Matching Items (84)
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
Nucleosomes are the basic repetitive unit of eukaryotic chromatin and are responsible for packing DNA inside the nucleus of the cell. They consist of a complex of eight histone proteins (two copies of four proteins H2A, H2B, H3 and H4) around which 147 base pairs of DNA are wrapped in ~1.67 superhelical turns. Although the nucleosomes are stable protein-DNA complexes, they undergo spontaneous conformational changes that occur in an asynchronous fashion. This conformational dynamics, defined by the "site-exposure" model, involves the DNA unwrapping from the protein core and exposing itself transiently before wrapping back. Physiologically, this allows regulatory proteins to bind to their target DNA sites during cellular processes like replication, DNA repair and transcription. Traditional biochemical assays have stablished the equilibrium constants for the accessibility to various sites along the length of the nucleosomal DNA, from its end to the middle of the dyad axis. Using fluorescence correlation spectroscopy (FCS), we have established the position dependent rewrapping rates for nucleosomes. We have also used Monte Carlo simulation methods to analyze the applicability of FRET fluctuation spectroscopy towards conformational dynamics, specifically motivated by nucleosome dynamics. Another important conformational change that is involved in cellular processes is the disassembly of nucleosome into its constituent particles. The exact pathway adopted by nucleosomes is still not clear. We used dual color fluorescence correlation spectroscopy to study the intermediates during nucleosome disassembly induced by changing ionic strength. Studying the nature of nucleosome conformational change and the kinetics is very important in understanding gene expression. The results from this thesis give a quantitative description to the basic unit of the chromatin.
ContributorsGurunathan, Kaushik (Author) / Levitus, Marcia (Thesis advisor) / Lindsay, Stuart (Committee member) / Woodbury, Neal (Committee member) / Yan, Hao (Committee member) / Arizona State University (Publisher)
Created2011
Description
The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system, with a projective Hilbert space regarded as the phase space. This thesis extends the theory by including some aspects of the symplectic topology of the quantum phase space. It is shown that the quantum mechanical uncertainty principle is a special case of an inequality from J-holomorphic map theory, that is, J-holomorphic curves minimize the difference between the quantum covariance matrix determinant and a symplectic area. An immediate consequence is that a minimal determinant is a topological invariant, within a fixed homology class of the curve. Various choices of quantum operators are studied with reference to the implications of the J-holomorphic condition. The mean curvature vector field and Maslov class are calculated for a lagrangian torus of an integrable quantum system. The mean curvature one-form is simply related to the canonical connection which determines the geometric phases and polarization linear response. Adiabatic deformations of a quantum system are analyzed in terms of vector bundle classifying maps and related to the mean curvature flow of quantum states. The dielectric response function for a periodic solid is calculated to be the curvature of a connection on a vector bundle.
ContributorsSanborn, Barbara (Author) / Suslov, Sergei K (Thesis advisor) / Suslov, Sergei (Committee member) / Spielberg, John (Committee member) / Quigg, John (Committee member) / Menéndez, Jose (Committee member) / Jones, Donald (Committee member) / Arizona State University (Publisher)
Created2011
Description
Healthy mitochondria are essential for cell survival. Described herein is the synthesis of a family of novel aminoquinone antioxidants designed to alleviate oxidative stress and prevent the impairment of cellular function. In addition, a library of bleomycin disaccharide analogues has also been synthesized to better probe the tumor targeting properties of bleomycin. The first study involves the synthesis of a benzoquinone natural product and analogues that closely resemble the redox core of the natural product geldanamycin. The synthesized 5-amino-3-tridecyl-1,4-benzoquinone antioxidants were tested for their ability to protect Friedreich's ataxia (FRDA) lymphocytes from induced oxidative stress. Some of the analogues synthesized conferred cytoprotection in a dose-dependent manner in FRDA lymphocytes at micromolar concentrations. The biological assays suggest that the modification of the 2-hydroxyl and N-(3-carboxypropyl) groups in the natural product can improve its antioxidant activity and significantly enhance its ability to protect mitochondrial function under conditions of oxidative stress. The second project focused on the synthesis of a library of bleomycin disaccharide-dye conjugates and monitored their cellular uptake by fluorescence microscopy. The studies reveal that the position of the carbamoyl group plays an important role in modulating the cellular uptake of the disaccharide. It also led to the discovery of novel disaccharides with improved tumor selectivity.
ContributorsMathilakathu Madathil, Manikandadas (Author) / Hecht, Sidney M. (Thesis advisor) / Rose, Seth (Committee member) / Woodbury, Neal (Committee member) / Arizona State University (Publisher)
Created2013
Description
This dissertation is intended to tie together a body of work which utilizes a variety of methods to study applied mathematical models involving heterogeneity often omitted with classical modeling techniques. I posit three cogent classifications of heterogeneity: physiological, behavioral, and local (specifically connectivity in this work). I consider physiological heterogeneity using the method of transport equations to study heterogeneous susceptibility to diseases in open populations (those with births and deaths). I then present three separate models of behavioral heterogeneity. An SIS/SAS model of gonorrhea transmission in a population of highly active men-who-have-sex-with-men (MSM) is presented to study the impact of safe behavior (prevention and self-awareness) on the prevalence of this endemic disease. Behavior is modeled in this examples via static parameters describing consistent condom use and frequency of STD testing. In an example of behavioral heterogeneity, in the absence of underlying dynamics, I present a generalization to ``test theory without an answer key" (also known as cultural consensus modeling or CCM). CCM is commonly used to study the distribution of cultural knowledge within a population. The generalized framework presented allows for selecting the best model among various extensions of CCM: multiple subcultures, estimating the degree to which individuals guess yes, and making competence homogenous in the population. This permits model selection based on the principle of information criteria. The third behaviorally heterogeneous model studies adaptive behavioral response based on epidemiological-economic theory within an $SIR$ epidemic setting. Theorems used to analyze the stability of such models with a generalized, non-linear incidence structure are adapted and applied to the case of standard incidence and adaptive incidence. As an example of study in spatial heterogeneity I provide an explicit solution to a generalization of the continuous time approximation of the Albert-Barabasi scale-free network algorithm. The solution is found by recursively solving the differential equations via integrating factors, identifying a pattern for the coefficients and then proving this observed pattern is consistent using induction. An application to disease dynamics on such evolving structures is then studied.
ContributorsMorin, Benjamin (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Hiebeler, David (Thesis advisor) / Hruschka, Daniel (Committee member) / Suslov, Sergei (Committee member) / Arizona State University (Publisher)
Created2012
Description
It has been well established that mitochondria play a critical role in the pathology of Friedreich's Ataxia. This disease is believed to be caused by a deficiency of frataxin, which research suggests is responsible for iron sulfur cluster assembly. This incomplete assembly of iron sulfur clusters is believed to be linked with dysfunctional complexes in the mitochondrial respiratory chain, increased oxidative stress, and potential cell death. Increased understanding of the pathophysiology of this disease has enabled the development of various therapeutic strategies aimed at restoring mitochondrial respiration. This thesis contains an analysis of the biological activity of several classes of antioxidants against oxidative stress induced by diethyl maleate in Friedreich's Ataxia lymphocytes and CEM leukemia cells. Analogues of vitamin E α-tocopherol have been shown to protect cells under oxidative stress. However, these same analogues show various levels of inhibition towards the electron transport chain complex I. Bicyclic pyridinols containing a ten carbon substituent provided favorable cytoprotection. N-hydroxy-4-pyridone compounds were observed to provide little protection. Similarly, analogues of CoQ10 in the form of pyridinol and pyrimidinol compounds also preserved cell viability at low concentrations.
ContributorsJaruvangsanti, Jennifer (Author) / Hecht, Sidney (Thesis advisor) / Woodbury, Neal (Committee member) / Skibo, Edward (Committee member) / Arizona State University (Publisher)
Created2012
Description
The field of biomedical research relies on the knowledge of binding interactions between various proteins of interest to create novel molecular targets for therapeutic purposes. While many of these interactions remain a mystery, knowledge of these properties and interactions could have significant medical applications in terms of understanding cell signaling and immunological defenses. Furthermore, there is evidence that machine learning and peptide microarrays can be used to make reliable predictions of where proteins could interact with each other without the definitive knowledge of the interactions. In this case, a neural network was used to predict the unknown binding interactions of TNFR2 onto LT-ɑ and TRAF2, and PD-L1 onto CD80, based off of the binding data from a sampling of protein-peptide interactions on a microarray. The accuracy and reliability of these predictions would rely on future research to confirm the interactions of these proteins, but the knowledge from these methods and predictions could have a future impact with regards to rational and structure-based drug design.
ContributorsPoweleit, Andrew Michael (Author) / Woodbury, Neal (Thesis director) / Diehnelt, Chris (Committee member) / Chiu, Po-Lin (Committee member) / School of Molecular Sciences (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
Lung cancer is the leading cause of cancer-related deaths in the US. Low-dose computed tomography (LDCT) scans are speculated to reduce lung cancer mortality. However LDCT scans impose multiple risks including false-negative results, false- positive results, overdiagnosis, and cancer due to repeated exposure to radiation. Immunosignaturing is a new method proposed to screen and detect lung cancer, eliminating the risks associated with LDCT scans. Known and blinded primary blood sera from participants with lung cancer and no cancer were run on peptide microarrays and analyzed. Immunosignatures for each known sample collectively indicated 120 peptides unique to lung cancer and non-cancer participants. These 120 peptides were used to determine the status of the blinded samples. Verification of the results from Vanderbilt is pending.
ContributorsNguyen, Geneva Trieu (Author) / Woodbury, Neal (Thesis director) / Zhao, Zhan-Gong (Committee member) / Stafford, Phillip (Committee member) / Barrett, The Honors College (Contributor) / Department of Chemistry and Biochemistry (Contributor) / Department of Psychology (Contributor)
Created2015-05
Description
With a quantum efficiency of nearly 100%, the electron transfer process that occurs within the reaction center protein of the photosynthetic bacteria Rhodobacter (Rh.) sphaeroides is a paragon for understanding the complexities, intricacies, and overall systemization of energy conversion and storage in natural systems. To better understand the way in which photons of light are captured, converted into chemically useful forms, and stored for biological use, an investigation into the reaction center protein, specifically into its cascade of cofactors, was undertaken. The purpose of this experimentation was to advance our knowledge and understanding of how differing protein environments and variant cofactors affect the spectroscopic aspects of and electron transfer kinetics within the reaction of Rh. sphaeroides. The native quinone, ubiquinone, was extracted from its pocket within the reaction center protein and replaced by non-native quinones having different reduction/oxidation potentials. It was determined that, of the two non-native quinones tested—1,2-naphthaquinone and 9,10- anthraquinone—the substitution of the anthraquinone (lower redox potential) resulted in an increased rate of recombination from the P+QA- charge-separated state, while the substitution of the napthaquinone (higher redox potential) resulted in a decreased rate of recombination.
ContributorsSussman, Hallie Rebecca (Author) / Woodbury, Neal (Thesis director) / Redding, Kevin (Committee member) / Lin, Su (Committee member) / School of Molecular Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2015-12
Description
Advances in peptide microarray technology have allowed for the creation of fast-paced and modular experiments within affinity ligand discovery. Previously, low density peptide arrays of 10,000 peptides were used to identify low affinity peptide ligands for a target protein; an approach that can be subsequently improved upon with a number of techniques. VDAP[a] offers more information about the relative affinity of protein-peptide interactions via signal intensity in contrast to high throughput screening (HTS) and display technologies which offer binary data. Now, high density peptide arrays with 130,000 to 330,000 peptides are available that allow screening across peptide libraries of greater diversity. With this increase in scale and diversity, faster analytical tools are needed to adequately characterize array data. Using the statistical power available in the R programming language, we have created a flexible analysis package that efficiently processes high density peptide array data from a variety of layouts, rank existing peptide hits, and utilize signal intensity data to generate new hits. This analysis provides a user-friendly method to efficiently analyze high density peptide array data, generate peptide leads for targeted therapeutic development, and further improve peptide array technologies.
ContributorsMoore, Cody Allen (Author) / Woodbury, Neal (Thesis director) / Diehnelt, Chris (Committee member) / Barrett, The Honors College (Contributor)
Created2015-12