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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
Motor learning is the process of improving task execution according to some measure of performance. This can be divided into skill learning, a model-free process, and adaptation, a model-based process. Prior studies have indicated that adaptation results from two complementary learning systems with parallel organization. This report attempted to answer the question of whether a similar interaction leads to savings, a model-free process that is described as faster relearning when experiencing something familiar. This was tested in a two-week reaching task conducted on a robotic arm capable of perturbing movements. The task was designed so that the two sessions differed in their history of errors. By measuring the change in the learning rate, the savings was determined at various points. The results showed that the history of errors successfully modulated savings. Thus, this supports the notion that the two complementary systems interact to develop savings. Additionally, this report was part of a larger study that will explore the organizational structure of the complementary systems as well as the neural basis of this motor learning.
ContributorsRuta, Michael (Author) / Santello, Marco (Thesis director) / Blais, Chris (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / School of Molecular Sciences (Contributor) / School of Human Evolution & Social Change (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
Neurostimulation methods currently include deep brain stimulation (DBS), optogenetic, transcranial direct-current stimulation (tDCS), and transcranial magnetic stimulation (TMS). TMS and tDCS are noninvasive techniques whereas DBS and optogenetic require surgical implantation of electrodes or light emitting devices. All approaches, except for optogenetic, have been implemented in clinical settings because they have demonstrated therapeutic utility and clinical efficacy for neurological and psychiatric disorders. When applied for therapeutic applications, these techniques suffer from limitations that hinder the progression of its intended use to treat compromised brain function. DBS requires an invasive surgical procedure that surfaces complications from infection, longevity of electrical components, and immune responses to foreign materials. Both TMS and tDCS circumvent the problems seen with DBS as they are noninvasive procedures, but they fail to produce the spatial resolution required to target specific brain structures. Realizing these restrictions, we sought out to use ultrasound as a neurostimulation modality. Ultrasound is capable of achieving greater resolution than TMS and tDCS, as we have demonstrated a ~2mm lateral resolution, which can be delivered noninvasively. These characteristics place ultrasound superior to current neurostimulation methods. For these reasons, this dissertation provides a developed protocol to use transcranial pulsed ultrasound (TPU) as a neurostimulation technique. These investigations implement electrophysiological, optophysiological, immunohistological, and behavioral methods to elucidate the effects of ultrasound on the central nervous system and raise questions about the functional consequences. Intriguingly, we showed that TPU was also capable of stimulating intact sub-cortical circuits in the anesthetized mouse. These data reveal that TPU can evoke synchronous oscillations in the hippocampus in addition to increasing expression of brain-derived neurotrophic factor (BDNF). Considering these observations, and the ability to noninvasively stimulate neuronal activity on a mesoscale resolution, reveals a potential avenue to be effective in clinical settings where current brain stimulation techniques have shown to be beneficial. Thus, the results explained by this dissertation help to pronounce the significance for these protocols to gain translational recognition.
ContributorsTufail, Yusuf Zahid (Author) / Tyler, William J (Thesis advisor) / Duch, Carsten (Committee member) / Muthuswamy, Jitendran (Committee member) / Santello, Marco (Committee member) / Tillery, Stephen H (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
An accurate sense of upper limb position is crucial to reaching movements where sensory information about upper limb position and target location is combined to specify critical features of the movement plan. This dissertation was dedicated to studying the mechanisms of how the brain estimates the limb position in space and the consequences of misestimation of limb position on movements. Two independent but related studies were performed. The first involved characterizing the neural mechanisms of limb position estimation in the non-human primate brain. Single unit recordings were obtained in area 5 of the posterior parietal cortex in order to examine the role of this area in estimating limb position based on visual and somatic signals (proprioceptive, efference copy). When examined individually, many area 5 neurons were tuned to the position of the limb in the workspace but very few neurons were modulated by visual feedback. At the population level however decoding of limb position was somewhat more accurate when visual feedback was provided. These findings support a role for area 5 in limb position estimation but also suggest that visual signals regarding limb position are only weakly represented in this area, and only at the population level. The second part of this dissertation focused on the consequences of misestimation of limb position for movement production. It is well known that limb movements are inherently variable. This variability could be the result of noise arising at one or more stages of movement production. Here we used biomechanical modeling and simulation techniques to characterize movement variability resulting from noise in estimating limb position ('sensing noise') and in planning required movement vectors ('planning noise'), and compared that to the variability expected due to noise in movement execution. We found that the effects of sensing and planning related noise on movement variability were dependent upon both the planned movement direction and the initial configuration of the arm and were different in many respects from the effects of execution noise.
ContributorsShi, Ying (Author) / Buneo, Christopher A (Thesis advisor) / Helms Tillery, Stephen (Committee member) / Santello, Marco (Committee member) / He, Jiping (Committee member) / Santos, Veronica (Committee member) / Arizona State University (Publisher)
Created2011
Description
Anticipatory planning of digit positions and forces is critical for successful dexterous object manipulation. Anticipatory (feedforward) planning bypasses the inherent delays in reflex responses and sensorimotor integration associated with reactive (feedback) control. It has been suggested that feedforward and feedback strategies can be distinguished based on the profile of grip and load force rates during the period between initial contact with the object and object lift. However, this has not been validated in tasks that do not constrain digit placement. The purposes of this thesis were (1) to validate the hypothesis that force rate profiles are indicative of the control strategy used for object manipulation and (2) to test this hypothesis by comparing manipulation tasks performed with and without digit placement constraints. The first objective comprised two studies. In the first study an additional light or heavy mass was added to the base of the object. In the second study a mass was added, altering the object's center of mass (CM) location. In each experiment digit force rates were calculated between the times of initial digit contact and object lift. Digit force rates were fit to a Gaussian bell curve and the goodness of fit was compared across predictable and unpredictable mass and CM conditions. For both experiments, a predictable object mass and CM elicited bell shaped force rate profiles, indicative of feedforward control. For the second objective, a comparison of performance between subjects who performed the grasp task with either constrained or unconstrained digit contact locations was conducted. When digit location was unconstrained and CM was predictable, force rates were well fit to a bell shaped curve. However, the goodness of fit of the force rate profiles to the bell shaped curve was weaker for the constrained than the unconstrained digit placement condition. These findings seem to indicate that brain can generate an appropriate feedforward control strategy even when digit placement is unconstrained and an infinite combination of digit placement and force solutions exists to lift the object successfully. Future work is needed that investigates the role digit positioning and tactile feedback has on anticipatory control of object manipulation.
ContributorsCooperhouse, Michael A (Author) / Santello, Marco (Thesis advisor) / Helms Tillery, Stephen (Committee member) / Buneo, Christopher (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
In order to successfully implement a neural prosthetic system, it is necessary to understand the control of limb movements and the representation of body position in the nervous system. As this development process continues, it is becoming increasingly important to understand the way multiple sensory modalities are used in limb representation. In a previous study, Shi et al. (2013) examined the multimodal basis of limb position in the superior parietal lobule (SPL) as monkeys reached to and held their arm at various target locations in a frontal plane. Visual feedback was withheld in half the trials, though non-visual (i.e. somatic) feedback was available in all trials. Previous analysis showed that some of the neurons were tuned to limb position and that some neurons had their response modulated by the presence or absence of visual feedback. This modulation manifested in decreases in firing rate variability in the vision condition as compared to nonvision. The decreases in firing rate variability, as shown through decreases in both the Fano factor of spike counts and the coefficient of variation of the inter-spike intervals, suggested that changes were taking place in both trial-by-trial and intra-trial variability. I sought to further probe the source of the change in intra-trial variability through spectral analysis. It was hypothesized that the presence of temporal structure in the vision condition would account for a regularity in firing that would have decreased intra-trial variability. While no peaks were apparent in the spectra, differences in spectral power between visual conditions were found. These differences are suggestive of unique temporal spiking patterns at the individual neuron level that may be influential at the population level.
ContributorsDyson, Keith (Author) / Buneo, Christopher A (Thesis advisor) / Helms-Tillery, Stephen I (Committee member) / Santello, Marco (Committee member) / Arizona State University (Publisher)
Created2013
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