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 ...

Women In Stem, 2021 Ouachita Baptist University

#### Women In Stem, Dyandra M. Johnson

*Arkansas Women in STEM Conference*

My poster is about the life of Katherine Johnson, its a summary of her achievements, educational background, and her family life. The purpose of my poster is to provide information about this amazing woman that was apart of STEM. I've found that she had accomplished a lot through using Mathematics, and how she contributed so much to NASA.

Skolem Number Of Subgraphs On The Triangular Lattice, 2021 Southern Connecticut State University

#### Skolem Number Of Subgraphs On The Triangular Lattice, Braxton Carrigan, Garrett Green

*Communications on Number Theory and Combinatorial Theory*

A Skolem sequence can be thought of as a labelled path where any two vertices with the same label are that distance apart. This concept has naturally been generalized to graph labelling. This brings rise to the question; “what is the smallest set of consecutive positive integers we can use to properly Skolem label a graph?” This is known as the Skolem number of the graph. In this paper we give the Skolem number for three natural vertex induced subgraphs of the triangular lattice graph.

Superoscillations And Analytic Extension In Schur Analysis, 2021 Chapman University

#### Superoscillations And Analytic Extension In Schur Analysis, Daniel Alpay, Fabrizio Colombo, Irene Sabadini

*Mathematics, Physics, and Computer Science Faculty Articles and Research*

We give applications of the theory of superoscillations to various questions, namely extension of positive definite functions, interpolation of polynomials and also of Rfunctions; we also discuss possible applications to signal theory and prediction theory of stationary stochastic processes. In all cases, we give a constructive procedure, by way of a limiting process, to get the required results.

Connectivity Of Matroids And Polymatroids, 2021 Louisiana State University and Agricultural and Mechanical College

#### Connectivity Of Matroids And Polymatroids, Zachary R. Gershkoff

*LSU Doctoral Dissertations*

This dissertation is a collection of work on matroid and polymatroid connectivity. Connectivity is a useful property of matroids that allows a matroid to be decomposed naturally into its connected components, which are like blocks in a graph. The Cunningham-Edmonds tree decomposition further gives a way to decompose matroids into 3-connected minors. Much of the research below concerns alternate senses in which matroids and polymatroids can be connected. After a brief introduction to matroid theory in Chapter 1, the main results of this dissertation are given in Chapters 2 and 3. Tutte proved that, for an element e of a ...

Inducibility Of 4-Vertex Tournaments, 2021 University of Colorado, Denver

#### Inducibility Of 4-Vertex Tournaments, Dalton Burke, Bernard Lidicky, Florian Pfender, Michael Phillips

*Mathematics Publications*

We determine the inducibility of all tournaments with at most 4 vertices together with the extremal constructions. The 4-vertex tournament containing an oriented C3 and one source vertex has a particularly interesting extremal construction. It is an unbalanced blow-up of an edge, where the sink vertex is replaced by a quasi-random tournament and the source vertex is iteratively replaced by a copy of the construction itself.

An Image Segmentation Technique With Statistical Strategies For Pesticide Efficacy Assessment, 2021 California State University, Monterey Bay

#### An Image Segmentation Technique With Statistical Strategies For Pesticide Efficacy Assessment, Steven B. Kim, Dong Sub Kim, Xiaoming Mo

*Mathematics and Statistics Faculty Publications and Presentations*

Image analysis is a useful technique to evaluate the efficacy of a treatment for weed control. In this study, we address two practical challenges in the image analysis. First, it is challenging to accurately quantify the efficacy of a treatment when an entire experimental unit is not affected by the treatment. Second, RGB codes, which can be used to identify weed growth in the image analysis, may not be stable due to various surrounding factors, human errors, and unknown reasons. To address the former challenge, the technique of image segmentation is considered. To address the latter challenge, the proportion of ...

Modeling The Ecological Dynamics Of A Three-Species Fish Population In The Chesapeake Bay, 2021 Christopher Newport University

#### Modeling The Ecological Dynamics Of A Three-Species Fish Population In The Chesapeake Bay, Iordanka N. Panayotova, Maila B. Hallare

*CODEE Journal*

We present an inquiry-based project that is designed for a mathematical modeling class of undergraduate junior or senior students. It discusses a three-species mathematical model that simulates the biological interactions among three important fish species in the Chesapeake Bay: the prey Atlantic menhaden and its two competing predators, the striped bass and the non-native blue catfish. The model also considers the following ecological issues related to these three species: the overfishing of menhaden, the invasiveness of the blue catfish, and the harvesting of blue catfish as a method to control the population. A series of modeling scenarios are considered based ...

Qualitative Analysis Of A Resource Management Model And Its Application To The Past And Future Of Endangered Whale Populations, 2021 University of Nebraska - Lincoln

#### Qualitative Analysis Of A Resource Management Model And Its Application To The Past And Future Of Endangered Whale Populations, Glenn Ledder

*CODEE Journal*

Observed whale dynamics show drastic historical population declines, some of which have not been reversed in spite of restrictions on harvesting. This phenomenon is not explained by traditional predator prey models, but we can do better by using models that incorporate more sophisticated assumptions about consumer-resource interaction. To that end, we derive the Holling type 3 consumption rate model and use it in a one-variable differential equation obtained by treating the predator population in a predator-prey model as a parameter rather than a dynamic variable. The resulting model produces dynamics in which low and high consumption levels lead to single ...

Engaging Students Early By Internationalizing The Undergraduate Calculus Course, 2021 Albany State University

#### Engaging Students Early By Internationalizing The Undergraduate Calculus Course, Chinenye Ofodile

*CODEE Journal*

Today's world is global. However, despite increasing numbers and diversity of participants in Study Abroad programs, only 10% of U. S. college students get that experience. There is an ever-growing need for students to become aware of and experience other cultures, to understand why others think and act differently. Internationalization is the conscious effort, begun nearly 40 years ago, to integrate an international, intercultural, and global dimension into the purpose, functions, and delivery of post-secondary education.

Albany State University began a Global Program Initiative in the 1990s. In 2016, we extended into mathematics the curriculum innovations of this program ...

Facing The Pandemic Together: Forming A Collaborative Research Group, 2021 Niagara University

#### Facing The Pandemic Together: Forming A Collaborative Research Group, Michael C. Barg

*CODEE Journal*

This is an account of how a reading and writing project in an introductory differential equations course was transitioned to a professor-student research group collaborative project, in response to the global COVID-19 pandemic. Adapting on the fly to the ever-evolving pandemic, we collected data, estimated parameters in our models, and computed numerical solutions to SIR-based systems of differential equations. This is a description of what we did and how we found comfort in the project in this time of great uncertainty. The collaboration yielded successes and more questions than we had answers for, but the situation provided an opportunity of ...

Epidemiology And The Sir Model: Historical Context To Modern Applications, 2021 Worcester Polytechnic Institute

#### Epidemiology And The Sir Model: Historical Context To Modern Applications, Francesca Bernardi, Manuchehr Aminian

*CODEE Journal*

We suggest the use of historical documents and primary sources, as well as data and articles from recent events, to teach students about mathematical epidemiology. We propose a project suitable -- in different versions -- as part of a class syllabus, as an undergraduate research project, and as an extra credit assignment. Throughout this project, students explore mathematical, historical, and sociological aspects of the SIR model and approach data analysis and interpretation. Based on their work, students form opinions on public health decisions and related consequences. Feedback from students has been encouraging.

We begin our project by having students read excerpts of ...

Engaging Learners: Differential Equations In Today's World, 2021 Claremont Colleges

#### Engaging Learners: Differential Equations In Today's World

*CODEE Journal*

Engaging Learners: Differential Equations in Today's World

CODEE Journal, Volume 14, Issue 1

Using A Hybrid Agent-Based And Equation Based Model To Test School Closure Policies During A Measles Outbreak, 2021 Technological University Dublin

#### Using A Hybrid Agent-Based And Equation Based Model To Test School Closure Policies During A Measles Outbreak, Elizabeth Hunter, John D. Kelleher

*Articles*

### Background

In order to be prepared for an infectious disease outbreak it is important to know what interventions will or will not have an impact on reducing the outbreak. While some interventions might have a greater effect in mitigating an outbreak, others might only have a minor effect but all interventions will have a cost in implementation. Estimating the effectiveness of an intervention can be done using computational modelling. In particular, comparing the results of model runs with an intervention in place to control runs where no interventions were used can help to determine what interventions will have the greatest ...

Nonlinear Potential Analysis On Sobolev Multiplier Spaces, 2021 Louisiana State University

#### Nonlinear Potential Analysis On Sobolev Multiplier Spaces, Keng Hao Ooi

*LSU Doctoral Dissertations*

We characterize preduals and Kothe duals to a class of Sobolev multiplier type spaces. Our results fit in well with the modern theory of function spaces of harmonic analysis and are also applicable to nonlinear partial differential equations. As a maneuver, we make use of several tools from nonlinear potential theory, weighted norm inequalities, and the theory of Banach function spaces to obtain our results. After characterizing the preduals, we establish a capacitary strong type inequality which resolves a special case of a conjecture by David R. Adams. As a consequence, we obtain several equivalent norms for Choquet integrals associated ...

Determining Biases In The Card-Chameleon Cryptosystem, 2021 Kutztown University of Pennsylvania

#### Determining Biases In The Card-Chameleon Cryptosystem, Isaac Reiter, Eric Landquist

*Communications on Number Theory and Combinatorial Theory*

Throughout history, spies, soldiers, and others have relied on so-called {\em hand ciphers} to send encrypted messages. Since the creation of Pontifex (also known as Solitaire) by Bruce Schneier in 1999, a number of hand ciphers utilizing a standard deck of playing cards have emerged. Since there are $52! \approx 2^{225.58}$ possible ways to order a deck of cards, there are over 225 bits of entropy in a well-shuffled deck of cards. Theoretically, this can provide enough security to rival modern computer-based cryptosystems. In this paper, we describe and analyze one such playing card cipher, Card-Chameleon, created by ...

New Representations For A Semi-Markov Chain And Related Filters, 2021 University of South Australia, Campus Central - City West, GPO Box 2471

#### New Representations For A Semi-Markov Chain And Related Filters, Robert J. Elliott, W. P. Malcolm

*Journal of Stochastic Analysis*

No abstract provided.