Matching Items (43)
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
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
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
Random peptide microarrays are a powerful tool for both the treatment and diagnostics of infectious diseases. On the treatment side, selected random peptides on the microarray have either binding or lytic potency against certain pathogens cells, thus they can be synthesized into new antimicrobial agents, denoted as synbodies (synthetic antibodies). On the diagnostic side, serum containing specific infection-related antibodies create unique and distinct "pathogen-immunosignatures" on the random peptide microarray distinct from the healthy control serum, and this different mode of binding can be used as a more precise measurement than traditional ELISA tests. My thesis project is separated into these two parts: the first part falls into the treatment side and the second one focuses on the diagnostic side. My first chapter shows that a substitution amino acid peptide library helps to improve the activity of a recently reported synthetic antimicrobial peptide selected by the random peptide microarray. By substituting one or two amino acids of the original lead peptide, the new substitutes show changed hemolytic effects against mouse red blood cells and changed potency against two pathogens: Staphylococcus aureus and Pseudomonas aeruginosa. Two new substitutes are then combined together to form the synbody, which shows a significantly antimicrobial potency against Staphylococcus aureus (<0.5uM). In the second chapter, I explore the possibility of using the 10K Ver.2 random peptide microarray to monitor the humoral immune response of dengue. Over 2.5 billion people (40% of the world's population) live in dengue transmitting areas. However, currently there is no efficient dengue treatment or vaccine. Here, with limited dengue patient serum samples, we show that the immunosignature has the potential to not only distinguish the dengue infection from non-infected people, but also the primary dengue infection from the secondary dengue infections, dengue infection from West Nile Virus (WNV) infection, and even between different dengue serotypes. By further bioinformatic analysis, we demonstrate that the significant peptides selected to distinguish dengue infected and normal samples may indicate the epitopes responsible for the immune response.
ContributorsWang, Xiao (Author) / Johnston, Stephen Albert (Thesis advisor) / Blattman, Joseph (Committee member) / Arntzen, Charles (Committee member) / Arizona State University (Publisher)
Created2013
Description
Cancer is one of the most serious global diseases. We have focused on cancer immunoprevention. My thesis projects include developing a prophylactic primary and metastatic cancer vaccines, early cancer detection and investigation of genes involved in tumor development. These studies were focused on frame-shift (FS) antigens. The FS antigens are generated by genomic mutations or abnormal RNA processing, which cause a portion of a normal protein to be translated out of frame. The concept of the prophylactic cancer vaccine is to develop a general cancer vaccine that could prevent healthy people from developing different types of cancer. We have discovered a set of cancer specific FS antigens. One of the FS candidates, structural maintenance of chromosomes protein 1A (SMC1A) FS, could start to accumulate at early stages of tumor and be specifically exposed to the immune system by tumor cells. Prophylactic immunization with SMC1A-FS could significantly inhibit primary tumor development in different murine tumor models and also has the potential to inhibit tumor metastasis. The SMC1A-FS transcript was detected in the plasma of the 4T1/BALB/c mouse tumor model. The tumor size was correlated with the transcript ratio of the SMC1A-FS verses the WT in plasma, which could be measured by regular RT-PCR. This unique cancer biomarker has a practical potential for a large population cancer screen, as well as clinical tumor monitoring. With a set of mimotope peptides, antibodies against SMC1A-FS peptide were detected in different cancer patients, including breast cancer, pancreas cancer and lung cancer with a 53.8%, 56.5% and 12.5% positive rate respectively. This suggested that the FS antibody could be a biomarker for early cancer detection. The characterization of SMC1A suggested that: First, the deficiency of the SMC1A is common in different tumors and able to promote tumor initiation and development; second, the FS truncated protein may have nucleolus function in normal cells. Mis-control of this protein may promote tumor development. In summary, we developed a systematic general cancer prevention strategy through the variety immunological and molecular methods. The results gathered suggest the SMC1A-FS may be useful for the detection and prevention of cancer.
ContributorsShen, Luhui (Author) / Johnston, Stephen Albert (Thesis advisor) / Chang, Yung (Committee member) / Miller, Laurence (Committee member) / Sykes, Kathryn (Committee member) / Jacobs, Bertram (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
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
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
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