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Articles 31 - 53 of 53
Full-Text Articles in Physical Sciences and Mathematics
Orderability And Rigidity In Contact Geometry, Peter Weigel
Orderability And Rigidity In Contact Geometry, Peter Weigel
Open Access Dissertations
We study the existence of positive loops of contactomorphisms on a Liouville-fillable contact manifold (&Sgr;, ξ = ker(α)). Previous results (see [1]) show that a large class of Liouville-fillable contact manifolds admit contractible positive loops. In contrast, we show that for any Liouville-fillable (&Sgr;, α) with dim(&Sgr;) ≥ 7, there exists a Liouville-fillable contact structure ξ' on &Sgr; which admits no positive loop at all. Further, ξ' can be chosen to agree with ξ' on the complement of a Darboux ball. We then define a relative version of orderability for a Legendrian submanifold, and discuss the relationship between the two …
Permutohedra, Configuration Spaces And Spineless Cacti, Yongheng Zhang
Permutohedra, Configuration Spaces And Spineless Cacti, Yongheng Zhang
Open Access Dissertations
It has been known that the configuration space F(R2, n) of n distinct ordered points in R2 deformation retracts to a regular CW complex with n!permutohedra Pn as the top dimensional cells. In this paper, we show that there exists a similar but different permutohedral structure of the spaceCact(n) of spineless cacti with n lobes. Based on these structures, direct homotopy equivalences between F (R2, n) and Cact(n) are then given. It is well known that the little 2-discs space D2(n) is homotopy equivalent toF(R2, n). …
Uncertainty Quantification And Calibration Of Physical Models, Xian He
Uncertainty Quantification And Calibration Of Physical Models, Xian He
Open Access Dissertations
An ecosystem model is a representation of a real complex ecological system, and is usually described by sophisticated mathematical models. Terrestrial Ecosystem Model (TEM) is one of the ecosystem models, that describes the dynamics of car- bon, nitrogen, water and other vegetation related variables. There are uncertainties in the TEM which are attributed to inaccurate input data, insufficient knowledge of the parameters, inherent randomness and simplification of the physical model. Quantification of uncertainty of such an ecosystem model is computationally very heavy. Bayesian calibration method has been used as an efficient way to calibrate and quantify uncertainties of the computer …
Parallel Symmetric Eigenvalue Problem Solvers, Alicia Marie Klinvex
Parallel Symmetric Eigenvalue Problem Solvers, Alicia Marie Klinvex
Open Access Dissertations
Sparse symmetric eigenvalue problems arise in many computational science and engineering applications: in structural mechanics, nanoelectronics, and spectral reordering, for example. Often, the large size of these problems requires the development of eigensolvers that scale well on parallel computing platforms. In this dissertation, we describe two such eigensolvers, TraceMin and TraceMin-Davidson. These methods are different from many other eigensolvers in that they do not require accurate linear solves to be performed at each iteration in order to find the smallest eigenvalues and their associated eigenvectors. After introducing these closely related eigensolvers, we discuss alternative methods for solving the saddle point …
Investigating Synergy: Mathematical Models For The Coupled Dynamics Of Hiv And Hsv-2 And Other Endemic Diseases, Christina M Alvey
Investigating Synergy: Mathematical Models For The Coupled Dynamics Of Hiv And Hsv-2 And Other Endemic Diseases, Christina M Alvey
Open Access Dissertations
This dissertation presents epidemiological models that investigate synergy: synergy between HIV and HSV-2 or between humans and mosquitoes in a malaria study. Each of the three coupled disease models addresses different epidemiological questions with regard to gender or disease structure in the context of sexually-transmitted diseases (STDs), while the malaria model focuses on age-structure of the human population. ^ Mounting evidence indicates that HSV-2 infection may increase susceptibility to HIV infection and that co-infection may increase infectiousness. Accordingly, antiviral treatment of people with HSV-2 may mitigate the incidence of HIV in populations where both pathogens occur. To better understand the …
Applications Of Microlocal Analysis To Some Hyperbolic Inverse Problems, Andrew J Homan
Applications Of Microlocal Analysis To Some Hyperbolic Inverse Problems, Andrew J Homan
Open Access Dissertations
This thesis compiles my work on three inverse problems: ultrasound recovery in thermoacoustic tomography, cancellation of singularities in synthetic aperture radar, and the injectivity and stability of some generalized Radon transforms. Each problem is approached using microlocal methods. In the context of thermoacoustic tomography under the damped wave equation, I show uniqueness and stability of the problem with complete data, provide a reconstruction algorithm for small attenuation with complete data, and obtain stability estimates for visible singularities with partial data. The chapter on synthetic aperture radar constructs microlocally several infinite-dimensional families of ground reflectivity functions which appear microlocally regular when …
Functional Inequalities And The Curvature Dimension Inequality On Totally Geodesic Foliations, Bumsik Kim
Functional Inequalities And The Curvature Dimension Inequality On Totally Geodesic Foliations, Bumsik Kim
Open Access Dissertations
We discover following analytic / geometric properties on Riemannian foliations with bundle-like metric and totally geodesic leaves, or shortly, totally geodesic foliations. Under a certain curvature condition, we obtain (1) Sobolev-isoperimetric inequalities, global Poincar\'e inqualities, and a lower bound for Cheeger's isoperimetric constant, (2) Poincar\'e inequalities on balls and uniqueness of positive(or $L^p,p\geq 1$) solutions for the subelliptic heat equation, (3) A lower bound for the first non-zero eigenvalue of sub-Laplacians (Lichnerowicz theorem), and Obata's sphere theorem. In this context, the curvature condition is a sub-Riemannian analogue of lower bounds for Ricci curvature tensor. Earlier, it is given by Baudoin-Garofalo's …
A Pure-Jump Market-Making Model For High-Frequency Trading, Chi Wai Law
A Pure-Jump Market-Making Model For High-Frequency Trading, Chi Wai Law
Open Access Dissertations
We propose a new market-making model which incorporates a number of realistic features relevant for high-frequency trading. In particular, we model the dependency structure of prices and order arrivals with novel self- and cross-exciting point processes. Furthermore, instead of assuming the bid and ask prices can be adjusted continuously by the market maker, we formulate the market maker's decisions as an optimal switching problem. Moreover, the risk of overtrading has been taken into consideration by allowing each order to have different size, and the market maker can make use of market orders, which are treated as impulse control, to get …
G-Frobenius Manifolds, Byeongho Lee
G-Frobenius Manifolds, Byeongho Lee
Open Access Dissertations
The goal of this dissertation is to introduce the notion of G-Frobenius manifolds for any finite group G. This work is motivated by the fact that any G-Frobenius algebra yields an ordinary Frobenius algebra by taking its G-invariants. We generalize this on the level of Frobenius manifolds. To define a G-Frobenius manifold as a braided-commutative generalization of the ordinary commutative Frobenius manifold, we develop the theory of G-braided spaces. These are defined as G-graded G-modules with certain braided-commutative "rings of functions", generalizing the commutative rings of power series on ordinary vector spaces. As the genus zero part of any ordinary …
A P-Adic Spectral Triple, Sumedha Hemamalee Rathnayake
A P-Adic Spectral Triple, Sumedha Hemamalee Rathnayake
Open Access Dissertations
We construct a spectral triple for the C*-algebra of continuous functions on the space of p-adic integers. On the technical level we utilize a weighted rooted tree obtained from a coarse grained approximation of the space combined with the forward derivative D on the tree. Our spectral triple satisfies the properties of a compact spectral metric space and the metric on the space of p-adic integers induced by the spectral triple is equivalent to the usual p-adic metric. Furthermore, we show that the spectrum of the operator D*D is closely related to the roots of a certain …
Modeling, Optimization, And Sensitivity Analysis Of A Continuous Multi-Segment Crystallizer For Production Of Active Pharmaceutical Ingredients, Bradley James Ridder
Modeling, Optimization, And Sensitivity Analysis Of A Continuous Multi-Segment Crystallizer For Production Of Active Pharmaceutical Ingredients, Bradley James Ridder
Open Access Dissertations
We have investigated the simulation-based, steady-state optimization of a new type of crystallizer for the production of pharmaceuticals. The multi-segment, multi-addition plug-flow crystallizer (MSMA-PFC) offers better control over supersaturation in one dimension compared to a batch or stirred-tank crystallizer. Through use of a population balance framework, we have written the governing model equations of population balance and mass balance on the crystallizer segments. The solution of these equations was accomplished through either the method of moments or the finite volume method. The goal was to optimize the performance of the crystallizer with respect to certain quantities, such as maximizing the …
A 2-Categorical Extension Of The Reshetikhin--Turaev Theory, Yu Tsumara
A 2-Categorical Extension Of The Reshetikhin--Turaev Theory, Yu Tsumara
Open Access Dissertations
We concretely construct a 2-categorically extended topological quantum field theory that extends the Reshetikhin-Turaev TQFT to cobordisms with corners. The source category will be a well chosen 2-category of decorated cobordisms with corners and the target bicategory will be the Kapranov-Voevodsky 2-vector spaces.
Nonparametric Variable Selection And Dimension Reduction Methods And Their Applications In Pharmacogenomics, Jingyi Zhu
Nonparametric Variable Selection And Dimension Reduction Methods And Their Applications In Pharmacogenomics, Jingyi Zhu
Open Access Dissertations
Nowadays it is common to collect large volumes of data in many fields with an extensive amount of variables, but often a small or moderate number of samples. For example, in the analysis of genomic data, the number of genes can be very large, varying from tens of thousands to several millions, whereas the number of samples is several hundreds to thousands. Pharmacogenomics is an example of genomics data analysis that we are considering here. Pharmacogenomics research uses whole-genome genetic information to predict individuals' drug response. Because whole-genome data are high dimensional and their relationships to drug response are complicated, …
Probabilistic Uncertainty Quantification And Experiment Design For Nonlinear Models: Applications In Systems Biology, Vu Cao Duy Thien Dinh
Probabilistic Uncertainty Quantification And Experiment Design For Nonlinear Models: Applications In Systems Biology, Vu Cao Duy Thien Dinh
Open Access Dissertations
Despite the ever-increasing interest in understanding biology at the system level, there are several factors that hinder studies and analyses of biological systems. First, unlike systems from other applied fields whose parameters can be effectively identified, biological systems are usually unidentifiable, even in the ideal case when all possible system outputs are known with high accuracy. Second, the presence of multivariate bifurcations often leads the system to behaviors that are completely different in nature. In such cases, system outputs (as function of parameters/inputs) are usually discontinuous or have sharp transitions across domains with different behaviors. Finally, models from systems biology …
On The Occurrences Of Motifs In Recursive Trees, With Applications To Random Structures, Mohan Gopaladesikan
On The Occurrences Of Motifs In Recursive Trees, With Applications To Random Structures, Mohan Gopaladesikan
Open Access Dissertations
In this dissertation we study three problems related to motifs and recursive trees. In the first problem we consider a collection of uncorrelated motifs and their occurrences on the fringe of random recursive trees. We compute the exact mean and variance of the multivariate random vector of the counts of occurrences of the motifs. We further use the Cramér-Wold device and the contraction method to show an asymptotic convergence in distribution to a multivariate normal random variable with this mean and variance. ^ The second problem we study is that of the probability that a collection of motifs (of the …
The Scientific Theories Of Michael Faraday And James Clerk Maxwell, Shannon P. Israelsen
The Scientific Theories Of Michael Faraday And James Clerk Maxwell, Shannon P. Israelsen
The Purdue Historian
This paper explores the role of mathematical formalism in physics theories through an analysis of the work of physicists Michael Faraday and James Clerk Maxwell in the field of electromagnetism. After a brief description of the educational backgrounds of each scientist, their views on the nature of physics theory and its relationship to mathematics are contrasted. Faraday sought a mathematics-free theory to describe the results of his experiments, producing a family of concepts that became the roots of electromagnetic field theory. Maxwell built upon these concepts, giving them robust mathematical expression and incorporating them into one unified theoretical picture. An …
Spatiotemporal Crime Analysis, James Q. Tay, Abish Malik, Sherry Towers, David Ebert
Spatiotemporal Crime Analysis, James Q. Tay, Abish Malik, Sherry Towers, David Ebert
The Summer Undergraduate Research Fellowship (SURF) Symposium
There has been a rise in the use of visual analytic techniques to create interactive predictive environments in a range of different applications. These tools help the user sift through massive amounts of data, presenting most useful results in a visual context and enabling the person to rapidly form proactive strategies. In this paper, we present one such visual analytic environment that uses historical crime data to predict future occurrences of crimes, both geographically and temporally. Due to the complexity of this analysis, it is necessary to find an appropriate statistical method for correlative analysis of spatiotemporal data, as well …
Lecture-Free Calculus For Science And Engineering, Benjamin Wiles
Lecture-Free Calculus For Science And Engineering, Benjamin Wiles
IMPACT Symposium
Plane Analytic Geometry and Calculus I (MA 16100) is a historically difficult, required course for engineering and science majors. The traditional configuration consists of 250 students meeting in a large lecture 3 times per week and twice per week in smaller recitations of size 40. Additionally, those who repeat the course often continue to encounter difficulty. A scalable re-design has been implemented to attempt to address the needs of students that are not being met in the traditional configuration by diverting resources from lecture to problem sessions and from traditional Q&A recitations to student-driven presentation/collaboration-based recitations. The students work in …
An Epidemic Model Structured By The Time Since Last Infection, Jorge Alturo Alfaro Murillo
An Epidemic Model Structured By The Time Since Last Infection, Jorge Alturo Alfaro Murillo
Open Access Dissertations
Epidemiological models structured by time since infection have their origin in the seminal work of 1927 by Kermack and McKendrick. Compared to ordinary differential equations (ODE) models, they are able to capture differences in infectivity of the individuals in a more suitable manner. Their use declined in the second half of the 20th century, probably because the theory for ODE models is more robust, complete and has proved successful in providing insights and predictions for many epidemiological problems. Nevertheless, it is important to understand in what occasions the inclusion of time since infection may alter the outcomes in a significant …
Exploring The Effects Of Conversational Repair As A Scaffolding Strategy To Promote Mathematics Explanations Of Students With Learning Disabilities, Jia Liu
Open Access Dissertations
Conversational repair often occurs in conversations when people attempt to address communicative breakdowns or inaccuracy by way of repeating what have been said or putting them in another way. The review of literature on conversational repair revealed that as an important concept in pragmatic aspect of language, it is an effective strategy to improve communication of different populations with disabilities. However, it is rarely studied in the domain of mathematics and with the population with learning disabilities/difficulties (LD). In current reform-based, discourse-oriented mathematics classrooms, students with LD encounter difficulties articulating or explaining well their reasoning processes due to the mathematical …
A Jackknife Empirical Likelihood Approach To Goodness Of Fit U-Statistic Testing With Side Information, Qun Lin
Open Access Dissertations
Motivated by applications to goodness of fit U-statistics testing, the jackknife empirical likelihood of Jing, et al. (2009) is justified with an alternative approach, and the Wilks theorem for vector U-statistics is proved. This generalizes Owen's empirical likelihood theorem for a vector mean to a vector U-statistics-based mean and includes the jackknife empirical likelihood of U-statistics with side information as a special case. The results are generalized to allow for the constraints to use estimated criteria functions and for the number of constraints to grow with the sample size. The latter is needed to handle naturally occurring nuisance parameters in …
Methods For Increasing Domains Of Convergence In Iterative Linear System Solvers, David Michael Imberti
Methods For Increasing Domains Of Convergence In Iterative Linear System Solvers, David Michael Imberti
Open Access Dissertations
In this thesis, we introduce and improve various methods for increasing the domains of convergence for iterative linear system solvers. We rely on the following three approaches: making the iteration adaptive, or nesting an inner iteration inside of a previously determined outer iteration; using deflation and projections to manipulate the spectra inherent to the iteration; and/or focusing on reordering schemes. We will analyze a specific combination of these three strategies. In particular, we propose to examine the influence of nesting a Flexible Generalized Minimum Residual algorithm together with an inner Recursive Projection Method using a banded preconditioner resulting from the …
Global Dimension Of Ci: Compete Or Collaborate, Arden L. Bement Jr.
Global Dimension Of Ci: Compete Or Collaborate, Arden L. Bement Jr.
PPRI Digital Library
No abstract provided.