Mathematics Commons^™

Using Geographic Information To Explore Player-Specific Movement And Its Effects On Play Success In The Nfl, Hayley Horn, Eric Laigaie, Alexander Lopez, Shravan Reddy

SMU Data Science Review

American Football is a billion-dollar industry in the United States. The analytical aspect of the sport is an ever-growing domain, with open-source competitions like the NFL Big Data Bowl accelerating this growth. With the amount of player movement during each play, tracking data can prove valuable in many areas of football analytics. While concussion detection, catch recognition, and completion percentage prediction are all existing use cases for this data, player-specific movement attributes, such as speed and agility, may be helpful in predicting play success. This research calculates player-specific speed and agility attributes from tracking data and supplements them with descriptive …

Photonic Sensors Based On Integrated Ring Resonators, Jaime Da Silva

Mechanical Engineering Research Theses and Dissertations

This thesis investigates the application of integrated ring resonators to different sensing applications. The sensors proposed here rely on the principle of optical whispering gallery mode (WGM) resonance shifts of the resonators. Three distinct sensing applications are investigated to demonstrate the concept: a photonic seismometer, an evanescent field sensor, and a zero-drift Doppler velocimeter. These concepts can be helpful in developing lightweight, compact, and highly sensitive sensors. Successful implementation of these sensors could potentially address sensing requirements for both space and Earth-bound applications. The feasibility of this class of sensors is assessed for seismic, proximity, and vibrational measurements.

Bridging The Chasm Between Fundamental, Momentum, And Quantitative Investing, Allen Hoskins, Jeff Reed, Robert Slater

SMU Data Science Review

A chasm exists between the active public equity investment management industry's fundamental, momentum, and quantitative styles. In this study, the researchers explore ways to bridge this gap by leveraging domain knowledge, fundamental analysis, momentum, crowdsourcing, and data science methods. This research also seeks to test the developed tools and strategies during the volatile time period of 2020 and 2021.

Supplementary Material For The Article “Using Generative Ai For Literature Searches And Scholarly Writing: Is The Integrity Of The Scientific Discourse In Jeopardy?", Paul G. Schmidt, Amnon J. Meir

Mathematics Research

Supplementing our paper "Using Generative AI for Literature Searches and Scholarly Writing: Is the Integrity of the Scientific Discourse in Jeopardy?" [1], we furnish and analyze the evidence of AI-induced contamination of the scientific literature that we alluded to in Section 2 of the paper (Section 1 below). We also provide a comprehensive list of references, encompassing the titles in the bibliography of [1], the titles cited in [1], but not included in the bibliography, and the titles cited in Section 1 below, but not in [1]. Further, we summarize two specific conversations with ChatGPT, corroborating the observations in Section …

Classification Of Pixel Tracks To Improve Track Reconstruction From Proton-Proton Collisions, Kebur Fantahun, Jobin Joseph, Halle Purdom, Nibhrat Lohia

SMU Data Science Review

In this paper, machine learning techniques are used to reconstruct particle collision pathways. CERN (Conseil européen pour la recherche nucléaire) uses a massive underground particle collider, called the Large Hadron Collider or LHC, to produce particle collisions at extremely high speeds. There are several layers of detectors in the collider that track the pathways of particles as they collide. The data produced from collisions contains an extraneous amount of background noise, i.e., decays from known particle collisions produce fake signal. Particularly, in the first layer of the detector, the pixel tracker, there is an overwhelming amount of background noise that …

Nonlinear Photonics In Twisted And Nonlocal Structures, Austin Copeland

Mathematics Theses and Dissertations

We provide a theoretical framework for the observed confinement of light modes within a twisted coreless photonic crystal fiber. Asymptotic methods are applied through ray theory and field theory in both the linear and nonlinear regime. We find the modes have a radially symmetric chirp and the envelope will decay away from the axis of propagation. Secondly, we study the stability and singularity formation of unidirectional beams as described by the Schrodinger equation. We propose a novel extension to the modeling equation to include a fractional Laplacian in one spatial dimension and a standard second derivative in a second dimension. …

Universal Vector Neural Machine Translation With Effective Attention, Joshua Yi, Satish Mylapore, Ryan Paul, Robert Slater

SMU Data Science Review

Neural Machine Translation (NMT) leverages one or more trained neural networks for the translation of phrases. Sutskever intro- duced a sequence to sequence based encoder decoder model which be- came the standard for NMT based systems. Attention mechanisms were later introduced to address the issues with the translation of long sen- tences and improving overall accuracy. In this paper, we propose two improvements to the encoder decoder based NMT approach. Most trans- lation models are trained as one model for one translation. We introduce a neutral/universal model representation that can be used to predict more than one language depending on …

Model Selection And Experimental Design Of Biological Networks With Algebraic Geometry, Anyu Zhang

Mathematics Theses and Dissertations

Model selection based on experimental data is an essential challenge in biological data science. In decades, the volume of biological data from varied sources, including laboratory experiments, field observations, and patient health records has seen an unprecedented increase. Mainly when collecting data is expensive or time-consuming, as it is often in the case with clinical trials and biomolecular experiments, the problem of selecting information-rich data becomes crucial for creating relevant models.

Motivated by certain geometric relationships between data, we partitioned input data sets, especially data sets that correspond to a unique basis, into equivalence classes with the same basis to …

Role Of Combinatorial Complexity In Genetic Networks, Sharon Yang

SMU Journal of Undergraduate Research

A common motif found in genetic networks is the formation of large complexes. One difficulty in modeling this motif is the large number of possible intermediate complexes that can form. For instance, if a complex could contain up to 10 different proteins, 210 possible intermediate complexes can form. Keeping track of all complexes is difficult and often ignored in mathematical models. Here we present an algorithm to code ordinary differential equations (ODEs) to model genetic networks with combinatorial complexity. In these routines, the general binding rules, which counts for the majority of the reactions, are implemented automatically, thus the users …

Improving Vix Futures Forecasts Using Machine Learning Methods, James Hosker, Slobodan Djurdjevic, Hieu Nguyen, Robert Slater

SMU Data Science Review

The problem of forecasting market volatility is a difficult task for most fund managers. Volatility forecasts are used for risk management, alpha (risk) trading, and the reduction of trading friction. Improving the forecasts of future market volatility assists fund managers in adding or reducing risk in their portfolios as well as in increasing hedges to protect their portfolios in anticipation of a market sell-off event. Our analysis compares three existing financial models that forecast future market volatility using the Chicago Board Options Exchange Volatility Index (VIX) to six machine/deep learning supervised regression methods. This analysis determines which models provide best …

Modeling Stochastically Intransitive Relationships In Paired Comparison Data, Ryan Patrick Alexander Mcshane

Statistical Science Theses and Dissertations

If the Warriors beat the Rockets and the Rockets beat the Spurs, does that mean that the Warriors are better than the Spurs? Sophisticated fans would argue that the Warriors are better by the transitive property, but could Spurs fans make a legitimate argument that their team is better despite this chain of evidence?

We first explore the nature of intransitive (rock-scissors-paper) relationships with a graph theoretic approach to the method of paired comparisons framework popularized by Kendall and Smith (1940). Then, we focus on the setting where all pairs of items, teams, players, or objects have been compared to …

Yelp’S Review Filtering Algorithm, Yao Yao, Ivelin Angelov, Jack Rasmus-Vorrath, Mooyoung Lee, Daniel W. Engels

SMU Data Science Review

In this paper, we present an analysis of features influencing Yelp's proprietary review filtering algorithm. Classifying or misclassifying reviews as recommended or non-recommended affects average ratings, consumer decisions, and ultimately, business revenue. Our analysis involves systematically sampling and scraping Yelp restaurant reviews. Features are extracted from review metadata and engineered from metrics and scores generated using text classifiers and sentiment analysis. The coefficients of a multivariate logistic regression model were interpreted as quantifications of the relative importance of features in classifying reviews as recommended or non-recommended. The model classified review recommendations with an accuracy of 78%. We found that reviews …

Near-Optimal Control Of Switched Systems With Continuous-Time Dynamics Using Approximate Dynamic Programming, Tohid Sardarmehni

Mechanical Engineering Research Theses and Dissertations

Optimal control is a control method which provides inputs that minimize a performance index subject to state or input constraints [58]. The existing solutions for finding the exact optimal control solution such as Pontryagin’s minimum principle and dynamic programming suffer from curse of dimensionality in high order dynamical systems. One remedy for this problem is finding near optimal solution instead of the exact optimal solution to avoid curse of dimensionality [31]. A method for finding the approximate optimal solution is through Approximate Dynamic Programming (ADP) methods which are discussed in the subsequent chapters.

In this dissertation, optimal switching in switched …

Understanding Natural Keyboard Typing Using Convolutional Neural Networks On Mobile Sensor Data, Travis Siems

Computer Science and Engineering Theses and Dissertations

Mobile phones and other devices with embedded sensors are becoming increasingly ubiquitous. Audio and motion sensor data may be able to detect information that we did not think possible. Some researchers have created models that can predict computer keyboard typing from a nearby mobile device; however, certain limitations to their experiment setup and methods compelled us to be skeptical of the models’ realistic prediction capability. We investigate the possibility of understanding natural keyboard typing from mobile phones by performing a well-designed data collection experiment that encourages natural typing and interactions. This data collection helps capture realistic vulnerabilities of the security …

Asian Carp Could Help Us Solve Hunger Problem, Michael (Dung) Tran

Collection of Engaged Learning

Bighead carp and silver carp (Invader Species – Asian Carp) invaded the Illinois River waterway over a decade ago. Populations of these fishes have apparently grown dense in the lower and middle Illinois Rivers and both species are approaching the Chicago Area Waterway System (CAWS) and potentially making their way into Great Lakes. So far, positive DNA of Asian Carp has been found beyond the defensive electrical barrier, which means they have made their way to Great Lakes somehow. Asian Carp are fast growing, aggressive, and adaptable fish that are outcompeting native fish species for food and habitat in much …

Experimental Design Models, J. Leroy Folks

Journal of the Graduate Research Center

If we were to assume a linear relationship between x and y described by the model y = a + βx + e it is unlikely that we would consider writing the model as y = a + bx + cx + e. It is even more unlikely that we would apply the least squares principle by minimizing Σe2 with respect to a, b, and c. Yet a similar thing happens in experimental design. In fact, it is common practice to use less than full-rank models where the parameters are not defined and, in cases where they are defined, to …

A Property Of The Mean Stieltjes Integral, J. A. Dyer

Journal of the Graduate Research Center

The purpose of this note is to consider the following problem. Suppose [a,b] is an interval, f a function in [a,b] and g a function which has a derivative in [a,b].

On The Estimation Of Parameters When The Observations Are Subject To Measurement Error, Paul D. Minton, Vanamamalai Seshadri

Journal of the Graduate Research Center

Maximum likelihood estimation of parameters is considered in the situation where a measurement x is taken to mean "x + d." The maximum likelihood estimator for the parameter of the exponential distribution is found for this case and compared with the usual estimator.

A Geometrically Characterized Reference Frame For The Study Of Cartan Hypersurfaces In N-Dimensional Projective Space, W. Dale Maness

Journal of the Graduate Research Center

In the projective differential geometry of ordinary space a problem of fundamental importance is that of obtaining a covariantly determined reference frame for the definition of local point coordinates and associated power series developments for the equations of curves and surfaces. Much of the celebrated memoir [1] of G. M. Green was devoted to this problem for a surface or 2-dimensional Cartan variety. However, the complete geometric characterization of the reference frame used by Green was not completed until sixteen years later by Bell [2]. In this paper, an extension of Green's "relation R" is given for a linear (n-2)-space …

A Proof Of A Theorem On Giffin's Paradox, Don E. Edmondson

Journal of the Graduate Research Center

For the uninitiated, Giflin's paradox is the name of a condition from economic analysis. One considers a consumer with a certain income faced with the decision of how much of two goods to purchase. Intuitively, one anticipates that this will depend upon the prices to be paid for the goods, and anticipates that if a price is increased the amount purchased by the consumer will decrease ( the other price being constant). If it happens that with an increase in price of a good, the demand for that good increases, then this paradoxical situation is called Giflin's Paradox. The theorem …

Some Decomposition Theorems For The Vector Space Of Matrix Summability Operators, Ed Kelly Jr., Tetsundo Sekiguchi

Journal of the Graduate Research Center

Consider the set T = {(aij) I aij are real } of matrix summability operators on the set B of bounded sequences of real numbers.

The Estimation Of Parameters In Regression Functions Subject To Certain Restraints, Paul D. Minton, Alfred E. Crofts Jr.

Journal of the Graduate Research Center

We consider two types of problems in maximum likelihood estimation of parameters of linear functions subject to certain restraints. One is a family of lines with equal slopes or intercepts; the other is a pair of lines constrained to meet at a predetermined point. In the case of normally distributed errors with equal variances within each set, the solutions are identical with least squares solutions. In addition to linear functions, non-linear functions which are transformable to linearity may be treated under these methods.

A Formula For A Class Of Steady State Solutions, Don E. Edmondson

Journal of the Graduate Research Center

An integral representation formula is developed to cope with the problem of determining and studying the steady state solutions of a class of differential equations. The class of differential equations studied is y' + yf = g, where f and g are continuous functions admitting period T > 0. The formula then defines a function admitting period T and serves to allow an analysis of the differential equation above. Theorem I delineates some of the properties of the function and Theorem II provides answers to the steady state questions. An application is made to a capacitance circuit problem.