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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
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
Background: Human papillomavirus (HPV) is the cause of 99.7% of cervical cancers. Research of cervical cancer has made this disease mostly curable in the developing world. Head and neck cancer, which is increasingly caused by HPV, still is associated with a mortality rate of 50,000 in the US annually. This study proposed to evaluate the biology of HPV-16 in head and neck tumors by using RT-qPCR to measure the RNA expression and its relation to physical status of the virus. Methods: This study was to develop an assay that uses RT-qPCR to determine the quantitative expression of HPV-16 RNA coding for proteins E1, E2, E4, E5, E6, and E7 in tumor samples. The assay development started with creation of primers. It went on to test the primers on template DNA through traditional PCR and then on DNA from HPV-16 positive cell lines, SiHa and CaSki, using RT-qPCR. This paper also describes the troubleshooting methods taken for the PCR reaction. Once the primers are verified, the RT-qPCR process can be carried out on RNA purified from tumor samples. Results: No primer sets have been confirmed to produce a product through PCR or RT-qPCR. The primer sequences match up correctly with known sequences for HPV-16 E1, E2, E4, E5, E6, and E7. RT-qPCR showed results consistent with the hypothesis. Conclusion: The RT-qPCR protocol must be optimized to confirm the primer sequences work as desired. Then primers will be used to study physical status and RNA expression in HPV-positive and HPV-negative head and neck tumor samples. This assay can help shed light on which proteins are expressed most in tumors of the head and neck and will aid in the development of future screening and treatment options.
ContributorsKhazanovich, Jakob (Author) / Anderson, Karen (Thesis director) / Mangone, Marco (Committee member) / Sundaresan, Sri Krishna (Committee member) / Barrett, The Honors College (Contributor)
Created2015-05
Description
Duchenne Muscular Dystrophy (DMD) is an X-linked recessive disease characterized by progressive muscle loss and weakness. This disease arises from a mutation that occurs on a gene that encodes for dystrophin, which results in observable muscle death and inflammation; however, the genetic changes that result from dystrophin's dysfunctionality remain unknown. Current DMD research uses mdx mice as a model, and while very useful, does not allow the study of cell-autonomous transcriptome changes during the progression of DMD due to the strong inflammatory response, perhaps hiding important therapeutic targets. C. elegans, which has a very weak inflammatory response compared to mdx mice and humans, has been used in the past to study DMD with some success. The worm ortholog of the dystrophin gene has been identified as dys-1 since its mutation phenocopies the progression of the disease and a portion of the human dystrophin gene alleviates symptoms. Importantly, the extracted RNA transcriptome from dys-1 worms showed significant change in gene expression, which needs to be further investigated with the development of a more robust model. Our lab previously published a method to isolate high-quality muscle-specific RNA from worms, which could be used to study such changes at higher resolution. We crossed the dys-1 worms with our muscle-specific strain and demonstrated that the chimeric strain exhibits similar behavioral symptoms as DMD patients as characterized by a shortened lifespan, difficulty in movement, and a decrease in speed. The presence of dys-1 and other members of the dystrophin complex in the body muscle were supported by the development of a resulting phenotype due to RNAi knockdown of each component in the body muscle; however, further experimentation is needed to reinforce this conclusion. Thus, the constructed chimeric C. elegans strain possesses unique characteristics that will allow the study of genetic changes, such as transcriptome rearrangements and dysregulation of miRNA, and how they affect the progression of DMD.
ContributorsNguyen, Thuy-Duyen Cao (Author) / Mangone, Marco (Thesis director) / Newbern, Jason (Committee member) / Duchaine, Thomas (Committee member) / School of Social Transformation (Contributor) / School of Life Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
microRNAs (miRNAs) are short ~22nt non-coding RNAs that regulate gene output at the post-transcriptional level. Via targeting of degenerate elements primarily in 3'untranslated regions (3'UTR) of mRNAs, miRNAs can target thousands of varying genes and suppress their protein translation. The precise mechanistic function and bio- logical role of miRNAs is not fully understood and yet it is a major contributor to a pleth- ora of diseases, including neurological disorders, muscular disorders, and cancer. Cer- tain model organisms are valuable in understanding the function of miRNA and there- fore fully understanding the biological significance of miRNA targeting. Here I report a mechanistic analysis of miRNA targeting in C. elegans, and a bioinformatic approach to aid in further investigation of miRNA targeted sequences. A few of the biologically significant mechanisms discussed in this thesis include alternative polyadenylation, RNA binding proteins, components of the miRNA recognition machinery, miRNA secondary structures, and their polymorphisms. This thesis also discusses a novel bioinformatic approach to studying miRNA biology, including computational miRNA target prediction software, and sequence complementarity. This thesis allows a better understanding of miRNA biology and presents an ideal strategy for approaching future research in miRNA targeting.
ContributorsWeigele, Dustin Keith (Author) / Mangone, Marco (Thesis director) / Katchman, Benjamin (Committee member) / Barrett, The Honors College (Contributor) / Department of Chemistry and Biochemistry (Contributor) / School of Life Sciences (Contributor)
Created2014-12
Description
The Cannabis plant has historical roots with human beings. The plant produces compounds called cannabinoids, which are responsible for the physiological affects of Cannabis and make it a research candidate for medicinal use. Analysis of the plant and its components will help build a better database that could be used to develop a complete roster of medicinal benefits. Research regarding the cellular protein receptors that bind the cannabinoids may not only help provide reasons explaining why the Cannabis plant could be medicinally relevant, but will also help explain how the receptors originated. The receptors may have been present in organisms before the present day Cannabis plant. So why would there be receptors that bind to cannabinoids? Searching for an endocannabinoid system could help explain the purpose of the cannabinoid receptors and their current structures in humans. Using genetic technologies we are able to take a closer look into the evolutionary history of cannabinoids and the receptors that bind them.
ContributorsSalasnek, Reed Samuel (Author) / Capco, David (Thesis director) / Mangone, Marco (Committee member) / Stump, Edmund (Committee member) / Barrett, The Honors College (Contributor) / School of Life Sciences (Contributor)
Created2014-05
Description
A coincidence reporter construct, consisting of the p21-promoter and two luciferase genes (Firefly and Renilla), was constructed for the screening of drugs that might inhibit Olig2's tumorigenic role in glioblastoma. The reporter construct was tested using an Olig2 inhibitor, HSP990, as well as short hairpin RNA targeting Olig2. Further confirmatory analysis is needed before the reporter cell line is ready for high-throughput screening at the NIH and lead compound selection.
ContributorsCusimano, Joseph Michael (Author) / LaBaer, Joshua (Thesis director) / Mangone, Marco (Committee member) / Mehta, Shwetal (Committee member) / Barrett, The Honors College (Contributor) / Department of Chemistry and Biochemistry (Contributor)
Created2014-05
Description
Background: Breast cancer is the most frequently diagnosed cancer and the leading cause of cancer deaths in females worldwide, accounting for 23% of all new cancer cases and 14% of all total cancer deaths in 2008. Five tumor-normal pairs of primary breast epithelial cells were treated for infinite proliferation by using a ROCK inhibitor and mouse feeder cells. Methods: Raw paired-end, 100x coverage RNA-Seq data was aligned to the Human Reference Genome Version 19 using BWA and Tophat. Gene differential expression analysis was completed using Cufflinks and Cuffdiff. Interactive Genome Viewer was used for data visualization. Results: 15 genes were found to be down-regulated by at least one log-fold change in 4/5 of tumor samples. 75 genes were found to be down-regulated in 3/5 of our tumor samples by at least one log-fold change. 11 genes were found to be up-regulated in 4/5 of our tumor samples, and 68 genes were identified to be up-regulated in 3/5 of the tumor samples by at least one-fold change. Conclusion: Expression changes in genes such as AZGP1, AGER, ALG11, and S1007 suggest a disruption in the glycosylation pathway. No correlation was found between Cufflink's Her2 gene-expression and DAKO score classification.
ContributorsHernandez, Fernando (Author) / Anderson, Karen (Thesis director) / Mangone, Marco (Committee member) / Park, Jin (Committee member) / Barrett, The Honors College (Contributor) / Department of Information Systems (Contributor)
Created2013-05
Description
miRNAs are short non-coding regulatory RNAs that have an important roles in a wide range of biological processes. Dysfunction of miRNA regulation has also been shown to occur in diseases such as cancer. Despite the widespread influence of miRNAs in these contexts, the vast majority of miRNA targets are poorly characterized. The aim of this research project was to gain a better understating of miRNA targeting by using the model organism C. elegans. In order to do this I adapted a novel high-throughput assay to detect miRNA targets for use with the C. elegans 3`UTRome. As a proof of principle I performed this assay on 96 C. elegans 3`UTRs using high-throughput techniques. The results revealed miRNA interactions with two predicted 3`UTR targets for the miRNA lin-4 and ten unpredicted targets. The results also corroborated previous findings that certain worm miRNAs require special modifications to be expressed in human cells.
ContributorsKotagama, Kasuen Indrajith Bandara (Author) / Mangone, Marco (Thesis director) / Anderson, Karen (Committee member) / Barrett, The Honors College (Contributor) / Department of Chemistry and Biochemistry (Contributor)
Created2013-12