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- Genre: Doctoral Dissertation
- Language: English
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
Cardiovascular disease (CVD) remains the leading cause of mortality, resulting in 1 out of 4 deaths in the United States at the alarming rate of 1 death every 36 seconds, despite great efforts in ongoing research. In vitro research to study CVDs has had limited success, due to lack of biomimicry and structural complexity of 2D models. As such, there is a critical need to develop a 3D, biomimetic human cardiac tissue within precisely engineered in vitro platforms. This PhD dissertation involved development of an innovative anisotropic 3D human stem cell-derived cardiac tissue on-a-chip model (i.e., heart on-a-chip), with an enhanced maturation tissue state, as demonstrated through extensive biological assessments. To demonstrate the potential of the platform to study cardiac-specific diseases, the developed heart on-a-chip was used to model myocardial infarction (MI) due to exposure to hypoxia. The successful induction of MI on-a-chip (heart attack-on-a-chip) was evidenced through fibrotic tissue response, contractile dysregulation, and transcriptomic regulation of key pathways.This dissertation also described incorporation of CRISPR/Cas9 gene-editing to create a human induced pluripotent stem cell line (hiPSC) with a mutation in KCNH2, the gene implicated in Long QT Syndrome Type 2 (LQTS2). This novel stem cell line, combined with the developed heart on-a-chip technology, led to creation of a 3D human cardiac on-chip tissue model of LQTS2 disease.. Extensive mechanistic biological and electrophysiological characterizations were performed to elucidate the mechanism of R531W mutation in KCNH2, significantly adding to existing knowledge about LQTS2. In summary, this thesis described creation of a LQTS2 cardiac on-a-chip model, incorporated with gene-edited hiPSC-cardiomyocytes and hiPSC-cardiac fibroblasts, to study mechanisms of LQTS2.
Overall, this dissertation provides broad impact for fundamental studies toward cardiac biological studies as well as drug screening applications. Specifically, the developed heart on-a-chip from this dissertation provides a unique alternative platform to animal testing and 2D studies that recapitulates the human myocardium, with capabilities to model critical CVDs to study disease mechanisms, and/or ultimately lead to development of future therapeutic strategies.
ContributorsVeldhuizen, Jaimeson (Author) / Nikkhah, Mehdi (Thesis advisor) / Brafman, David (Committee member) / Ebrahimkhani, Mo (Committee member) / Migrino, Raymond Q (Committee member) / Plaisier, Christopher (Committee member) / Arizona State University (Publisher)
Created2021
Description
The advent of CRISPR/Cas9 revolutionized the field of genetic engineering and gave rise to the development of new gene editing tools including prime editing. Prime editing is a versatile gene editing method that mediates precise insertions and deletions and can perform all 12 types of point mutations. In turn, prime editing represents great promise in the design of new gene therapies and disease models where editing was previously not possible using current gene editing techniques. Despite advancements in genome modification technologies, parallel enrichment strategies of edited cells remain lagging behind in development. To this end, this project aimed to enhance prime editing using transient reporter for editing enrichment (TREE) technology to develop a method for the rapid generation of clonal isogenic cell lines for disease modeling. TREE uses an engineered BFP variant that upon a C-to-T conversion will convert to GFP after target modification. Using flow cytometry, this BFP-to-GFP conversion assay enables the isolation of edited cell populations via a fluorescent reporter of editing. Prime induced nucleotide engineering using a transient reporter for editing enrichment (PINE-TREE), pairs prime editing with TREE technology to efficiently enrich for prime edited cells. This investigation revealed PINE-TREE as an efficient editing and enrichment method compared to a conventional reporter of transfection (RoT) enrichment strategy. Here, PINE-TREE exhibited a significant increase in editing efficiencies of single nucleotide conversions, small insertions, and small deletions in multiple human cell types. Additionally, PINE-TREE demonstrated improved clonal cell editing efficiency in human induced pluripotent stem cells (hiPSCs). Most notably, PINE-TREE efficiently generated clonal isogenic hiPSCs harboring a mutation in the APOE gene for in vitro modeling of Alzheimer’s Disease. Collectively, results gathered from this study exhibited PINE-TREE as a valuable new tool in genetic engineering to accelerate the generation of clonal isogenic cell lines for applications in developmental biology, disease modeling, and drug screening.
ContributorsKostes, William Warner (Author) / Brafman, David (Thesis advisor) / Jacobs, Bertram (Committee member) / Lapinaite, Audrone (Committee member) / Tian, Xiaojun (Committee member) / Wang, Xiao (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
Ecology has been an actively studied topic recently, along with the rapid development of human microbiota-based technology. Scientists have made remarkable progress using bioinformatics tools to identify species and analyze composition. However, a thorough understanding of interspecies interactions of microbial ecosystems is still lacking, which has been a significant obstacle in the further development of related technologies. In this work, a genetic circuit design principle with synthetic biology approaches is developed to form two-strain microbial consortia with different inter-strain interactions. The microbial systems are well-defined and inducible. Co-culture experiment results show that our microbial consortia behave consistently with previous ecological knowledge and thus serves as excellent model systems to simulate ecosystems with similar interactions. Colony patterns also emerge when co-culturing multiple species on solid media. With the engineered microbial consortia, image-processing based methods were developed to quantify the shape of co-culture colonies and distinguish microbial consortia with different interactions. Factors that affect the population ratios were identified through induction and variations in the inoculation process. Further time-lapse experiments revealed the basic rules of colony growth, composition variation, patterning, and how spatial factors impact the co-culture colony.
ContributorsChen, Xingwen (Author) / Wang, Xiao (Thesis advisor) / Kuang, Yang (Committee member) / Tian, Xiaojun (Committee member) / Brafman, David (Committee member) / Plaisier, Christopher (Committee member) / Arizona State University (Publisher)
Created2022
Description
Annually, approximately 1.7 million people suffer a traumatic brain injury (TBI) in the United States. After initial insult, a TBI persists as a series of molecular and cellular events that lead to cognitive and motor deficits which have no treatment. In addition, the injured brain activates the regenerative niches of the adult brain presumably to reduce damage. The subventricular zone (SVZ) niche contains neural progenitor cells (NPCs) that generate astrocytes, oligodendrocyte, and neuroblasts. Following TBI, the injury microenvironment secretes signaling molecules like stromal cell derived factor-1a (SDF-1a). SDF-1a gradients from the injury contribute to the redirection of neuroblasts from the SVZ towards the lesion which may differentiate into neurons and integrate into existing circuitry. This repair mechanism is transient and does not lead to complete recovery of damaged tissue. Further, the mechanism by which SDF-1a gradients reach SVZ cells is not fully understood. To prolong NPC recruitment to the injured brain, exogenous SDF-1a delivery strategies have been employed. Increases in cell recruitment following stroke, spinal cord injury, and TBI have been demonstrated following SDF-1a delivery. Exogenous delivery of SDF-1a is limited by its 28-minute half-life and clearance from the injury microenvironment. Biomaterials-based delivery improves stability of molecules like SDF-1a and offer control of its release.
This dissertation investigates SDF-1a delivery strategies for neural regeneration in three ways: 1) elucidating the mechanisms of spatiotemporal SDF-1a signaling across the brain, 2) developing a tunable biomaterials system for SDF-1a delivery to the brain, 3) investigating SDF-1a delivery on SVZ-derived cell migration following TBI. Using in vitro, in vivo, and in silico analyses, autocrine/paracrine signaling was necessary to produce SDF-1a gradients in the brain. Native cell types engaged in autocrine/paracrine signaling. A microfluidics device generated injectable hyaluronic-based microgels that released SDF-1a peptide via enzymatic cleavage. Microgels (±SDF-1a peptide) were injected 7 days post-TBI in a mouse model and evaluated for NPC migration 7 days later using immunohistochemistry. Initial staining suggested complex presence of astrocytes, NPCs, and neuroblasts throughout the frontoparietal cortex.
Advancement of chemokine delivery was demonstrated by uncovering endogenous chemokine propagation in the brain, generating new approaches to maximize chemokine-based neural regeneration.
ContributorsHickey, Kassondra (Author) / Stabenfeldt, Sarah E (Thesis advisor) / Holloway, Julianne (Committee member) / Caplan, Michael (Committee member) / Brafman, David (Committee member) / Newbern, Jason (Committee member) / Arizona State University (Publisher)
Created2021
Description
The RNA editing enzyme adenosine deaminase acting on double stranded RNA 2 (ADAR2) converts adenosine into inosine in regions of double stranded RNA. Here, it was discovered that this critical function of ADAR2 was dysfunctional in amyotrophic lateral sclerosis (ALS) mediated by the C9orf72 hexanucleotide repeat expansion, the most common genetic abnormality associated with ALS. Typically a nuclear protein, ADAR2 was localized in cytoplasmic accumulations in postmortem tissue from C9orf72 ALS patients. The mislocalization of ADAR2 was confirmed using immunostaining in a C9orf72 mouse model and motor neurons differentiated from C9orf72 patient induced pluripotent stem cells. Notably, the cytoplasmic accumulation of ADAR2 coexisted in neurons with cytoplasmic accumulations of TAR DNA binding protein 43 (TDP-43). Interestingly, ADAR2 overexpression in mammalian cell lines induced nuclear depletion and cytoplasmic accumulation of TDP-43, reflective of the pathology observed in ALS patients. The mislocalization of TDP-43 was dependent on the catalytic activity of ADAR2 and the ability of TDP-43 to bind directly to inosine containing RNA. In addition, TDP-43 nuclear export was significantly elevated in cells with increased RNA editing. Together these results describe a novel cellular mechanism by which alterations in RNA editing drive the nuclear export of TDP-43 leading to its cytoplasmic mislocalization. Considering the contribution of cytoplasmic TDP-43 to the pathogenesis of ALS, these findings represent a novel understanding of how the formation of pathogenic cytoplasmic TDP-43 accumulations may be initiated. Further research exploring this mechanism will provide insights into opportunities for novel therapeutic interventions.
ContributorsMoore, Stephen Philip (Author) / Sattler, Rita (Thesis advisor) / Zarnescu, Daniela (Committee member) / Brafman, David (Committee member) / Van Keuren-Jensen, Kendall (Committee member) / Mangone, Marco (Committee member) / Arizona State University (Publisher)
Created2021
Description
The GGGGCC (G4C2) hexanucleotide repeat expansion (HRE) in the C9orf72 gene is the most common genetic abnormality associated with both amyotrophic lateral sclerosis (ALS) and frontotemporal dementia (FTD), two devastatingly progressive neurodegenerative diseases. The discovery of this genetic link confirmed that ALS and FTD reside along a spectrum with clinical and pathological commonalities. Historically understood as diseases resulting in neuronal death, the role of non-neuronal cells like astrocytes is still wholly unresolved. With evidence of cortical neurodegeneration leading to cognitive impairments in C9orf72-ALS/FTD, there is a need to investigate the role of cortical astrocytes in this disease spectrum. Here, a patient-derived induced pluripotent stem cell (iPSC) cortical astrocyte model was developed to investigate consequences of C9orf72-HRE pathogenic features in this cell type. Although there were no significant C9orf72-HRE pathogenic features in cortical astrocytes, transcriptomic, proteomic and phosphoproteomic profiles elucidated global disease-related phenotypes. Specifically, aberrant expression of astrocytic-synapse proteins and secreted factors were identified. SPARCL1, a pro-synaptogenic secreted astrocyte factor was found to be selectively decreased in C9orf72-ALS/FTD iPSC-cortical astrocytes. This finding was further validated in human tissue analyses, indicating that cortical astrocytes in C9orf72-ALS/FTD exhibit a reactive transformation that is characterized by a decrease in SPARCL1 expression. Considering the evidence for substantial astrogliosis and synaptic failure leading to cognitive impairments in C9orf72-ALS/FTD, these findings represent a novel understanding of how cortical astrocytes may contribute to the cortical neurodegeneration in this disease spectrum.
ContributorsBustos, Lynette (Author) / Sattler, Rita (Thesis advisor) / Newbern, Jason (Committee member) / Zarnescu, Daniela (Committee member) / Brafman, David (Committee member) / Mehta, Shwetal (Committee member) / Arizona State University (Publisher)
Created2023
Description
APOE encodes for a lipid transport protein and has three allelic variants-APOE ε2, ε3 and ε4 each of which differentially modulate the risk for Alzheimer’s disease (AD). The presence of the ε4 allele of APOE greatly increases AD risk compared to the presence of the more prevalent and risk neutral ε3 allele. An imbalance in the generation and clearance of amyloid beta (Aβ) peptides has been hypothesized to play a key role in driving the disease. APOE4 impacts several AD-relevant cellular processes. However, it is unclear whether these effects represent a gain of toxic function or a loss of function, specifically as it relates to modulating amyloid beta (Aβ) levels. Here, a set of APOE knockout (KO) and APOE4 isogenic human induced pluripotent stem cells (hiPSCs) were generated from a parental APOE3 hiPSC line with a highly penetrant familial AD (fAD) mutation to investigate this with respect to Aβ secretion in neural cultures and Aβ uptake in monocultures of microglia-like cells (iMGLs). Conversion of APOE3 to E4 as well as functionally knocking APOE out from the APOE3 parental line, result in elevated Aβ levels in neural cultures, likely through multiple mechanisms including the altered processing of the precursor protein to Aβ called amyloid precursor protein (APP). In pure neuronal cultures, a shift in the processing of APP was observed with the Aβ-generating amyloidogenic pathway being favored in both APOE3 as well as APOE4 neurons compared to APOE KO neurons, with APOE4 neurons exhibiting a greater shift. In iMGLs derived from the isogenic hiPSC lines, expression of APOE, regardless of the isoform, lowered the uptake of Aβ. Overall, APOE4 modulates Aβ levels through distinct loss of protective and gain of function effects. Dissecting these effects would contribute towards a better understanding of the design of potential APOE-targeted therapeutics in the future.
ContributorsRajaram Srinivasan, Gayathri (Author) / Brafman, David (Thesis advisor) / Plaisier, Christopher (Committee member) / Newbern, Jason (Committee member) / Stabenfeldt, Sarah (Committee member) / Wang, Xiao (Committee member) / Arizona State University (Publisher)
Created2024