Loop Homology Of Bi-Secondary Structures, 2019 Illinois State University

#### Loop Homology Of Bi-Secondary Structures, Andrei Bura

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Design Of Experiments For Unique Wiring Diagram Identification, 2019 California Polytechnic State University, San Luis Obispo

#### Design Of Experiments For Unique Wiring Diagram Identification, Elena Dimitrova

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

The Energy-Spectrum Of Bicompatible Sequences, 2019 Illinois State University

#### The Energy-Spectrum Of Bicompatible Sequences, Wenda Huang

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

On An Enhancement Of Rna Probing Data Using Information Theory, 2019 University of Virginia

#### On An Enhancement Of Rna Probing Data Using Information Theory, Thomas J.X. Li, Christian M. Reidys

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Topology And Dynamics Of Gene Regulatory Networks: A Meta-Analysis, 2019 Illinois State University

#### Topology And Dynamics Of Gene Regulatory Networks: A Meta-Analysis, Claus Kadelka

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Modeling Control Methods To Manage The Sylvatic Plague In Black-Tailed Prairie Dog Towns, 2019 University of Tennessee, Knoxville

#### Modeling Control Methods To Manage The Sylvatic Plague In Black-Tailed Prairie Dog Towns, David C. Elzinga, Shelby R. Stowe, Leland Russell

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Using Agent-Based Modeling To Investigate The Existence Of Herd Immunity Thresholds For Infectious Diseases On Randomly Generated Contact Networks, 2019 University of Portland

#### Using Agent-Based Modeling To Investigate The Existence Of Herd Immunity Thresholds For Infectious Diseases On Randomly Generated Contact Networks, Hannah Callender Highlander, Owen Price

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Oscillation In Mathematical Epidemiology, 2019 Bates College

#### Oscillation In Mathematical Epidemiology, Meredith Greer

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

A Concise Workbook For College Algebra 2nd Edition, 2019 Queensborough Community College

#### A Concise Workbook For College Algebra 2nd Edition, Fei Ye

*Open Educational Resources*

This is the second edition of the book "A Concise Workbook for College Algebra". In this new edition, some tips and notes, more exercises and examples were added.

A Study On Discrete And Discrete Fractional Pharmacokinetics-Pharmacodynamics Models For Tumor Growth And Anti-Cancer Effects, 2019 Western Kentucky University

#### A Study On Discrete And Discrete Fractional Pharmacokinetics-Pharmacodynamics Models For Tumor Growth And Anti-Cancer Effects, Ferhan Atici, Ngoc Nguyen

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Research For Educators: Modeling Graph Theory For Nontraditional Math Researchers, 2019 Illinois State University

#### Research For Educators: Modeling Graph Theory For Nontraditional Math Researchers, Erwin Cornelius

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

A Model For Cross-Institutional Collaboration: Addressing Diminishing Resources In Academia, 2019 Illinois State University

#### A Model For Cross-Institutional Collaboration: Addressing Diminishing Resources In Academia, Claudia Kolakowski

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

An Optimal Edg Method For Distributed Control Of Convection Diffusion Pdes, 2019 Missouri University of Science and Technology

#### An Optimal Edg Method For Distributed Control Of Convection Diffusion Pdes, X. Zhang, Y. Zhang, John R. Singler

*Mathematics and Statistics Faculty Research & Creative Works*

We propose an embedded discontinuous Galerkin (EDG) method to approximate the solution of a distributed control problem governed by convection diffusion PDEs, and obtain optimal a priori error estimates for the state, dual state, their uxes, and the control. Moreover, we prove the optimize-then-discretize (OD) and discrtize-then-optimize (DO) approaches coincide. Numerical results confirm our theoretical results.

Exercises Integrating High School Mathematics With Robot Motion Planning, 2019 Loyola University Chicago

#### Exercises Integrating High School Mathematics With Robot Motion Planning, Ronald I. Greenberg, George K. Thiruvathukal

*Computer Science: Faculty Publications and Other Works*

This paper presents progress in developing exercises for high school students incorporating level-appropriate mathematics into robotics activities. We assume mathematical foundations ranging from algebra to precalculus, whereas most prior work on integrating mathematics into robotics uses only very elementary mathematical reasoning or, at the other extreme, is comprised of technical papers or books using calculus and other advanced mathematics. The exercises suggested are relevant to any differerential-drive robot, which is an appropriate model for many different varieties of educational robots. They guide students towards comparing a variety of natural navigational strategies making use of typical movement primitives. The exercises align ...

Beauty, Bees, And God: The Fibonacci Sequence As A Theological Springboard In Secondary Mathematics, 2019 Divine Child High School

#### Beauty, Bees, And God: The Fibonacci Sequence As A Theological Springboard In Secondary Mathematics, John D. Brahier

*Journal of Catholic Education*

Catholic schools primarily should be in the business of making saints. This article identifies and explores a meaningful, engaging point of contact between mathematics and theology for high school math classes, the Fibonacci Sequence. This sequence serves as an engaging introduction to sequences and series; more importantly, the topic can be used as a springboard to theological discussions. The paper will provide a brief historical background to the Fibonacci Sequence, an explanation of how it can be used in a high school math classroom, and an exploration of three different theological touchpoints that the Fibonacci Sequence offers.

Diffusion And Consensus On Weakly Connected Directed Graphs, 2019 Portland State University

#### Diffusion And Consensus On Weakly Connected Directed Graphs, J. J. P. Veerman, Ewan Kummel

*Mathematics and Statistics Faculty Publications and Presentations*

Let G be a weakly connected directed graph with asymmetric graph Laplacian L. Consensus and diffusion are dual dynamical processes defined on G by x˙=−Lx for consensus and p˙=−pL for diffusion. We consider both these processes as well their discrete time analogues. We define a basis of row vectors {γ¯i}ki=1 of the left null-space of L and a basis of column vectors {γi}ki=1 of the right null-space of L in terms of the partition of G into strongly connected components. This allows for complete characterization of the asymptotic behavior of both diffusion and ...

Crank--Nicolson Alternative Direction Implicit Method For Space-Fractional Diffusion Equations With Nonseparable Coefficients, 2019 Department of Mathematics, Hong Kong Baptist University

#### Crank--Nicolson Alternative Direction Implicit Method For Space-Fractional Diffusion Equations With Nonseparable Coefficients, Xue-Lei Lin, Michael K. Ng, Hai-Wei Sun

*HKBU Staff Publication*

In this paper, we study the Crank--Nicolson alternative direction implicit (ADI) method for two-dimensional Riesz space-fractional diffusion equations with nonseparable coefficients. Existing ADI methods are only shown to be unconditional stable when coefficients are some special separable functions. The main contribution of this paper is to show under mild assumptions the unconditional stability of the proposed Crank--Nicolson ADI method in discrete $\ell^2$ norm and the consistency of cross perturbation terms arising from the Crank--Nicolson ADI method. Also, we demonstrate that several consistent spatial discretization schemes satisfy the required assumptions. Numerical results are presented to examine the accuracy and the ...

Closed-Form Probability Distribution Of Number Of Infections At A Given Time In A Stochastic Sis Epidemic Model, 2019 Marshall University

#### Closed-Form Probability Distribution Of Number Of Infections At A Given Time In A Stochastic Sis Epidemic Model, Olusegun M. Otunuga

*Olusegun Michael Otunuga*

We study the effects of external fluctuations in the transmission rate of certain diseases and how these affect the distribution of the number of infected individuals over time. To do this, we introduce random noise in the transmission rate in a deterministic SIS model and study how the number of infections changes over time. The objective of this work is to derive and analyze the closed form probability distribution of the number of infections at a given time in the resulting stochastic SIS epidemic model. Using the Fokker-Planck equation, we reduce the differential equation governing the number of infections to ...

Making Kr+1-Free Graphs R-Partite, 2019 University of Illinois at Urbana-Champaign

#### Making Kr+1-Free Graphs R-Partite, József Balogh, Felix Christian Clemen, Mikhail Lavrov, Bernard Lidický, Florian Pfender

*Mathematics Publications*

The Erdős–Simonovits stability theorem states that for all ε > 0 there exists α > 0 such that if G is a Kr+1-free graph on n vertices with e(G) > ex(n, Kr+1) − αn2, then one can remove εn2 edges from G to obtain an r-partite graph. Fu¨redi gave a short proof that one can choose α = ε. We give a bound for the relationship of α and ε which is asymptotically sharp as ε → 0.

Spanning Eulerian Subgraphs And Catlin’S Reduced Graphs, 2019 Butler University

#### Spanning Eulerian Subgraphs And Catlin’S Reduced Graphs, Wei-Guo Chen, Zhi-Hong Chen

*Zhi-Hong Chen*

A graph G is collapsible if for every even subset R ⊆ V (G), there is a spanning connected subgraph H_{R} of G whose set of odd degree vertices is R. A graph is reduced if it has no nontrivial collapsible subgraphs. Catlin [4] showed that the existence of spanning Eulerian subgraphs in a graph G can be determined by the reduced graph obtained from G by contracting all the collapsible subgraphs of G. In this paper, we present a result on 3-edge-connected reduced graphs of small orders. Then, we prove that a 3-edge-connected graph G of order n either ...