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Description
Nonlinear dispersive equations model nonlinear waves in a wide range of physical and mathematics contexts. They reinforce or dissipate effects of linear dispersion and nonlinear interactions, and thus, may be of a focusing or defocusing nature. The nonlinear Schrödinger equation or NLS is an example of such equations. It appears as a model in hydrodynamics, nonlinear optics, quantum condensates, heat pulses in solids and various other nonlinear instability phenomena. In mathematics, one of the interests is to look at the wave interaction: waves propagation with different speeds and/or different directions produces either small perturbations comparable with linear behavior, or creates solitary waves, or even leads to singular solutions. This dissertation studies the global behavior of finite energy solutions to the $d$-dimensional focusing NLS equation, $i partial _t u+Delta u+ |u|^{p-1}u=0, $ with initial data $u_0in H^1,; x in Rn$; the nonlinearity power $p$ and the dimension $d$ are chosen so that the scaling index $s=frac{d}{2}-frac{2}{p-1}$ is between 0 and 1, thus, the NLS is mass-supercritical $(s>0)$ and energy-subcritical $(s<1).$ For solutions with $ME[u_0]<1$ ($ME[u_0]$ stands for an invariant and conserved quantity in terms of the mass and energy of $u_0$), a sharp threshold for scattering and blowup is given. Namely, if the renormalized gradient $g_u$ of a solution $u$ to NLS is initially less than 1, i.e., $g_u(0)<1,$ then the solution exists globally in time and scatters in $H^1$ (approaches some linear Schr"odinger evolution as $ttopminfty$); if the renormalized gradient $g_u(0)>1,$ then the solution exhibits a blowup behavior, that is, either a finite time blowup occurs, or there is a divergence of $H^1$ norm in infinite time. This work generalizes the results for the 3d cubic NLS obtained in a series of papers by Holmer-Roudenko and Duyckaerts-Holmer-Roudenko with the key ingredients, the concentration compactness and localized variance, developed in the context of the energy-critical NLS and Nonlinear Wave equations by Kenig and Merle. One of the difficulties is fractional powers of nonlinearities which are overcome by considering Besov-Strichartz estimates and various fractional differentiation rules.
ContributorsGuevara, Cristi Darley (Author) / Roudenko, Svetlana (Thesis advisor) / Castillo_Chavez, Carlos (Committee member) / Jones, Donald (Committee member) / Mahalov, Alex (Committee member) / Suslov, Sergei (Committee member) / Arizona State University (Publisher)
Created2011
Description
The goal of this project was to design and create a genetic construct that would allow for <br/>tumor growth to be induced in the center of the wing imaginal disc of Drosophila larvae, the <br/>R85E08 domain, using a heat shock. The resulting transgene would be combined with other <br/>transgenes in a single fly that would allow for simultaneous expression of the oncogene and, in <br/>the surrounding cells, other genes of interest. This system would help establish Drosophila as a <br/>more versatile and reliable model organism for cancer research. Furthermore, pilot studies were <br/>performed, using elements of the final proposed system, to determine if tumor growth is possible <br/>in the center of the disc, which oncogene produces the best results, and if oncogene expression <br/>induced later in development causes tumor growth. Three different candidate genes were <br/>investigated: RasV12, PvrACT, and Avli.
ContributorsSt Peter, John Daniel (Author) / Harris, Rob (Thesis director) / Varsani, Arvind (Committee member) / School of Molecular Sciences (Contributor) / Department of Psychology (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
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
It is possible in a properly controlled environment, such as industrial metrology, to make significant headway into the non-industrial constraints on image-based position measurement using the techniques of image registration and achieve repeatable feature measurements on the order of 0.3% of a pixel, or about an order of magnitude improvement on conventional real-world performance. These measurements are then used as inputs for a model optimal, model agnostic, smoothing for calibration of a laser scribe and online tracking of velocimeter using video input. Using appropriate smooth interpolation to increase effective sample density can reduce uncertainty and improve estimates. Use of the proper negative offset of the template function has the result of creating a convolution with higher local curvature than either template of target function which allows improved center-finding. Using the Akaike Information Criterion with a smoothing spline function it is possible to perform a model-optimal smooth on scalar measurements without knowing the underlying model and to determine the function describing the uncertainty in that optimal smooth. An example of empiric derivation of the parameters for a rudimentary Kalman Filter from this is then provided, and tested. Using the techniques of Exploratory Data Analysis and the "Formulize" genetic algorithm tool to convert the spline models into more accessible analytic forms resulted in stable, properly generalized, KF with performance and simplicity that exceeds "textbook" implementations thereof. Validation of the measurement includes that, in analytic case, it led to arbitrary precision in measurement of feature; in reasonable test case using the methods proposed, a reasonable and consistent maximum error of around 0.3% the length of a pixel was achieved and in practice using pixels that were 700nm in size feature position was located to within ± 2 nm. Robust applicability is demonstrated by the measurement of indicator position for a King model 2-32-G-042 rotameter.
ContributorsMunroe, Michael R (Author) / Phelan, Patrick (Thesis advisor) / Kostelich, Eric (Committee member) / Mahalov, Alex (Committee member) / Arizona State University (Publisher)
Created2012
Description
Members of the Delphinidae family are widely distributed across the world’s oceans. We used a viral metagenomic approach to identify viruses in orca (Orcinus orca) and short-finned pilot whale (Globicephala macrorhynchus) muscle, kidney, and liver samples from deceased animals. From orca tissue samples (muscle, kidney, and liver), we identified a novel polyomavirus (Polyomaviridae), three cressdnaviruses, and two genomoviruses (Genomoviridae). In the short-finned pilot whale we were able to identify one genomovirus in a kidney sample. The presence of unclassified cressdnavirus within two samples (muscle and kidney) of the same animal supports the possibility these viruses might be widespread within the animal. The orca polyomavirus identified here is the first of its species and is not closely related to the only other dolphin polyomavirus previously discovered. The identification and verification of these viruses expands the current knowledge of viruses that are associated with the Delphinidae family.
ContributorsSmith, Kendal Ryan (Author) / Varsani, Arvind (Thesis director) / Kraberger, Simona (Committee member) / Dolby, Greer (Committee member) / School of Life Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
Phage therapy has been around for more than a century, but has regained interest in the field of medicine and holds significant potential to act as a treatment against a deadly bacterial infection in various cactus species. It was discovered that bacteriophages isolated from soil samples of potato plants were able to suppress Pectobacterium carotovorum, ‘Pectobacterium’ being within the family Pectobacteriaceae which contains the ‘Erwinia’ genus that causes soft rot diseases in various plants (Jones, 2012). The two scientists had co-inoculated “... the phage with the phytobacterium” (Jones, 2012) in order to suppress the growth and prevent the infection from occurring.
ContributorsFry, Danielle Elizabeth (Author) / Geiler-Samerotte, Kerry (Thesis director) / Pfeifer, Susanne (Committee member) / Varsani, Arvind (Committee member) / College of Health Solutions (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05
Description
Following the journey through the sewerage system, wastewater is subject to a series of purification procedures, prior to water reuse and disposal of the resultant sewage sludge. Biosolids, also known as treated sewage sludge, deemed fit for application on land, is a nutrient-rich, semisolid byproduct of biological wastewater treatment. Technological progression in metagenomics has allowed for large-scale analysis of complex viral communities in a number of samples, including wastewater. Members of the Microviridae family are non-enveloped, ssDNA bacteriophages, and are known to infect enterobacteria. Members of the Genomoviridae family similarly are non-enveloped, ssDNA viruses, but are presumed to infect fungi rather than eubacteria. As these two families of viruses are not relatively documented and their diversity poorly classified, this study aimed to analyze the presence of genomoviruses and the diversity of microviruses in nine samples representative of wastewater in Arizona and other regions of the United States. Using a metagenomic approach, the nucleic acids of genomoviruses and microviruses were isolated, assembled into complete genomes, and characterized through visual analysis: a heat chart showing percent coverage for genomoviruses and a circular phylogenetic tree showing diversity of microviruses. The heat map results for the genomoviruses showed a large presence of 99 novel sequences in all nine wastewater samples. Additionally, the 535 novel microviruses displayed great diversity in the cladogram, both in terms of sub-family and isolation source. Further research should be conducted in order to classify the taxonomy of microviruses and the diversity of genomoviruses. Finally, this study suggests future exploration of the viral host, prior to entering the wastewater system.
ContributorsSchreck, Joshua Reuben (Author) / Varsani, Arvind (Thesis director) / Rolf, Halden (Committee member) / Misra, Rajeev (Committee member) / School of Film, Dance and Theatre (Contributor) / School of Life Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05
Description
Yellow-bellied marmots (Marmota flavivent) are semi-fossorial ground-dwelling sciurid rodents native to the western United States. They are facultatively social and live in colonies that may contain over 50 individuals. Marmot populations are well studied in terms of their diet, life cycle, distribution, and behavior, however, knowledge about viruses associated with marmots is very limited. In this study we aim to identify DNA viruses by non-invasive sampling of their feces. Viral DNA was extracted from fecal material of 35 individual marmots collected in Colorado and subsequently submitted to rolling circle amplification for circular molecule enrichment. Using a viral metagenomics approach which included high-throughput sequencing and verification of viral genomes using PCR, cloning and sequencing, a diverse group of single-stranded (ss) DNA viruses were identified. Diverse ssDNA viruses were identified that belong to two established families, Genomoviridae (n=7) and Anelloviridae (n=1) and several others that belong to unclassified circular replication associated encoding single-stranded (CRESS) DNA virus groups (n=19). There were also circular DNA molecules extracted (n=4) that appear to encode one viral-like gene and are composed of <1545 nt. The viruses that belonged to the family Genomoviridae clustered with those in the Gemycircularvirus genus. The genomoviruses were extracted from 6 samples. These clustered with gemycircularvirus extracted from arachnids and feces. The anellovirus, extracted from one sample, identified here has a genome sequence that is most similar to those from other rodent species, lagomorphs, and mosquitos. The CRESS viruses identified here were extracted from 9 samples and are novel and cluster with others identified from avian species. This study gives a snapshot of viruses associated with marmots based on fecal sampling.
ContributorsKhalifeh, Anthony (Author) / Varsani, Arvind (Thesis director) / Kraberger, Simona (Committee member) / Dolby, Greer (Committee member) / School of Life Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05
Description
To date, there have been few, if any, studies evaluating the venom toxin levels in dogs that have been naturally envenomated by pit vipers. Understanding venom toxin pharmacokinetics in a clinical setting is important for a variety of reasons, including the potential to better elucidate treatment options, prognosis, and other factors associated with pit viper envenomation. In addition, dogs serve as a comparative species to humans for evaluating pit viper envenomations. This pilot study’s primary objective was to address the question of “What do we see?” in dogs presenting for rattlesnake envenomation. To answer this question, we obtained serum from envenomated dogs presenting at three veterinary clinics, then used enzyme-linked immunosorbent assay (ELISA) and western blot analysis to measure total venom and key toxins in sera. Phospholipase A2, a primary venom toxin, was identified in a few samples by the western blot, and contributed to the positive correlation between percent echinocytes in the blood and venom concentration. Medical data records were compared to venom concentrations measured using ELISA to determine whether there were any significant correlations. First, the hematological results were compared. Clotting times showed a strong positive correlation, clotting times and platelets showed a negative correlation, while echinocytes and platelets showed no correlation. When compared to venom concentration, clotting times showed a negative correlation, while age showed a positive correlation. Weight and platelets were also compared to venom concentration, but no significant correlations were found. The logistics of this study provided a real-world model where time elapsed between envenomation and hospital admission, thus giving a realistic look at what occurs in both animal and human medicine.
ContributorsNelson, Alexis (Co-author, Co-author) / DeNardo, Dale (Thesis director) / Woods, Craig (Thesis director) / Varsani, Arvind (Committee member) / Harrington Bioengineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
Human papillomavirus (HPV) is the causative agent of cervical cancer. Persistent infection with high-risk HPV 16, 18 or 45 species is associated with the development and progression of cervical cancer. HPV genotyping and Pap smear tests are the regular methods used to detect pre-invasive cervical lesions, but there is a need for developing a rapid biomarker to profile immunity to these viruses. The viral E7 oncogene is expressed in most HPV-associated cancers and anti-E7 antibodies can be detected in the blood of patients with cervical cancer. This research was focused on viral E7 oncogene expression to be used in development of low-cost point of care tests, enabling patients from low resource settings to detect the asymptotic stage of cervical cancer and be able to seek treatment early. In order to produce the E7 protein in vitro to measure antibody levels, GST tagged E7 genes from HPV 16, 18 and 45 species were inserted into the pDEST15 vector and expressed in E. coli BL21DE3 cells that were induced with 1mM of IPTG. The E7-GST fused expressed protein was then purified using glutathione beads and resolved on sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE). Protein expression was 5.8 \u03bcg/ml for HPV 16E7 in 500 ml culture and for the 500 ml culture of HPV 18 E7 and 45 E7 were 10.5 \u03bcg/ml and 10.5 \u03bcg/ml for HPV 18E7 and 45E7 respectively. High yield values are showing high expression levels of GST-tagged E7 recombinant protein which can be used for serotyping a number of individuals. This shows that HPV E7 can be produced in large quantities that can potentially be used in point of care tests that can help identify women at risk of cervical cancer. In conclusion, the E7 protein produced in this study can potentially be used to induce humoral responses in patients\u2019 sera for understanding the immune response of cervical cancer.
ContributorsMakuyana, Ntombizodwa (Author) / Anderson, Karen (Thesis director) / Ewaisha, Radwa (Committee member) / Varsani, Arvind (Committee member) / Hou, Ching-Wen (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / School of Molecular Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-12