Matching Items (31)
Filtering by
- Resource Type: Text
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
This research project investigated known and novel differential genetic variants and their associated molecular pathways involved in Type II diabetes mellitus for the purpose of improving diagnosis and treatment methods. The goal of this investigation was to 1) identify the genetic variants and SNPs in Type II diabetes to develop a gene regulatory pathway, and 2) utilize this pathway to determine suitable drug therapeutics for prevention and treatment. Using a Gene Set Enrichment Analysis (GSEA), a set of 1000 gene identifiers from a Mayo Clinic database was analyzed to determine the most significant genetic variants related to insulin signaling pathways involved in Type II Diabetes. The following genes were identified: NRAS, KRAS, PIK3CA, PDE3B, TSC1, AKT3, SOS1, NEU1, PRKAA2, AMPK, and ACC. In an extensive literature review and cross-analysis with Kegg and Reactome pathway databases, novel SNPs located on these gene variants were identified and used to determine suitable drug therapeutics for treatment. Overall, understanding how genetic mutations affect target gene function related to Type II Diabetes disease pathology is crucial to the development of effective diagnosis and treatment. This project provides new insight into the molecular basis of the Type II Diabetes, serving to help untangle the regulatory complexity of the disease and aid in the advancement of diagnosis and treatment. Keywords: Type II Diabetes mellitus, Gene Set Enrichment Analysis, genetic variants, KEGG Insulin Pathway, gene-regulatory pathway
ContributorsBucklin, Lindsay (Co-author) / Davis, Vanessa (Co-author) / Holechek, Susan (Thesis director) / Wang, Junwen (Committee member) / Nyarige, Verah (Committee member) / School of Human Evolution & Social Change (Contributor) / School of Life Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
This research project investigated known and novel differential genetic variants and their associated molecular pathways involved in Type II diabetes mellitus for the purpose of improving diagnosis and treatment methods. The goal of this investigation was to 1) identify the genetic variants and SNPs in Type II diabetes to develop a gene regulatory pathway, and 2) utilize this pathway to determine suitable drug therapeutics for prevention and treatment. Using a Gene Set Enrichment Analysis (GSEA), a set of 1000 gene identifiers from a Mayo Clinic database was analyzed to determine the most significant genetic variants related to insulin signaling pathways involved in Type II Diabetes. The following genes were identified: NRAS, KRAS, PIK3CA, PDE3B, TSC1, AKT3, SOS1, NEU1, PRKAA2, AMPK, and ACC. In an extensive literature review and cross-analysis with Kegg and Reactome pathway databases, novel SNPs located on these gene variants were identified and used to determine suitable drug therapeutics for treatment. Overall, understanding how genetic mutations affect target gene function related to Type II Diabetes disease pathology is crucial to the development of effective diagnosis and treatment. This project provides new insight into the molecular basis of the Type II Diabetes, serving to help untangle the regulatory complexity of the disease and aid in the advancement of diagnosis and treatment.
ContributorsDavis, Vanessa Brooke (Co-author) / Bucklin, Lindsay (Co-author) / Holechek, Susan (Thesis director) / Wang, Junwen (Committee member) / School of Molecular Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
A numerical study of wave-induced momentum transport across the tropopause in the presence of a stably stratified thin inversion layer is presented and discussed. This layer consists of a sharp increase in static stability within the tropopause. The wave propagation is modeled by numerically solving the Taylor-Goldstein equation, which governs the dynamics of internal waves in stably stratified shear flows. The waves are forced by a flow over a bell shaped mountain placed at the lower boundary of the domain. A perfectly radiating condition based on the group velocity of mountain waves is imposed at the top to avoid artificial wave reflection. A validation for the numerical method through comparisons with the corresponding analytical solutions will be provided. Then, the method is applied to more realistic profiles of the stability to study the impact of these profiles on wave propagation through the tropopause.
ContributorsCole, Alexandra Shea (Author) / Moustaoui, Mohamed (Thesis director) / Kostelich, Eric (Committee member) / Mahalov, Alex (Committee member) / School of International Letters and Cultures (Contributor) / School of Geographical Sciences and Urban Planning (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2017-05
Description
High throughput transcriptome data analysis like Single-cell Ribonucleic Acid sequencing (scRNA-seq) and Circular Ribonucleic Acid (circRNA) data have made significant breakthroughs, especially in cancer genomics. Analysis of transcriptome time series data is core in identifying time point(s) where drastic changes in gene transcription are associated with homeostatic to non-homeostatic cellular transition (tipping points). In Chapter 2 of this dissertation, I present a novel cell-type specific and co-expression-based tipping point detection method to identify target gene (TG) versus transcription factor (TF) pairs whose differential co-expression across time points drive biological changes in different cell types and the time point when these changes are observed. This method was applied to scRNA-seq data sets from a SARS-CoV-2 study (18 time points), a human cerebellum development study (9 time points), and a lung injury study (18 time points). Similarly, leveraging transcriptome data across treatment time points, I developed methodologies to identify treatment-induced and cell-type specific differentially co-expressed pairs (DCEPs). In part one of Chapter 3, I presented a pipeline that used a series of statistical tests to detect DCEPs. This method was applied to scRNA-seq data of patients with non-small cell lung cancer (NSCLC) sequenced across cancer treatment times. However, this pipeline does not account for correlations among multiple single cells from the same sample and correlations among multiple samples from the same patient. In Part 2 of Chapter 3, I presented a solution to this problem using a mixed-effect model. In Chapter 4, I present a summary of my work that focused on the cross-species analysis of circRNA transcriptome time series data. I compared circRNA profiles in neonatal pig and mouse hearts, identified orthologous circRNAs, and discussed regulation mechanisms of cardiomyocyte proliferation and myocardial regeneration conserved between mouse and pig at different time points.
ContributorsNyarige, Verah Mocheche (Author) / Liu, Li (Thesis advisor) / Wang, Junwen (Thesis advisor) / Dinu, Valentin (Committee member) / Arizona State University (Publisher)
Created2022
Description
Beta-Amyloid(Aβ) plaques and tau protein tangles in the brain are now widely recognized as the defining hallmarks of Alzheimer’s disease (AD), followed by structural atrophy detectable on brain magnetic resonance imaging (MRI) scans. However, current methods to detect Aβ/tau pathology are either invasive (lumbar puncture) or quite costly and not widely available (positron emission tomography (PET)). And one of the particular neurodegenerative regions is the hippocampus to which the influence of Aβ/tau on has been one of the research projects focuses in the AD pathophysiological progress.
In this dissertation, I proposed three novel machine learning and statistical models to examine subtle aspects of the hippocampal morphometry from MRI that are associated with Aβ /tau burden in the brain, measured using PET images. The first model is a novel unsupervised feature reduction model to generate a low-dimensional representation of hippocampal morphometry for each individual subject, which has superior performance in predicting Aβ/tau burden in the brain. The second one is an efficient federated group lasso model to identify the hippocampal subregions where atrophy is strongly associated with abnormal Aβ/Tau. The last one is a federated model for imaging genetics, which can identify genetic and transcriptomic influences on hippocampal morphometry. Finally, I stated the results of these three models that have been published or submitted to peer-reviewed conferences and journals.
ContributorsWu, Jianfeng (Author) / Wang, Yalin (Thesis advisor) / Li, Baoxin (Committee member) / Liang, Jianming (Committee member) / Wang, Junwen (Committee member) / Wu, Teresa (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
Climate is a critical determinant of agricultural productivity, and the ability to accurately predict this productivity is necessary to provide guidance regarding food security and agricultural management. Previous predictions vary in approach due to the myriad of factors influencing agricultural productivity but generally suggest long-term declines in productivity and agricultural land suitability under climate change. In this paper, I relate predicted climate changes to yield for three major United States crops, namely corn, soybeans, and wheat, using a moderate emissions scenario. By adopting data-driven machine learning approaches, I used the following machine learning methods: random forest (RF), extreme gradient boosting (XGB), and artificial neural networks (ANN) to perform comparative analysis and ensemble methodology. I omitted the western US due to the region's susceptibility to water stress and the prevalence of artificial irrigation as a means to compensate for dry conditions. By considering only climate, the model's results suggest an ensemble mean decline in crop yield of 23.4\% for corn, 19.1\% for soybeans, and 7.8\% for wheat between the years of 2017 and 2100. These results emphasize potential negative impacts of climate change on the current agricultural industry as a result of shifting bio-climactic conditions.
ContributorsSwarup, Shray (Author) / Eikenberry, Steffen (Thesis director) / Mahalov, Alex (Committee member) / Barrett, The Honors College (Contributor) / Computer Science and Engineering Program (Contributor)
Created2023-05
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