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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
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
Plasma and serum are the most commonly used liquid biospecimens in biomarker research. These samples may be subjected to several pre-analytical variables (PAVs) during collection, processing and storage. Exposure to thawed conditions (temperatures above -30 °C) is a PAV that is hard to control, and track and could provide misleading information, that fail to accurately reveal the in vivo biological reality, when unaccounted for. Hence, assays that can empirically check the integrity of plasma and serum samples are crucial. As a solution to this issue, an assay titled ΔS-Cys-Albumin was developed and validated. The reference range of ΔS-Cys-Albumin in cardio vascular patients was determined and the change in ΔS-Cys-Albumin values in different samples over time course incubations at room temperature, 4 °C and -20 °C were evaluated. In blind challenges, this assay proved to be successful in identifying improperly stored samples individually and as groups. Then, the correlation between the instability of several clinically important proteins in plasma from healthy and cancer patients at room temperature, 4 °C and -20 °C was assessed. Results showed a linear inverse relationship between the percentage of proteins destabilized and ΔS-Cys-Albumin regardless of the specific time or temperature of exposure, proving ΔS-Cys-Albumin as an effective surrogate marker to track the stability of clinically relevant analytes in plasma. The stability of oxidized LDL in serum at different temperatures was assessed in serum samples and it stayed stable at all temperatures evaluated. The ΔS-Cys-Albumin requires the use of an LC-ESI-MS instrument which limits its availability to most clinical research laboratories. To overcome this hurdle, an absorbance-based assay that can be measured using a plate reader was developed as an alternative to the ΔS-Cys-Albumin assay. Assay development and analytical validation procedures are reported herein. After that, the range of absorbance in plasma and serum from control and cancer patients were determined and the change in absorbance over a time course incubation at room temperature, 4 °C and -20 °C was assessed. The results showed that the absorbance assay would act as a good alternative to the ΔS-Cys-Albumin assay.
ContributorsJehanathan, Nilojan (Author) / Borges, Chad (Thesis advisor) / Guo, Jia (Committee member) / Van Horn, Wade (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
Type 1 diabetes (T1D) is the result of an autoimmune attack against the insulin-producing β-cells of the pancreas causing hyperglycemia and requiring the individual to rely on life-long exogenous insulin. With the age of onset typically occurring in childhood, there is increased physical and emotional stress to the child as well as caregivers to maintain appropriate glucose levels. The majority of T1D patients have antibodies to one or more antigens: insulin, IA-2, GAD65, and ZnT8. Although antibodies are detectable years before symptoms occur, the initiating factors and mechanisms of progression towards β-cell destruction are still not known. The search for new autoantibodies to elucidate the autoimmune process in diabetes has been slow, with proteome level screenings on native proteins only finding a few minor antigens. Post-translational modifications (PTM)—chemical changes that occur to the protein after translation is complete—are an unexplored way a self-protein could become immunogenic. This dissertation presents the first large sale screening of autoantibodies in T1D to nitrated proteins. The Contra Capture Protein Array (CCPA) allowed for fresh expression of hundreds of proteins that were captured on a secondary slide by tag-specific ligand and subsequent modification with peroxynitrite. The IgG and IgM humoral response of 48 newly diagnosed T1D subjects and 48 age-matched controls were screened against 1632 proteins highly or specifically expressed in pancreatic cells. Top targets at 95% specificity were confirmed with the same serum samples using rapid antigenic protein in situ display enzyme-linked immunosorbent assay (RAPID ELISA) a modified sandwich ELISA employing the same cell-free expression as the CCPA. For validation, 8 IgG and 5 IgM targets were evaluated with an independent serum sample set of 94 T1D subjects and 94 controls. The two best candidates at 90% specificity were estrogen receptor 1 (ESR1) and phosphatidylinositol 4-kinase type 2 beta (PI4K2B) which had sensitivities of 22% (p=.014) and 25% (p=.045), respectively. Receiver operating characteristic (ROC) analyses found an area under curve (AUC) of 0.6 for ESR1 and 0.58 for PI4K2B. These studies demonstrate the ability and value for high-throughput autoantibody screening to modified antigens and the frequency of Type 1 diabetes.
ContributorsHesterman, Jennifer (Author) / LaBaer, Joshua (Thesis advisor) / Borges, Chad (Committee member) / Sweazea, Karen (Committee member) / Mangone, Marco (Committee member) / Arizona State University (Publisher)
Created2022
Description
Antibodies are the immunoglobulins which are secreted by the B cells after a microbial invasion. They are stable and stays in the serum for a long time which makes them an excellent biomarker for disease diagnosis. Inflammatory bowel disease is a type of autoimmune disease where the immune system mistakenly attacks the commensal bacteria and leads to inflammation. We studied antibody response of 100 Crohn’s disease (CD), 100 ulcerative colitis (UC) and 100 healthy controls against 1,173 bacterial and 397 viral proteins. We found some anti-bacterial antibodies higher in CD compared to controls while some antibodies lower in UC compared to controls. We were able to build biomarker panels with AUCs of 0.81, 0.87, and 0.82 distinguishing CD vs. control, UC vs. control, and CD vs. UC, respectively. Subgroup analysis based on the Montreal classification revealed that penetrating CD behavior (B3), colonic CD location (L2), and extensive UC (E3) exhibited highest antibody reactivity among all patients. We also wanted to study the reason for the presence of autoantibodies in the sera of healthy individuals. A meta-analysis of 9 independent biomarker study was performed to find 77 common autoantibodies shared by healthy individuals. There was no gender bias; however, the number of autoantibodies increased with age, plateauing around adolescence. Molecular mimicry likely contributed to the elicitation of a subset of these common autoantibodies as 21 common autoantigens had 7 or more ungapped amino acid matches with viral proteins. Intrinsic properties of protein like hydrophilicity, basicity, aromaticity, and flexibility were enriched for common autoantigens. Subcellular localization and tissue expression analysis indicated the sequestration of some autoantigens from circulating autoantibodies can explain the absence of autoimmunity in these healthy individuals.
ContributorsShome, Mahasish (Author) / LaBaer, Joshua (Thesis advisor) / Borges, Chad (Committee member) / Stephanopoulos, Nicholas (Committee member) / Arizona State University (Publisher)
Created2021
Description
Transient protein-protein and protein-molecule interactions fluctuate between associated and dissociated states. They are widespread in nature and mediate most biological processes. These interactions are complex and are strongly influenced by factors such as concentration, structure, and environment. Understanding and utilizing these types of interactions is useful from both a fundamental and design perspective. In this dissertation, transient protein interactions are used as the sensing element of a biosensor for small molecule detection. This is done by using a transcription factor-small molecule pair that mediates the activation of a CRISPR/Cas12a complex. Activation of the Cas12a enzyme results in an amplified readout mechanism that is either fluorescence or paper based. This biosensor can successfully detect 9 different small molecules including antibiotics with a tuneable detection limit ranging from low µM to low nM. By combining protein and nucleic acid-based systems, this biosensor has the potential to report on almost any protein-molecule interaction, linking this to the intrinsic amplification that is possible when working with nucleic acid-based technologies. The second part of this dissertation focuses on understanding protein-molecule interactions at a more fundamental level, and, in so doing, exploring design rules required to generalize sensors like the ones described above. This is done by training a neural network algorithm with binding data from high density peptide micro arrays incubated with specific protein targets. Because the peptide sequences were chosen simply to evenly, though sparsely, represent all sequence space, the resulting network provides a comprehensive sequence/binding relationship for a given target protein. While past work had shown that this works well on the arrays, here I have explored how well the neural networks thus trained, predict sequence-dependent binding in the context of protein-protein and peptide-protein interactions. Amino acid sequences, either free in solution or embedded in protein structure, will display somewhat different binding properties than sequences affixed to the surface of a high-density array. However, the neural network trained on array sequences was able to both identify binding regions in between proteins and predict surface plasmon resonance-based binding propensities for peptides with statistically significant levels of accuracy.
ContributorsSwingle, Kirstie Lynn (Author) / Woodbury, Neal W (Thesis advisor) / Green, Alexander A (Thesis advisor) / Stephanopoulos, Nicholas (Committee member) / Borges, Chad (Committee member) / Arizona State University (Publisher)
Created2022
Description
Earth-system models describe the interacting components of the climate system and
technological systems that affect society, such as communication infrastructures. Data
assimilation addresses the challenge of state specification by incorporating system
observations into the model estimates. In this research, a particular data
assimilation technique called the Local Ensemble Transform Kalman Filter (LETKF) is
applied to the ionosphere, which is a domain of practical interest due to its effects
on infrastructures that depend on satellite communication and remote sensing. This
dissertation consists of three main studies that propose strategies to improve space-
weather specification during ionospheric extreme events, but are generally applicable
to Earth-system models:
Topic I applies the LETKF to estimate ion density with an idealized model of
the ionosphere, given noisy synthetic observations of varying sparsity. Results show
that the LETKF yields accurate estimates of the ion density field and unobserved
components of neutral winds even when the observation density is spatially sparse
(2% of grid points) and there is large levels (40%) of Gaussian observation noise.
Topic II proposes a targeted observing strategy for data assimilation, which uses
the influence matrix diagnostic to target errors in chosen state variables. This
strategy is applied in observing system experiments, in which synthetic electron density
observations are assimilated with the LETKF into the Thermosphere-Ionosphere-
Electrodynamics Global Circulation Model (TIEGCM) during a geomagnetic storm.
Results show that assimilating targeted electron density observations yields on
average about 60%–80% reduction in electron density error within a 600 km radius of
the observed location, compared to 15% reduction obtained with randomly placed
vertical profiles.
Topic III proposes a methodology to account for systematic model bias arising
ifrom errors in parametrized solar and magnetospheric inputs. This strategy is ap-
plied with the TIEGCM during a geomagnetic storm, and is used to estimate the
spatiotemporal variations of bias in electron density predictions during the
transitionary phases of the geomagnetic storm. Results show that this strategy reduces
error in 1-hour predictions of electron density by about 35% and 30% in polar regions
during the main and relaxation phases of the geomagnetic storm, respectively.
technological systems that affect society, such as communication infrastructures. Data
assimilation addresses the challenge of state specification by incorporating system
observations into the model estimates. In this research, a particular data
assimilation technique called the Local Ensemble Transform Kalman Filter (LETKF) is
applied to the ionosphere, which is a domain of practical interest due to its effects
on infrastructures that depend on satellite communication and remote sensing. This
dissertation consists of three main studies that propose strategies to improve space-
weather specification during ionospheric extreme events, but are generally applicable
to Earth-system models:
Topic I applies the LETKF to estimate ion density with an idealized model of
the ionosphere, given noisy synthetic observations of varying sparsity. Results show
that the LETKF yields accurate estimates of the ion density field and unobserved
components of neutral winds even when the observation density is spatially sparse
(2% of grid points) and there is large levels (40%) of Gaussian observation noise.
Topic II proposes a targeted observing strategy for data assimilation, which uses
the influence matrix diagnostic to target errors in chosen state variables. This
strategy is applied in observing system experiments, in which synthetic electron density
observations are assimilated with the LETKF into the Thermosphere-Ionosphere-
Electrodynamics Global Circulation Model (TIEGCM) during a geomagnetic storm.
Results show that assimilating targeted electron density observations yields on
average about 60%–80% reduction in electron density error within a 600 km radius of
the observed location, compared to 15% reduction obtained with randomly placed
vertical profiles.
Topic III proposes a methodology to account for systematic model bias arising
ifrom errors in parametrized solar and magnetospheric inputs. This strategy is ap-
plied with the TIEGCM during a geomagnetic storm, and is used to estimate the
spatiotemporal variations of bias in electron density predictions during the
transitionary phases of the geomagnetic storm. Results show that this strategy reduces
error in 1-hour predictions of electron density by about 35% and 30% in polar regions
during the main and relaxation phases of the geomagnetic storm, respectively.
ContributorsDurazo, Juan, Ph.D (Author) / Kostelich, Eric J. (Thesis advisor) / Mahalov, Alex (Thesis advisor) / Tang, Wenbo (Committee member) / Moustaoui, Mohamed (Committee member) / Platte, Rodrigo (Committee member) / Arizona State University (Publisher)
Created2018
Description
Measuring molecular interaction with membrane proteins is critical for understanding cellular functions, validating biomarkers and screening drugs. Despite the importance, developing such a capability has been a difficult challenge, especially for small molecules binding to membrane proteins in their native cellular environment. The current mainstream practice is to isolate membrane proteins from the cell membranes, which is difficult and often lead to the loss of their native structures and functions. In this thesis, novel detection methods for in situ quantification of molecular interactions with membrane proteins are described.
First, a label-free surface plasmon resonance imaging (SPRi) platform is developed for the in situ detection of the molecular interactions between membrane protein drug target and its specific antibody drug molecule on cell surface. With this method, the binding kinetics of the drug-target interaction is quantified for drug evaluation and the receptor density on the cell surface is also determined.
Second, a label-free mechanically amplification detection method coupled with a microfluidic device is developed for the detection of both large and small molecules on single cells. Using this method, four major types of transmembrane proteins, including glycoproteins, ion channels, G-protein coupled receptors (GPCRs) and tyrosine kinase receptors on single whole cells are studied with their specific drug molecules. The basic principle of this method is established by developing a thermodynamic model to express the binding-induced nanometer-scale cellular deformation in terms of membrane protein density and cellular mechanical properties. Experiments are carried out to validate the model.
Last, by tracking the cell membrane edge deformation, molecular binding induced downstream event – granule exocytosis is measured with a dual-optical imaging system. Using this method, the single granule exocytosis events in single cells are monitored and the temporal-spatial distribution of the granule fusion-induced cell membrane deformation are mapped. Different patterns of granule release are resolved, including multiple release events occurring close in time and position. The label-free cell membrane deformation tracking method was validated with the simultaneous fluorescence recording. And the simultaneous cell membrane deformation detection and fluorescence recording allow the study of the propagation of the granule release-induced membrane deformation along cell surfaces.
First, a label-free surface plasmon resonance imaging (SPRi) platform is developed for the in situ detection of the molecular interactions between membrane protein drug target and its specific antibody drug molecule on cell surface. With this method, the binding kinetics of the drug-target interaction is quantified for drug evaluation and the receptor density on the cell surface is also determined.
Second, a label-free mechanically amplification detection method coupled with a microfluidic device is developed for the detection of both large and small molecules on single cells. Using this method, four major types of transmembrane proteins, including glycoproteins, ion channels, G-protein coupled receptors (GPCRs) and tyrosine kinase receptors on single whole cells are studied with their specific drug molecules. The basic principle of this method is established by developing a thermodynamic model to express the binding-induced nanometer-scale cellular deformation in terms of membrane protein density and cellular mechanical properties. Experiments are carried out to validate the model.
Last, by tracking the cell membrane edge deformation, molecular binding induced downstream event – granule exocytosis is measured with a dual-optical imaging system. Using this method, the single granule exocytosis events in single cells are monitored and the temporal-spatial distribution of the granule fusion-induced cell membrane deformation are mapped. Different patterns of granule release are resolved, including multiple release events occurring close in time and position. The label-free cell membrane deformation tracking method was validated with the simultaneous fluorescence recording. And the simultaneous cell membrane deformation detection and fluorescence recording allow the study of the propagation of the granule release-induced membrane deformation along cell surfaces.
ContributorsZhang, Fenni (Author) / Tao, Nongjian (Thesis advisor) / Chae, Junseok (Committee member) / Borges, Chad (Committee member) / Jing, Tianwei (Committee member) / Wang, Shaopeng (Committee member) / Arizona State University (Publisher)
Created2018
Description
Measurements of different molecular species from single cells have the potential to reveal cell-to-cell variations, which are precluded by population-based measurements. An increasing percentage of researches have been focused on proteins, for its central roles in biological processes. Immunofluorescence (IF) has been a well-established protein analysis platform. To gain comprehensive insights into cell biology and diagnostic pathology, a crucial direction would be to increase the multiplexity of current single cell protein analysis technologies.
An azide-based chemical cleavable linker has been introduced to design and synthesis novel fluorescent probes. These probes allow cyclic immunofluorescence staining which leads to the feasibility of highly multiplexed single cell in situ protein profiling. These highly multiplexed imaging-based platforms have the potential to quantify more than 100 protein targets in cultured cells and more than 50 protein targets in single cells in tissues.
This approach has been successfully applied in formalin-fixed paraffin-embedded (FFPE) brain tissues. Multiplexed protein expression level results reveal neuronal heterogeneity in the human hippocampus.
An azide-based chemical cleavable linker has been introduced to design and synthesis novel fluorescent probes. These probes allow cyclic immunofluorescence staining which leads to the feasibility of highly multiplexed single cell in situ protein profiling. These highly multiplexed imaging-based platforms have the potential to quantify more than 100 protein targets in cultured cells and more than 50 protein targets in single cells in tissues.
This approach has been successfully applied in formalin-fixed paraffin-embedded (FFPE) brain tissues. Multiplexed protein expression level results reveal neuronal heterogeneity in the human hippocampus.
ContributorsLiao, Renjie (Author) / Guo, Jia (Thesis advisor) / Borges, Chad (Committee member) / Liu, Yan (Committee member) / Arizona State University (Publisher)
Created2019