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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
A synbody is a newly developed protein binding peptide which can be rapidly produced by chemical methods. The advantages of the synbody producing process make it a potential human proteome binding reagent. Most of the synbodies are designed to bind to specific proteins. The peptides incorporated in a synbody are discovered with peptide microarray technology. Nevertheless, the targets for unknown synbodies can also be discovered by searching through a protein mixture. The first part of this thesis mainly focuses on the process of target searching, which was performed with immunoprecipitation assays and mass spectrometry analysis. Proteins are pulled down from the cell lysate by certain synbodies, and then these proteins are identified using mass spectrometry. After excluding non-specific bindings, the interaction between a synbody and its real target(s) can be verified with affinity measurements. As a specific example, the binding between 1-4-KCap synbody and actin was discovered. This result proved the feasibility of the mass spectrometry based method and also suggested that a high throughput synbody discovery platform for the human proteome could be developed. Besides the application of synbody development, the peptide microarray technology can also be used for immunosignatures. The composition of all types of antibodies existing in one's blood is related to an individual's health condition. A method, called immunosignaturing, has been developed for early disease diagnosis based on this principle. CIM10K microarray slides work as a platform for blood antibody detection in immunosignaturing. During the analysis of an immunosignature, the data from these slides needs to be validated by using landing light peptides. The second part of this thesis focuses on the validation of the data. A biotinylated peptide was used as a landing light on the new CIM10K slides. The data was collected in several rounds of tests and indicated that the variation among landing lights was significantly reduced by using the newly prepared biotinylated peptide compared with old peptide mixture. Several suggestions for further landing light improvement are proposed based on the results.
ContributorsSun, Minyao (Author) / Johnston, Stephen Albert (Thesis advisor) / Diehnelt, Chris Wayne (Committee member) / Stafford, Phillip (Committee member) / Arizona State University (Publisher)
Created2011
Description
Immunosignaturing is a new immunodiagnostic technology that uses random-sequence peptide microarrays to profile the humoral immune response. Though the peptides have little sequence homology to any known protein, binding of serum antibodies may be detected, and the pattern correlated to disease states. The aim of my dissertation is to analyze the factors affecting the binding patterns using monoclonal antibodies and determine how much information may be extracted from the sequences. Specifically, I examined the effects of antibody concentration, competition, peptide density, and antibody valence. Peptide binding could be detected at the low concentrations relevant to immunosignaturing, and a monoclonal's signature could even be detected in the presences of 100 fold excess naive IgG. I also found that peptide density was important, but this effect was not due to bivalent binding. Next, I examined in more detail how a polyreactive antibody binds to the random sequence peptides compared to protein sequence derived peptides, and found that it bound to many peptides from both sets, but with low apparent affinity. An in depth look at how the peptide physicochemical properties and sequence complexity revealed that there were some correlations with properties, but they were generally small and varied greatly between antibodies. However, on a limited diversity but larger peptide library, I found that sequence complexity was important for antibody binding. The redundancy on that library did enable the identification of specific sub-sequences recognized by an antibody. The current immunosignaturing platform has little repetition of sub-sequences, so I evaluated several methods to infer antibody epitopes. I found two methods that had modest prediction accuracy, and I developed a software application called GuiTope to facilitate the epitope prediction analysis. None of the methods had sufficient accuracy to identify an unknown antigen from a database. In conclusion, the characteristics of the immunosignaturing platform observed through monoclonal antibody experiments demonstrate its promise as a new diagnostic technology. However, a major limitation is the difficulty in connecting the signature back to the original antigen, though larger peptide libraries could facilitate these predictions.
ContributorsHalperin, Rebecca (Author) / Johnston, Stephen A. (Thesis advisor) / Bordner, Andrew (Committee member) / Taylor, Thomas (Committee member) / Stafford, Phillip (Committee member) / Arizona State University (Publisher)
Created2011
Description
African Swine Fever (ASF), endemic in many African countries, is now spreading to other continents. Though ASF is capable of incurring serious economic losses in affected countries, no vaccine exists to provide immunity to animals. Disease control relies largely on rapid diagnosis and the implementation of movement restrictions and strict eradication programs. Developing a scalable, accurate and low cost diagnostic for ASF will be of great help for the current situation. CIM's 10K random peptide microarray is a new high-throughput platform that allows systematic investigations of immune responses associated with disease and shows promise as a diagnostic tool. In this study, this new technology was applied to characterize the immune responses of ASF virus (ASFV) infections and immunizations. Six sets of sera from ASFV antigen immunized pigs, 6 sera from infected pigs and 20 sera samples from unexposed pigs were tested and analyzed statistically. Results show that both ASFV antigen immunized pigs and ASFV viral infected pigs can be distinguished from unexposed pigs. Since it appears that immune responses to other viral infections are also distinguishable on this platform, it holds the potential of being useful in developing a new ASF diagnostic. The ability of this platform to identify specific ASFV antibody epitopes was also explored. A subtle motif was found to be shared among a set of peptides displaying the highest reactivity for an antigen specific antibody. However, this motif does not seem to match with any antibody epitopes predicted by a linear antibody epitope prediction.
ContributorsXiao, Liang (Author) / Sykes, Kathryn (Thesis advisor) / Zhao, Zhan-Gong (Committee member) / Stafford, Phillip (Committee member) / Arizona State University (Publisher)
Created2011
Description
The use of synthetic cathinones or "bath salts" has risen dramatically in recent years with one of the most popular being Methylendioxypyrovalerone (MDPV). Following the temporary legislative ban on the sale and distribution of this compound , a multitude of other cathinone derivatives have been synthesized. The current study seeks to compare the abuse potential of MDPV with one of the emergent synthetic cathinones 4-methylethcathinone (4-MEC), based on their respective ability to lower current thresholds in an intracranial self-stimulation (ICSS) paradigm. Following acute administration (0.1, 0.5, 1 and 2 mg/kg i.p.) MDPV was found to significantly lower ICSS thresholds at all doses tested (F4,35=11.549, p<0.001). However, following acute administration (0.3,1,3,10,30 mg/kg i.p) 4-MEC produced no significant ICSS threshold depression (F5,135= 0.622, p = 0.684). Together these findings suggest that while MDPV may possess significant abuse potential, other synthetic cathinones such as 4-MEC may have a drastically reduced potential for abuse.
ContributorsWegner, Scott Andrew (Author) / Olive, M. Foster (Thesis director) / Presson, Clark (Committee member) / Sanabria, Federico (Committee member) / Barrett, The Honors College (Contributor) / Department of Chemistry and Biochemistry (Contributor) / Department of Psychology (Contributor)
Created2013-05
Description
Food system and health characteristics were evaluated across the last Waorani hunter-gatherer group in Amazonian Ecuador and a remote neighboring Kichwa indigenous subsistence agriculture community. Hunter-gatherer food systems like the Waorani foragers may not only be nutritionally, but also pharmaceutically beneficial because of high dietary intake of varied plant phytochemical compounds. A modern diet that reduces these dietary plant defense phytochemicals below levels typical in human evolutionary history may leave humans vulnerable to diseases that were controlled through a foraging diet. Few studies consider the health impact of the recent drastic reduction of plant phytochemical content in the modern global food system, which has eliminated essential components of food because they are not considered "nutrients". The antimicrobial and anti-inflammatory nature of the food system may not only regulate infectious pathogens and inflammatory disease, but also support beneficial microbes in human hosts, reducing vulnerability to chronic diseases. Waorani foragers seem immune to certain infections with very low rates of chronic disease. Does returning to certain characteristics of a foraging food system begin to restore the human body microbe balance and inflammatory response to evolutionary norms, and if so, what implication does this have for the treatment of disease? Several years of data on dietary and health differences across the foragers and the farmers was gathered. There were major differences in health outcomes across the board. In the Waorani forager group there were no signs of infection in serious wounds such as 3rd degree burns and spear wounds. The foragers had one-degree lower body temperature than the farmers. The Waorani had an absence of signs of chronic diseases including vision and blood pressure that did not change markedly with age while Kichwa farmers suffered from both chronic diseases and physiological indicators of aging. In the Waorani forager population, there was an absence of many common regional infectious diseases, from helminthes to staphylococcus. Study design helped control for confounders (exercise, environment, genetic factors, non-phytochemical dietary intake). This study provides evidence of the major role total phytochemical dietary intake plays in human health, often not considered by policymakers and nutritional and agricultural scientists.
ContributorsLondon, Douglas (Author) / Tsuda, Takeyuki (Thesis advisor) / Beezhold, Bonnie L (Committee member) / Hruschka, Daniel (Committee member) / Eder, James (Committee member) / Arizona State University (Publisher)
Created2012
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
We propose a novel solution to prevent cancer by developing a prophylactic cancer. Several sources of antigens for cancer vaccines have been published. Among these, antigens that contain a frame-shift (FS) peptide or viral peptide are quite attractive for a variety of reasons. FS sequences, from either mistake in RNA processing or in genomic DNA, may lead to generation of neo-peptides that are foreign to the immune system. Viral peptides presumably would originate from exogenous but integrated viral nucleic acid sequences. Both are non-self, therefore lessen concerns about development of autoimmunity. I have developed a bioinformatical approach to identify these aberrant transcripts in the cancer transcriptome. Their suitability for use in a vaccine is evaluated by establishing their frequencies and predicting possible epitopes along with their population coverage according to the prevalence of major histocompatibility complex (MHC) types. Viral transcripts and transcripts with FS mutations from gene fusion, insertion/deletion at coding microsatellite DNA, and alternative splicing were identified in NCBI Expressed Sequence Tag (EST) database. 48 FS chimeric transcripts were validated in 50 breast cell lines and 68 primary breast tumor samples with their frequencies from 4% to 98% by RT-PCR and sequencing confirmation. These 48 FS peptides, if translated and presented, could be used to protect more than 90% of the population in Northern America based on the prediction of epitopes derived from them. Furthermore, we synthesized 150 peptides that correspond to FS and viral peptides that we predicted would exist in tumor patients and we tested over 200 different cancer patient sera. We found a number of serological reactive peptide sequences in cancer patients that had little to no reactivity in healthy controls; strong support for the strength of our bioinformatic approach. This study describes a process used to identify aberrant transcripts that lead to a new source of antigens that can be tested and used in a prophylactic cancer vaccine. The vast amount of transcriptome data of various cancers from the Cancer Genome Atlas (TCGA) project will enhance our ability to further select better cancer antigen candidates.
ContributorsLee, HoJoon (Author) / Johnston, Stephen A. (Thesis advisor) / Kumar, Sudhir (Committee member) / Miller, Laurence (Committee member) / Stafford, Phillip (Committee member) / Sykes, Kathryn (Committee member) / Arizona State University (Publisher)
Created2012
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
Immunosignaturing is a technology that allows the humoral immune response to be observed through the binding of antibodies to random sequence peptides. The immunosignaturing microarray is based on complex mixtures of antibodies binding to arrays of random sequence peptides in a multiplexed fashion. There are computational and statistical challenges to the analysis of immunosignaturing data. The overall aim of my dissertation is to develop novel computational and statistical methods for immunosignaturing data to access its potential for diagnostics and drug discovery. Firstly, I discovered that a classification algorithm Naive Bayes which leverages the biological independence of the probes on our array in such a way as to gather more information outperforms other classification algorithms due to speed and accuracy. Secondly, using this classifier, I then tested the specificity and sensitivity of immunosignaturing platform for its ability to resolve four different diseases (pancreatic cancer, pancreatitis, type 2 diabetes and panIN) that target the same organ (pancreas). These diseases were separated with >90% specificity from controls and from each other. Thirdly, I observed that the immunosignature of type 2 diabetes and cardiovascular complications are unique, consistent, and reproducible and can be separated by 100% accuracy from controls. But when these two complications arise in the same person, the resultant immunosignature is quite different in that of individuals with only one disease. I developed a method to trace back from informative random peptides in disease signatures to the potential antigen(s). Hence, I built a decipher system to trace random peptides in type 1 diabetes immunosignature to known antigens. Immunosignaturing, unlike the ELISA, has the ability to not only detect the presence of response but also absence of response during a disease. I observed, not only higher but also lower peptides intensities can be mapped to antigens in type 1 diabetes. To study immunosignaturing potential for population diagnostics, I studied effect of age, gender and geographical location on immunosignaturing data. For its potential to be a health monitoring technology, I proposed a single metric Coefficient of Variation that has shown potential to change significantly when a person enters a disease state.
ContributorsKukreja, Muskan (Author) / Johnston, Stephen Albert (Thesis advisor) / Stafford, Phillip (Committee member) / Dinu, Valentin (Committee member) / Arizona State University (Publisher)
Created2012