Energy On Spheres And Discreteness Of Minimizing Measures, 2021 The University of Texas Rio Grande Valley

#### Energy On Spheres And Discreteness Of Minimizing Measures, Dmitriy Bilyk, Alexey Glazyrin, Ryan Matzke, Josiah Park, Oleksandr Vlasiuk

*Mathematical and Statistical Sciences Faculty Publications and Presentations*

In the present paper we study the minimization of energy integrals on the sphere with a focus on an interesting clustering phenomenon: for certain types of potentials, optimal measures are discrete or are supported on small sets. In particular, we prove that the support of any minimizer of the *p*-frame energy has empty interior whenever *p* is not an even integer. A similar effect is also demonstrated for energies with analytic potentials which are not positive definite. In addition, we establish the existence of discrete minimizers for a large class of energies, which includes energies with polynomial potentials.

Geometrization Of Hawking Radiation Via Ricci Flow, 2021 Winona State University

#### Geometrization Of Hawking Radiation Via Ricci Flow, Alexander Cassem

*Ramaley Research Celebration*

In 1982, Richard S. Hamilton formulated Ricci flow along manifolds of three dimensions of positive Ricci curvature as an attempt to resolve Poincaré’s Conjecture. However, it took until 2006 by Grigori Perelman to resolve the conjecture with Ricci flow. Since then, research in pure mathematics on Ricci Flow increased exponentially, and people began to apply it towards physics. For example, Ricci flow has been found to be the Renormalization Group flow of the bosonic string and sigma model. However, Ricci flow’s analogous counterpart being the heat equation, makes it appear to have more applications. For this reason, we ...

Emerald Ash Borer And The Application Of Biological Control In Virginia, 2021 University of Richmond

#### Emerald Ash Borer And The Application Of Biological Control In Virginia, Shuheng Chen, Yihui Wu, Shengjie Liu

*Arts & Sciences Student Symposium*

The emerald ash borer (Agrilus planipennis; EAB) is an invasive wood-boring beetle whose larvae feed on ash phloem. After only 1-5 years of infestation, the larvae create extensive tunnels under the bark that disrupt the tree’s ability to transport water and nutrients, which eventually girdles and kills the tree. Since 2008, EAB has spread to all but the eastern-most counties in Virginia. Bological control is one strategy to limit EAB populations. In this project we study control by native agents (woodpeckers) and imported agents (parasitoid wasps).

Mathematical models of host-parasitoid interactions and simulations based on both models and field ...

Reducing The Maximum Degree Of A Graph: Comparisons Of Bounds, 2021 Department of Mathematics, Faculty of Science, University of Malta, Malta

#### Reducing The Maximum Degree Of A Graph: Comparisons Of Bounds, Peter Borg

*Theory and Applications of Graphs*

Let $\lambda(G)$ be the smallest number of vertices that can be removed from a non-empty graph $G$ so that the resulting graph has a smaller maximum degree. Let $\lambda_{\rm e}(G)$ be the smallest number of edges that can be removed from $G$ for the same purpose. Let $k$ be the maximum degree of $G$, let $t$ be the number of vertices of degree $k$, let $M(G)$ be the set of vertices of degree $k$, let $n$ be the number of vertices in the closed neighbourhood of $M(G)$, and let $m$ be the number of edges ...

Getting Over It, 2021 University of Richmond

#### Getting Over It, Thomas Kade, Kevorc Ibrahimian, Max Simpson

*Arts & Sciences Student Symposium*

The research extended a 2D motion planning system to three dimensional environments. The updated system is now able to plan the motion for robots over 3D terrains modeled by polyhedrons.

The School Mathematics Study Group: Lessons In Mathematics Education, 2021 University of Richmond

#### The School Mathematics Study Group: Lessons In Mathematics Education, Madeline Polhill

*Arts & Sciences Student Symposium*

This work argues that the "new math" project called the School Mathematics Study Group offers a valuable case study for mathematics educators seeking to venture into the future better informed about both the successes and failures of previous projects. Understanding this project requires recognizing that the School Mathematics Study Group was wholly a product of the forces—personal, educational, mathematical, and political—that shaped it. Admittedly, some of the SMSG's shortcomings resulted from its members' lack of understanding of the changes needed in mathematics education. Still, the majority of the SMSG's public vilification resulted through no fault of ...

Determination Of The Traits In Leguminous Crops Under Saline Condition, 2021 Gulistan state University

#### Determination Of The Traits In Leguminous Crops Under Saline Condition, Tojiddin Kuliev, Karomat Ismailova

*Karakalpak Scientific Journal*

In this study, the variability and determination of genetic traits for winter legume crop varieties the Vostok-55 (*Pisum arvense** *L) and Mirzachul-1 (*Vicia villoza Roth** *L) were investigated under moderate saline soil condition. Results show that the weight of the bean was marked as variable and highly deterministic, and the height of the plants was the most stable. The selection of plants based on these traits is the most effective way of salinity. Both variety the forage pea Vostok-55 and vetch Mirzachul-1 is highly recommended as a sideration and forage crop in saline lands.

Compact Representations Of Uncertainty In Clustering, 2021 University of Massachusetts Amherst

#### Compact Representations Of Uncertainty In Clustering, Craig Stuart Greenberg

*Doctoral Dissertations*

Flat clustering and hierarchical clustering are two fundamental tasks, often used to discover meaningful structures in data, such as subtypes of cancer, phylogenetic relationships, taxonomies of concepts, and cascades of particle decays in particle physics. When multiple clusterings of the data are possible, it is useful to represent uncertainty in clustering through various probabilistic quantities, such as the distribution over partitions or tree structures, and the marginal probabilities of subpartitions or subtrees.

Many compact representations exist for structured prediction problems, enabling the efficient computation of probability distributions, e.g., a trellis structure and corresponding Forward-Backward algorithm for Markov models that ...

Stitching Dedekind Cuts To Construct The Real Numbers, 2021 Saint Edwards University

#### Stitching Dedekind Cuts To Construct The Real Numbers, Michael P. Saclolo

*Analysis*

No abstract provided.

Examining Middle School Students' Methods Of Justification, 2021 Undergraduate

#### Examining Middle School Students' Methods Of Justification, Leslie Reyes- Hernandez

*Mathematics*

Researching students’ thinking is imperative to improving the education system throughout the world. From extensive research, it is noted that students are unaccustomed and struggle with providing valid mathematical justifications (e.g. Inglis & Alcock 2012). The National Council of Teachers of Mathematics (NCTM, 2000) and Common Core State Standards of Mathematics (CCSSM, 2010) suggest that students should have several opportunities to construct mathematical arguments across all grade levels. To take a closer look at this educational phenomenon, we prompt fifth to eighth-grade students with nine mathematical tasks. Within our research, we focus on tasks based on number properties, algebraic thinking ...

Squigonometry, 2021 Undergraduate

#### Squigonometry, Andrew Hatfield, Riley Klette, Christopher Moore, Beth Warden

*Mathematics*

Trigonometry is the study of circular functions - functions defined on the unit circle where distances are measured with respect to the Euclidean norm. In our research, we develop a parallel theory of trigonometric and inverse trigonometric functions for the p-norm. This is called squigonometry because the resulting functions are defined on a squircle. This approach leads to new transcendental periods, formulas, and identities. It also extends to exponential, hyperbolic, and logarithmic functions in the p-norm.

A Direct Method For Modeling And Simulations Of Elliptic And Parabolic Interface Problems, 2021 Old Dominion University

#### A Direct Method For Modeling And Simulations Of Elliptic And Parabolic Interface Problems, Kumudu Gamage, Yan Peng

*College of Sciences Posters*

Interface problems have many applications in fluid dynamics, molecular biology, electromagnetism, material science, heat distribution in engines, and hyperthermia treatment of cancer. Mathematically, interface problems commonly lead to partial differential equations (PDE) whose in- put data are discontinuous or singular across the interfaces in the solution domain. Many standard numerical methods designed for smooth solutions poorly work for interface problems as solutions of the interface problems are mostly non-smoothness or discontinuous. Moving interface problems depends on the accuracy of the gradient of the solution at the interface. Therefore, it became essential to derive a method for interface problems that gives ...

Math 102: Mathematics In Contemporary Society, 2021 City University of New York (CUNY)

#### Math 102: Mathematics In Contemporary Society, Cuny School Of Professional Studies

*Open Educational Resources*

Designed to provide students with an understanding of the mathematical ideas and methods found in the social sciences, the arts, and business, this course covers the fundamentals of statistics, scatter plots, graphics in the media, problem-solving strategies, dimensional analysis, and mathematical modeling. Students can expect to explore real world applications.

Math 215: Introduction To Statistics, 2021 City University of New York (CUNY)

#### Math 215: Introduction To Statistics, Cuny School Of Professional Studies

*Open Educational Resources*

Introduces the basic principles of statistics and probability, with an emphasis on understanding the underlying concepts, real-world applications, and the underlying story that the numbers tell. Uses Microsoft Excel’s statistical functions to analyze data. Provides an introduction to probability, descriptive statistics, hypothesis testing, and inferential statistics.

Mathematical Modeling Of The Candida Albicans Yeast To Hyphal Transition Reveals Novel Control Strategies, 2021 Pennsylvania State University

#### Mathematical Modeling Of The Candida Albicans Yeast To Hyphal Transition Reveals Novel Control Strategies, David J. Wooten, Jorge Gómez Tejeda Zañudo, David Murrugarra, Austin M. Perry, Anna Dongari-Bagtzoglou, Reinhard Laubenbacher, Clarissa J. Nobile, Réka Albert

*Mathematics Faculty Publications*

*Candida albicans*, an opportunistic fungal pathogen, is a significant cause of human infections, particularly in immunocompromised individuals. Phenotypic plasticity between two morphological phenotypes, yeast and hyphae, is a key mechanism by which *C*. *albicans* can thrive in many microenvironments and cause disease in the host. Understanding the decision points and key driver genes controlling this important transition and how these genes respond to different environmental signals is critical to understanding how *C*. *albicans* causes infections in the host. Here we build and analyze a Boolean dynamical model of the *C*. *albicans* yeast to hyphal transition, integrating multiple environmental factors and ...

Entropic Dynamics Of Networks, 2021 Department of Physics, University at Albany, State University of New York

#### Entropic Dynamics Of Networks, Felipe Xavier Costa, Pedro Pessoa

*Northeast Journal of Complex Systems (NEJCS)*

Here we present the entropic dynamics formalism for networks. That is, a framework for the dynamics of graphs meant to represent a network derived from the principle of maximum entropy and the rate of transition is obtained taking into account the natural information geometry of probability distributions. We apply this framework to the Gibbs distribution of random graphs obtained with constraints on the node connectivity. The information geometry for this graph ensemble is calculated and the dynamical process is obtained as a diffusion equation. We compare the steady state of this dynamics to degree distributions found on real-world networks.

Emergent Hierarchy Through Conductance-Based Degree Constraints, 2021 Air Force Research Laboratory / Clarkson University

#### Emergent Hierarchy Through Conductance-Based Degree Constraints, Christopher Tyler Diggans, Jeremie Fish, Erik M. Bollt

*Northeast Journal of Complex Systems (NEJCS)*

The presence of hierarchy in many real-world networks is not yet fully understood. We observe that complex interaction networks are often coarse-grain models of vast modular networks, where tightly connected subgraphs are agglomerated into nodes for simplicity of representation and computational feasibility. The emergence of hierarchy in such growing complex networks may stem from one particular property of these ignored subgraphs: their graph conductance. Being a quantification of the main bottleneck of flow through the coarse-grain node, this scalar quantity implies a structural limitation and supports the consideration of heterogeneous degree constraints. The internal conductance values of the subgraphs are ...

The Conditional Strong Matching Preclusion Of Augmented Cubes, 2021 American University of Kuwait

#### The Conditional Strong Matching Preclusion Of Augmented Cubes, Mohamad Abdallah, Eddie Cheng

*Theory and Applications of Graphs*

The strong matching preclusion is a measure for the robustness of interconnection networks in the presence of node and/or link failures. However, in the case of random link and/or node failures, it is unlikely to find all the faults incident and/or adjacent to the same vertex. This motivates Park et al. to introduce the conditional strong matching preclusion of a graph. In this paper we consider the conditional strong matching preclusion problem of the augmented cube $AQ_n$, which is a variation of the hypercube $Q_n$ that possesses favorable properties.

Characterizing 2-Trees Relative To Chordal And Series-Parallel Graphs, 2021 Wright State University

#### Characterizing 2-Trees Relative To Chordal And Series-Parallel Graphs, Terry A. Mckee

*Theory and Applications of Graphs*

The 2-connected 2-tree graphs are defined as being constructible from a single 3-cycle by recursively appending new degree-2 vertices so as to form 3-cycles that have unique edges in common with the existing graph. Such 2-trees can be characterized both as the edge-minimal chordal graphs and also as the edge-maximal series-parallel graphs. These are also precisely the 2-connected graphs that are simultaneously chordal and series-parallel, where these latter two better-known types of graphs have themselves been both characterized and applied in numerous ways that are unmotivated by their interaction with 2-trees and with each other.

Toward providing such motivation, the ...

Max Cuts In Triangle-Free Graphs, 2021 University of Illinois at Urbana-Champaign

#### Max Cuts In Triangle-Free Graphs, József Balogh, Felix Christian Clemen, Bernard Lidicky

*Mathematics Publications*

A well-known conjecture by Erdős states that every triangle-free graph on n vertices can be made bipartite by removing at most n2/25 edges. This conjecture was known for graphs with edge density at least 0.4 and edge density at most 0.172. Here, we will extend the edge density for which this conjecture is true; we prove the conjecture for graphs with edge density at most 0.2486 and for graphs with edge density at least 0.3197. Further, we prove that every triangle-free graph can be made bipartite by removing at most n2/23.5 edges improving ...