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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
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
Chronic restraint stress impairs hippocampal-mediated spatial learning and memory, which improves following a post-stress recovery period. Here, we investigated whether brain derived neurotrophic factor (BDNF), a protein important for hippocampal function, would alter the recovery from chronic stress-induced spatial memory deficits. Adult male Sprague-Dawley rats were infused into the hippocampus with adeno- associated viral vectors containing the coding sequence for short interfering (si)RNA directed against BDNF or a scrambled sequence (Scr), with both containing the coding information for green fluorescent protein to aid in anatomical localization. Rats were then chronically restrained (wire mesh, 6h/d/21d) and assessed for spatial learning and memory using a radial arm water maze (RAWM) either immediately after stressor cessation (Str-Imm) or following a 21-day post-stress recovery period (Str-Rec). All groups learned the RAWM task similarly, but differed on the memory retention trial. Rats in the Str-Imm group, regardless of viral vector contents, committed more errors in the spatial reference memory domain than did non-stressed controls. Importantly, the typical improvement in spatial memory following recovery from chronic stress was blocked with the siRNA against BDNF, as Str-Rec-siRNA performed worse on the RAWM compared to the non-stressed controls or Str-Rec-Scr. These effects were specific for the reference memory domain as repeated entry errors that reflect spatial working memory were unaffected by stress condition or viral vector contents. These results demonstrate that hippocampal BDNF is necessary for the recovery from stress-induced hippocampal dependent spatial memory deficits in the reference memory domain.
ContributorsOrtiz, J. Bryce (Author) / Conrad, Cheryl D. (Thesis advisor) / Olive, M. Foster (Committee member) / Taylor, Sara (Committee member) / Bimonte-Nelson, Heather A. (Committee member) / Arizona State University (Publisher)
Created2013
Description
The brain is a fundamental target of the stress response that promotes adaptation and survival but the repeated activation of the stress response has the potential alter cognition, emotion, and motivation, key functions of the limbic system. Three structures of the limbic system in particular, the hippocampus, medial prefrontal cortex (mPFC), and amygdala, are of special interest due to documented structural changes and their implication in post-traumatic stress disorder (PTSD). One of many notable chronic stress-induced changes include dendritic arbor restructuring, which reflect plasticity patterns in parallel with the direction of alterations observed in functional imaging studies in PTSD patients. For instance, chronic stress produces dendritic retraction in the hippocampus and mPFC, but dendritic hypertrophy in the amygdala, consistent with functional imaging in patients with PTSD. Some have hypothesized that these limbic region's modifications contribute to one's susceptibility to develop PTSD following a traumatic event. Consequently, we used a familiar chronic stress procedure in a rat model to create a vulnerable brain that might develop traits consistent with PTSD when presented with a challenge. In adult male rats, chronic stress by wire mesh restraint (6h/d/21d) was followed by a variety of behavioral tasks including radial arm water maze (RAWM), fear conditioning and extinction, and fear memory reconsolidation to determine chronic stress effects on behaviors mediated by these limbic structures. In chapter 2, we corroborated past findings that chronic stress caused hippocampal CA3 dendritic retraction. Importantly, we present new findings that CA3 dendritic retraction corresponded with poor spatial memory in the RAWM and that these outcomes reversed after a recovery period. In chapter 3, we also showed that chronic stress impaired mPFC-mediated extinction memory, findings that others have reported. Using carefully assessed behavior, we present new findings that chronic stress impacted nonassociative fear by enhancing contextual fear during extinction that generalized to a new context. Moreover, the generalization behavior corresponded with enhanced functional activation in the hippocampus and amygdala during fear extinction memory retrieval. In chapter 5, we showed for the first time that chronic stress enhanced amygdala functional activation during fear memory retrieval, i.e., reactivation. Moreover, these enhanced fear memories were resistant to protein synthesis interference to disrupt a previously formed memory, called reconsolidation in a novel attempt to weaken chronic stress enhanced traumatic memory. Collectively, these studies demonstrated the plastic and dynamic effects of chronic stress on limbic neurocircuitry implicated in PTSD. We showed that chronic stress created a structural and functional imbalance across the hippocampus, mPFC, and amygdala, which lead to a PTSD-like phenotype with persistent and exaggerated fear following fear conditioning. These behavioral disruptions in conjunction with morphological and functional imaging data reflect a chronic stress-induced imbalance between hippocampal and mPFC regulation in favor of amygdala function overdrive, and supports a novel approach for traumatic memory processing in PTSD.
ContributorsHoffman, Ann (Author) / Conrad, Cheryl D. (Thesis advisor) / Olive, M. Foster (Committee member) / Hammer, Jr., Ronald P. (Committee member) / Sanabria, Federico (Committee member) / Arizona State University (Publisher)
Created2013
Description
The maternal separation (MS) paradigm is an animal model of early life stress. Animals subjected to MS during the first two weeks of life display altered behavioral and neuroendocrinological stress responses as adults. MS also produces altered responsiveness to and self-administration (SA) of various drugs of abuse including cocaine, ethanol, opioids, and amphetamine. Methamphetamine (METH) causes great harm to both the individual user and to society; yet, no studies have examined the effects of MS on METH SA. This study was performed to examine the effects of MS on the acquisition of METH SA, extinction, and reinstatement of METH-seeking behavior in adulthood. Given the known influence of early life stress and drug exposure on epigenetic processes, group differences in levels of the epigenetic marker methyl CpG binding protein 2 (MeCP2) in the nucleus accumbens (NAc) core were also investigated. Long-Evans pups and dams were separated on postnatal days (PND) 2-14 for either 180 (MS180) or 15 min (MS15). Male offspring were allowed to acquire METH SA (0.05 mg/kg/infusion) in 15 2-hr daily sessions starting at PND67, followed by extinction training and cue-induced reinstatement of METH-seeking behavior. Rats were then assessed for MeCP2 levels in the NAc core by immunohistochemistry. The MS180 group self-administered significantly more METH and acquired SA earlier than the MS15 group. No group differences in extinction or cue-induced reinstatement were observed. MS15 rats had significantly elevated MeCP2-immunoreactive cells in the NAc core as compared to MS180 rats. Together, these data suggest that MS has lasting influences on METH SA as well as epigenetic processes in the brain reward circuitry.
ContributorsLewis, Candace (Author) / Olive, Micheal F (Thesis advisor) / Conrad, Cheryl (Committee member) / Neisewander, Janet (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
Description
Sports related concussions, or mild traumatic brain injuries (mTBI), have recently increased in prevalence, and thus gained a great deal of recognition from the public and the media. While the acute symptoms associated with concussions are well known, which include headaches, dizziness, vomiting, and fatigue, recent research has indicated that there can be severe chronic consequences of multiple conditions. Most notably, a disease called Chronic Traumatic Encephalopathy (CTE) has been linked to multiple mTBIs, which produces symptoms similar to Alzheimer's disease and dementia, in addition to personality changes, increased suicidality, and in some cases death. This knowledge has led the NFL to take steps to protect their players, and increase both the understanding and awareness of the problems associated with multiple concussions. This comes with many problems, however, as players and fans alike are quick to resist any type of change to the rules or policies present in football, in fear that it may damage the integrity of the game. The NFL is thus forced into a difficult position, and must balance public opinion and player safety. There are things that can be done, however, that do not threaten the game itself, such as investing in concussion research and safety equipment design that will more effectively protect the brain from concussions.
ContributorsAiello, Mimi Elizabeth (Author) / Olive, M. Foster (Thesis director) / Bimonte-Nelson, Heather (Committee member) / Camp, Bryan (Committee member) / Barrett, The Honors College (Contributor) / Department of Psychology (Contributor)
Created2013-05
Description
An introduction to neuroscientific thought aimed at an audience that is not educated in biology. Meant to be readable and easily understood by anyone with a high school education. The first section is completed in its entirety, with outlines for the proposed final sections to be completed over the next few years.
ContributorsNelson, Nicholas Alan (Author) / Olive, M. Foster (Thesis director) / Brewer, Gene (Committee member) / Barrett, The Honors College (Contributor) / Department of Psychology (Contributor) / School of Life Sciences (Contributor) / School of Historical, Philosophical and Religious Studies (Contributor)
Created2014-05
ContributorsChandler, N. Kayla (Author) / Neisewander, Janet (Thesis director) / Sanabria, Federico (Committee member) / Olive, M. Foster (Committee member) / Barrett, The Honors College (Contributor) / College of Liberal Arts and Sciences (Contributor)
Created2013-05
Description
Major Depressive Disorder (MDD) affects over 300 million people worldwide, with the hippocampus showing decreased volume and activity in patients with MDD. The current study investigated whether a novel preclinical model of depression, unpredictable intermittent restraint (UIR), would decrease hippocampal neuronal dendritic complexity. Adult Sprague Dawley rats (24 male, 24 female) were equally divided into 4 groups: control males (CON-M), UIR males (UIR-M), control females (CON-F) and UIR females (UIR-F). UIR groups received restraint and shaking on an orbital shaker on a randomized schedule for 30 or 60 minutes/day for two to six days in a row for 26 days (21 total UIR days) before behavioral testing commenced. UIR continued and was interspersed between behavioral test days. At the end of behavioral testing, brains were processed. The behavior is published and not part of my honor’s thesis; my contribution involved quantifying and analyzing neurons in the hippocampus. Several neuronal types are found in the CA3 subregion of the hippocampus and I focused on short shaft (SS) neurons, which show different sensitivities to stress than the more common long shaft (LS) variety. Brains sections were mounted to slides and Golgi stained. SS neurons were drawn using a microscope with camera lucida attachment and quantified using the number of bifurcations and dendritic intersections as metrics for dendritic complexity in the apical and basal areas separately. The hypothesis that SS neurons in the CA3 region of the hippocampus would exhibit apical dendritic simplification in both sexes after UIR was not supported by our findings. In contrast, following UIR, SS apical dendrites were more complex in both sexes compared to controls. Although unexpected, we believe that the UIR paradigm was an effective stressor, robust enough to illicit neuronal adaptations. It appears that the time from the end of UIR to when the brain tissue was collected, or the post-stress recovery period, and/or repeated behavioral testing may have played a role in the observed increased neuronal complexity. Future studies are needed to parse out these potential effects.
ContributorsAcuna, Amanda Marie (Author) / Conrad, Cheryl (Thesis director) / Corbin, William (Committee member) / Olive, M. Foster (Committee member) / School of Life Sciences (Contributor) / Department of Psychology (Contributor) / Barrett, The Honors College (Contributor)
Created2020-12