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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

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
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Description
For over a century, researchers have been investigating collective cognition, in which a group of individuals together process information and act as a single cognitive unit. However, I still know little about circumstances under which groups achieve better (or worse) decisions than individuals. My dissertation research directly addressed this longstanding

For over a century, researchers have been investigating collective cognition, in which a group of individuals together process information and act as a single cognitive unit. However, I still know little about circumstances under which groups achieve better (or worse) decisions than individuals. My dissertation research directly addressed this longstanding question, using the house-hunting ant Temnothorax rugatulus as a model system. Here I applied concepts and methods developed in psychology not only to individuals but also to colonies in order to investigate differences of their cognitive abilities. This approach is inspired by the superorganism concept, which sees a tightly integrated insect society as the analog of a single organism. I combined experimental manipulations and models to elucidate the emergent processes of collective cognition. My studies show that groups can achieve superior cognition by sharing the burden of option assessment among members and by integrating information from members using positive feedback. However, the same positive feedback can lock the group into a suboptimal choice in certain circumstances. Although ants are obligately social, my results show that they can be isolated and individually tested on cognitive tasks. In the future, this novel approach will help the field of animal behavior move towards better understanding of collective cognition.
ContributorsSasaki, Takao (Author) / Pratt, Stephen C (Thesis advisor) / Amazeen, Polemnia (Committee member) / Liebig, Jürgen (Committee member) / Janssen, Marco (Committee member) / Fewell, Jennifer (Committee member) / Hölldobler, Bert (Committee member) / Arizona State University (Publisher)
Created2013
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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

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
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Description
The spread of invasive species may be greatly affected by human responses to prior species spread, but models and estimation methods seldom explicitly consider human responses. I investigate the effects of management responses on estimates of invasive species spread rates. To do this, I create an agent-based simulation model of

The spread of invasive species may be greatly affected by human responses to prior species spread, but models and estimation methods seldom explicitly consider human responses. I investigate the effects of management responses on estimates of invasive species spread rates. To do this, I create an agent-based simulation model of an insect invasion across a county-level citrus landscape. My model provides an approximation of a complex spatial environment while allowing the "truth" to be known. The modeled environment consists of citrus orchards with insect pests dispersing among them. Insects move across the simulation environment infesting orchards, while orchard managers respond by administering insecticide according to analyst-selected behavior profiles and management responses may depend on prior invasion states. Dispersal data is generated in each simulation and used to calculate spread rate via a set of estimators selected for their predominance in the empirical literature. Spread rate is a mechanistic, emergent phenomenon measured at the population level caused by a suite of latent biological, environmental, and anthropogenic. I test the effectiveness of orchard behavior profiles on invasion suppression and evaluate the robustness of the estimators given orchard responses. I find that allowing growers to use future expectations of spread in management decisions leads to reduced spread rates. Acting in a preventative manner by applying insecticide before insects are actually present, orchards are able to lower spread rates more than by reactive behavior alone. Spread rates are highly sensitive to spatial configuration. Spatial configuration is hardly a random process, consisting of many latent factors often not accounted for in spread rate estimation. Not considering these factors may lead to an omitted variables bias and skew estimation results. The ability of spread rate estimators to predict future spread varies considerably between estimators, and with spatial configuration, invader biological parameters, and orchard behavior profile. The model suggests that understanding the latent factors inherent to dispersal is important for selecting phenomenological models of spread and interpreting estimation results. This indicates a need for caution when evaluating spread. Although standard practice, current empirical estimators may both over- and underestimate spread rate in the simulation.
ContributorsShanafelt, David William (Author) / Fenichel, Eli P (Thesis advisor) / Richards, Timothy (Committee member) / Janssen, Marco (Committee member) / Arizona State University (Publisher)
Created2012
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DescriptionThis paper provides an analysis of the differences in impacts made by companies that promote their sustainability efforts. A comparison of companies reveals that the ones with greater supply chain influence and larger consumer bases can make more concrete progress in terms of accomplishment for the sustainability realm.
ContributorsBeaubien, Courtney Lynn (Author) / Anderies, John (Thesis director) / Allenby, Brad (Committee member) / Janssen, Marco (Committee member) / Barrett, The Honors College (Contributor) / School of Life Sciences (Contributor)
Created2013-05
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Description

Despite the fact that seizures are commonly associated with autism spectrum disorder (ASD), the effectiveness of treatments for seizures has not been well studied in individuals with ASD. This manuscript reviews both traditional and novel treatments for seizures associated with ASD. Studies were selected by systematically searching major electronic databases

Despite the fact that seizures are commonly associated with autism spectrum disorder (ASD), the effectiveness of treatments for seizures has not been well studied in individuals with ASD. This manuscript reviews both traditional and novel treatments for seizures associated with ASD. Studies were selected by systematically searching major electronic databases and by a panel of experts that treat ASD individuals. Only a few anti-epileptic drugs (AEDs) have undergone carefully controlled trials in ASD, but these trials examined outcomes other than seizures. Several lines of evidence point to valproate, lamotrigine, and levetiracetam as the most effective and tolerable AEDs for individuals with ASD. Limited evidence supports the use of traditional non-AED treatments, such as the ketogenic and modified Atkins diet, multiple subpial transections, immunomodulation, and neurofeedback treatments. Although specific treatments may be more appropriate for specific genetic and metabolic syndromes associated with ASD and seizures, there are few studies which have documented the effectiveness of treatments for seizures for specific syndromes. Limited evidence supports l-carnitine, multivitamins, and N-acetyl-l-cysteine in mitochondrial disease and dysfunction, folinic acid in cerebral folate abnormalities and early treatment with vigabatrin in tuberous sclerosis complex. Finally, there is limited evidence for a number of novel treatments, particularly magnesium with pyridoxine, omega-3 fatty acids, the gluten-free casein-free diet, and low-frequency repetitive transcranial magnetic simulation. Zinc and l-carnosine are potential novel treatments supported by basic research but not clinical studies. This review demonstrates the wide variety of treatments used to treat seizures in individuals with ASD as well as the striking lack of clinical trials performed to support the use of these treatments. Additional studies concerning these treatments for controlling seizures in individuals with ASD are warranted.

ContributorsFrye, Richard E. (Author) / Rossignol, Daniel (Author) / Casanova, Manuel F. (Author) / Brown, Gregory L. (Author) / Martin, Victoria (Author) / Edelson, Stephen (Author) / Coben, Robert (Author) / Lewine, Jeffrey (Author) / Slattery, John C. (Author) / Lau, Chrystal (Author) / Hardy, Paul (Author) / Fatemi, S. Hossein (Author) / Folsom, Timothy D. (Author) / MacFabe, Derrick (Author) / Adams, James (Author) / Ira A. Fulton Schools of Engineering (Contributor)
Created2013-09-13
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Description

There is a growing body of scientific evidence that the health of the microbiome (the trillions of microbes that inhabit the human host) plays an important role in maintaining the health of the host and that disruptions in the microbiome may play a role in certain disease processes. An increasing

There is a growing body of scientific evidence that the health of the microbiome (the trillions of microbes that inhabit the human host) plays an important role in maintaining the health of the host and that disruptions in the microbiome may play a role in certain disease processes. An increasing number of research studies have provided evidence that the composition of the gut (enteric) microbiome (GM) in at least a subset of individuals with autism spectrum disorder (ASD) deviates from what is usually observed in typically developing individuals. There are several lines of research that suggest that specific changes in the GM could be causative or highly associated with driving core and associated ASD symptoms, pathology, and comorbidities which include gastrointestinal symptoms, although it is also a possibility that these changes, in whole or in part, could be a consequence of underlying pathophysiological features associated with ASD. However, if the GM truly plays a causative role in ASD, then the manipulation of the GM could potentially be leveraged as a therapeutic approach to improve ASD symptoms and/or comorbidities, including gastrointestinal symptoms.

One approach to investigating this possibility in greater detail includes a highly controlled clinical trial in which the GM is systematically manipulated to determine its significance in individuals with ASD. To outline the important issues that would be required to design such a study, a group of clinicians, research scientists, and parents of children with ASD participated in an interdisciplinary daylong workshop as an extension of the 1st International Symposium on the Microbiome in Health and Disease with a Special Focus on Autism (www.microbiome-autism.com). The group considered several aspects of designing clinical studies, including clinical trial design, treatments that could potentially be used in a clinical trial, appropriate ASD participants for the clinical trial, behavioral and cognitive assessments, important biomarkers, safety concerns, and ethical considerations. Overall, the group not only felt that this was a promising area of research for the ASD population and a promising avenue for potential treatment but also felt that further basic and translational research was needed to clarify the clinical utility of such treatments and to elucidate possible mechanisms responsible for a clinical response, so that new treatments and approaches may be discovered and/or fostered in the future.

ContributorsFrye, Richard E. (Author) / Slattery, John (Author) / MacFabe, Derrick F. (Author) / Allen-Vercoe, Emma (Author) / Parker, William (Author) / Rodakis, John (Author) / Adams, James (Author) / Krajmalnik-Brown, Rosa (Author) / Bolte, Ellen (Author) / Kahler, Stephen (Author) / Jennings, Jana (Author) / James, Jill (Author) / Cerniglia, Carl E. (Author) / Midtvedt, Tore (Author) / Ira A. Fulton Schools of Engineering (Contributor)
Created2015-05-07
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Description

The evolution of cooperation is a fundamental problem in biology, especially for non-relatives, where indirect fitness benefits cannot counter within-group inequalities. Multilevel selection models show how cooperation can evolve if it generates a group-level advantage, even when cooperators are disadvantaged within their group. This allows the possibility of group selection,

The evolution of cooperation is a fundamental problem in biology, especially for non-relatives, where indirect fitness benefits cannot counter within-group inequalities. Multilevel selection models show how cooperation can evolve if it generates a group-level advantage, even when cooperators are disadvantaged within their group. This allows the possibility of group selection, but few examples have been described in nature. Here we show that group selection can explain the evolution of cooperative nest founding in the harvester ant Pogonomyrmex californicus. Through most of this species’ range, colonies are founded by single queens, but in some populations nests are instead founded by cooperative groups of unrelated queens. In mixed groups of cooperative and single-founding queens, we found that aggressive individuals had a survival advantage within their nest, but foundress groups with such non-cooperators died out more often than those with only cooperative members. An agent-based model shows that the between-group advantage of the cooperative phenotype drives it to fixation, despite its within-group disadvantage, but only when population density is high enough to make between-group competition intense. Field data show higher nest density in a population where cooperative founding is common, consistent with greater density driving the evolution of cooperative foundation through group selection.

ContributorsShaffer, Zachary (Author) / Sasaki, Takao (Author) / Haney, Brian (Author) / Janssen, Marco (Author) / Pratt, Stephen (Author) / Fewell, Jennifer (Author) / College of Liberal Arts and Sciences (Contributor)
Created2016-07-28
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Description

Background: Despite the high prevalence of seizure, epilepsy and abnormal electroencephalograms in individuals with autism spectrum disorder (ASD), there is little information regarding the relative effectiveness of treatments for seizures in the ASD population. In order to determine the effectiveness of traditional and non-traditional treatments for improving seizures and influencing other

Background: Despite the high prevalence of seizure, epilepsy and abnormal electroencephalograms in individuals with autism spectrum disorder (ASD), there is little information regarding the relative effectiveness of treatments for seizures in the ASD population. In order to determine the effectiveness of traditional and non-traditional treatments for improving seizures and influencing other clinical factor relevant to ASD, we developed a comprehensive on-line seizure survey.

Methods: Announcements (by email and websites) by ASD support groups asked parents of children with ASD to complete the on-line surveys. Survey responders choose one of two surveys to complete: a survey about treatments for individuals with ASD and clinical or subclinical seizures or abnormal electroencephalograms, or a control survey for individuals with ASD without clinical or subclinical seizures or abnormal electroencephalograms. Survey responders rated the perceived effect of traditional antiepileptic drug (AED), non-AED seizure treatments and non-traditional ASD treatments on seizures and other clinical factors (sleep, communication, behavior, attention and mood), and listed up to three treatment side effects.

Results: Responses were obtained concerning 733 children with seizures and 290 controls. In general, AEDs were perceived to improve seizures but worsened other clinical factors for children with clinical seizure. Valproic acid, lamotrigine, levetiracetam and ethosuximide were perceived to improve seizures the most and worsen other clinical factors the least out of all AEDs in children with clinical seizures. Traditional non-AED seizure and non-traditional treatments, as a group, were perceived to improve other clinical factors and seizures but the perceived improvement in seizures was significantly less than that reported for AEDs. Certain traditional non-AED treatments, particularly the ketogenic diet, were perceived to improve both seizures and other clinical factors. For ASD individuals with reported subclinical seizures, other clinical factors were reported to be worsened by AEDs and improved by non-AED traditional seizure and non-traditional treatments. The rate of side effects was reportedly higher for AEDs compared to traditional non-AED treatments.

Conclusion: Although this survey-based method only provides information regarding parental perceptions of effectiveness, this information may be helpful for selecting seizure treatments in individuals with ASD.

ContributorsFrye, Richard E. (Author) / Sreenivasula, Swapna (Author) / Adams, James (Author) / Ira A. Fulton Schools of Engineering (Contributor)
Created2011-05-18
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Description
Climate change presents the urgent need for effective sustainable water management that is capable of preserving natural resources while maintaining economical stability. States like California rely heavily on groundwater pumping for agricultural use, contributing to land subsidence and insufficient returns to water resources. The recent California drought has impacted agricultural

Climate change presents the urgent need for effective sustainable water management that is capable of preserving natural resources while maintaining economical stability. States like California rely heavily on groundwater pumping for agricultural use, contributing to land subsidence and insufficient returns to water resources. The recent California drought has impacted agricultural production of certain crops. In this thesis, we present an agent-based model of farmers adapting to drought conditions by making crop choice decisions, much like the decisions Californian farmers have made. We use the Netlogo platform to capture the 2D spatial view of an agricultural system with changes in annual rainfall due to drought conditions. The goal of this model is to understand some of the simple rules farmers may follow to self-govern their consumption of a water resource. Farmer agents make their crop decisions based on deficit irrigation crop production function and a net present value discount rate. The farmers choose between a thirsty crop with a high production cost and a dry crop with a low production cost. Simulations results show that farmers switch crops in accordance with limited water and land resources. Farmers can maintain profit and yield by following simple rules of crop switching based on future yields and optimal irrigation. In drought conditions, individual agents expecting lower annual rainfall were able to increase their total profits. The maintenance of crop yield and profit is evidence of successful adaptation when farmers switch to crops that require less water.
ContributorsGokool, Rachael Shanta (Author) / Janssen, Marco (Thesis director) / Eakin, Hallie (Committee member) / School of Human Evolution and Social Change (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05