 is essential for therapeutic development. The human TRPV1 (hTRPV1) voltage-sensing like domain (VSLD; transmembrane helices S1-S4) contains the canonical vanilloid ligand binding site and significantly contributes to thermosensing. Nuclear magnetic resonance (NMR)-detected studies probe the role of the hTRPV1-VSLD in TRPV1 polymodal function. The hTRPV1-VSLD is identified as an allosteric hub for all three primary TRPV1 activation modes and demonstrates plasticity in chemical ligand modulation. The presented results underscore molecular features in the VSLD that dictate TRPV1 function, highlighting important considerations for future therapeutic design.
ContributorsOwens, Aerial M. (Author) / Van Horn, Wade D. (Thesis advisor) / Levitus, Marcia (Committee member) / LaBaer, Joshua (Committee member) / Arizona State University (Publisher)
Created2023
Description
The Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) pandemic, declared in March 2020 resulted in an unprecedented scientific effort that led to the deployment in less than a year of several vaccines to prevent severe disease, hospitalizations, and death from coronavirus disease 2019 (COVID-19). Most vaccine models focus on the production of neutralizing antibodies against the spike (S) to prevent infection. As the virus evolves, new variants emerge that evade neutralizing antibodies produced by natural infection and vaccination, while memory T cell responses are long-lasting and resilient to most of the changes found in variants of concern (VOC). Several lines of evidence support the study of T cell-mediated immunity in SARS-CoV-2 infections. First, T cell reactivity against SARS-CoV-2 is found in both (cluster of differentiation) CD4+ and CD8+ T cell compartments in asymptomatic, mild, and severe recovered COVID-19 patients. Second, an early and stronger CD8+ T cell response correlates with less severe COVID-19 disease [1-4]. Third, both CD4+ and CD8+ T cells that are reactive to SARS-CoV-2 viral antigens are found in healthy unexposed individuals suggesting that cross-reactive and conserved epitopes may be protective against infection.
The current study is focused on the T cell-mediated response, with special attention to conserved, non-spike-cross-reactive epitopes that may be protective against SARS-CoV-2. The first chapter reviews the importance of epitope prediction in understanding the T cell-mediated responses to a pathogen. The second chapter centers on the validation of SARS-CoV-2 CD8+ T cell predicted peptides to find conserved, immunodominant, and immunoprevalent epitopes that can be incorporated into the next generation of vaccines against severe COVID-19 disease. The third chapter explores pre-existing immunity to SARS-CoV-2 in a pre-pandemic cohort and finds two highly immunogenic epitopes that are conserved among human common cold coronaviruses (HCoVs). To end, the fourth chapter explores the concept of T cell receptor (TCR) cross-reactivity by isolating SARS-CoV-2-reactive TCRs to elucidate the mechanisms of cross-reactivity to SARS-CoV-2 and other human coronaviruses (HCoVs).
ContributorsCarmona, Jacqueline (Author) / Anderson, Karen S (Thesis advisor) / Lake, Douglas (Thesis advisor) / Maley, Carlo (Committee member) / Mangone, Marco (Committee member) / LaBaer, Joshua (Committee member) / Arizona State University (Publisher)
Created2023
Description
Climate change is one of the most pressing issues affecting the world today. One of the impacts of climate change is on the transmission of mosquito-borne diseases (MBDs), such as West Nile Virus (WNV). Climate is known to influence vector and host demography as well as MBD transmission. This dissertation addresses the questions of how vector and host demography impact WNV dynamics, and how expected and likely climate change scenarios will affect demographic and epidemiological processes of WNV transmission. First, a data fusion method is developed that connects non-autonomous logistic model parameters to mosquito time series data. This method captures the inter-annual and intra-seasonal variation of mosquito populations within a geographical location. Next, a three-population WNV model between mosquito vectors, bird hosts, and human hosts with infection-age structure for the vector and bird host populations is introduced. A sensitivity analysis uncovers which parameters have the most influence on WNV outbreaks. Finally, the WNV model is extended to include the non-autonomous population model and temperature-dependent processes. Model parameterization using historical temperature and human WNV case data from the Greater Toronto Area (GTA) is conducted. Parameter fitting results are then used to analyze possible future WNV dynamics under two climate change scenarios. These results suggest that WNV risk for the GTA will substantially increase as temperature increases from climate change, even under the most conservative assumptions. This demonstrates the importance of ensuring that the warming of the planet is limited as much as possible.
ContributorsMancuso, Marina (Author) / Milner, Fabio A (Thesis advisor) / Kuang, Yang (Committee member) / Kostelich, Eric (Committee member) / Eikenberry, Steffen (Committee member) / Manore, Carrie (Committee member) / Arizona State University (Publisher)
Created2023
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