The Brother Joseph W. Stander Symposium recognizes and celebrates academic excellence in undergraduate and graduate education. This annual event provides an opportunity for students from all disciplines to showcase their intellectual and artistic accomplishments. The Stander Symposium represents the Marianist tradition of education through community and is the principal campus-wide event in which faculty and students actualize our mission to be a "community of learners."
19th Annual Integration Bee, a mathematics interactive competition: The students compete in teams of 2-3 people. This is organized in a similar way to the traditional spelling bee. Teams will be evaluating integrals that are projected on a screen. If a team incorrectly evaluates an integral, the team is eliminated from the competition. After the elimination rounds, we will hold the lightning rounds. The first 'y' many teams to correctly evaluate the given integrals will proceed to the next round. We do this until there is a 1st, 2nd, and 3rd place team. First, second, and third place teams will receive math T-shirts. The Department of Mathematics will host a pizza lunch in the Science Center Atrium from noon to 1 p.m. prior to the Integration Bee.
Grant Eifert, Rebekah Revadelo
Repairable adhesive elastomers are emerging materials employed in compelling applications such as soft robotics, biosensing, tissue regeneration, and wearable electronics. Facilitating adhesion requires strong interactions, while self-healing requires bond dynamicity. This contrast in desired bond characteristics presents a challenge in the design of healable adhesive elastomers. Furthermore, 3D printability of this novel class of materials has received limited attention, restricting the potential design space of as-built geometries. Here, we report a series of 3D-printable elastomeric materials with self-healing ability and adhesive properties. Repairability is obtained using Thiol-Michael dynamic crosslinkers incorporated into the polymer backbone, while adhesion is facilitated with acrylate monomers. The adhesive properties were tested by performing lap shear tests and measured across different lap materials and formulations of the tested material. We successfully 3D printed complex functional structures using a commercial digital light processing (DLP) printer. Shape-selective lifting of low surface energy Teflon objects is achieved using soft robotic actuators with designed geometries, wherein contour matching leads to increased adhesion and successful lifting capacity. The demonstrated utility of these adhesive elastomer materials provides unique capabilities to easily program soft robot functionality.
Vatsa Sanjay Patel
Photobombing occurs very often in photography. This causes trouble for the human subjects of the photographs. Thus, there is a valid requirement to eliminate photobombing from captured images. In this study, we do a comparative analysis of this topic. In order to accomplish this, we first collect a dataset of photographs including unwanted and distracting components that must be removed in order to detect photobombing. Then, we annotate the photobombed areas that have a tendency to be eliminated. The photobombed portions are then removed using various picture inpainting techniques. The photobombing removal results are compared to a manually created ground truth. Many performance measures are employed in our benchmark to compare the efficacy of various techniques. Experiments yield illuminating data that indicate the efficacy of image inpainting techniques for this specific issue.
A Century of Disturbance and Dynamics During the Establishment of White Oak (Quercus alba) Dominance in Forests of Southeastern Ohio: Implications for Sustainable Forest Management
The current structure and composition of forest ecosystems throughout eastern North America has been determined greatly by historic natural disturbances and successional processes. The white oak tree (Quercus alba) has the largest range among tree species in eastern North America (the Atlantic to the Great Plains, the Great Lakes to the Gulf) and has historical dominance of the canopy. White oaks are a broadleaved tree species that form stands with conifers (Pinus spp.) and/or other broadleaved species (Carya spp., Fraxinus spp., Acer spp., Populus spp., etc.) The white oak group (Leucobalanus) was an important ecosystem service for Indigenous Peoples of eastern North America for hundreds of years and the European colonizers of the 18th and 19th centuries. Among Indigenous groups, oaks (including Q. macrocarpa and Q. rubra) were cultivated and managed for increased growing success. Acorns were used for flour and medicinal mixtures. Branches were used for basket weaving. Stems were used for cabins, canoes, and shelters. In addition to popular human uses, the white oak is of paramount importance for a variety of wildlife, including fungi and bacteria. Q. alba is known to be both historically and culturally important to forest ecosystems, however it is one of numerous species currently experiencing massive regeneration issues with its young offspring. Recruitment failure and a subsequent forest transition of substituting shade-tolerant maple species for oak species could give rise to a largescale shift in biodiversity, wildlife nutrition, and soil characteristics across the Eastern Deciduous Forest (EDF). In addition to a changing climate, the white oak, a paragon of EDF tree species, could quickly become much less secure in conservation status. We examined 65 cross section samples of white oak (n= 62), chestnut oak (n= 2), and shagbark hickory (n= 1) trees for their growth release history and fire scar history. Analyzing and comparing both periods of growth and fire throughout history gave insight into how the current forest came to be and the important factors necessary for successful oak regeneration. Results showed that growth releases and fire occurrence do not have a strong correlation. Only 2 samples exhibited a release within a time lag period of 3 years following a fire. There was a ~70-year period where a fire did not occur, but releases still happened frequently. However, a short period of fires within the 1920s were quickly followed by releases. Foresting the area in order to aid in the Civil War effort between 1850-1875 allowed numerous young oak samples to release, and a similar pattern was seen near WWII. We hypothesize that similar periodic thinning/cutting was done throughout the ~70-year period without fires for these releases to have occurred.
We present a compact Michelson interferometer-based Fourier transform spectrometer on a silicon photonic chip. In contrast to a conventional Mach Zehnder interferometer (MZI) designs demonstrated elsewhere, our design doubles the optical path difference between the two unbalanced arms of the interferometer thereby effectively doubling the spectral resolution while still maintaining the same geometric length in a MZI. Our design centered at 1550nm thus achieves ~0.8nm spectral resolution with a 40micron geometric path length difference between the two arms of the interferometer in contrast to ~1.6nm spectral resolution in the corresponding MZI. Devices have been fabricated and results will be presented.
Aaron Hendricks, Jarod Mendoza
In this project, we’ll use computational methods to study hypothetical biomolecular reaction kinetics. The concentrations of five chemicals are modeled by a system of five coupled differential equations. It is important for any physical system to be simulated as accurately as possible. We will compare the numerical solution of the system using Euler’s Method and the Runge-Kutta methods.
Over many decades Latin America has been experiencing a shift in dietary habits, due in part to an overconsumption of sugary, processed foods- as well as an increase in sugar sweetened beverage consumption. Many sugar sweetened beverage companies have extensive marketing campaigns in this region therefore promoting increases in intake. This increase in intake is contributing to negative health outcomes including type 2 diabetes and decaying oral health. A comprehensive literature review was completed to examine the various marketing strategies used by sugar sweetened beverage companies to promote intake as well as the political tactics used to deter consumption. The purpose of the review was to provide a foundation for future research related to determining interventions to deter sugar sweetened beverage intake in Latin America.
Engaging in high-impact physical activities may not be suitable for individuals with disabilities and senior adults to maintain their fitness needs due to the risk of injury or exacerbating pre-existing conditions. Adaptive yoga provides a low-impact alternative that offers tailored exercises to different age groups and individuals with disabilities. However, post-pandemic travel can make attending yoga sessions challenging. To address this, the augmented-reality based yoga system provides a way to learn and practice yoga in an immersive mixed-reality environment at comfort of comfort of their home or preferred location. The application uses a database of yoga poses and a mixed-reality environment with a virtual instructor to guide users and allow them to interact with both virtual and real-world elements. The application provides different yoga routines based on user details, and live feedback with the help of a smartphone camera to correct and validate yoga poses. Moreover, the application tracks the user's progress and provides digital rewards to motivate them further. The user can also workout with family or friends represented by virtual avatars in a joint yoga session, promoting a sense of community and belonging. Adaptive yoga provides numerous health benefits, including strengthened bones, enhanced balance and flexibility, improved quality of sleep, and reduced stress, depression, and anxiety, promoting mental fitness and clarity for the elderly. The proposed application makes learning yoga engaging and enjoyable while providing various health benefits. Also, the application ensures exercises are practiced correctly and safely with the help of live feedback. The proposed application provides a convenient and accessible solution for post-pandemic times. The social aspect can help promote overall mental health and well-being, enhancing a sense of community and belonging. The proposed application has significant implications for promoting active and healthy aging.
Advanced composite materials consist of continuous fibers of carbon or glass embedded in a polymer matrix, such as epoxy. This hybrid material system forms a high-strength and lightweight structure that is increasingly used in a wide variety of applications, including aerospace, marine structure and vehicles, energy production, sporting goods, and general infrastructure. There are numerous manufacturing processes for making these products, but all of them involve combining the matrix with a high concentration of reinforcing fibers, resulting in a highly compacted laminate structure. T-joint composite parts have been widely used in the construction of products in several applications, especially in aerospace. Recently, there has been increased interest in investigating T-joint strength behavior and failure mechanisms through a combination of experimental and numerical approaches. These parts require a filler material in the voided deltoid region, where the base and flange meet, to ensure their strength and damage tolerance. To provide structural integrity, including a filler material in the deltoid region is necessary for finished composite parts. Conventionally, the deltoid region fills up with resin during molding, or a rolled-up piece of fabric is placed in the region prior to molding to reinforce the resin. Neither approach is ideal for several reasons including fiber distortion and uncontrolled permeability in the deltoid region. In this research, a tensile pull-off test is used to investigate the strength of T-joint parts with different custom porosity of 3D printed parts used as the filler material. The maximum force required to fail the structure, as well as the total elongation to failure, were compared for a carbon/epoxy composite T-joint structure.
For the 2022 Formula One (F1) season, F1 introduced a new set of technical regulations that reduce the complexity of the aerodynamic devices such as the spoiler, often called wings. The objective of this regulation change is to reduce the amount of turbulence produced allowing the cars to trail behind one another closer, making for easier overtaking and increasing the competitiveness of the sport. The present study evaluates and quantifies the aerodynamic performance of a 2022 F1 rear wing by using computational fluid dynamic (CFD) analyses. Both a study of a 2022 and 2021 specification rear wing is assessed to determine how the new technical regulations affect the turbulence in the wake of the car. The study is performed by taking cut planes in the fluid domain downstream of the rear wing model and integrating over the plane to determine the turbulence behind the wing. With this analysis, a comparison between the two rear wing specifications can be performed to determine the magnitude of impact the new technical regulations produce. From this, a conclusion can be made regarding the effectiveness of the 2022 F1 technical regulations, and whether the regulation change was justified.
A Factor Based Portfolio Weighing Model for the S&P 500 Health Care Sector (XLV): An Empirical Analysis of Portfolio Returns, 2009-2022
Nathan Jabaay, Kevin Cullen
In this study, I use firm revenue growth as my factor weight. I carry out two empirical tests: (1) my revenue growth factor based portfolio weighing model outperforms an equal weight portfolio model over the period 2009-2022; (2) firm revenue growth is a priced-in risk factor in the equity market. For my first test, I compare the long run cumulative returns for the revenue growth factor based portfolio weighing model to the returns for the equal weight portfolio, 2009-2022. For my second test, I determine if my portfolio weighing model generates excess returns over the broad market benchmark, the S&P 500 index, for the period 2009-2022. I use two investment strategies, a buy and hold strategy and an adjustable shares strategy, to generate the returns for my portfolio weighing model.
Recent experimental studies suggest that thin-film crystalline silicon is viable as a high-efficiency material for energy conversion in solar cells. A theoretical study on the optical properties of two-dimensional (2D) silicon thin films is needed to gain insights into the structure-property correlation of this material. In our project, we made Density Functional Theory calculations of multiple 2D silicon thin films of different structures. We first constructed their model structures from bulk silicon by cutting it along the (100), (110), and (111) low-Miller-index faces, varying the number of silicon atomic layers from two to eight layers, and exposing the bare surfaces or terminating them with hydrogen atoms. We then relaxed the atomic coordinates and in-plane lattice vectors of the 2D films. Next, we calculated the surface energies for the thin films with bare surfaces and modelled the octahedral crystal habit of silicon. From electronic structure calculations, we found that the 2D films with bare surfaces possess metallic in-gap states near the Fermi level, whereas hydrogen termination on the surfaces can render semiconducting thin films suitable for optical applications. Finally, we calculated the optical properties of the semiconducting thin films from the complex dielectric function at different levels of approximation, giving frequency-, face-index-, and thickness-dependent absorption coefficients. We found that the absorption coefficients increase with increasing thicknesses, asymptotically approaching that of the bulk structure. Among the three face indices studied, the (111) films have the lowest surface energy and achieve the highest absorption coefficients, making (111) the most favorable face index for thin-film silicon solar cell applications.
Jonathan Shepelak, Terrence Oliss, Michael Dimisa, Carson Karn, Benjamin Burkett, Ahmad S GH B Alazemi, Bader S M M M Alotaibi, Mohammad E M M Alazmi, Clara Schulze, Rachel Reid, Miguel Reyes, Makoro Kebe, William Uhlenbrock, Sean Coney, Andrew Koltas, Conner Kelley, David Hughes, Bobbi Gunn, Sheora Watkins, Charles Lynch, Michael Adedokun, Elizabeth Andreu, James Boldt, Bryon Helbling, Alexandra Cooney, Michael Cooney, Mia Huckleberry, Saad M S Z Alazemi, Anthony Rizkallah, Soud M S M Alazmi, Drew Gueterman, Piper Ashley, Alvaro Guerrero Valera, Ace Kinman
These presentations examine topics which shape contemporary African experience with a goal of introducing the audience to why and how Africa will shape events in the twenty-first century. The topic presented in include infectious diseases, Muammar Gadhafi, Human Trafficking, Blood Diamond, and civil conflict.
This study examines the relationship between one’s siblings’ internalizing and externalizing problems, and the effect those behaviors may have on one’s relationship with one’s parents. Previous research indicated that siblings’ relationships are some of the most long-lasting and important relationships in an individual’s life. Family research has also shown that there are situations in which children’s internalizing and externalizing behaviors can shape their relationship with their parents. However, no previous research to my knowledge has explored whether one’s sibling’s behaviors influences one’s own parent-child relationship. During this study, data from the United States Department of Labor and National Longitudinal Survey of Youth (NLSY79) as well as the Children of the National Longitudinal Survey of Youth (CNLSY) was analyzed. Internalizing and externalizing behaviors were evaluated through the Behavior Problems Index (BPI). The child’s perception of parenting was evaluated based on four scales: Autonomy, Disharmony, Intimacy, and Joint Activity (Hart et al., 1999). When siblings are further apart in age, there was an association found between internalizing and externalizing behaviors and Joint Activities, resulting in the younger child spending less time with parents. Disharmony between parents and children was found to be only correlated with the child’s own externalizing behaviors, not with a siblings’ externalizing behaviors. These findings do not provide clear support for the possibility that sibling behavior problems have influence on one's own parent-child relationship.
American Fracture, Digital Rage: Evaluating the Influence of Conspiratorial Rhetoric on the U.S. Catholic Community
It has been well documented that religious individuals and groups continue to play roles in both the complex global web of polarization, extremism, and terroristic violence and in the reciprocal forces of peacebuilding, justice work, and public reconciliation. My graduate thesis research examines the historical antecedents and current characteristics of digital spaces like #CatholicTwitter (and, in particular, the degree to which both conspiratorial and extremist rhetoric flow throughout them) to assess how such social media spaces both mediate the American Catholic experience and affect the civic health of the United States at large. This thesis speaks to all those interested in understanding, assessing, and combatting civic fragmentation, polarization, and extremism; enters into a growing scholarly conversation exploring the various ways Catholic individuals and institutions both affect and are affected by conspiratorial discourse, misinformation, and disinformation; and point toward potential reconciliatory paths forward. As a Catholic and Marianist institution, the University of Dayton "encourages its members to judge for themselves how institutions are performing their purposes (and) to expose deficiencies in their structures and operations..." through inquiry, dialogue, and praxis. In that spirit, I write in hopes of helping advance our campus community's communal mission to function as a university for the common good.
A Multi-Sector Portfolio Weighting Model with Firm Revenue Growth the Factor Weight: An Empirical Analysis of Portfolio Returns, 2009-2022
Daniel Montgomery, Vincent Rullo
In this study we conduct two empirical tests. First, we determine if the revenue growth factor weighted multi-sector portfolio outperforms an equal weight portfolio over the period 2009-2022. Second, we test to see if revenue growth is a “priced-in risk factor” by determining if the long term returns to our portfolio weighting model are in excess of the returns to the broad market index S&P 500.60 stocks from six S&P 500 sectors make up the portfolio. The six sectors are: (1) Consumer Discretionary, (2) Healthcare, (3) Industrials, (4) Information Technology, (5) Real Estate, and (6) Communication Services. Historically, these six sectors contribute most of the returns to the S&P 500. To generate our returns, we use two investment strategies: (1) Buy and Hold, and (2) Adjustable Shares.
Listeria monocytogenes is a prevalent food-borne pathogen, and a clear understanding of its pathogenesis can enhance our capability to treat infections. L. monocytogenes is ingested through contaminated foods, enters the intestinal lumen, and is able to spread throughout the rest of the body. The intracellular life cycle of L. monocytogenes requires the regulated expressions of a variety of virulence genes. We previously found that exposure to short chain fatty acids (SCFAs), fermentation byproducts present in the intestines, resulted in significant changes in L. monocytogenes pathogenesis. This research, divided into two major projects, aimed to understand the relationship between L. monocytogenes, its host, and the exposure to SCFAs. Project one evaluated the effect of prior anaerobic exposure of SCFAs, specifically propionate, on strain 07PF0776, a cardiotropic clinical isolate. Hemolytic assays were used to measure the activity of secreted LLO as an indication of bacterial virulence. This project also assessed intracellular growth and actin polymerization of L. monocytogenes in cardiac myoblast cells and macrophages. To further investigate the mechanism underlying L. monocytogenes response to SCFAs, project two explored the role of CodY, a transcription factor in response to levels of branched chain amino acids, in the opposing effects of propionate on LLO production. By comparing the culture supernatant LLO activities in strain 10403s and a mutant with a codY gene deletion (ΔcodY), I discovered that CodY was required for the increase in LLO production in response to anaerobic propionate exposure. Together, the results of these projects provide further evidence for the relationship between SCFA exposure and L. monocytogenes pathogenesis. Ultimately, these findings can be utilized to improve the understanding of L. monocytogenes and develop effective prevention and treatment methods.
The Movies Dataset, available on Kaggle, is a comprehensive dataset containing information on movies released between 1990 and 2017. In this project, we aim to analyze variables that have significant predictive power on the success of a movie and to build a recommendation system based on users' profiles.Firstly, we will explore the dataset and preprocess it to extract relevant information for our analysis. We will then perform exploratory data analysis to identify potential predictors of a movie's success, such as budget, genre, runtime, release date, and rating. We will use regression techniques to model the relationship between these predictors and a movie's success, as measured by box office revenue and user ratings. The results of our analysis will provide insights into the factors that contribute to a movie's commercial and critical success.In the second part of the project, we will develop a recommendation system that suggests movies to users based on their preferences. We will incorporate content-based filtering techniques, where we analyze the movie's features and recommend movies that are similar in genre, cast, or storyline to those the user has previously enjoyed. This can be a tricky problem as movie ratings are often times purely subjective and highly variable.Overall, this project will provide a comprehensive analysis of the movies dataset and a recommendation system that can help users discover new movies that match their preferences.
M M Shaifur Rahman
Deep learning (DL) is currently one of the most popular branch of Machine Learning and uses Deep Convolutional Neural Network (DCNN) architectures. It can transform medical diagnostics. DCNN predictions are significantly dependent on high-quality input data. However, large-scale images are challenging to operate with classical deep-learning architectures due to their vast memory and computational requirements. Currently, one of the popular approaches to deal with large-scale input images is to resize the large image to a smaller dimension which decays the performance of the overall system. Another popular approach to overcome large-scale image problems is to sequentially crop the high-resolution image into multiple smaller images to fit in the computation memory (GPU). In this work, we demonstrate a novel approach to training and inference in higher-resolution input images (e.g., 1024 x 1024) with DCNN. Our proposed architectures are constructed with state-of-the-art DCNN backbone models such as ResNet101, DenseNet-121 and EfficientNet. Finally, the models are evaluated using large-scale diabetic retinopathy datasets (e.g., Dataset for Diabetic Retinopathy, Kaggle 2019 BD). The experimental results are compared against existing deep learning methods and demonstrate significant improvements in accuracy.
The purpose of this study is to increase the understanding of power system resilience through pattern recognition of disaster-induced system disruption. This study consists of analyzing power system failure and recovery patterns in a post-extreme event environment to determine relevant pattern characteristics relating to power system resilience. Specifically, the methodology of this study consists of (1) collecting and processing data from power system failures induced by natural disasters categorized by power companies, states, counties, and natural disaster occurrence.; (2) developing failure and recovery curves for the collected data; (3) investigating and establishing statistical distribution models that correlate to the goodness of fit for plotted curves best characterizing the system behaviour for each extreme external occurrence; and (4) creating a quantitative algorithm for specifying the resilience of such engineered systems. The resultant algorithm will assist in answering questions about the resiliency of power systems. Since modern society relies extensively on power systems to survive, this increased insight into power system resilience will provide better situational awareness for stakeholders during future decision-making discussions regarding power system construction.
What keeps roller coasters safe? Why do you so rarely ever hear about roller coaster trains colliding? The answer is simple: blocking systems. A block is a section of track only one train may occupy at one time; at the end of each block is a method of stopping and holding a train reliably should the next block not be clear. Examples of this are chain lift hills, magnetic brakes paired with drive tires, or friction brakes that clamp onto a brake fin secured to the bottom of the train. For my project, I would like to design a simple logic system that utilizes proximity sensors to prevent trains from colliding with each other. Along with the sensors, I will be using other miniature versions of common roller coaster components and design a simple track layout for the trains to follow.
An anisotropic transfer matrix approach to profiled optical field propagation through hyperbolic metamaterials
We extend the transfer matrix method to study the propagation of beams and arbitrary profiled fields through anisotropic metamaterial slabs, and to demonstrate the negative refractive index property resulting in linear self-focusing of beams in hyperbolic metamaterials. Specifically, the transfer matrix method, commonly used to analyze bi-directional plane wave propagation, is developed to analyze beam propagation. By expressing a Gaussian beam as an angular spectrum of plane waves, an anisotropic transfer matrix, which is also obtained using the eigenvalues mentioned above, can be applied to calculate the beam spectrum at an arbitrary distance of propagation through a hyperbolic metamaterial. With given incident and emergent media, say, air, linear self-focusing within the metamaterial slab and subsequent reimaging in the emergent medium are numerically investigated for one transverse dimensional TM polarized Gaussian beam. Simulation results are compared with results from the unidirectional transfer function approach. The anisotropic transfer matrix method can be used to study beam transmission and reflection at the interfaces, and can be applied to analyze optical propagation through anisotropic metamaterial on uniaxial electro-optic substrates. The technique can be extended to arbitrary initial optical field profiles in one transverse dimension to assess the imaging quality of metamaterial slabs.
Sohini Sengupta (presenting author); other authors: Fajer A. Almanea, Venkateswar Rao, Jinchen Han, Soubantika Palchoudhury (faculty advisor)
Cu3MX4 (M = V, Nb, and Ta; X = S, Se, and Te) compounds, also known as the sulvanite family, have recently emerged as promising materials for optoelectronic devices, including solar photovoltaics (PV) due to their tunable band gaps, high optical absorption coefficients and composition consisting of comparatively earth-abundant elements. These several nanocrystal compositions of the Cu3VS4−xSex (x = 0, 1, 2, 3) series were synthesized in the solution phase. The solution-phase synthesis methods allow for the control of particle size and morphology, which conventional solid-state synthesis fails to achieve. Based on experimental band gap characterization via ultraviolet visible spectroscopy,the multinary Copper vanadium chalcogenides possess an intermediate band (IB), making them promising candidates for the absorber layer in solar PV. The optical direct band gap trend shows a decrease with increasing Se content. The IB solar cells are designed to incorporate an energy band that is partially filled with electrons within the forbidden bandgap of a semiconductor, in order to provide a large photogenerated current while maintaining a high output voltage. A detailed material characterization of these new multinary nanocrystals was conducted using x-ray diffraction, photoluminescence spectroscopy, and scanning electron microscopy to further understand the structure-property relation of these nanocrystals.
A new single molecule 4-difluoro-4-bora-3a,4a-diaza-s-indacene (BODIPY) dyedesigned to conjugate to the peripheral amines of proteins have been synthesized. Thesynthetic route taken toward these dyes along with their characterization by 1 H NMR willbe described. This dye offers extraordinary absorption and emission properties withinthe far-visible region of the electromagnetic spectrum. Details of their spectroscopicproperties along with first attempts to conjugate this dye to proteins will be presented.
Connect Four is a popular game in which two players take turns placing game chips down an upright six-by-seven grid. The goal is to get four chips in a line (vertically, horizontally, or diagonally). Connect Four has been extensively studied and it has been determined that the player who moves first has an advantage. We studied an upright three-by-three grid in which the objective is to get three chips in a line. We also considered other games on three-by-three grids such as Tic-Tac-Toe and Dawson’s Chess.