Thinking Poker Through Game Theory, 2016 California State University, San Bernardino

#### Thinking Poker Through Game Theory, Damian Palafox

*Electronic Theses, Projects, and Dissertations*

Poker is a complex game to analyze. In this project we will use the mathematics of game theory to solve some simplified variations of the game. Probability is the building block behind game theory. We must understand a few concepts from probability such as distributions, expected value, variance, and enumeration methods to aid us in studying game theory. We will solve and analyze games through game theory by using different decision methods, decision trees, and the process of domination and simplification. Poker models, with and without cards, will be provided to illustrate optimal strategies. Extensions to those models will be ...

The Evolution Of Cryptology, 2016 California State University - San Bernardino

#### The Evolution Of Cryptology, Gwendolyn Rae Souza

*Electronic Theses, Projects, and Dissertations*

We live in an age when our most private information is becoming exceedingly difficult to keep private. Cryptology allows for the creation of encryptive barriers that protect this information. Though the information is protected, it is not entirely inaccessible. A recipient may be able to access the information by decoding the message. This possible threat has encouraged cryptologists to evolve and complicate their encrypting methods so that future information can remain safe and become more difficult to decode. There are various methods of encryption that demonstrate how cryptology continues to evolve through time. These methods revolve around different areas of ...

Abrupt Transitions From Low To High Firing Frequencies In Neurons And Neuronal Networks, 2016 Tufts University

#### Abrupt Transitions From Low To High Firing Frequencies In Neurons And Neuronal Networks, Ryusei Melody Takeuchi, Christoph Borgers

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

In-111 Uptake In Spect Images Of Murine Tumors With Varying Antigen Expression: A Topological Approach, 2016 College of the Holy Cross

#### In-111 Uptake In Spect Images Of Murine Tumors With Varying Antigen Expression: A Topological Approach, Sarah J. Tymochko

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Can Including Time Delay In Epidemic Models Significantly Improve Predictions Concerning Intervention Strategies?, 2016 College of William and Mary

#### Can Including Time Delay In Epidemic Models Significantly Improve Predictions Concerning Intervention Strategies?, Adrienna N. Bingham, Leah Shaw

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

A Topological Analysis Of Targeted In-111 Up- Take In Spect Images Of Murine Tumors., 2016 College of the Holy Cross

#### A Topological Analysis Of Targeted In-111 Up- Take In Spect Images Of Murine Tumors., David Damiano

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

General Models For Ecological Drivers Of Poverty, 2016 Harvard Medical School

#### General Models For Ecological Drivers Of Poverty, Calistus Ngeh Ngonghala

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Force Generation And Contraction Of Random Actomyosin Bundles., 2016 Courant Institute (NYU)

#### Force Generation And Contraction Of Random Actomyosin Bundles., Dietmar B. Oelz

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Statistics In League Of Legends: Analyzing Runes For Last-Hitting, 2016 Augustana College, Rock Island Illinois

#### Statistics In League Of Legends: Analyzing Runes For Last-Hitting, Brian M. Hook

*Mathematics: Student Scholarship & Creative Works*

While other sports have statisticians to evaluate players and their stats, in electronic sports there is a need for statisticians to evaluate different parts of the game. League of Legends is the most popular of ESports and is the focus of this discussion. The mechanic of focus here is runes which give boosts to the players stats in-game like being able to do extra damage. We will be finding the effectiveness of these runes by looking at gold efficiency, help with last hitting, and extra damage dealt through the use of Python.

Totally Positive Density Matrices And Linear Preservers, 2016 University of Guelph

#### Totally Positive Density Matrices And Linear Preservers, David Kribs, Jeremy Levick, Rajesh Pereira

*Electronic Journal of Linear Algebra*

The intersection between the set of totally nonnegative matrices, which are of interest in many areas of matrix theory and its applications, and the set of density matrices, which provide the mathematical description of quantum states, are investigated. The single qubit case is characterized, and several equivalent conditions for a quantum channel to preserve the set in that case are given. Higher dimensional cases are also discussed.

Modelling The Impact Of Climate Change On The Polar Bear Population In Western Hudson Bay, 2016 The University of Western Ontario

#### Modelling The Impact Of Climate Change On The Polar Bear Population In Western Hudson Bay, Nicole Bastow

*Electronic Thesis and Dissertation Repository*

The aim of this thesis is to model the impact of climate change on polar bear populations. The first model is a discrete matrix model with time-dependent parameters, which are influenced by temperature increases. Sensitivity analysis is done on the model. Numerical simulations predict there exist several scenarios that result in polar bear extinction. When the impact of climate warming is low the population is predicted to die out in 300 years and for higher levels of impact the population can be extinct within 6. The second model is a system of continuous delay differential equations with time-dependent parameters, also ...

Growing Networks With Positive And Negative Links, 2016 College of William and Mary

#### Growing Networks With Positive And Negative Links, Corynne Smith Dech

*College of William & Mary Undergraduate Honors Theses*

Scale-free networks grown via preferential attachment have been used to model real-world networks such as the Internet, citation networks, and social networks. Here we investigate signed scale-free networks where a link represents a positive or negative connection. We present analytic results and simulations for a growing signed network model and compare the signed network to an unsigned scale-free network. We discuss several options for preferential attachment in a signed network model. Lastly we measure preferential attachment in a real-world network and discuss the advantages and disadvantages of data fitting methods.

An Overview Of Cryptography (Updated Version, March 3, 2016), 2016 Embry-Riddle Aeronautical University - Daytona Beach

#### An Overview Of Cryptography (Updated Version, March 3, 2016), Gary Kessler

*Gary C. Kessler*

Higher Numerical Ranges Of Quaternion Matrices, 2016 Department of Mathematics, IAU-Shahrood University, Shahrood, Iran

#### Higher Numerical Ranges Of Quaternion Matrices, Narjes Haj Aboutalebi, Gholamreza Aghamollaei, Hossein Momenaee Kermani

*Electronic Journal of Linear Algebra*

Let n and k be two positive integers and k n. In this paper, the notion of k−numerical range of n−square quaternion matrices is introduced. Some algebraic and geometrical properties are investigated. In particular, a necessary and sufficient condition for the convexity of the k−numerical range of a quaternion matrix is given. Moreover, a new description of 1−numerical range of normal quaternion matrices is also stated.

Procesy Cieplne I Aparaty (Lab), 2016 Wroclaw University of Technology

The Mathematics Of Scientific Research: Scientometrics, Citation Metrics, And Impact Factors, 2016 Wayne State University

#### The Mathematics Of Scientific Research: Scientometrics, Citation Metrics, And Impact Factors, Clayton Hayes

*Library Scholarly Publications*

This talk will consist of an introduction to the rationale behind the establishment of the field of Scientometrics, which attempts to measure and analyze the body of research done in the sciences. This is primarily through analyzing the connections between scientific journals, articles, and authors. I will cover the foundational works of Price and Garfield in the fields of citation networks and impact factor, respectively, and will give some historical context for these developments. I will also speak briefly on more recent developments in these areas, such as the Eigenfactor, author citation metrics, and (time permitting) alternative metrics.

**Audience**: The ...

Using Mathematical Research Methods To Solve A Problem In Music Theory Instruction, Specifically, The Teaching Of Secondary Dominant Chords, 2016 University of Akron

#### Using Mathematical Research Methods To Solve A Problem In Music Theory Instruction, Specifically, The Teaching Of Secondary Dominant Chords, Angela Ulrich

*Honors Research Projects*

The mathematical method for research is used to find a solution to a problem in music theory: understanding and identifying secondary dominant chords. By reviewing and assessing the teaching methods of university professors and theory textbooks, and comparing those findings with student reviews, a new method for teaching the concept is developed. The proposed system incorporates aural, visual, and kinetic exercises to serve every learner. The literature review and sample unit plan are followed by a possible procedure for testing the effectiveness of the new method.

Subgroups Of Finite Wreath Product Groups For P=3, 2016 University of Akron

#### Subgroups Of Finite Wreath Product Groups For P=3, Jessica L. Gonda

*Honors Research Projects*

Let M be the additive abelian group of 3-by-3 matrices whose entries are from the ring of integers modulo 9. The problem of determining all the normal subgroups of the regular wreath product group P=Z_{9}≀(Z_{3} × Z_{3}) that are contained in its base subgroup is equivalent to the problem of determining the subgroups of M that are invariant under two particular endomorphisms of M. In this thesis we give a partial solution to the latter problem by implementing a systematic approach using concepts from group theory and linear algebra.

Mathematical Models For Infectious Disease Transmission With Stochastic Simulation Of Measles Outbreaks, 2016 Georgia Southern University

#### Mathematical Models For Infectious Disease Transmission With Stochastic Simulation Of Measles Outbreaks, Valerie Welty

*University Honors Program Theses*

As they are the leading cause of death among children and adolescents worldwide, it is of extreme importance to control the spread of infectious diseases. Information gained from mathematical modeling of these events often proves quite useful in establishing policy decisions to accomplish this goal. Human behavior, however, is quite difficult to recreate when using equations with pre-determined results, such as deterministic differential equations often used with epidemic models. Because of this, the focus of the research was to create a simulation of an outbreak, specifically of measles, by using an imaginary population experiencing simulated stochastic events on a discrete ...

A Computational Investigation Of Large Gaps In Contingency Tables, 2016 James Madison University

#### A Computational Investigation Of Large Gaps In Contingency Tables, Noah J. Watson

*Senior Honors Projects*

Integer programming can be used to find upper and lower bounds on the cells of a multi-dimensional contingency table using the information from the released margins. The linear relaxation of these programs also provides bounds and the discrepancy between these bounds, the integer programming gap, can be large. While the more notable examples of large gaps have been shown to be rare, here we provide some results on the rarity of large gaps on small tables.