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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
Many forms of programmable matter have been proposed for various tasks. We use an abstract model of self-organizing particle systems for programmable matter which could be used for a variety of applications, including smart paint and coating materials for engineering or programmable cells for medical uses. Previous research using this model has focused on shape formation and other spatial configuration problems, including line formation, compression, and coating. In this work we study foundational computational tasks that exceed the capabilities of the individual constant memory particles described by the model. These tasks represent new ways to use these self-organizing systems, which, in conjunction with previous shape and configuration work, make the systems useful for a wider variety of tasks. We present an implementation of a counter using a line of particles, which makes it possible for the line of particles to count to and store values much larger than their individual capacities. We then present an algorithm that takes a matrix and a vector as input and then sets up and uses a rectangular block of particles to compute the matrix-vector multiplication. This setup also utilizes the counter implementation to store the resulting vector from the matrix-vector multiplication. Operations such as counting and matrix multiplication can leverage the distributed and dynamic nature of the self-organizing system to be more efficient and adaptable than on traditional linear computing hardware. Such computational tools also give the systems more power to make complex decisions when adapting to new situations or to analyze the data they collect, reducing reliance on a central controller for setup and output processing. Finally, we demonstrate an application of similar types of computations with self-organizing systems to image processing, with an implementation of an image edge detection algorithm.
ContributorsPorter, Alexandra Marie (Author) / Richa, Andrea (Thesis director) / Xue, Guoliang (Committee member) / School of Music (Contributor) / Computer Science and Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-12
Description
Division of Labor among social insects is frequently discussed in regards to the colony's worker population. However, before a colony achieves a worker population, a queen is required to perform all of the tasks necessary for her survival: foraging, building the colony, and brood care. A simple ODE model was developed through the use of a framework of replicator equations in dynamical environments to investigate how queen ants perform and distribute all of the tasks necessary for her and her colony's survival by incorporating individual internal thresholds and environmental stimulus. Modi�cations to the internal threshold, risk of performing the task, and the rate of increase of the environmental stimulus were also explored. Because of the simplicity of the model, it could also be used to measure the task performance of larger populations of social insects. However, the model has only been applied to the data collected from Pogonomyrmex barbatus single queen ants.
ContributorsKincade, Katherine Margaret (Author) / Kang, Yun (Thesis director) / Fewell, Jennifer (Committee member) / Lanchier, Nicolas (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Computer Science and Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2016-12
Description
Many programmable matter systems have been proposed and realized recently, each often tailored toward a particular task or physical setting. In our work on self-organizing particle systems, we abstract away from specific settings and instead describe programmable matter as a collection of simple computational elements (to be referred to as particles) with limited computational power that each perform fully distributed, local, asynchronous algorithms to solve system-wide problems of movement, configuration, and coordination. In this thesis, we focus on the compression problem, in which the particle system gathers as tightly together as possible, as in a sphere or its equivalent in the presence of some underlying geometry. While there are many ways to formalize what it means for a particle system to be compressed, we address three different notions of compression: (1) local compression, in which each individual particle utilizes local rules to create an overall convex structure containing no holes, (2) hole elimination, in which the particle system seeks to detect and eliminate any holes it contains, and (3) alpha-compression, in which the particle system seeks to shrink its perimeter to be within a constant factor of the minimum possible value. We analyze the behavior of each of these algorithms, examining correctness and convergence where appropriate. In the case of the Markov Chain Algorithm for Compression, we provide improvements to the original bounds for the bias parameter lambda which influences the system to either compress or expand. Lastly, we briefly discuss contributions to the problem of leader election--in which a particle system elects a single leader--since it acts as an important prerequisite for compression algorithms that use a predetermined seed particle.
ContributorsDaymude, Joshua Jungwoo (Author) / Richa, Andrea (Thesis director) / Kierstead, Henry (Committee member) / Computer Science and Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Many current cryptographic algorithms will eventually become easily broken by Shor's Algorithm once quantum computers become more powerful. A number of new algorithms have been proposed which are not compromised by quantum computers, one of which is the Supersingular Isogeny Diffie-Hellman Key Exchange Protocol (SIDH). SIDH works by having both parties perform random walks between supersingular elliptic curves on isogeny graphs of prime degree and eventually end at the same location, a shared secret.<br/><br/>This thesis seeks to explore some of the theory and concepts underlying the security of SIDH, especially as it relates to finding supersingular elliptic curves, generating isogeny graphs, and implementing SIDH. As elliptic curves and SIDH may be an unfamiliar topic to many readers, the paper begins by providing a brief introduction to elliptic curves, isogenies, and the SIDH Protocol. Next, the paper investigates more efficient methods of generating supersingular elliptic curves, which are important for visualizing the isogeny graphs in the algorithm and the setup of the protocol. Afterwards, the paper focuses on isogeny maps of various degrees, attempting to visualize isogeny maps similar to those used in SIDH. Finally, the paper looks at an implementation of SIDH in PARI/GP and work is done to see the effects of using isogenies of degree greater than 2 and 3 on the security, runtime, and practicality of the algorithm.
ContributorsSteele, Aaron J (Author) / Jones, John (Thesis director) / Childress, Nancy (Committee member) / Computer Science and Engineering Program (Contributor, Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
In the modern world with the ever growing importance of technology, the challenge of information security is of increasing importance. Cryptographic algorithms used to encode information stored and transmitted over the internet must be constantly improving as methodology and technology for cyber attacks improve. RSA and Elliptic Curve cryptosystems such as El Gamal or Diffie-Hellman key exchange are often used as secure asymmetric cryptographic algorithms. However, quantum computing threatens the security of these algorithms. A relatively new algorithm that is based on isogenies between elliptic curves has been proposed in response to this threat. The new algorithm is thought to be quantum resistant as it uses isogeny walks instead of point addition to generate a shared secret key. In this paper we will analyze this algorithm in an attempt to understand the theory behind it. A main goal is to create isogeny graphs to visualize degree 2 and 3 isogeny walks that can be taken between supersingular elliptic curves over small fields to get a better understanding of the workings and security of the algorithm.
ContributorsLoucks, Sara J (Author) / Jones, John (Thesis director) / Bremner, Andrew (Committee member) / Computer Science and Engineering Program (Contributor) / School of Film, Dance and Theatre (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05