Matching Items (118)
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
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
In an effort to begin validating the large number of discovered candidate biomarkers, proteomics is beginning to shift from shotgun proteomic experiments towards targeted proteomic approaches that provide solutions to automation and economic concerns. Such approaches to validate biomarkers necessitate the mass spectrometric analysis of hundreds to thousands of human samples. As this takes place, a serendipitous opportunity has become evident. By the virtue that as one narrows the focus towards "single" protein targets (instead of entire proteomes) using pan-antibody-based enrichment techniques, a discovery science has emerged, so to speak. This is due to the largely unknown context in which "single" proteins exist in blood (i.e. polymorphisms, transcript variants, and posttranslational modifications) and hence, targeted proteomics has applications for established biomarkers. Furthermore, besides protein heterogeneity accounting for interferences with conventional immunometric platforms, it is becoming evident that this formerly hidden dimension of structural information also contains rich-pathobiological information. Consequently, targeted proteomics studies that aim to ascertain a protein's genuine presentation within disease- stratified populations and serve as a stepping-stone within a biomarker translational pipeline are of clinical interest. Roughly 128 million Americans are pre-diabetic, diabetic, and/or have kidney disease and public and private spending for treating these diseases is in the hundreds of billions of dollars. In an effort to create new solutions for the early detection and management of these conditions, described herein is the design, development, and translation of mass spectrometric immunoassays targeted towards diabetes and kidney disease. Population proteomics experiments were performed for the following clinically relevant proteins: insulin, C-peptide, RANTES, and parathyroid hormone. At least thirty-eight protein isoforms were detected. Besides the numerous disease correlations confronted within the disease-stratified cohorts, certain isoforms also appeared to be causally related to the underlying pathophysiology and/or have therapeutic implications. Technical advancements include multiplexed isoform quantification as well a "dual- extraction" methodology for eliminating non-specific proteins while simultaneously validating isoforms. Industrial efforts towards widespread clinical adoption are also described. Consequently, this work lays a foundation for the translation of mass spectrometric immunoassays into the clinical arena and simultaneously presents the most recent advancements concerning the mass spectrometric immunoassay approach.
ContributorsOran, Paul (Author) / Nelson, Randall (Thesis advisor) / Hayes, Mark (Thesis advisor) / Ros, Alexandra (Committee member) / Williams, Peter (Committee member) / Arizona State University (Publisher)
Created2011
Description
Signal processing techniques have been used extensively in many engineering problems and in recent years its application has extended to non-traditional research fields such as biological systems. Many of these applications require extraction of a signal or parameter of interest from degraded measurements. One such application is mass spectrometry immunoassay (MSIA) which has been one of the primary methods of biomarker discovery techniques. MSIA analyzes protein molecules as potential biomarkers using time of flight mass spectrometry (TOF-MS). Peak detection in TOF-MS is important for biomarker analysis and many other MS related application. Though many peak detection algorithms exist, most of them are based on heuristics models. One of the ways of detecting signal peaks is by deploying stochastic models of the signal and noise observations. Likelihood ratio test (LRT) detector, based on the Neyman-Pearson (NP) lemma, is an uniformly most powerful test to decision making in the form of a hypothesis test. The primary goal of this dissertation is to develop signal and noise models for the electrospray ionization (ESI) TOF-MS data. A new method is proposed for developing the signal model by employing first principles calculations based on device physics and molecular properties. The noise model is developed by analyzing MS data from careful experiments in the ESI mass spectrometer. A non-flat baseline in MS data is common. The reasons behind the formation of this baseline has not been fully comprehended. A new signal model explaining the presence of baseline is proposed, though detailed experiments are needed to further substantiate the model assumptions. Signal detection schemes based on these signal and noise models are proposed. A maximum likelihood (ML) method is introduced for estimating the signal peak amplitudes. The performance of the detection methods and ML estimation are evaluated with Monte Carlo simulation which shows promising results. An application of these methods is proposed for fractional abundance calculation for biomarker analysis, which is mathematically robust and fundamentally different than the current algorithms. Biomarker panels for type 2 diabetes and cardiovascular disease are analyzed using existing MS analysis algorithms. Finally, a support vector machine based multi-classification algorithm is developed for evaluating the biomarkers' effectiveness in discriminating type 2 diabetes and cardiovascular diseases and is shown to perform better than a linear discriminant analysis based classifier.
ContributorsBuddi, Sai (Author) / Taylor, Thomas (Thesis advisor) / Cochran, Douglas (Thesis advisor) / Nelson, Randall (Committee member) / Duman, Tolga (Committee member) / Arizona State University (Publisher)
Created2012
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
Cancer claims hundreds of thousands of lives every year in US alone. Finding ways for early detection of cancer onset is crucial for better management and treatment of cancer. Thus, biomarkers especially protein biomarkers, being the functional units which reflect dynamic physiological changes, need to be discovered. Though important, there are only a few approved protein cancer biomarkers till date. To accelerate this process, fast, comprehensive and affordable assays are required which can be applied to large population studies. For this, these assays should be able to comprehensively characterize and explore the molecular diversity of nominally "single" proteins across populations. This information is usually unavailable with commonly used immunoassays such as ELISA (enzyme linked immunosorbent assay) which either ignore protein microheterogeneity, or are confounded by it. To this end, mass spectrometric immuno assays (MSIA) for three different human plasma proteins have been developed. These proteins viz. IGF-1, hemopexin and tetranectin have been found in reported literature to show correlations with many diseases along with several carcinomas. Developed assays were used to extract entire proteins from plasma samples and subsequently analyzed on mass spectrometric platforms. Matrix assisted laser desorption ionization (MALDI) and electrospray ionization (ESI) mass spectrometric techniques where used due to their availability and suitability for the analysis. This resulted in visibility of different structural forms of these proteins showing their structural micro-heterogeneity which is invisible to commonly used immunoassays. These assays are fast, comprehensive and can be applied in large sample studies to analyze proteins for biomarker discovery.
ContributorsRai, Samita (Author) / Nelson, Randall (Thesis advisor) / Hayes, Mark (Thesis advisor) / Borges, Chad (Committee member) / Ros, Alexandra (Committee member) / Arizona State University (Publisher)
Created2012
Description
Some of the most talented, innovative, and experimental artists are students, but they are often discouraged by the price of higher education and lack of scholarship or funding opportunities. Additionally, the art industry has become stagnant. Traditional brick-and-mortar galleries are not willing to represent young, unknown artists. Their overhead is simply too high for risky choices.
The Student Art Project is art patronage for the 21st century—a curated online gallery featuring exceptional student artists. The Student Art Project is a highly curated experience for buyers. Only five artists are featured each month. Buyers are not bombarded with thousands of different products and separate artists “shops”. They can read artists bios and find art they connect with.
Student artists apply through an online form. Once accepted to the program, artists receive a $200 materials stipend to create an exclusive collection of 5-10 pieces. Original artwork and limited edition prints are sold through our website. These collections can potentially fund an entire year of college tuition, a life-changing amount for many students.
Brick-and-mortar galleries typically take 40-60% of the retail price of artwork. The Student Art Project will only take 30%, which we will use to reinvest in future artists. Other art websites, like Etsy, require the artists to ship, invoice, and communicate with customers. For students, this means less time spent in the classroom and less time developing their craft. The Student Art Project handles all business functions for our artists, allowing them to concentrate on what really matters, their education.
The Student Art Project is art patronage for the 21st century—a curated online gallery featuring exceptional student artists. The Student Art Project is a highly curated experience for buyers. Only five artists are featured each month. Buyers are not bombarded with thousands of different products and separate artists “shops”. They can read artists bios and find art they connect with.
Student artists apply through an online form. Once accepted to the program, artists receive a $200 materials stipend to create an exclusive collection of 5-10 pieces. Original artwork and limited edition prints are sold through our website. These collections can potentially fund an entire year of college tuition, a life-changing amount for many students.
Brick-and-mortar galleries typically take 40-60% of the retail price of artwork. The Student Art Project will only take 30%, which we will use to reinvest in future artists. Other art websites, like Etsy, require the artists to ship, invoice, and communicate with customers. For students, this means less time spent in the classroom and less time developing their craft. The Student Art Project handles all business functions for our artists, allowing them to concentrate on what really matters, their education.
ContributorsDangler, Rebecca Leigh (Author) / Trujillo, Rhett (Thesis director) / Coleman, Sean (Committee member) / Barrett, The Honors College (Contributor) / Herberger Institute for Design and the Arts (Contributor) / Department of Management (Contributor)
Created2015-05
Description
Drought is one of the most pressing issues affecting the future of the standard of living here in Phoenix. With the threat of water rationing and steep price hikes looming on the horizon for water customers in California, the desert southwest, and in drought-stricken communities worldwide, industrial designers are in a prime position to help improve the experience of water conservation so that consumers are willing to start taking conscious steps toward rethinking their relationship with water usage.
In a research group, several designers sought to understand the depth and complexity of this highly politicized issue by interviewing a wide variety of stakeholders, including sustainability experts, landscapers, water company executives, small business owners, reservoir forest rangers, and many more. Data synthesis led to the conclusion that residential water use is a lifestyle issue, and the only real way to conserve involves a significant shift in the collective idea of an “ideal” home—lawns, pools, and overwatered landscaping contribute to 70% of all water use by residences in the Phoenix area. The only real way to conserve involves increasing population density and creating communal green spaces.
DR. DISH is a dishwashing device that is meant to fit into the high-density living spaces that are rapidly being built in the face of the massive exodus of people into the world’s cities. To help busy apartment and condominium dwellers conserve water and time, DR. DISH converts a standard kitchen sink into a small dishwasher, which uses significantly less water than hand-washing dishes or rinsing dishes before putting them into a conventional dishwasher. Using advanced filtration technology and a powerful rinse cycle, a load dishes can be cleaned with about 2 gallons of water. Fully automating the dishwashing process also saves the user time and minimizes unpleasant contact with food residue and grease.
This device is meant to have a significant impact upon the water use of households that do not have a dishwasher, or simply do not use their dishwasher. With a low target price point and myriad convenient features, DR. DISH is a high-tech solution that promises water savings at a time when every effort toward conservation is absolutely critical. As we move toward a new era in determining water rights and imposing mandatory restrictions upon each and every person living in affected areas, creating conservation solutions that will be relevant for the lifestyles of the future is especially important, and the agility of designers in coming up with products that quickly cut consumer water consumption will be a key factor in determining whether humanity will be able to adapt to a new era in our relationship with natural resources.
In a research group, several designers sought to understand the depth and complexity of this highly politicized issue by interviewing a wide variety of stakeholders, including sustainability experts, landscapers, water company executives, small business owners, reservoir forest rangers, and many more. Data synthesis led to the conclusion that residential water use is a lifestyle issue, and the only real way to conserve involves a significant shift in the collective idea of an “ideal” home—lawns, pools, and overwatered landscaping contribute to 70% of all water use by residences in the Phoenix area. The only real way to conserve involves increasing population density and creating communal green spaces.
DR. DISH is a dishwashing device that is meant to fit into the high-density living spaces that are rapidly being built in the face of the massive exodus of people into the world’s cities. To help busy apartment and condominium dwellers conserve water and time, DR. DISH converts a standard kitchen sink into a small dishwasher, which uses significantly less water than hand-washing dishes or rinsing dishes before putting them into a conventional dishwasher. Using advanced filtration technology and a powerful rinse cycle, a load dishes can be cleaned with about 2 gallons of water. Fully automating the dishwashing process also saves the user time and minimizes unpleasant contact with food residue and grease.
This device is meant to have a significant impact upon the water use of households that do not have a dishwasher, or simply do not use their dishwasher. With a low target price point and myriad convenient features, DR. DISH is a high-tech solution that promises water savings at a time when every effort toward conservation is absolutely critical. As we move toward a new era in determining water rights and imposing mandatory restrictions upon each and every person living in affected areas, creating conservation solutions that will be relevant for the lifestyles of the future is especially important, and the agility of designers in coming up with products that quickly cut consumer water consumption will be a key factor in determining whether humanity will be able to adapt to a new era in our relationship with natural resources.
ContributorsMarcinkowski, Margaret Nicole (Author) / Shin, Dosun (Thesis director) / McDermott, Lauren (Committee member) / Barrett, The Honors College (Contributor) / The Design School (Contributor) / Herberger Institute for Design and the Arts (Contributor)
Created2015-05
Description
Fire Shelter Foam Assist is meant as a firefighter's last effort of survival when a wildfire threatens their position. When deployed, it will cover the firefighter as the fire blows over. By reducing the time of deployment and simplifying the process, firefighters will have more time to ensure the area around them is cleared. The Fire Shelter Foam Assist has features that allow it to auto deploy around the firefighter through the use of fire foam retardant. The fire foam retardant inflates the shelter as well as provides an extra layer of protection against the wildfire.
ContributorsSmith, Tori Elizabeth (Author) / Shin, Dosun (Thesis director) / McDermott, Lauren (Committee member) / Barrett, The Honors College (Contributor) / Herberger Institute for Design and the Arts (Contributor) / The Design School (Contributor)
Created2015-05
Description
After researching pediatric cancer experiences, an opportunity emerged creating a less intimidating environment for children undergoing chemotherapy. By means of adding a creative component to their IV pole and disguising machinery, children will be a part of an Imagination Voyage adventure. Creative themes allow for a journey on a pirate ship, or being in a fantasy castle by captivating children in playtime. The design allows for a frightening experience to become a positive one.
ContributorsHerold, Brittany Ann (Author) / Shin, Dosun (Thesis director) / McDermott, Lauren (Committee member) / Barrett, The Honors College (Contributor) / Herberger Institute for Design and the Arts (Contributor) / School of Sustainability (Contributor) / The Design School (Contributor)
Created2015-05