Matching Items (126)
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 theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system, with a projective Hilbert space regarded as the phase space. This thesis extends the theory by including some aspects of the symplectic topology of the quantum phase space. It is shown that the quantum mechanical uncertainty principle is a special case of an inequality from J-holomorphic map theory, that is, J-holomorphic curves minimize the difference between the quantum covariance matrix determinant and a symplectic area. An immediate consequence is that a minimal determinant is a topological invariant, within a fixed homology class of the curve. Various choices of quantum operators are studied with reference to the implications of the J-holomorphic condition. The mean curvature vector field and Maslov class are calculated for a lagrangian torus of an integrable quantum system. The mean curvature one-form is simply related to the canonical connection which determines the geometric phases and polarization linear response. Adiabatic deformations of a quantum system are analyzed in terms of vector bundle classifying maps and related to the mean curvature flow of quantum states. The dielectric response function for a periodic solid is calculated to be the curvature of a connection on a vector bundle.
ContributorsSanborn, Barbara (Author) / Suslov, Sergei K (Thesis advisor) / Suslov, Sergei (Committee member) / Spielberg, John (Committee member) / Quigg, John (Committee member) / Menéndez, Jose (Committee member) / Jones, Donald (Committee member) / Arizona State University (Publisher)
Created2011
Description
This dissertation is intended to tie together a body of work which utilizes a variety of methods to study applied mathematical models involving heterogeneity often omitted with classical modeling techniques. I posit three cogent classifications of heterogeneity: physiological, behavioral, and local (specifically connectivity in this work). I consider physiological heterogeneity using the method of transport equations to study heterogeneous susceptibility to diseases in open populations (those with births and deaths). I then present three separate models of behavioral heterogeneity. An SIS/SAS model of gonorrhea transmission in a population of highly active men-who-have-sex-with-men (MSM) is presented to study the impact of safe behavior (prevention and self-awareness) on the prevalence of this endemic disease. Behavior is modeled in this examples via static parameters describing consistent condom use and frequency of STD testing. In an example of behavioral heterogeneity, in the absence of underlying dynamics, I present a generalization to ``test theory without an answer key" (also known as cultural consensus modeling or CCM). CCM is commonly used to study the distribution of cultural knowledge within a population. The generalized framework presented allows for selecting the best model among various extensions of CCM: multiple subcultures, estimating the degree to which individuals guess yes, and making competence homogenous in the population. This permits model selection based on the principle of information criteria. The third behaviorally heterogeneous model studies adaptive behavioral response based on epidemiological-economic theory within an $SIR$ epidemic setting. Theorems used to analyze the stability of such models with a generalized, non-linear incidence structure are adapted and applied to the case of standard incidence and adaptive incidence. As an example of study in spatial heterogeneity I provide an explicit solution to a generalization of the continuous time approximation of the Albert-Barabasi scale-free network algorithm. The solution is found by recursively solving the differential equations via integrating factors, identifying a pattern for the coefficients and then proving this observed pattern is consistent using induction. An application to disease dynamics on such evolving structures is then studied.
ContributorsMorin, Benjamin (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Hiebeler, David (Thesis advisor) / Hruschka, Daniel (Committee member) / Suslov, Sergei (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
Cancer remains one of the leading killers throughout the world. Death and disability due to lung cancer in particular accounts for one of the largest global economic burdens a disease presents. The burden on third-world countries is especially large due to the unusually large financial stress that comes from late tumor detection and expensive treatment options. Early detection using inexpensive techniques may relieve much of the burden throughout the world, not just in more developed countries. I examined the immune responses of lung cancer patients using immunosignatures – patterns of reactivity between host serum antibodies and random peptides. Immunosignatures reveal disease-specific patterns that are very reproducible. Immunosignaturing is a chip-based method that has the ability to display the antibody diversity from individual sera sample with low cost. Immunosignaturing is a medical diagnostic test that has many applications in current medical research and in diagnosis. From a previous clinical study, patients diagnosed for lung cancer were tested for their immunosignature vs. healthy non-cancer volunteers. The pattern of reactivity against the random peptides (the ‘immunosignature’) revealed common signals in cancer patients, absent from healthy controls. My study involved the search for common amino acid motifs in the cancer-specific peptides. My search through the hundreds of ‘hits’ revealed certain motifs that were repeated more times than expected by random chance. The amino acids that were the most conserved in each set include tryptophan, aspartic acid, glutamic acid, proline, alanine, serine, and lysine. The most overall conserved amino acid observed between each set was D - aspartic acid. The motifs were short (no more than 5-6 amino acids in a row), but the total number of motifs I identified was large enough to assure significance. I utilized Excel to organize the large peptide sequence libraries, then CLUSTALW to cluster similar-sequence peptides, then GLAM2 to find common themes in groups of peptides. In so doing, I found sequences that were also present in translated cancer expression libraries (RNA) that matched my motifs, suggesting that immunosignatures can find cancer-specific antigens that can be both diagnostic and potentially therapeutic.
ContributorsShiehzadegan, Shima (Author) / Johnston, Stephen (Thesis director) / Stafford, Phillip (Committee member) / School of Life Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2015-12
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 influenza virus, also known as "the flu", is an infectious disease that has constantly affected the health of humanity. There is currently no known cure for Influenza. The Center for Innovations in Medicine at the Biodesign Institute located on campus at Arizona State University has been developing synbodies as a possible Influenza therapeutic. Specifically, at CIM, we have attempted to design these initial synbodies to target the entire Influenza virus and preliminary data leads us to believe that these synbodies target Nucleoprotein (NP). Given that the synbody targets NP, the penetration of cells via synbody should also occur. Then by Western Blot analysis we evaluated for the diminution of NP level in treated cells versus untreated cells. The focus of my honors thesis is to explore how synthetic antibodies can potentially inhibit replication of the Influenza (H1N1) A/Puerto Rico/8/34 strain so that a therapeutic can be developed. A high affinity synbody for Influenza can be utilized to test for inhibition of Influenza as shown by preliminary data. The 5-5-3819 synthetic antibody's internalization in live cells was visualized with Madin-Darby Kidney Cells under a Confocal Microscope. Then by Western Blot analysis we evaluated for the diminution of NP level in treated cells versus untreated cells. Expression of NP over 8 hours time was analyzed via Western Blot Analysis, which showed NP accumulation was retarded in synbody treated cells. The data obtained from my honors thesis and preliminary data provided suggest that the synthetic antibody penetrates live cells and targets NP. The results of my thesis presents valuable information that can be utilized by other researchers so that future experiments can be performed, eventually leading to the creation of a more effective therapeutic for influenza.
ContributorsHayden, Joel James (Author) / Diehnelt, Chris (Thesis director) / Johnston, Stephen (Committee member) / Legutki, Bart (Committee member) / Barrett, The Honors College (Contributor) / Department of Psychology (Contributor) / Department of Chemistry and Biochemistry (Contributor)
Created2014-05
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