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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
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
Like individual organisms, complex social groups are able to maintain predictable trajectories of growth, from initial colony foundation to mature reproductively capable units. They do so while simultaneously responding flexibly to variation in nutrient availability and intake. Leafcutter ant colonies function as tri-trophic systems, in which the ants harvest vegetation to grow a fungus that, in turn, serves as food for the colony. Fungal growth rates and colony worker production are interdependent, regulated by nutritional and behavioral feedbacks. Fungal growth and quality are directly affected by worker foraging decisions, while worker production is, in turn, dependent on the amount and condition of the fungus. In this dissertation, I first characterized the growth relationship between the workers and the fungus of the desert leafcutter ant Acromyrmex versicolor during early stages of colony development, from colony foundation by groups of queens through the beginnings of exponential growth. I found that this relationship undergoes a period of slow growth and instability when workers first emerge, and then becomes allometrically positive. I then evaluated how mass and element ratios of resources collected by the ants are translated into fungus and worker population growth, and refuse, finding that colony digestive efficiency is comparable to digestive efficiencies of other herbivorous insects and ruminants. To test how colonies behaviorally respond to perturbations of the fungus garden, I quantified activity levels and task performance of workers in colonies with either supplemented or diminished fungus gardens, and found that colonies adjusted activity and task allocation in response to the fungus garden size. Finally, to identify possible forms of nutrient limitation, I measured how colony performance was affected by changes in the relative amounts of carbohydrates, protein, and phosphorus available in the resources used to grow the fungus garden. From this experiment, I concluded that colony growth is primarily carbohydrate-limited.
ContributorsClark, Rebecca, 1981- (Author) / Fewell, Jennifer H (Thesis advisor) / Mueller, Ulrich (Committee member) / Liebig, Juergen (Committee member) / Elser, James (Committee member) / Harrison, Jon (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
The repression of reproductive competition and the enforcement of altruism are key components to the success of animal societies. Eusocial insects are defined by having a reproductive division of labor, in which reproduction is relegated to one or few individuals while the rest of the group members maintain the colony and help raise offspring. However, workers have retained the ability to reproduce in most insect societies. In the social Hymenoptera, due to haplodiploidy, workers can lay unfertilized male destined eggs without mating. Potential conflict between workers and queens can arise over male production, and policing behaviors performed by nestmate workers and queens are a means of repressing worker reproduction. This work describes the means and results of the regulation of worker reproduction in the ant species Aphaenogaster cockerelli. Through manipulative laboratory studies on mature colonies, the lack of egg policing and the presence of physical policing by both workers and queens of this species are described. Through chemical analysis and artificial chemical treatments, the role of cuticular hydrocarbons as indicators of fertility status and the informational basis of policing in this species is demonstrated. An additional queen-specific chemical signal in the Dufour's gland is discovered to be used to direct nestmate aggression towards reproductive competitors. Finally, the level of actual worker-derived males in field colonies is measured. Together, these studies demonstrate the effectiveness of policing behaviors on the suppression of worker reproduction in a social insect species, and provide an example of how punishment and the threat of punishment is a powerful force in maintaining cooperative societies.
ContributorsSmith, Adrian A. (Author) / Liebig, Juergen (Thesis advisor) / Hoelldobler, Bert (Thesis advisor) / Gadau, Juergen (Committee member) / Johnson, Robert A. (Committee member) / Pratt, Stephen (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
Meteorology is an uncommon term rarely resonating through elementary classrooms. However, it is a concept found in both fourth and sixth grade Arizona science standards. As issues involving the environment are becoming more pertinent, it is important to study and understand atmospheric processes along with fulfilling the standards for each grade level. This thesis project teaches the practical skills of weather map reading and weather forecasting through the creation and execution of an after school lesson with the aide of seven teen assistants.
ContributorsChoulet, Shayna (Author) / Walters, Debra (Thesis director) / Oliver, Jill (Committee member) / Balling, Robert (Committee member) / Barrett, The Honors College (Contributor) / College of Liberal Arts and Sciences (Contributor)
Created2012-12
Description
Plants are essential to human life. They release oxygen into the atmosphere for us to breathe. They also provide shelter, medicine, clothing, tools, and food. For many people, the food that is on their tables and in their supermarkets isn't given much thought. Where did it come from? What part of the plant is it? How does it relate to others in the plant kingdom? How do other cultures use this plant? The most many of us know about them is that they are at the supermarket when we need them for dinner (Nabhan, 2009) (Vileisis, 2008).
ContributorsBarron, Kara (Author) / Landrum, Leslie (Thesis director) / Swanson, Tod (Committee member) / Pigg, Kathleen (Committee member) / Barrett, The Honors College (Contributor) / College of Liberal Arts and Sciences (Contributor)
Created2012-12
DescriptionBased on previous research and findings it is proven that a non-profit class to create awareness will be beneficial in the prevention of eating disorders. This analysis will provide significant research to defend the proposed class.
ContributorsAllen, Brittany (Author) / Chung, Deborah (Author) / Fey, Richard (Thesis director) / Peck, Sidnee (Committee member) / Mazurkiewicz, Milena (Committee member) / Barrett, The Honors College (Contributor) / W. P. Carey School of Business (Contributor) / College of Liberal Arts and Sciences (Contributor)
Created2012-12