On The Spatial Modelling Of Biological Invasions, 2022 The University of Western Ontario

#### On The Spatial Modelling Of Biological Invasions, Tedi Ramaj

*Electronic Thesis and Dissertation Repository*

We investigate problems of biological spatial invasion through the use of spatial modelling. We begin by examining the spread of an invasive weed plant species through a forest by developing a system of partial differential equations (PDEs) involving an invasive weed and a competing native plant species. We find that extinction of the native plant species may be achieved by increasing the carrying capacity of the forest as well as the competition coefficient between the species. We also find that the boundary conditions exert long-term control on the biomass of the invasive weed and hence should be considered when implementing …

Solving Clostridioides Difficile: Mathematical Models Of Transmission And Control In Healthcare Settings, 2022 Lewis University

#### Solving Clostridioides Difficile: Mathematical Models Of Transmission And Control In Healthcare Settings, Cara Sulyok, Max Lewis, Laila Mahrat, Brittany Stephenson, Malen De La Fuente Arruabarrena, David Kovalev, Justyna Sliwinska

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

Modularity And Boolean Network Decomposition, 2022 University of Florida

#### Modularity And Boolean Network Decomposition, Matthew Wheeler

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

Canalization And Other Design Principles Of Gene Regulatory Networks, 2022 Illinois State University

#### Canalization And Other Design Principles Of Gene Regulatory Networks, Claus Kadelka

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

Model-Free Identification Of Relevant Variables From Response Data, 2022 University of Dayton

#### Model-Free Identification Of Relevant Variables From Response Data, Alan Veliz-Cuba, David Murrugarra

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

On Analysis Of Effectiveness Controlling Covid-19 With Quarantine And Vaccination Compartments In Indonesia, 2022 Illinois State University

#### On Analysis Of Effectiveness Controlling Covid-19 With Quarantine And Vaccination Compartments In Indonesia, Prihantini Prihantini

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

Compilación De Procesos Investigativos En Educación Matemática, 2022 Universidad de Cundinamarca

#### Compilación De Procesos Investigativos En Educación Matemática, Martha Lidia Barreto Moreno, Yeferson Castellanos Novoa, María Alejandra Mayorga Henao, Diana Marcela Contento Sarmiento, Jesús Antonio Villarraga Palomino, Andrés Alberto Gutiérrez Morales, Juan David Firigua Bejarano, Yineth Marleidy Parra Ubaque, Lady Johanna Silva Marín

*Educación*

En el libro Compilación de procesos de investigación en educación matemática, consta de cuatro capítulos donde se presentan los procesos desarrollados en el marco de proyectos de investigación a nivel de pregrado y postgrado en Educación.

El primer capítulo consiste en la sistematización de la acción docente desarrollada en el marco de los Talleres Itinerantes de Alfabetización Computacional en la provincia de Sumapaz, propuesta de innovación para implementar procesos didácticos que contribuyan al desarrollo del pensamiento matemático computacional en educación básica primaria rural.

El segundo capítulo contiene el proceso investigativo que dio continuidad al trabajo realizado en la Fase1, sobre …

Machine Learning To Predict Warhead Fragmentation In-Flight Behavior From Static Data, 2022 Embry-Riddle Aeronautical University

#### Machine Learning To Predict Warhead Fragmentation In-Flight Behavior From Static Data, Katharine Larsen

*Doctoral Dissertations and Master's Theses*

Accurate characterization of fragment fly-out properties from high-speed warhead detonations is essential for estimation of collateral damage and lethality for a given weapon. Real warhead dynamic detonation tests are rare, costly, and often unrealizable with current technology, leaving fragmentation experiments limited to static arena tests and numerical simulations. Stereoscopic imaging techniques can now provide static arena tests with time-dependent tracks of individual fragments, each with characteristics such as fragment IDs and their respective position vector. Simulation methods can account for the dynamic case but can exclude relevant dynamics experienced in real-life warhead detonations. This research leverages machine learning methodologies to …

On Cantor Sets Defined By Generalized Continued Fractions, 2022 College of the Canyons

#### On Cantor Sets Defined By Generalized Continued Fractions, Danielle Hedvig, Masha Gorodetski

*Rose-Hulman Undergraduate Mathematics Journal*

We study a special class of generalized continuous fractions, both in real and complex settings, and show that in many cases, the set of numbers that can be represented by a continued fraction for that class form a Cantor set. Specifically, we study generalized continued fractions with a fixed absolute value and a variable coefficient sign. We ask the same question in the complex setting, allowing the coefficient's argument to be a multiple of \pi/2. The numerical experiments we conducted showed that in these settings the set of numbers formed by such continued fractions is a Cantor set for large …

Dynamical Systems And Matching Symmetry In Beta-Expansions, 2022 California Polytechnic State University, San Luis Obispo

#### Dynamical Systems And Matching Symmetry In Beta-Expansions, Karl Zieber

*Master's Theses*

Symbolic dynamics, and in particular β-expansions, are a ubiquitous tool in studying more complicated dynamical systems. Applications include number theory, fractals, information theory, and data storage.

In this thesis we will explore the basics of dynamical systems with a special focus on topological dynamics. We then examine symbolic dynamics and β-transformations through the lens of sequence spaces. We discuss observations from recent literature about how matching (the property that the itinerary of 0 and 1 coincide after some number of iterations) is linked to when T_{β,⍺} generates a subshift of finite type. We prove the set of ⍺ in …

(R1882) Effects Of Viscosity, Oblateness, And Finite Straight Segment On The Stability Of The Equilibrium Points In The Rr3bp, 2022 Lady Shri Ram College for Women

#### (R1882) Effects Of Viscosity, Oblateness, And Finite Straight Segment On The Stability Of The Equilibrium Points In The Rr3bp, Bhavneet Kaur, Sumit Kumar, Rajiv Aggarwal

*Applications and Applied Mathematics: An International Journal (AAM)*

Associating the influences of viscosity and oblateness in the finite straight segment model of the Robe’s problem, the linear stability of the collinear and non-collinear equilibrium points for a small solid sphere *m*_{3} of density \rho_{3} are analyzed. This small solid sphere is moving inside the first primary *m*_{1} whose hydrostatic equilibrium figure is an oblate spheroid and it consists of an incompressible homogeneous fluid of density \rho_{1}. The second primary *m*_{2} is a finite straight segment of length 2*l*. The existence of the equilibrium points is discussed after deriving the pertinent …

Universality And Synchronization In Complex Quadratic Networks (Cqns), 2022 State University of New York at New Paltz

#### Universality And Synchronization In Complex Quadratic Networks (Cqns), Anca R. Radulescu, Danae Evans

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Gene Drives And The Consequences Of Over-Suppression, 2022 Virginia Commonwealth University

#### Gene Drives And The Consequences Of Over-Suppression, Cole Butler

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Real-Time Interactive Simulation Of Large Bird Flocks: Toward Understanding Murmurations, 2022 Georgia Institute of Technology

#### Real-Time Interactive Simulation Of Large Bird Flocks: Toward Understanding Murmurations, Maxfield R. Comstock

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Dimension Theory Of Conformal Iterated Function Systems, 2022 University of Connecticut

#### Dimension Theory Of Conformal Iterated Function Systems, Sharon Sneha Spaulding

*Honors Scholar Theses*

This thesis is an expository investigation of the conformal iterated function system (CIFS) approach to fractals and their dimension theory. Conformal maps distort regions, subject to certain constraints, in a controlled way. Let $\mathcal{S} = (X, E, \{\phi_e\}_{e \in E})$ be an iterated function system where $X$ is a compact metric space, $E$ is a countable index set, and $\{\phi_e\}_{e \in E}$ is a family of injective and uniformly contracting maps. If the family of maps $\{\phi_e\}_{e \in E}$ is also conformal and satisfies the open set condition, then the distortion properties of conformal maps can be extended to the …

The Butterfly Effect Of Fractals, 2022 Murray State University

#### The Butterfly Effect Of Fractals, Cody Watkins

*Honors College Theses*

This thesis applies concepts in fractal geometry to the relatively new field of mathematics known as chaos theory, with emphasis on the underlying foundation of the field: the butterfly effect. We begin by reviewing concepts useful for an introduction to chaos theory by defining terms such as fractals, transformations, affine transformations, and contraction mappings, as well as proving and demonstrating the contraction mapping theorem. We also show that each fractal produced by the contraction mapping theorem is unique in its fractal dimension, another term we define. We then show and demonstrate iterated function systems and take a closer look at …

Finite Subdivision Rules For Matings Of Quadratic Thurston Maps With Few Postcritical Points, 2022 Bellarmine University

#### Finite Subdivision Rules For Matings Of Quadratic Thurston Maps With Few Postcritical Points, Jeremiah Zonio

*Undergraduate Theses*

A finite subdivision rule is set of instructions for repeatedly subdividing a partitioning of a given space. This turns out to be incredibly useful when attempting to describe a process known as polynomial mating. Polynomial mating is a way of gluing together two spaces which two polynomials may act upon such that the glued borders of each space respects the dynamics described by each polynomial. For matings of Misiurewicz polynomials, the spaces we are gluing together are 1-dimensional and are thus all border. This poses a conceptual difficulty which this paper attempts to resolve by using finite subdivison rules to …

Dynamics Of Mutualism In A Two Prey, One Predator System With Variable Carrying Capacity, 2022 University of North Florida

#### Dynamics Of Mutualism In A Two Prey, One Predator System With Variable Carrying Capacity, Randy Huy Lee

*UNF Graduate Theses and Dissertations*

We considered the livelihood of two prey species in the presence of a predator species. To understand this phenomenon, we developed and analyzed two mathematical models considering indirect and direct mutualism of two prey species and the influence of one predator species. Both types of mutualism are represented by an increase in the preys' carrying capacities based on direct and indirect interactions between the prey. Because of mutualism, as the death rate parameter of the predator species goes through some critical value, the model shows transcritical bifurcation. Additionally, in the direct mutualism model, as the death rate parameter decreases to …

An Integrated Computational Pipeline To Construct Patient-Specific Cancer Models, 2022 University of Kentucky

#### An Integrated Computational Pipeline To Construct Patient-Specific Cancer Models, Daniel Plaugher

*Theses and Dissertations--Mathematics*

Precision oncology largely involves tumor genomics to guide therapy protocols. Yet, it is well known that many commonly mutated genes cannot be easily targeted. Even when genes can be targeted, resistance to therapy is quite common. A rising field with promising results is that of mathematical biology, where *in silico* models are often used for the discovery of general principles and novel hypotheses that can guide the development of new treatments. A major goal is that eventually *in silico* models will accurately predict clinically relevant endpoints and find optimal control interventions to stop (or reverse) disease progression. Thus, it is …

Exo-Sir: An Epidemiological Model To Analyze The Impact Of Exogenous Spread Of Infection, 2022 LNMIIT, India

#### Exo-Sir: An Epidemiological Model To Analyze The Impact Of Exogenous Spread Of Infection, Nirmal Kumar Sivaraman, Manas Gaur, Shivansh Baijal, Sakthi Balan Muthiah, Amit Sheth

*Publications*

Epidemics like Covid-19 and Ebola have impacted people's lives significantly. The impact of mobility of people across the countries or states in the spread of epidemics has been significant. The spread of disease due to factors local to the population under consideration is termed the endogenous spread. The spread due to external factors like migration, mobility, etc. is called the exogenous spread. In this paper, we introduce the Exo-SIR model, an extension of the popular SIR model and a few variants of the model. The novelty in our model is that it captures both the exogenous and endogenous spread of …