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Articles 1 - 10 of 10
Full-Text Articles in Other Mathematics
Rigid Body Constrained Motion Optimization And Control On Lie Groups And Their Tangent Bundles, Brennan S. Mccann
Rigid Body Constrained Motion Optimization And Control On Lie Groups And Their Tangent Bundles, Brennan S. Mccann
Doctoral Dissertations and Master's Theses
Rigid body motion requires formulations where rotational and translational motion are accounted for appropriately. Two Lie groups, the special orthogonal group SO(3) and the space of quaternions H, are commonly used to represent attitude. When considering rigid body pose, that is spacecraft position and attitude, the special Euclidean group SE(3) and the space of dual quaternions DH are frequently utilized. All these groups are Lie groups and Riemannian manifolds, and these identifications have profound implications for dynamics and controls. The trajectory optimization and optimal control problem on Riemannian manifolds presents significant opportunities for theoretical development. Riemannian optimization is an attractive …
Multilayer Network Model Of Gender Bias And Homophily In Hierarchical Structures, Emerson Mcmullen
Multilayer Network Model Of Gender Bias And Homophily In Hierarchical Structures, Emerson Mcmullen
HMC Senior Theses
Although women have made progress in entering positions in academia and
industry, they are still underrepresented at the highest levels of leadership.
Two factors that may contribute to this leaky pipeline are gender bias,
the tendency to treat individuals differently based on the person’s gender
identity, and homophily, the tendency of people to want to be around those
who are similar to themselves. Here, we present a multilayer network model
of gender representation in professional hierarchies that incorporates these
two factors. This model builds on previous work by Clifton et al. (2019), but
the multilayer network framework allows us to …
Role Of Inhibition And Spiking Variability In Ortho- And Retronasal Olfactory Processing, Michelle F. Craft
Role Of Inhibition And Spiking Variability In Ortho- And Retronasal Olfactory Processing, Michelle F. Craft
Theses and Dissertations
Odor perception is the impetus for important animal behaviors, most pertinently for feeding, but also for mating and communication. There are two predominate modes of odor processing: odors pass through the front of nose (ortho) while inhaling and sniffing, or through the rear (retro) during exhalation and while eating and drinking. Despite the importance of olfaction for an animal’s well-being and specifically that ortho and retro naturally occur, it is unknown whether the modality (ortho versus retro) is transmitted to cortical brain regions, which could significantly instruct how odors are processed. Prior imaging studies show different …
Stroke Clustering And Fitting In Vector Art, Khandokar Shakib
Stroke Clustering And Fitting In Vector Art, Khandokar Shakib
Senior Independent Study Theses
Vectorization of art involves turning free-hand drawings into vector graphics that can be further scaled and manipulated. In this paper, we explore the concept of vectorization of line drawings and study multiple approaches that attempt to achieve this in the most accurate way possible. We utilize a software called StrokeStrip to discuss the different mathematics behind the parameterization and fitting involved in the drawings.
Sum Of Cubes Of The First N Integers, Obiamaka L. Agu
Sum Of Cubes Of The First N Integers, Obiamaka L. Agu
Electronic Theses, Projects, and Dissertations
In Calculus we learned that Sum^{n}_{k=1} k = [n(n+1)]/2 , that Sum^{n}_{k=1} k^2 = [n(n+1)(2n+1)]/6 , and that Sum^{n}_{k=1} k^{3} = (n(n+1)/2)^{2}. These formulas are useful when solving for the area below quadratic or cubic function over an interval [a, b]. This tedious process, solving for areas under a quadratic or a cubic, served as motivation for the introduction of Riemman integrals. For the overzealous math student, these steps were replaced by a simpler method of evaluating antiderivatives at the endpoints a and b. From my recollection, a former instructor informed us to do the value of memorizing these formulas. …
Mathematical Models: The Lanchester Equations And The Zombie Apocalypse, Hailey Bauer
Mathematical Models: The Lanchester Equations And The Zombie Apocalypse, Hailey Bauer
Undergraduate Theses and Capstone Projects
This research study used mathematical models to analyze and depicted specific battle situations and the outcomes of the zombie apocalypse. The original models that predicted warfare were the Lanchester models, while the zombie apocalypse models were fictional expansions upon mathematical models used to examine infectious diseases. In this paper, I analyzed and compared different mathematical models by examining each model’s set of assumptions and the impact of the change in variables on the population classes. The purpose of this study was to understand the basics of the discrete dynamical systems and to determine the similarities between imaginary and realistic models. …
Theoretical Analysis Of Nonlinear Differential Equations, Emily Jean Weymier
Theoretical Analysis Of Nonlinear Differential Equations, Emily Jean Weymier
Electronic Theses and Dissertations
Nonlinear differential equations arise as mathematical models of various phenomena. Here, various methods of solving and approximating linear and nonlinear differential equations are examined. Since analytical solutions to nonlinear differential equations are rare and difficult to determine, approximation methods have been developed. Initial and boundary value problems will be discussed. Several linear and nonlinear techniques to approximate or solve the linear or nonlinear problems are demonstrated. Regular and singular perturbation theory and Magnus expansions are our particular focus. Each section offers several examples to show how each technique is implemented along with the use of visuals to demonstrate the accuracy, …
The Mathematics Of Cancer: Fitting The Gompertz Equation To Tumor Growth, Dyjuan Tatro
The Mathematics Of Cancer: Fitting The Gompertz Equation To Tumor Growth, Dyjuan Tatro
Senior Projects Spring 2018
Mathematical models are finding increased use in biology, and partuculary in the field of cancer research. In relation to cancer, systems of differential equations have been proven to model tumor growth for many types of cancer while taking into account one or many features of tumor growth. One feature of tumor growth that models must take into account is that tumors do not grow exponentially. One model that embodies this feature is the Gomperts Model of Cell Growth. By fitting this model to long-term breast cancer study data, this project ascertains gompertzian parameters that can be used to predicts tumor …
Epistasis In Predator-Prey Relationships, Iuliia Inozemtseva
Epistasis In Predator-Prey Relationships, Iuliia Inozemtseva
Electronic Theses and Dissertations
Epistasis is the interaction between two or more genes to control a single phenotype. We model epistasis of the prey in a two-locus two-allele problem in a basic predator- prey relationship. The resulting model allows us to examine both population sizes as well as genotypic and phenotypic frequencies. In the context of several numerical examples, we show that if epistasis results in an undesirable or desirable phenotype in the prey by making the particular genotype more or less susceptible to the predator or dangerous to the predator, elimination of undesirable phenotypes and then genotypes occurs.
Validation Of Weak Form Thermal Analysis Algorithms Supporting Thermal Signature Generation, Elton Lewis Freeman
Validation Of Weak Form Thermal Analysis Algorithms Supporting Thermal Signature Generation, Elton Lewis Freeman
Masters Theses
Extremization of a weak form for the continuum energy conservation principle differential equation naturally implements fluid convection and radiation as flux Robin boundary conditions associated with unsteady heat transfer. Combining a spatial semi-discretization via finite element trial space basis functions with time-accurate integration generates a totally node-based algebraic statement for computing. Closure for gray body radiation is a newly derived node-based radiosity formulation generating piecewise discontinuous solutions, while that for natural-forced-mixed convection heat transfer is extracted from the literature. Algorithm performance, mathematically predicted by asymptotic convergence theory, is subsequently validated with data obtained in 24 hour diurnal field experiments for …