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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
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
It is possible in a properly controlled environment, such as industrial metrology, to make significant headway into the non-industrial constraints on image-based position measurement using the techniques of image registration and achieve repeatable feature measurements on the order of 0.3% of a pixel, or about an order of magnitude improvement on conventional real-world performance. These measurements are then used as inputs for a model optimal, model agnostic, smoothing for calibration of a laser scribe and online tracking of velocimeter using video input. Using appropriate smooth interpolation to increase effective sample density can reduce uncertainty and improve estimates. Use of the proper negative offset of the template function has the result of creating a convolution with higher local curvature than either template of target function which allows improved center-finding. Using the Akaike Information Criterion with a smoothing spline function it is possible to perform a model-optimal smooth on scalar measurements without knowing the underlying model and to determine the function describing the uncertainty in that optimal smooth. An example of empiric derivation of the parameters for a rudimentary Kalman Filter from this is then provided, and tested. Using the techniques of Exploratory Data Analysis and the "Formulize" genetic algorithm tool to convert the spline models into more accessible analytic forms resulted in stable, properly generalized, KF with performance and simplicity that exceeds "textbook" implementations thereof. Validation of the measurement includes that, in analytic case, it led to arbitrary precision in measurement of feature; in reasonable test case using the methods proposed, a reasonable and consistent maximum error of around 0.3% the length of a pixel was achieved and in practice using pixels that were 700nm in size feature position was located to within ± 2 nm. Robust applicability is demonstrated by the measurement of indicator position for a King model 2-32-G-042 rotameter.
ContributorsMunroe, Michael R (Author) / Phelan, Patrick (Thesis advisor) / Kostelich, Eric (Committee member) / Mahalov, Alex (Committee member) / Arizona State University (Publisher)
Created2012
Description
Honey bee workers display remarkable flexibility in the aging process. This plasticity is closely tied to behavioral maturation. Workers who initiate foraging behavior at earlier ages have shorter lifespans, and much of the variation in total lifespan can be explained by differences in pre-foraging lifespan. Vitellogenin (Vg), a yolk precursor protein, influences worker lifespan both as a regulator of behavioral maturation and through anti-oxidant and immune functions. Experimental reduction of Vg mRNA, and thus Vg protein levels, in wild-type bees results in precocious foraging behavior, decreased lifespan, and increased susceptibility to oxidative damage. We sought to separate the effects of Vg on lifespan due to behavioral maturation from those due to immune and antioxidant function using two selected strains of honey bees that differ in their phenotypic responsiveness to Vg gene knockdown. Surprisingly, we found that lifespans lengthen in the strain described as behaviorally and hormonally insensitive to Vg reduction. We then performed targeted gene expression analyses on genes hypothesized to mediate aging and lifespan: the insulin-like peptides (Ilp1 and 2) and manganese superoxide dismutase (mnSOD). The two honey bee Ilps are the most upstream components in the insulin-signaling pathway, which influences lifespan in Drosophila melanogaster and other organisms, while manganese superoxide dismutase encodes an enzyme with antioxidant functions in animals. We found expression differences in the llps in fat body related to behavior (llp1 and 2) and genetic background (Ilp2), but did not find strain by treatment effects. Expression of mnSOD was also affected by behavior and genetic background. Additionally, we observed a differential response to Vg knockdown in fat body expression of mnSOD, suggesting that antioxidant pathways may partially explain the strain-specific lifespan responses to Vg knockdown.
ContributorsIhle, Kate (Author) / Fondrk, M. Kim (Author) / Page, Robert (Author) / Amdam, Gro (Author) / College of Liberal Arts and Sciences (Contributor) / School of Life Sciences (Contributor)
Created2015-01-01
Description
The brain is considered the crux of identity, yet human behavior may be influenced by bacteria in gut microbiomes. Honeybees can exchange bacteria through their many social behaviors, making their microbiomes, and the effect they have on honeybee behavior, of interest. There is recent evidence suggesting the presence of bacteria existing in human brains, which can be investigated in honeybee brains due to their well-documented structure. The purpose of this study is to establish if lipopolysaccharide—a molecule on bacteria membranes—is present in the honeybee brain and if it colocalizes with vitellogenin—an immune mediator. Additionally, this study also seeks to establish the efficacy of embedding tissue samples in resin and performing immunohistochemistry for vitellogenin and lipopolysaccharide on sections.
ContributorsStrange, Amalie Sofie (Co-author) / Strange, Amalie (Co-author) / Amdam, Gro (Thesis director) / Baluch, Page (Committee member) / School of International Letters and Cultures (Contributor) / School of Life Sciences (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2020-05
Description
Background
The reproductive ground plan hypothesis of social evolution suggests that reproductive controls of a solitary ancestor have been co-opted during social evolution, facilitating the division of labor among social insect workers. Despite substantial empirical support, the generality of this hypothesis is not universally accepted. Thus, we investigated the prediction of particular genes with pleiotropic effects on ovarian traits and social behavior in worker honey bees as a stringent test of the reproductive ground plan hypothesis. We complemented these tests with a comprehensive genome scan for additional quantitative trait loci (QTL) to gain a better understanding of the genetic architecture of the ovary size of honey bee workers, a morphological trait that is significant for understanding social insect caste evolution and general insect biology.
Results
Back-crossing hybrid European x Africanized honey bee queens to the Africanized parent colony generated two study populations with extraordinarily large worker ovaries. Despite the transgressive ovary phenotypes, several previously mapped QTL for social foraging behavior demonstrated ovary size effects, confirming the prediction of pleiotropic genetic effects on reproductive traits and social behavior. One major QTL for ovary size was detected in each backcross, along with several smaller effects and two QTL for ovary asymmetry. One of the main ovary size QTL coincided with a major QTL for ovary activation, explaining 3/4 of the phenotypic variance, although no simple positive correlation between ovary size and activation was observed.
Conclusions
Our results provide strong support for the reproductive ground plan hypothesis of evolution in study populations that are independent of the genetic stocks that originally led to the formulation of this hypothesis. As predicted, worker ovary size is genetically linked to multiple correlated traits of the complex division of labor in worker honey bees, known as the pollen hoarding syndrome. The genetic architecture of worker ovary size presumably consists of a combination of trait-specific loci and general regulators that affect the whole behavioral syndrome and may even play a role in caste determination. Several promising candidate genes in the QTL intervals await further study to clarify their potential role in social insect evolution and the regulation of insect fertility in general.
The reproductive ground plan hypothesis of social evolution suggests that reproductive controls of a solitary ancestor have been co-opted during social evolution, facilitating the division of labor among social insect workers. Despite substantial empirical support, the generality of this hypothesis is not universally accepted. Thus, we investigated the prediction of particular genes with pleiotropic effects on ovarian traits and social behavior in worker honey bees as a stringent test of the reproductive ground plan hypothesis. We complemented these tests with a comprehensive genome scan for additional quantitative trait loci (QTL) to gain a better understanding of the genetic architecture of the ovary size of honey bee workers, a morphological trait that is significant for understanding social insect caste evolution and general insect biology.
Results
Back-crossing hybrid European x Africanized honey bee queens to the Africanized parent colony generated two study populations with extraordinarily large worker ovaries. Despite the transgressive ovary phenotypes, several previously mapped QTL for social foraging behavior demonstrated ovary size effects, confirming the prediction of pleiotropic genetic effects on reproductive traits and social behavior. One major QTL for ovary size was detected in each backcross, along with several smaller effects and two QTL for ovary asymmetry. One of the main ovary size QTL coincided with a major QTL for ovary activation, explaining 3/4 of the phenotypic variance, although no simple positive correlation between ovary size and activation was observed.
Conclusions
Our results provide strong support for the reproductive ground plan hypothesis of evolution in study populations that are independent of the genetic stocks that originally led to the formulation of this hypothesis. As predicted, worker ovary size is genetically linked to multiple correlated traits of the complex division of labor in worker honey bees, known as the pollen hoarding syndrome. The genetic architecture of worker ovary size presumably consists of a combination of trait-specific loci and general regulators that affect the whole behavioral syndrome and may even play a role in caste determination. Several promising candidate genes in the QTL intervals await further study to clarify their potential role in social insect evolution and the regulation of insect fertility in general.
ContributorsGraham, Allie M. (Author) / Munday, Michael D. (Author) / Kaftanoglu, Osman (Author) / Page, Robert (Author) / Amdam, Gro (Author) / Rueppell, Olav (Author) / College of Liberal Arts and Sciences (Contributor) / School of Life Sciences (Contributor)
Created2011-04-13
Description
As a biology major, many of my classes have included studying the fundamentals of genetics or investigating the way genetics influence heritability of certain diseases. When I began taking upper-division psychology courses, the genetic factors of psychological disorders became an important part of the material. I was exposed to a new idea: that genes were equally important in studying somatic diseases as they were to psychological disorders. As important as genetics are to psychology, they are not part of the required courses for the major; I found many of my peers in psychology courses did not have a grasp on genetic fundamentals in the same way biology majors did. This was a disconnect that I also found in my own life outside the classroom. Growing up, my mother consistently reminded me to limit my carbs and watch my sugars. Diabetes was very prevalent in my family and I was also at risk. I was repeatedly reminded of my own genes and the risk I faced in having this biological disorder. However, my friend whose father was an alcoholic did not warn her in the same way. While she did know of her father's history, she was not warned of the potential for her to become an alcoholic. While my behavior was altered due to my mother's warning and my own knowledge of the genetic risk of diabetes, I wondered if other people at genetic risk of psychological disorders also altered their behavior. Through my thesis, I hope to answer if students have the same perceived genetic knowledge of psychological diseases as they do for biological ones. In my experience, it is not as well known that psychological disorders have genetic factors. For example, alcohol is commonly used by college students. Alcohol use disorder is present in 16.2% of college aged students and "40-60% of the variance of risk explained by genetic influences." (DSM V, 2013) Compare this to diabetes that has "several common genetic variants that account for about 10% of the total genetic effects," but is much more openly discussed even though it is less genetically linked. (McVay, 2015)This stems from the stigma/taboo surrounding many psychological disorders. If students do know that psychological disorder are genetically influenced, I expect their knowledge to be skewed or inaccurate. As part of a survey, I hope to see how strong they believe the genetic risk of certain diseases are as well as where they gained this knowledge. I hypothesize that only students with a background in psychology will be able to correctly assign the genetic risk of the four presented diseases. Completing this thesis will require in-depth study of the genetic factors, an understanding of the way each disease is perceived and understood by the general population, and a statistical analysis of the survey responses. If the survey data turns out as I expect where students do not have a strong grasp of diseases that could potentially influence their own health, I hope to find a way to educate students on biological and psychological diseases, their genetic risk, and how to speak openly about them.
ContributorsParasher, Nisha (Author) / Amdam, Gro (Thesis director) / Toft, Carolyn Cavaugh (Committee member) / Ostwald, Madeleine (Committee member) / Department of Psychology (Contributor) / School of Life Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
Honeybees (Apis mellifera) are pollinators that face multiple challenges during foraging such as fungicides applied to floral sources. Fungicides are chemicals used to inhibit key fungal mechanisms like metabolism, but their effects remain relatively unknown in bees. In addition, studying the maturing bee can help us identify demographics that are more vulnerable to toxic materials like fungicides. The purpose of this study is test whether maturation and the fungicide Pristine influence the permeability of the blood-brain barrier. Specifically, we use a transportable dye to test how blood brain barrier transporter function responds to toxic insult and how it changes with age. Oral ingestion of Pristine by female workers did not have an effect on blood brain barrier permeability which suggests Pristine may have no or longer term consequences in the bee. However, blood brain barrier permeability changed with the bee's age which could be explained by the regulation of blood brain barrier transporters during natural transitions in hive task or the presence of hemolymph protein filtration
ContributorsPatel, Aamir S. (Author) / Amdam, Gro (Thesis director) / Harrison, Jon (Committee member) / Ozturk, Cahit (Committee member) / School of Life Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
Dire wolves have recently risen to fame as a result of the popular television program Game of Thrones, and thus many viewers know dire wolves as the sigil and loyal companions of the Stark house. Far fewer recognize dire wolves by their scientific name, Canis dirus, or understand the population history of this ‘fearsome wolf’ species that roamed the Americas until the megafaunal mass extinction event of the Late Pleistocene. Although numerous studies have examined the species using morphological and geographical methods, thus far their results have been either inconclusive or contradictory. Remaining questions include the relationships dire wolves share with other members of the Canis genus and the internal structure of their populations. Advancements in ancient DNA recovery methods may make it possible to study dire wolf specimens at the molecular level for the first time and may therefore prove useful in clarifying the answers to these questions. Eighteen dire wolf specimens were collected from across the United States and subjected to ancient DNA extraction, library preparation, amplification and purification, bait preparation and capture, and next-generation sequencing. There was an average of 76.9 unique reads and 5.73% coverage when mapped to the Canis familiaris reference genome in ultraconserved regions of the mitochondrial genome. The results indicate that endogenous ancient DNA was not successfully recovered and perhaps ancient DNA recovery methods have not advanced to the point of retrieving informative amounts of DNA from particularly old, thermally degraded specimens. Nevertheless, the ever-changing nature of ancient DNA research makes it vital to continually test the limitations of the field and suggests that ancient DNA recovery methods will prove useful in illuminating dire wolf population history at some point in the future.
ContributorsSkerry, Katherine Marie (Author) / Stone, Anne (Thesis director) / Amdam, Gro (Committee member) / Larson, Greger (Committee member) / School of Human Evolution and Social Change (Contributor) / School of Nutrition and Health Promotion (Contributor) / School of Life Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
Vitellogenin (vg) is a precursor protein of egg yolk in honeybees, but it is also known to have immunological functions. The purpose of this experiment was to determine the effect of vg on the viral load of deformed wing virus (DWV) in worker honey bees (Apis mellifera). I hypothesized that a reduction in vg expression would lead to an increase in the viral load. I collected 180 worker bees and split them into four groups: half the bees were subjected to a vg gene knockdown by injections of double stranded vg RNA, and the rest were injected with green fluorescent protein (gfp) double stranded RNA. Half of each group was thereafter injected with DWV, and half given a sham injection. The rate of mortality in all four groups was higher than expected, leaving only 17 bees total. I dissected these bees' fat bodies and extracted their RNA to test for vg and DWV. PCR results showed that, out of the small group of remaining bees, the levels of vg were not statistically different. Furthermore, both groups of virus-injected bees showed similar viral loads. Because of the high mortality rate bees and the lack of differing levels of vg transcript between experimental and control groups, I could not draw conclusions from these results. The high mortality could be caused by several factors: temperature-induced stress, repeated stress from the two injections, and stress from viral infection. In addition, it is possible that the vg dsRNA batch I used was faulty. This thesis exemplifies that information cannot safely be extracted when loss of sampling units result in a small datasets that do not represent the original sampling population.
ContributorsCrable, Emma Lewis (Author) / Amdam, Gro (Thesis director) / Wang, Ying (Committee member) / Dahan, Romain (Committee member) / School of Life Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2017-12