Matching Items (51)
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- All Subjects: Mathematics
- All Subjects: Physics
- Creators: School of Mathematical and Statistical Sciences
- Creators: Kostelich, Eric
- Member of: Barrett, The Honors College Thesis/Creative Project Collection
- Resource Type: Text
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
The current observable universe is made of matter due to baryon/antibaryon asymmetry. The Deep Underground Neutrino Experiment is an international experiment through the Fermi National Accelerator Laboratory that will study neutrinos. In this study, the detection efficiency for low energy supernova neutrinos was examined in order to improve energy reconstruction for neutrino energies less than 40 MeV. To do this, supernova neutrino events were simulated using the LarSoft simulation package with and without background. The ratios between the true data and reconstructed data were compared to identify the deficiencies of the detector, which were found to be low energies and high drift times. The ratio between the true and reconstructed data was improved by applying the physical limits of the detector. The efficiency of the improved ratio of the clean data was found to be 93.2% and the efficiency of the improved ratio with the data with background was 82.6%. The study suggests that a second photon detector at the far wall of the detector would help improve the resolutions at high drift times and low neutrino energies.
ContributorsProcter-Murphy, Rachel Grace (Co-author) / Procter-Murphy, Rachel (Co-author) / Ritchie, Barry (Thesis director) / LoSecco, John (Committee member) / School of Earth and Space Exploration (Contributor) / Department of Physics (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05
Description
In this project, we created a code that was able to simulate the dynamics of a three site Hubbard model ring connected to an infinite dissipative bath and driven by an electric field. We utilized the master equation approach, which will one day be able to be implemented efficiently on a quantum computer. For now we used classical computing to model one of the simplest nontrivial driven dissipative systems. This will serve as a verification of the master equation method and a baseline to test against when we are able to implement it on a quantum computer. For this report, we will mainly focus on classifying the DC component of the current around our ring. We notice several expected characteristics of this DC current including an inverse square tail at large values of the electric field and a linear response region at small values of the electric field.
ContributorsJohnson, Michael (Author) / Chamberlin, Ralph (Thesis director) / Ritchie, Barry (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Department of Physics (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05
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
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
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
There exists a notable gender gap in the field of economics. One explanation for this gap is the low supply of women entering the economics labor market. To understand the shortage of female economics students, I observe students at the undergraduate and graduate level. My data consists of a sample of current undergraduate students and a sample of past Ph.D. applicants at Arizona State University. The gender gaps in these samples, both at the undergraduate and graduate level, can largely be explained by the variation in mathematical preparation of the students. The data reveals that undergraduate male economics students are more frequently enrolled in higher level math courses compared to female undergraduate students. Likewise, a higher number of male Ph.D. applicants have stronger mathematical backgrounds relative to female Ph.D. applicants. This common factor might explain the higher supply of male students who apply and get accepted to postgraduate studies in economics, relative to female students, holding all else constant. I conclude with the following recommended interventions: make information regarding postgraduate opportunities in economics more readily available, and increase math requirements for a bachelor’s degree in economics at ASU.
ContributorsZafari, Zorah (Author) / Datta, Manjira (Thesis director) / Zafar, Basit (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / School of Social Transformation (Contributor, Contributor) / Department of Economics (Contributor) / Dean, W.P. Carey School of Business (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
Cryptocurrencies have become one of the most fascinating forms of currency and economics due to their fluctuating values and lack of centralization. This project attempts to use machine learning methods to effectively model in-sample data for Bitcoin and Ethereum using rule induction methods. The dataset is cleaned by removing entries with missing data. The new column is created to measure price difference to create a more accurate analysis on the change in price. Eight relevant variables are selected using cross validation: the total number of bitcoins, the total size of the blockchains, the hash rate, mining difficulty, revenue from mining, transaction fees, the cost of transactions and the estimated transaction volume. The in-sample data is modeled using a simple tree fit, first with one variable and then with eight. Using all eight variables, the in-sample model and data have a correlation of 0.6822657. The in-sample model is improved by first applying bootstrap aggregation (also known as bagging) to fit 400 decision trees to the in-sample data using one variable. Then the random forests technique is applied to the data using all eight variables. This results in a correlation between the model and data of 9.9443413. The random forests technique is then applied to an Ethereum dataset, resulting in a correlation of 9.6904798. Finally, an out-of-sample model is created for Bitcoin and Ethereum using random forests, with a benchmark correlation of 0.03 for financial data. The correlation between the training model and the testing data for Bitcoin was 0.06957639, while for Ethereum the correlation was -0.171125. In conclusion, it is confirmed that cryptocurrencies can have accurate in-sample models by applying the random forests method to a dataset. However, out-of-sample modeling is more difficult, but in some cases better than typical forms of financial data. It should also be noted that cryptocurrency data has similar properties to other related financial datasets, realizing future potential for system modeling for cryptocurrency within the financial world.
ContributorsBrowning, Jacob Christian (Author) / Meuth, Ryan (Thesis director) / Jones, Donald (Committee member) / McCulloch, Robert (Committee member) / Computer Science and Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
For colonies of ponerine ant species, sterility regulation after a founding queen's death is not totally achieved in the worker caste, and the possibility of sexual reproduction is opened to workers. The persisting survival of these colonies is dependent on capturing the optimal reproductive ratio; yet, an informational gap bounds the mechanisms detailing the selection of new reproductives and the suppression of ovarian development in rejected reproductives. We investigated the mechanisms of worker policing, one of the primary methods of ovarian suppression, through continuous video observation for a period of five days at the start of colony instability. Observations suggest policing in H. saltator is performed by a majority of a colony, including potential reproductives, and requires multiple events to fully discourage ovarian growth.
ContributorsChien, Jeffrey (Co-author) / Barat Ali, Fatima (Co-author) / Kang, Yun (Thesis director) / Liebig, Juergen (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Mechanical and Aerospace Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2018-12
Description
Within the context of the Finite-Difference Time-Domain (FDTD) method of simulating interactions between electromagnetic waves and matter, we adapt a known absorbing boundary condition, the Convolutional Perfectly-Matched Layer (CPML) to a background of Drude-dispersive medium. The purpose of this CPML is to terminate the virtual grid of scattering simulations by absorbing all outgoing radiation. In this thesis, we exposit the method of simulation, establish the Perfectly-Matched Layer as a domain which houses a spatial-coordinate transform to the complex plane, construct the CPML in vacuum, adapt the CPML to the Drude medium, and conclude with tests of the adapted CPML for two different scattering geometries.
ContributorsThornton, Brandon Maverick (Author) / Sukharev, Maxim (Thesis director) / Goodnick, Stephen (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Department of Physics (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05