Other Mathematics Commons^™

Msis-Capaldi: Modelling The Winter Tick Epizootic In Moose, Charlotte Beckford

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Integrating Quantitative Skills Into Biology Courses, Kathleen Hoffman, Sarah Leupen, Hannah Pie, Michelle Starz-Gaiano, Patricia Turner, Tory Williams

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modelling Impact Of Diverse Vegetation On Crop-Pollinator Interactions, Morgan N. Beetler

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

On A Stationary Random Knot, Andrey A. Dorogovtsev

Journal of Stochastic Analysis

No abstract provided.

Most Popular Genre's Of Videogames To Play For Hu Students, Asheria Upsher, Jean Orejuela, Joshua Scott

Harrisburg University Research Symposium: Highlighting Research, Innovation, & Creativity

Our Poster will show the most played and favored videogame genre's according to HU students.

Reducing Uncertainty In Sea-Level Rise Prediction: A Spatial-Variability-Aware Approach, Subhankar Ghosh, Shuai An, Arun Sharma, Jayant Gupta, Shashi Shekhar, Aneesh Subramanian

I-GUIDE Forum

Given multi-model ensemble climate projections, the goal is to accurately and reliably predict future sea-level rise while lowering the uncertainty. This problem is important because sea-level rise affects millions of people in coastal communities and beyond due to climate change's impacts on polar ice sheets and the ocean. This problem is challenging due to spatial variability and unknowns such as possible tipping points (e.g., collapse of Greenland or West Antarctic ice-shelf), climate feedback loops (e.g., clouds, permafrost thawing), future policy decisions, and human actions. Most existing climate modeling approaches use the same set of weights globally, during either regression or …

Backward Stochastic Differential Equations In A Semi-Markov Chain Model, Robert J. Elliott, Zhe Yang

Journal of Stochastic Analysis

No abstract provided.

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 …

Superoscillations And Fock Spaces, Daniel Alpay, Fabrizio Colombo, Kamal Diki, Irene Sabadini, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we use techniques in Fock spaces theory and compute how the Segal-Bargmann transform acts on special wave functions obtained by multiplying superoscillating sequences with normalized Hermite functions. It turns out that these special wave functions can be constructed also by computing the approximating sequence of the normalized Hermite functions. First, we start by treating the case when a superoscillating sequence is multiplied by the Gaussian function. Then, we extend these calculations to the case of normalized Hermite functions leading to interesting relations with Weyl operators. In particular, we show that the Segal-Bargmann transform maps superoscillating sequences onto …

Approaches To Assessing Nutrient Coupling In Open Ocean Datasets, James M. Moore, Claire P. Till

IdeaFest: Interdisciplinary Journal of Creative Works and Research from Cal Poly Humboldt

Nutrient coupling describes a process where the biogeochemical cycles of two elements are linked by being incorporated similarly into biomass. This paper uses data from the GEOTRACES GP16 cruise (Eastern Pacific Zonal Transect) to investigate the relationship between certain macronutrients generally coupled to trace elements in terms of their oceanic distributions with the notable exception of in an oxygen minimum zone: cadmium-phosphate and zinc-silicate. There are many methods applied to oceanographic data to correlate analyte concentrations; while they are often presented independently in literature, here we attempt to use them in conjunction for a more thorough interpretation. By compiling 1) …

The Mean Sum Of Squared Linking Numbers Of Random Piecewise-Linear Embeddings Of $K_N$, Yasmin Aguillon, Xingyu Cheng, Spencer Eddins, Pedro Morales

Rose-Hulman Undergraduate Mathematics Journal

DNA and other polymer chains in confined spaces behave like closed loops. Arsuaga et al. \cite{AB} introduced the uniform random polygon model in order to better understand such loops in confined spaces using probabilistic and knot theoretical techniques, giving some classification on the mean squared linking number of such loops. Flapan and Kozai \cite{flapan2016linking} extended these techniques to find the mean sum of squared linking numbers for random linear embeddings of complete graphs $K_n$ and found it to have order $\Theta(n(n!))$. We further these ideas by inspecting random piecewise-linear embeddings of complete graphs and give introductory-level summaries of the ideas …

On The Spectrum Of Quaquaversal Operators, Josiah Sugarman

Dissertations, Theses, and Capstone Projects

In 1998 Charles Radin and John Conway introduced the Quaquaversal Tiling. A three dimensional hierarchical tiling with the property that the orientations of its tiles approach a uniform distribution faster than what is possible for hierarchical tilings in two dimensions. The distribution of orientations is controlled by the spectrum of a certain Hecke operator, which we refer to as the Quaquaversal Operator. For example, by showing that the largest eigenvalue has multiplicity equal to one, Charles Radin and John Conway showed that the orientations of this tiling approach a uniform distribution. In 2008, Bourgain and Gamburd showed that this operator …

Differential Calculus: From Practice To Theory, Eugene Boman, Robert Rogers

Milne Open Textbooks

Differential Calculus: From Practice to Theory covers all of the topics in a typical first course in differential calculus. Initially it focuses on using calculus as a problem solving tool (in conjunction with analytic geometry and trigonometry) by exploiting an informal understanding of differentials (infinitesimals). As much as possible large, interesting, and important historical problems (the motion of falling bodies and trajectories, the shape of hanging chains, the Witch of Agnesi) are used to develop key ideas. Only after skill with the computational tools of calculus has been developed is the question of rigor seriously broached. At that point, the …

Geometry In Spectral Triples: Immersions And Fermionic Fuzzy Geometries, Luuk S. Verhoeven

Electronic Thesis and Dissertation Repository

We investigate the metric nature of spectral triples in two ways.

Given an oriented Riemannian embedding i:X->Y of codimension 1 we construct a family of unbounded KK-cycles i!(epsilon), each of which represents the shriek class of i in KK-theory. These unbounded KK-cycles are further equipped with connections, allowing for the explicit computation of the products of i! with the spectral triple of Y at the unbounded level. In the limit epsilon to 0 the product of these unbounded KK-cycles with the canonical spectral triple for Y admits an asymptotic expansion. The divergent part of this expansion is known and …

Double Barrier Backward Doubly Stochastic Differential Equations, Tadashi Hayashi

Journal of Stochastic Analysis

No abstract provided.

Symmetric Functions Algebras (Sfa) Iii: Stochastic And Constant Row Sum Matrices, Philip Feinsilver

Journal of Stochastic Analysis

No abstract provided.

Signings Of Graphs And Sign-Symmetric Signed Graphs, Ahmad Asiri

Theses and Dissertations

In this dissertation, we investigate various aspects of signed graphs, with a particular focus on signings and sign-symmetric signed graphs. We begin by examining the complete graph on six vertices with one edge deleted ($K_6$\textbackslash e) and explore the different ways of signing this graph up to switching isomorphism. We determine the frustration index (number) of these signings and investigate the existence of sign-symmetric signed graphs. We then extend our study to the $K_6$\textbackslash 2e graph and the McGee graph with exactly two negative edges. We investigate the distinct ways of signing these graphs up to switching isomorphism and demonstrate …

Math And Democracy, Kimberly A. Roth, Erika L. Ward

Journal of Humanistic Mathematics

Math and Democracy is a math class containing topics such as voting theory, weighted voting, apportionment, and gerrymandering. It was first designed by Erika Ward for math master’s students, mostly educators, but then adapted separately by both Erika Ward and Kim Roth for a general audience of undergraduates. The course contains materials that can be explored in mathematics classes from those for non-majors through graduate students. As such, it serves students from all majors and allows for discussion of fairness, racial justice, and politics while exploring mathematics that non-major students might not otherwise encounter. This article serves as a guide …

Dna Self-Assembly Of Trapezohedral Graphs, Hytham Abdelkarim

Electronic Theses, Projects, and Dissertations

Self-assembly is the process of a collection of components combining to form an organized structure without external direction. DNA self-assembly uses multi-armed DNA molecules as the component building blocks. It is desirable to minimize the material used and to minimize genetic waste in the assembly process. We will be using graph theory as a tool to find optimal solutions to problems in DNA self-assembly. The goal of this research is to develop a method or algorithm that will produce optimal tile sets which will self-assemble into a target DNA complex. We will minimize the number of tile and bond-edge types …

The G_2-Hitchin Component Of Triangle Groups: Dimension And Integer Points, Hannah E. Downs

Doctoral Dissertations

The image of $\PSL(2,\reals)$ under the irreducible representation into $\PSL(7,\reals)$ is contained in the split real form $G_{2}^{4,3}$ of the exceptional Lie group $G_{2}$. This irreducible representation therefore gives a representation $\rho$ of a hyperbolic triangle group $\Gamma(p,q,r)$ into $G_{2}^{4,3}$, and the \textit{Hitchin component} of the representation variety $\Hom(\Gamma(p,q,r),G_{2}^{4,3})$ is the component of $\Hom(\Gamma(p,q,r),G_{2}^{4,3})$ containing $\rho$.

This thesis is in two parts: (i) we give a simple, elementary proof of a formula for the dimension of this Hitchin component, this formula having been obtained earlier in [Alessandrini et al.], \citep{Alessandrini2023}, as part of a wider investigation using Higgs bundle techniques, …