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Articles 1 - 30 of 99
Full-Text Articles in Physical Sciences and Mathematics
Exploring Parameter Sensitivity Analysis In Mathematical Modeling With Ordinary Differential Equations, Viktoria Savatorova
Exploring Parameter Sensitivity Analysis In Mathematical Modeling With Ordinary Differential Equations, Viktoria Savatorova
CODEE Journal
This paper presents an exploration into parameter sensitivity analysis in mathematical modeling using ordinary differential equations (ODEs). Taking the first steps in understanding local sensitivity analysis through the direct differential method and global sensitivity analysis using metrics like Pearson, Spearman, PRCC, and Sobol’, we provide readers with a basic understanding of parameter sensitivity analysis for mathematical modeling using ODEs. As an illustrative application, the system of differential equations modeling population dynamics of several fish species with harvest considerations is utilized. The results of employing local and global sensitivity analysis are compared, shedding light on the strengths and limitations of each …
The "Benfordness" Of Bach Music, Chadrack Bantange, Darby Burgett, Luke Haws, Sybil Prince Nelson
The "Benfordness" Of Bach Music, Chadrack Bantange, Darby Burgett, Luke Haws, Sybil Prince Nelson
Journal of Humanistic Mathematics
In this paper we analyze the distribution of musical note frequencies in Hertz to see whether they follow the logarithmic Benford distribution. Our results show that the music of Johann Sebastian Bach and Johann Christian Bach is Benford distributed while the computer-generated music is not. We also find that computer-generated music is statistically less Benford distributed than human- composed music.
Math And Democracy, Kimberly A. Roth, Erika L. Ward
Math And Democracy, Kimberly A. Roth, Erika L. Ward
Journal of Humanistic Mathematics
Math and Democracy is a math class containing topics such as voting theory, weighted voting, apportionment, and gerrymandering. It was first designed by Erika Ward for math master’s students, mostly educators, but then adapted separately by both Erika Ward and Kim Roth for a general audience of undergraduates. The course contains materials that can be explored in mathematics classes from those for non-majors through graduate students. As such, it serves students from all majors and allows for discussion of fairness, racial justice, and politics while exploring mathematics that non-major students might not otherwise encounter. This article serves as a guide …
The Effect Of Age, Syntax Complexity, And Cognitive Ability On The Rate Of Semantic Illusions, Sara Anne Goring
The Effect Of Age, Syntax Complexity, And Cognitive Ability On The Rate Of Semantic Illusions, Sara Anne Goring
CGU Theses & Dissertations
Semantic illusions are recognition errors that occur when an individual fails to notice that information contradicts their prior knowledge (Barton & Sanford, 1993; Erickson & Mattson, 1981). For example, after hearing the question, “If a plane crashes while flying over state lines, where should the survivors be buried?” many start to consider the legality or appropriateness of the scenario despite knowing “survivors” should not be buried. Having more knowledge does not necessarily prevent individuals from overlooking illusory information/misinformation. Older adults tend to have greater crystallized intelligence than young adults, yet these age groups appear to detect illusory information at equivalent …
Application Of Sentiment Analysis And Machine Learning Techniques To Predict Daily Cryptocurrency Price Returns, Edward Wu
CMC Senior Theses
This paper examines the effects of social media sentiment relating to Bitcoin on the daily price returns of Bitcoin and other popular cryptocurrencies by utilizing sentiment analysis and machine learning techniques to predict daily price returns. Many investors think that social media sentiment affects cryptocurrency prices. However, the results of this paper find that social media sentiment relating to Bitcoin does not add significant predictive value to forecasting daily price returns for each of the six cryptocurrencies used for analysis and that machine learning models that do not assume linearity between the current day price return and previous daily price …
Beginner's Analysis Of Financial Stochastic Process Models, David Garcia
Beginner's Analysis Of Financial Stochastic Process Models, David Garcia
HMC Senior Theses
This thesis explores the use of geometric Brownian motion (GBM) as a financial model for predicting stock prices. The model is first introduced and its assumptions and limitations are discussed. Then, it is shown how to simulate GBM in order to predict stock price values. The performance of the GBM model is then evaluated in two different periods of time to determine whether it's accuracy has changed before and after March 23, 2020.
So Long My Friend, Bryan Mcnair
So Long My Friend, Bryan Mcnair
Journal of Humanistic Mathematics
No abstract provided.
Teiresias, Proportions, And Sexual Pleasure, Spyros Missiakoulis
Teiresias, Proportions, And Sexual Pleasure, Spyros Missiakoulis
Journal of Humanistic Mathematics
In this short article, I claim that Teiresias, the blind prophet of Apollo, in order to answer the question of whether “in sexual intercourse the woman had a larger share of pleasure than the man did”, measured the abstract concept of sexual pleasure and acted as a present-day scholar. With the help of numerical, not geometrical, proportions, he ended up with the conclusion “a man enjoyed one-tenth of the pleasure and a woman nine-tenths”.
Using Short Bursts To Optimize Redistricting In Georgia, Vedika Vishweshwar
Using Short Bursts To Optimize Redistricting In Georgia, Vedika Vishweshwar
CMC Senior Theses
Identifying extreme outliers in large state spaces is a difficult prob-
lem. I consider this problem in the context of finding political district-
ing plans that maximize the number of districts in which the majority
of the population is from a minority group, such as African Americans.
Since the set of all possible districting plans is enormous and unfeasi-
ble to examine in practice, this paper proposes a sampling method to
find these outlying plans. Specifically, this paper experiments with short
bursts in the context of minority voting rights in Georgia. Short bursts
are a type of Markov Chain in …
Containing Compounding Container Congestion, Curtis Salinger
Containing Compounding Container Congestion, Curtis Salinger
CMC Senior Theses
The Covid-19 pandemic caused major disruptions throughout the container shipping supply chain. Professor Dongping Song of Liverpool University wrote a paper discussing the logistical vulnerabilities in the supply chain, including the issue of congestion in ports. This paper examines the Port of Los Angeles from 2018-2021 as it relates to Song’s paper to see how its operations were impacted during the Covid-19 timeframe. It is found that labor shortages, chassis shortages, and change in trade behavior each contributed to the congestion. Unfortunately, the implemented policies were insufficient to bolster the port against sustained challenges and congestion continues to worsen.
The Uncertainty Of Confidence, Michael J. Leach
The Uncertainty Of Confidence, Michael J. Leach
Journal of Humanistic Mathematics
This is a free-verse poem about the estimation of population parameters in statistical models. The spacing of words is intended to reflect uncertainty.
Markov Chains For Computer Music Generation, Ilana Shapiro, Mark Huber
Markov Chains For Computer Music Generation, Ilana Shapiro, Mark Huber
Journal of Humanistic Mathematics
Random generation of music goes back at least to the 1700s with the introduction of Musical Dice Games. More recently, Markov chain models have been used as a way of extracting information from a piece of music and generating new music. We explain this approach and give Python code for using it to first draw out a model of the music and then create new music with that model.
A Gender And Race Theoretical And Probabilistic Analysis Of The Recent Title Ix Policy Changes, Jordan Wellington
A Gender And Race Theoretical And Probabilistic Analysis Of The Recent Title Ix Policy Changes, Jordan Wellington
Scripps Senior Theses
On May 6th, 2020, after extensive public comment and review, the Department of Education published the final rule for the new Title IX regulations, which took effect in schools on August 14th. Title IX is the nearly fifty year old piece of the Education Amendments that prohibits sexual discrimination in federally funded schools. Several of these changes, such as the inclusion of live hearings and cross examination of witnesses, have been widely criticized by victims’ rights advocates for potentially retraumatizing victims of sexual assault and discouraging students from pursuing a Title IX claim. While the impact of the new regulations …
Uncovering Object Categories In Infant Views, Naiti S. Bhatt
Uncovering Object Categories In Infant Views, Naiti S. Bhatt
Scripps Senior Theses
While adults recognize objects in a near-instant, infants must learn how to categorize the objects in their visual environments. Recent work has shown that egocentric head-mounted camera videos contain rich data that illuminate the infant experience (Clerkin et al., 2017; Franchak et al., 2011; Yoshida & Smith, 2008). While past work has focused on the social information in view, in this work, we aim to characterize the objects in infants’ at-home visual environments by modifying modern computer vision models for the infant view. To do so, we collected manual annotations of objects that infants seemed to be interacting within a …
Feature Investigation For Stock Returns Prediction Using Xgboost And Deep Learning Sentiment Classification, Seungho (Samuel) Lee
Feature Investigation For Stock Returns Prediction Using Xgboost And Deep Learning Sentiment Classification, Seungho (Samuel) Lee
CMC Senior Theses
This paper attempts to quantify predictive power of social media sentiment and financial data in stock prediction by utilizing a comprehensive set of stock-related fundamental and technical variables and social media sentiments. For conducting sentiment analysis, this study employs a pretrained finBERT model that provides three different sentiment classifications and respective softmax scores. Hence, the significance of these variables is evaluated with XGBoost regression and Shapley Additive exPlanations (SHAP) frameworks. Through investigating feature importance, this study finds that statistical properties of sentiment variables provide a stronger predictive power than a weighted sentiment score and that it is possible to quantify …
Using Twitter Api To Solve The Goat Debate: Michael Jordan Vs. Lebron James, Jordan Trey Leonard
Using Twitter Api To Solve The Goat Debate: Michael Jordan Vs. Lebron James, Jordan Trey Leonard
CMC Senior Theses
Using a Twitter API, I gather and analyze tweets by performing sentiment analysis to solve the GOAT debate among professional athletes with the primary focus on comparing Michael Jordan and LeBron James. Athletes from the National Football League (NFL), the National Basketball Association (NBA), Major League Baseball (MLB), and the National Collegiate Athletic Association (NCAA) Division 1 Men's and Women's Basketball were selected to compare how sentiment polarity varies across sports. Sentiment polarity is measured by labeling text as "positive", "neutral", or "negative" which allows us to determine which athlete/sport is highly favored among the Twitter community when it comes …
An Evaluation Of Knot Placement Strategies For Spline Regression, William Klein
An Evaluation Of Knot Placement Strategies For Spline Regression, William Klein
CMC Senior Theses
Regression splines have an established value for producing quality fit at a relatively low-degree polynomial. This paper explores the implications of adopting new methods for knot selection in tandem with established methodology from the current literature. Structural features of generated datasets, as well as residuals collected from sequential iterative models are used to augment the equidistant knot selection process. From analyzing a simulated dataset and an application onto the Racial Animus dataset, I find that a B-spline basis paired with equally-spaced knots remains the best choice when data are evenly distributed, even when structural features of a dataset are known …
Information Prioritization: A Comparison Between Utility Maximizers And Probability Matchers, Yusuf Ismaeel
Information Prioritization: A Comparison Between Utility Maximizers And Probability Matchers, Yusuf Ismaeel
CMC Senior Theses
This thesis examines the differences between probability matchers and utility maximizers in their preferences for information sources in a lab environment. In this paper, we consider the best source of information to be the most connected one. We conducted several linear probability model type regressions along with logit regressions. Furthermore, we also attempted to control and fix any potential misclassifications in classifying the cognitive strategy by using instrumental variables. The results show that utility maximizers will almost always choose the most informed node. Probability matchers, on the other hand, do not exhibit such a behavior as the probability matching strategy …
Neither “Post-War” Nor Post-Pregnancy Paranoia: How America’S War On Drugs Continues To Perpetuate Disparate Incarceration Outcomes For Pregnant, Substance-Involved Offenders, Becca S. Zimmerman
Neither “Post-War” Nor Post-Pregnancy Paranoia: How America’S War On Drugs Continues To Perpetuate Disparate Incarceration Outcomes For Pregnant, Substance-Involved Offenders, Becca S. Zimmerman
Pitzer Senior Theses
This thesis investigates the unique interactions between pregnancy, substance involvement, and race as they relate to the War on Drugs and the hyper-incarceration of women. Using ordinary least square regression analyses and data from the Bureau of Justice Statistics’ 2016 Survey of Prison Inmates, I examine if (and how) pregnancy status, drug use, race, and their interactions influence two length of incarceration outcomes: sentence length and amount of time spent in jail between arrest and imprisonment. The results collectively indicate that pregnancy decreases length of incarceration outcomes for those offenders who are not substance-involved but not evenhandedly -- benefitting white …
Quantifying Controllability In Temporal Networks With Uncertainty, James C. Boerkoel Jr., Lindsay Popowski, Michael Gao, Hemeng Li, Savana Ammons, Shyan Akmal
Quantifying Controllability In Temporal Networks With Uncertainty, James C. Boerkoel Jr., Lindsay Popowski, Michael Gao, Hemeng Li, Savana Ammons, Shyan Akmal
All HMC Faculty Publications and Research
Controllability for Simple Temporal Networks with Uncertainty (STNUs) has thus far been limited to three levels: strong, dynamic, and weak. Because of this, there is currently no systematic way for an agent to assess just how far from being controllable an uncontrollable STNU is. We provide new insights inspired by a geometric interpretation of STNUs to introduce the degrees of strong and dynamic controllability - continuous metrics that measure how far a network is from being controllable. We utilize these metrics to approximate the probabilities that an STNU can be dispatched successfully offline and online respectively. We introduce new methods …
Dynamic Control Of Probabilistic Simple Temporal Networks, James C. Boerkoel Jr., Michael Gao, Lindsay Popowski
Dynamic Control Of Probabilistic Simple Temporal Networks, James C. Boerkoel Jr., Michael Gao, Lindsay Popowski
All HMC Faculty Publications and Research
The controllability of a temporal network is defined as an agent’s ability to navigate around the uncertainty in its schedule and is well-studied for certain networks of temporal constraints. However, many interesting real-world problems can be better represented as Probabilistic Simple Temporal Networks (PSTNs) in which the uncertain durations are represented using potentially-unbounded probability density functions. This can make it inherently impossible to control for all eventualities. In this paper, we propose two new dynamic controllability algorithms that attempt to maximize the likelihood of successfully executing a schedule within a PSTN. The first approach, which we call MIN-LOSS DC, finds …
Novel Random Forest Methods And Algorithms For Autism Spectrum Disorders Research, Afrooz Jahedi
Novel Random Forest Methods And Algorithms For Autism Spectrum Disorders Research, Afrooz Jahedi
CGU Theses & Dissertations
Random Forest (RF) is a flexible, easy to use machine learning algorithm that was proposed by Leo Breiman in 2001 for building a predictor ensemble with a set of decision trees that grow in randomly selected subspaces of data. Its superior prediction accuracy has made it the most used algorithms in the machine learning field. In this dissertation, we use the random forest as the main building block for creating a proximity matrix for multivariate matching and diagnostic classification problems that are used for autism research (as an exemplary application). In observational studies, matching is used to optimize the balance …
A Multinational Study Of The Etiology And Clinical Teleology Of Moral Evaluations Of Patient Behaviors, Anna Yu Lee
A Multinational Study Of The Etiology And Clinical Teleology Of Moral Evaluations Of Patient Behaviors, Anna Yu Lee
CGU Theses & Dissertations
This dissertation is a collection of four studies which collectively explore a hypothesized construct of ‘moral evaluation of patient behaviors’ (MEPB) as a driver of health professionals’ readiness to interact humanistically with their patients. In these studies, ‘humanistic interactions’ refer to the non-technical, intangible skills and factors of clinical competence; the factors specifically explored in these studies were compassion toward patients, self-efficacy for treating patients, and optimism toward patient treatment. For the purpose of specificity, all factors were examined as they pertained to patients with substance use disorders. Survey data from a convenience sample of 524 health professionals (i.e. physicians, …
How Machine Learning And Probability Concepts Can Improve Nba Player Evaluation, Harrison Miller
How Machine Learning And Probability Concepts Can Improve Nba Player Evaluation, Harrison Miller
CMC Senior Theses
In this paper I will be breaking down a scholarly article, written by Sameer K. Deshpande and Shane T. Jensen, that proposed a new method to evaluate NBA players. The NBA is the highest level professional basketball league in America and stands for the National Basketball Association. They proposed to build a model that would result in how NBA players impact their teams chances of winning a game, using machine learning and probability concepts. I preface that by diving into these concepts and their mathematical backgrounds. These concepts include building a linear model using ordinary least squares method, the bias …
Causal Effect Random Forest Of Interaction Trees For Learning Individualized Treatment Regimes In Observational Studies: With Applications To Education Study Data, Luo Li
CGU Theses & Dissertations
Learning individualized treatment regimes (ITR) using observational data holds great interest in various fields, as treatment recommendations based on individual characteristics may improve individual treatment benefits with a reduced cost. It has long been observed that different individuals may respond to a certain treatment with significant heterogeneity. ITR can be defined as a mapping between individual characteristics to a treatment assignment. The optimal ITR is the treatment assignment that maximizes expected individual treatment effects. Rooted from personalized medicine, many studies and applications of ITR are in medical fields and clinical practice. Heterogeneous responses are also well documented in educational interventions. …
K-Means Stock Clustering Analysis Based On Historical Price Movements And Financial Ratios, Shu Bin
K-Means Stock Clustering Analysis Based On Historical Price Movements And Financial Ratios, Shu Bin
CMC Senior Theses
The 2015 article Creating Diversified Portfolios Using Cluster Analysis proposes an algorithm that uses the Sharpe ratio and results from K-means clustering conducted on companies' historical financial ratios to generate stock market portfolios. This project seeks to evaluate the performance of the portfolio-building algorithm during the beginning period of the COVID-19 recession. S&P 500 companies' historical stock price movement and their historical return on assets and asset turnover ratios are used as dissimilarity metrics for K-means clustering. After clustering, stock with the highest Sharpe ratio from each cluster is picked to become a part of the portfolio. The economic and …
Mathematics Versus Statistics, Mindy B. Capaldi
Mathematics Versus Statistics, Mindy B. Capaldi
Journal of Humanistic Mathematics
Mathematics and statistics are both important and useful subjects, but the former has maintained prominence in the American education system. On the other hand, statistics is more prevalent in daily life and is an increasingly marketable subject to know. This article gives a personal history of one mathematician’s bumpy road to learning and teaching statistics. Additionally, arguments for how and why to include statistics in the K-12 and college curricula are provided.
Choose Your Own Adventure: An Analysis Of Interactive Gamebooks Using Graph Theory, D'Andre Adams, Daniela Beckelhymer, Alison Marr
Choose Your Own Adventure: An Analysis Of Interactive Gamebooks Using Graph Theory, D'Andre Adams, Daniela Beckelhymer, Alison Marr
Journal of Humanistic Mathematics
"BEWARE and WARNING! This book is different from other books. You and YOU ALONE are in charge of what happens in this story." This is the captivating introduction to every book in the interactive novel series, Choose Your Own Adventure (CYOA). Our project uses the mathematical field of graph theory to analyze forty books from the CYOA book series for ages 9-12. We first began by drawing the digraphs of each book. Then we analyzed these digraphs by collecting structural data such as longest path length (i.e. longest story length) and number of vertices with outdegree zero (i.e. number …
Be Wary Of Black-Box Trading Algorithms, Gary N. Smith
Be Wary Of Black-Box Trading Algorithms, Gary N. Smith
Pomona Economics
Black-box algorithms now account for nearly a third of all U. S. stock trades. It is a mistake to think that these algorithms possess superhuman intelligence. In reality, computers do not have the common sense and wisdom that humans have accumulated by living. Trading algorithms are particularly dangerous because they are so efficient at discovering statistical patterns—but so utterly useless in judging whether the discovered patterns are meaningful.
The Paradox Of Big Data, Gary N. Smith
The Paradox Of Big Data, Gary N. Smith
Pomona Economics
Data-mining is often used to discover patterns in Big Data. It is tempting believe that because an unearthed pattern is unusual it must be meaningful, but patterns are inevitable in Big Data and usually meaningless. The paradox of Big Data is that data mining is most seductive when there are a large number of variables, but a large number of variables exacerbates the perils of data mining.