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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
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
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
The health benefits of physical activity are widely accepted. Emerging research also indicates that sedentary behaviors can carry negative health consequences regardless of physical activity level. This dissertation explored four projects that examined measurement properties of physical activity and sedentary behavior monitors. Project one identified the oxygen costs of four other care activities in seventeen adults. Pushing a wheelchair and pushing a stroller were identified as moderate-intensity activities. Minutes spent engaged in these activities contribute towards meeting the 2008 Physical Activity Guidelines. Project two identified the oxygen costs of common cleaning activities in sixteen adults. Mopping a floor was identified as moderate-intensity physical activity, while cleaning a kitchen and cleaning a bathtub were identified as light-intensity physical activity. Minutes spent engaged in mopping a floor contributes towards meeting the 2008 Physical Activity Guidelines. Project three evaluated the differences in number of minutes spent in activity levels when utilizing different epoch lengths in accelerometry. A shorter epoch length (1-second, 5-seconds) accumulated significantly more minutes of sedentary behaviors than a longer epoch length (60-seconds). The longer epoch length also identified significantly more time engaged in light-intensity activities than the shorter epoch lengths. Future research needs to account for epoch length selection when conducting physical activity and sedentary behavior assessment. Project four investigated the accuracy of four activity monitors in assessing activities that were either sedentary behaviors or light-intensity physical activities. The ActiGraph GT3X+ assessed the activities least accurately, while the SenseWear Armband and ActivPAL assessed activities equally accurately. The monitor used to assess physical activity and sedentary behaviors may influence the accuracy of the measurement of a construct.
ContributorsMeckes, Nathanael (Author) / Ainsworth, Barbara E (Thesis advisor) / Belyea, Michael (Committee member) / Buman, Matthew (Committee member) / Gaesser, Glenn (Committee member) / Wharton, Christopher (Christopher Mack), 1977- (Committee member) / Arizona State University (Publisher)
Created2012
Description
Cardiovascular disease (CVD) is the number one cause of death in the United States and type 2 diabetes (T2D) and obesity lead to cardiovascular disease. Obese adults are more susceptible to CVD compared to their non-obese counterparts. Exercise training leads to large reductions in the risk of CVD and T2D. Recent evidence suggests high-intensity interval training (HIT) may yield similar or superior benefits in a shorter amount of time compared to traditional continuous exercise training. The purpose of this study was to compare the effects of HIT to continuous (CONT) exercise training for the improvement of endothelial function, glucose control, and visceral adipose tissue. Seventeen obese men (N=9) and women (N=8) were randomized to eight weeks of either HIT (N=9, age=34 years, BMI=37.6 kg/m2) or CONT (N=8, age=34 years, BMI=34.6 kg/m2) exercise 3 days/week for 8 weeks. Endothelial function was assessed via flow-mediated dilation (FMD), glucose control was assessed via continuous glucose monitoring (CGM), and visceral adipose tissue and body composition was measured with an iDXA. Incremental exercise testing was performed at baseline, 4 weeks, and 8 weeks. There were no changes in weight, fat mass, or visceral adipose tissue measured by the iDXA, but there was a significant reduction in body fat that did not differ by group (46±6.3 to 45.4±6.6%, P=0.025). HIT led to a significantly greater improvement in FMD compared to CONT exercise (HIT: 5.1 to 9.0%; CONT: 5.0 to 2.6%, P=0.006). Average 24-hour glucose was not improved over the whole group and there were no group x time interactions for CGM data (HIT: 103.9 to 98.2 mg/dl; CONT: 99.9 to 100.2 mg/dl, P>0.05). When statistical analysis included only the subjects who started with an average glucose at baseline > 100 mg/dl, there was a significant improvement in glucose control overall, but no group x time interaction (107.8 to 94.2 mg/dl, P=0.027). Eight weeks of HIT led to superior improvements in endothelial function and similar improvements in glucose control in obese subjects at risk for T2D and CVD. HIT was shown to have comparable or superior health benefits in this obese sample with a 36% lower total exercise time commitment.
ContributorsSawyer, Brandon J (Author) / Gaesser, Glenn A (Thesis advisor) / Shaibi, Gabriel (Committee member) / Lee, Chong (Committee member) / Swan, Pamela (Committee member) / Buman, Matthew (Committee member) / Arizona State University (Publisher)
Created2013
Description
Purpose: The purpose of this study was to examine the acute effects of two novel intermittent exercise prescriptions on glucose regulation and ambulatory blood pressure. Methods: Ten subjects (5 men and 5 women, ages 31.5 ± 5.42 yr, height 170.38 ± 9.69 cm and weight 88.59 ± 18.91 kg) participated in this four-treatment crossover trial. All subjects participated in four trials, each taking place over three days. On the evening of the first day, subjects were fitted with a continuous glucose monitor (CGM). On the second day, subjects were fitted with an ambulatory blood pressure monitor (ABP) and underwent one of the following four conditions in a randomized order: 1) 30-min: 30 minutes of continuous exercise at 60 - 70% VO2peak; 2) Mod 2-min: twenty-one 2-min bouts of walking at 3 mph performed once every 20 minutes; 3) HI 2-min: eight 2-min bouts of walking at maximal incline performed once every hour; 4) Control: a no exercise control condition. On the morning of the third day, the CGM and ABP devices were removed. All meals were standardized during the study visits. Linear mixed models were used to compare mean differences in glucose and blood pressure regulation between the four trials. Results: Glucose concentrations were significantly lower following the 30-min (91.1 ± 14.9 mg/dl), Mod 2-min (93.7 ± 19.8 mg/dl) and HI 2-min (96.1 ± 16.4 mg/dl) trials as compared to the Control (101.1 ± 20 mg/dl) (P < 0.001 for all three comparisons). The 30-min trial was superior to the Mod 2-min, which was superior to the HI 2-min trial in lowering blood glucose levels (P < 0.001 and P = 0.003 respectively). Only the 30-min trial was effective in lowering systolic ABP (124 ± 12 mmHg) as compared to the Control trial (127 ± 14 mmHg; P < 0.001) for up to 11 hours post exercise. Conclusion: Performing frequent short (i.e., 2 minutes) bouts of moderate or high intensity exercise may be a viable alternative to traditional continuous exercise in improving glucose regulation. However, 2-min bouts of exercise are not effective in reducing ambulatory blood pressure in healthy adults.
ContributorsBhammar, Dharini Mukeshkumar (Author) / Gaesser, Glenn A (Thesis advisor) / Shaibi, Gabriel (Committee member) / Buman, Matthew (Committee member) / Swan, Pamela (Committee member) / Lee, Chong (Committee member) / Arizona State University (Publisher)
Created2013
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