Matching Items (38)
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- All Subjects: Mathematics
- Creators: School of Mathematical and Statistical Sciences
- Member of: Theses and Dissertations
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- Status: Published
Description
A one-way function (OWF) is a function that is computationally feasible to compute in one direction, but infeasible to invert. Many current cryptosystems make use of properties of OWFs to provide ways to send secure messages. This paper reviews some simple OWFs and examines their use in contemporary cryptosystems and other cryptographic applications. This paper also discusses the broader implications of OWF-based cryptography, including its relevance to fields such as complexity theory and quantum computing, and considers the importance of OWFs in future cryptographic development
ContributorsMcdowell, Jeremiah Tenney (Author) / Hines, Taylor (Thesis director) / Foy, Joseph (Committee member) / Sprung, Florian (Committee member) / School of Mathematical and Statistical Sciences (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2020-05
Description
Ion channels in the membranes of cells in the body allow for the creation of action potentials from external stimuli, allowing us to sense our surroundings. One particular channel, TRPM8, is a trans-membrane ion channel believed to be the primary cold sensor in humans. Despite this important biological role and intense study of the channel, TRPM8 is not fully understood mechanistically and has not been accurately modeled. Existing models of TRPM8 fail to account for menthol activation of the channel. In this paper we re-implement an established whole cell model for TRPM8 with gating by both voltage and temperature. Using experimental data obtained from the Van Horn lab at Arizona State University, we refined the model to represent more accurately the dynamics of the human TRPM8 channel and incorporate the channel activation through menthol agonist binding. Our new model provides a large improvement over preexisting models, and serves as a basis for future incorporation of other channel activators of TRPM8 and for the modeling of other channels in the TRP family.
ContributorsAckerman, David (Author) / Crook, Sharon (Thesis director) / Van Horn, Wade (Committee member) / School of Earth and Space Exploration (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
The objective of this paper is to find and describe trends in the fast Fourier transformed accelerometer data that can be used to predict the mechanical failure of large vacuum pumps used in industrial settings, such as providing drinking water. Using three-dimensional plots of the data, this paper suggests how a model can be developed to predict the mechanical failure of vacuum pumps.
ContributorsHalver, Grant (Author) / Taylor, Tom (Thesis director) / Konstantinos, Tsakalis (Committee member) / Fricks, John (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
This honors thesis explores and models the flow of air around a cylindrical arrow that is rotating as it moves through the air. This model represents the airflow around an archery arrow after it is released from the bow and rotates while it flies through the air. This situation is important in archery because an understanding of the airflow allows archers to predict the flight of the arrow. As a result, archers can improve their accuracy and ability to hit targets. However, not many computational fluid dynamic simulations modeling the airflow around a rotating archery arrow exist. This thesis attempts to further the understanding of the airflow around a rotating archery arrow by creating a mathematical model to numerically simulate the airflow around the arrow in the presence of this rotation. This thesis uses a linearized approximation of the Navier Stokes equations to model the airflow around the arrow and explains the reasoning for using this simplification of the fully nonlinear Navier Stokes equations. This thesis continues to describe the discretization of these linearized equations using the finite difference method and the boundary conditions used for these equations. A MATLAB code solves the resulting system of equations in order to obtain a numerical simulation of this airflow around the rotating arrow. The results of the simulation for each velocity component and the pressure distribution are displayed. This thesis then discusses the results of the simulation, and the MATLAB code is analyzed to verify the convergence of the solution. Appendix A includes the full MATLAB code used for the flow simulation. Finally, this thesis explains potential future research topics, ideas, and improvements to the code that can help further the understanding and create more realistic simulations of the airflow around a flying archery arrow.
ContributorsCholinski, Christopher John (Author) / Tang, Wenbo (Thesis director) / Herrmann, Marcus (Committee member) / Mechanical and Aerospace Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
The Jordan curve theorem states that any homeomorphic copy of a circle into R2 divides the plane into two distinct regions. This paper reconstructs one proof of the Jordan curve theorem before turning its attention toward generalizations of the theorem and their proofs and counterexamples. We begin with an introduction to elementary topology and the different notions of the connectedness of a space before constructing the first proof of the Jordan curve theorem. We then turn our attention to algebraic topology which we utilize in our discussion of the Jordan curve theorem’s generalizations. We end with a proof of the Jordan-Brouwer theorems, extensions of the Jordan curve theorem to higher dimensions.
ContributorsClark, Kacey (Author) / Kawski, Matthias (Thesis director) / Paupert, Julien (Committee member) / Department of Physics (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05
Description
A factor accounting for the COVID-19 pandemic was added to a generalized linear model to more accurately predict unpaid claims. COVID-19 has affected not just healthcare, but all sectors of the economy. Because of this, whether or not an automobile insurance claim is filed during the pandemic needs to be taken into account while estimating unpaid claims. Reserve-estimating functions such as glmReserve from the “ChainLadder” package in the statistical software R were experimented with to produce their own results. Because of their insufficiency, a manual approach to building the model turned out to be the most proficient method. Utilizing the GLM function, a model was built that emulated linear regression with a factor for COVID-19. The effects of such a model are analyzed based on effectiveness and interpretablility. A model such as this would prove useful for future calculations, especially as society is now returning to a “normal” state.
ContributorsKossler, Patrick (Author) / Zicarelli, John (Thesis director) / Milovanovic, Jelena (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2022-05
Description
The objective of this study is to build a model using R and RStudio that automates ratemaking procedures for Company XYZ’s actuaries in their commercial general liability pricing department. The purpose and importance of this objective is to allow actuaries to work more efficiently and effectively by using this model that outputs the results they otherwise would have had to code and calculate on their own. Instead of spending time working towards these results, the actuaries can analyze the findings, strategize accordingly, and communicate with business partners. The model was built from R code that was later transformed to Shiny, a package within RStudio that allows for the build-up of interactive web applications. The final result is a Shiny app that first takes in multiple datasets from Company XYZ’s data warehouse and displays different views of the data in order for actuaries to make selections on development and trend methods. The app outputs the re-created ratemaking exhibits showing the resulting developed and trended loss and premium as well as the experience-based indicated rate level change based on prior selections. The ratemaking process and Shiny app functionality will be detailed in this report.
ContributorsGilkey, Gina (Author) / Zicarelli, John (Thesis director) / Milovanovic, Jelena (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2022-05
Description
One common problem that occurs to students during breaks is the retrogression of knowledge due to lack of practice. This problem occurs for students at all levels of education but is especially harmful to students who are taking sequential classes such as Calculus for Engineers I and Calculus for Engineers II where the retention of topics taught in Calculus for Engineers I are required for students to succeed. One solution to this problem is the Keep in School Shape (KiSS) program. The KiSS program is a very efficient and easily accessible program that allows students to stay warmed up and ready to go when they start a sequential course by having daily review material during academic breaks.
During an academic break, students who are signed up for the KiSS program are sent a link through text message or email every day that allows them to access a multiple choice review problem. The review problem that they are given is a problem that presents material from the previous course that will be needed in the upcoming course. At the beginning of the review, students have the option to choose between a Level 1 or a Level 2 problem, where a Level 2 problem is related to its Level 1 counterpart but slightly more difficult. Before the students are permitted to solve the problem, they must first use a five point scale that indicates their confidence in their ability to solve the problem. After they complete either the Level 1 or Level 2 daily problem, those that got it wrong have the option to view a hint and try again or view a solution. The students that got the Level 1 daily problem right are also allowed to view the solution but will be permitted to go onto the next level right away whereas the students that got the Level 1 problem incorrect will need to try a similar problem before being able to move onto Level 2. For students who chose to do the Level 2 problem and were not very confident, they were given the option to solve a level 1 problem instead. Students who chose level 2 and got it wrong are given the options to view a hint and try again or simply view the solution before moving on to flashcard versions of the daily problems. Students who get the Level 2 problem correct are also given the option to continue practicing using the flashcards if they choose to.
Once a week, there is also a trivia day where students have the choice to complete solely a mathematical trivia question or complete both the trivia question along with a daily review problem. This feature allows students to take a day off from doing mathematics if they choose, but still stay engaged by doing a related activity.
Through this program, there is a lot to learn about whether doing Level 1 problems can help students improve their understanding of a concept enough to correctly solve a Level 2 problem. There are many factors to consider such as which question the student chose to answer first, student confidence, and student perseverance. Through the Summer Break 2023 KiSS program, there was data collected for every student answer for each day they accessed the daily KiSS activity. This thesis presents an analysis of the data showing how having two levels of problems is beneficial for students and the correlation between students’ results in Level 1 problems and Level 2 problems for students who chose to attempt both problems.
ContributorsWang, Ryan (Author) / Van de Sande, Carla (Thesis director) / Reiser, Mark (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2023-12