Physical Sciences and Mathematics Commons^™

A Stochastic Nonlinear Dynamical System For Smoothing Noisy Eye Gaze Data, Thoa Thieu, Roderick Melnik

School of Mathematical & Statistical Sciences Faculty Publications

In this study, we address the challenges associated with accurately determining gaze location on a screen, which is often compromised by noise from factors such as eye tracker limitations, calibration drift, ambient lighting changes, and eye blinks. We propose the use of an extended Kalman filter (EKF) to smooth the gaze data collected during eye-tracking experiments and systematically explore the interaction of different system parameters. Our results demonstrate that the EKF significantly reduces noise, leading to a marked improvement in tracking accuracy. Furthermore, we show that our proposed stochastic nonlinear dynamical model aligns well with real experimental data and holds …

Land-Use Transitions And Carbon Emissions Of Aquaculture Expansion In The Brazilian Amazon, Felipe S. Pacheco, Sebastian A. Heilpern, Rafael M. Almeida, Suresh A. Sethi, Marcela Miranda, Nicholas Ray, Laura Greenstreet, Joshua Fan, Brendan H. Rappazzo, Marcelo Gomes Da Silva

School of Earth, Environmental, & Marine Sciences Faculty Publications

Accounting for land-use change underlying food sector expansion is critical for conserving ecosystem integrity. This challenge is particularly acute in the Amazon, where the conversion of forests for food production is pronounced and has broad implications for global biodiversity and the cycling of water and carbon. Here, we analyze land-use transitions associated with aquaculture development in the Brazilian Amazon. We found that a 450-fold increase in aquaculture pond area from 1985 to 2022 occurred primarily on pasturelands (87%) but also included wetland conversion (4%) and deforestation (5%). Notably, continued growth can be sustained within already altered landscapes: In Rondônia, the …

Gw240925 And Gw250207: Astrophysical Calibration Of Gravitational Wave Detectors, A. G. Abac, I. Abouelfettouh, F. Acernese, Teviet Creighton, Mario C. Diaz, Raul Alberto Espinosa Perez, J. Lawrence, Francisco Llamas Villarreal, Soma Mukherjee, Gaukhar Nurbek, Volker Quetschke, Miriam Ramos Arevalo, Wenhui Wang

Physics & Astronomy Faculty Publications

GW240925 and GW250207 are two loud gravitational-wave signals from binary black hole coalescences observed with network signal-to-noise ratios ∼32 and ∼69, respectively, by the LIGO Hanford-LIGO Livingston-Virgo network. Gravitational-wave signals from coalescing binaries have characteristic phase and amplitude evolution predicted by general relativity. These signal waveforms, together with measured instrumental calibration uncertainties, are used to infer source parameters. However, for sufficiently loud detections, it is possible to constrain the calibration of the detectors directly using the signals themselves. We present the first informative astrophysical measurements of gravitational-wave detector calibration. For GW240925, we verify the inference of Hanford calibration from the …

Sustainability Challenges And Opportunities In A University Police Fleet: A Case Study Of Idling, Emissions, And Electrification Potential, Van Slusser

School of Political Science, Public Affairs, Legal and Security Studies Faculty Publications

This case study examines fleet sustainability challenges within the University of Texas Rio Grande Valley Police Department, a multicampus public safety agency operating aging gasoline vehicles central to daily patrol and administrative functions. Rising maintenance costs, increased vehicle downtime, and extensive idling created both operational strain and avoidable environmental impacts. Aging internal-combustion vehicles contributed to elevated emissions and fuel consumption, particularly under high-heat conditions and equipment demands typical of campus policing. Telematics monitoring indicated that approximately 48% of total engine-on time consisted of idling, highlighting a substantial source of avoidable fuel use and emissions. The study employed a qualitative case …

Hidden Symmetries Of The Classical 3×3 Magic Square, Vijender Nallapu, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

The classical 3×3 magic square is one of the most famous objects in recreational mathematics. Its defining feature is that every row, every column, and the two main diagonals have the same sum. However, beyond this well-known property, the square contains several hidden symmetries involving rotations, reflections, complementary pairs, parity, and balance around the central entry. In this article, we present an elementary exploration of these symmetries and show how the classical magic square provides a beautiful introduction to mathematical structure and pattern recognition.

Vedic Mathematics And Mental Computation: Fast Multiplication Techniques, Algebraic Foundations, And Historical Perspectives, Rakesh Bhatia, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

Mental computation has fascinated mathematicians, educators, and students for centuries. Various computational techniques allow arithmetic calculations to be performed rapidly without the use of calculators or computers. Among these methods, several popular techniques are associated with what is commonly known as Vedic Mathematics. In this article, we examine a collection of fast multiplication techniques, including multiplication near powers of ten, multiplication by eleven, squaring numbers ending in five, and the vertical-and-crosswise method. For each technique, we provide elementary mathematical explanations based on algebraic identities and place-value representations.

Curious Patterns And Identities Involving Consecutive Integers, Carlo Cattani, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

Consecutive integers exhibit numerous surprising patterns and elegant identities. In this article, we investigate several classical properties involving products, sums, divisibility, perfect squares, cubes, pronic numbers, triangular numbers, sums of squares, and Pythagorean triples. Using only elementary algebra, symmetry arguments, and mathematical induction, we establish a collection of identities that reveal rich connections among these classical topics. The exposition is intended for students, teachers, and recreational mathematicians, illustrating how simple observations about consecutive integers can lead to beautiful mathematical patterns and deeper insights into elementary number theory.

Phenotypic And Biochemical Responses Of High-Yield Tomato Varieties To Salinity And Drought Stress, Shahida Ferdousee, Myung Hwangbo, Md Sakil Arman, Muhammad Abul Kalam Azad, Ajit Ghosh, Jongsun Kim

School of Earth, Environmental, & Marine Sciences Faculty Publications

Abiotic stresses can influence plant growth and productivity by causing physiological, biochemical, molecular, and morphological changes. Salinity and drought are increasing in frequency and intensity because of climate change. Therefore, this study assessed four high-yield tomato cultivars under 150 mM NaCl and 260 mM mannitol treatments to characterize physiological (i.e., chlorophyll level, root/shoot length, and relative water content) and biochemical responses (i.e., GLY I/II and DLDH enzyme activities, proline, and hydrogen peroxide). Results indicated that the four BARI tomato varieties showed genotype- and treatment-specific physiological and biochemical responses rather than a single uniform tolerance pattern. BARI tomato 2 maintained relatively …

The Mathematics Of Calendar Patterns: Day-Of-Week Phenomena, Number Patterns, And Recreational Investigations, Vijender Nallapu, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

Calendars are among the most familiar mathematical structures encountered in everyday life. Beyond their practical use in organizing dates and measuring time, calendars contain a rich collection of numerical patterns, symmetries, and arithmetic relationships. Many of these patterns can be explored using only elementary mathematics, making calendars an attractive subject for recreational investigation and mathematical enrichment.

In this article we examine several mathematical properties arising from the structure of monthly calendars. We investigate arithmetic patterns associated with rows, columns, and rectangular blocks of dates, establish properties of calendar squares, and explore connections with modular arithmetic through day-of-week calculations. We also …

Gwtc-4.0: Constraints On The Cosmic Expansion Rate And Modified Gravitational-Wave Propagation, A. G. Abac, I. Abouelfettouh, Teviet Creighton, Mario C. Diaz, Raul Alberto Espinosa Perez, J. Lawrence, Francisco Llamas Villarreal, Soma Mukherjee, Volker Quetschke, Miriam Ramos Arevalo, Wenhui Wang

Physics & Astronomy Faculty Publications

We analyze data from 142 of the 218 gravitational-wave (GW) sources in the fourth LIGO-Virgo-KAGRA Collaboration (LVK) Gravitational-Wave Transient Catalog (GWTC-4.0) to estimate the Hubble constant H0 jointly with the population properties of merging compact binaries. We measure the luminosity distance and redshifted masses of GW sources directly; in contrast, we infer GW source redshifts statistically through (i) location of features in the compact object mass spectrum and merger rate evolution, and (ii) identifying potential host galaxies in the GW localization volume. Probing the relationship between source luminosity distances and redshifts obtained in this way yields constraints on cosmological parameters. …

A Granularity-Centered Taxonomy Of Personalized Federated Learning, Ei Ei Nyein Chan, Sergei Chuprov, Pretom Roy Ovi, Kamrul Hasan

Computer Science Faculty Publications

Personalized Federated Learning (PFL) has emerged as a key approach to address performance degradation in FL systems under heterogeneous client data. While existing surveys typically categorize PFL methods based on optimization strategies or system-level mechanisms, they often overlook a fundamental question: where is personalization embedded within the model architecture? In this survey, we bridge this knowledge gap and introduce a granularity-centered taxonomy that organizes PFL approaches according to the structural depth of personalization, ranging from head-layer and layer-wise adaptation to model-wise and parameter-wise customization. This novel perspective helps practitioners select appropriate personalization strategies based on model architecture, data heterogeneity, and …

Dry After-Ripening Increases Germination Of Critically Imperilled Physaria Thamnophila (Zapata Bladderpod), Christopher A. Gabler, Jerald T. Garrett

School of Earth, Environmental, & Marine Sciences Faculty Publications

Effective endangered plant conservation and recovery require empirical knowledge of seed dormancy release and responses to post-collection handling, yet such information is lacking for many rare taxa. Physaria thamnophila (Zapata bladderpod; Brassicaceae), a critically imperilled (G1) species endemic to southern Texas, USA, is poorly studied, and basic questions regarding seed storage and germination remain unresolved. We evaluated the effects of short-term cool-storage duration (14–180 d), storage temperature (refrigeration vs. freezing), dry after-ripening and maternal plant identity on germination probability and timing in P. thamnophila. Dry after-ripening and increased cool-storage duration consistently increased germination and shortened germination time, whereas storage temperature …

The 2025 Measles Outbreak In Texas, Tamer Oraby, Martial L. Ndeffo-Mbah

School of Mathematical & Statistical Sciences Faculty Publications

Background: In 2025, Texas experienced its largest measles outbreak in decades, reporting 762 cases by mid-August. Measles is a highly contagious but vaccine-preventable infection transmitted mainly among unvaccinated individuals and capable of causing severe outcomes.

Methods: We investigate counterfactual measles control scenarios based on daycare and school closures and reactive vaccination of infants and children, including mixed interventions. We analyze the 2025 Texas outbreak using an age-structured multi-stage SEIR model formulated as a system of ordinary differential equations. The model is fit to case data using Bayesian inference to estimate the effective reproduction number and generate posterior predictive trajectories under …

Influence Of Transboundary Wildfire Smoke On Fine Particulate Matter Concentrations At South Texas Border Schools, Sai Deepak Pinakana, Kabir Bahadur Shah, Owen Temby, Dawid K. Wladyka, Juan L. Gonzalez, Md Saydur Rahman, Katarzyna Sepielak, Amit U. Raysoni

School of Earth, Environmental, & Marine Sciences Faculty Publications

Exposure to air pollutants in indoor and outdoor school environments poses significant health risks to children due to their heightened vulnerability. Increasing wildfire frequency has intensified transboundary smoke transport, with border communities among the first to experience associated air quality impacts. While the impacts of wildfires on air quality are increasingly recognized through satellite observations and modeling, ground-based observations remain scarce in under-monitored regions. Low-cost air sensors were deployed across schools in the Roma and Rio Grande City areas of Starr County, along the U.S.–Mexico border, for 146-days from November 2023 to April 2024. The raw sensor measurements were corrected …

Human-Centered Electric Vehicle Adoption Framework For Smart Mobility: Modeling Perceived Range And Charging Anxiety As A Psychological Barrier, Fatemeh Nazari, Abolfazl (Kouros) Mohammadian, Thomas Stephens

Civil Engineering Faculty Publications

Electric vehicles (EVs) offer a transformative pathway toward reducing the environmental, economic, and health-related externalities of internal combustion engine vehicles in urban settings. Despite substantial advances in battery technology, charging infrastructure expansion, and supportive policy incentives, EV penetration remains limited which poses challenges for smart and sustainable mobility planning. A critical yet insufficiently modeled barrier to adoption lies in the psychological perceptions surrounding electric driving range and charging reliability, which is commonly framed as “range anxiety,” but more broadly reflecting perceived range and charging anxiety. To address this gap, this study introduces a latent psychological construct capturing individuals’ perceived range …

A Finite Element Model To Analyze Crack-Tip Fields In A Transversely Isotropic Strain-Limiting Elastic Solid, Saugata Ghosh, Dambaru Bhatta, S. M. Mallikarjunaiah

School of Mathematical & Statistical Sciences Faculty Publications

This paper presents a finite element model for the analysis of crack-tip fields in a transversely isotropic strain-limiting elastic body. A nonlinear constitutive relationship between stress and linearized strain characterizes the material response. This algebraically nonlinear relationship is critical as it mitigates the physically inconsistent strain singularities that arise at crack tips. These strain-limiting relationships ensure that strains remain bounded near the crack tip, representing a significant advancement in the formulation of boundary value problems (BVPs) within the context of first-order approximate constitutive models. For a transversely isotropic elastic material containing a crack, the equilibrium equation, derived from the balance …

Greenhouse Gas Flux Response In Biochar- And Compost-Amended Lawn Soils Under Simulated Water Saturation Conditions, Angel Salinas, Chu-Lin Cheng, Engil Pereira, Rafael M. Almeida, James Jihoon Kang

School of Earth, Environmental, & Marine Sciences Faculty Publications

Understanding greenhouse gas emission dynamics in lawn soils is important for improving climate change mitigation strategies in urban and suburban landscapes. In this greenhouse mesocosm study, carbon dioxide (CO2), methane (CH4), and nitrous oxide (N2O) fluxes were measured from 12 turfgrass soil columns arranged in an unreplicated, completely randomized 4 × 3 factorial design. Four amendment treatments (biochar, compost, bio-com [1:1 volume ratio of biochar and compost], and unamended control) were combined with three water-table conditions (full saturation, half saturation, and unsaturated), with a single column representing each treatment combination. Columns were irrigated at 1 cm day−1 for 24 days, …

Why Technical Readiness Is Not Enough: Institutional Barriers To Full Harvest Strategy Adoption In The International Pacific Halibut Commission, Evelyn Roozee, Owen Temby, Gordon M. Hickey

School of Earth, Environmental, & Marine Sciences Faculty Publications

Harvest strategies are increasingly promoted as a mechanism to reduce political discretion and align fisheries management with pre-agreed scientific objectives. While substantial progress has been made in tuna regional fisheries management organizations (RFMOs), non-tuna RFMOs have lagged behind. Existing research has focused primarily on technical modeling challenges, with comparatively limited attention to the governance dynamics shaping adoption. Using the International Pacific Halibut Commission (IPHC) as an instrumental case study, we examine the progress and delays in the development of a harvest strategy policy (HSP) through semi-structured interviews and participant observation. We find that the IPHC successfully addressed commonly cited barriers, …

Bayesian Variable Selection In High-Dimensional Ordinal Quantile Regression Models, Mai Dao, Md. Sakhawat Hossain, Zhuanzhuan Ma

School of Mathematical & Statistical Sciences Faculty Publications

Quantile regression (QR) provides a flexible statistical framework for modeling the entire conditional distribution of the response variable, making it useful for analysis in various fields. Despite its advantages, existing methods for QR often encounter numerical challenges in high-dimensional settings, especially for those with ordinal responses. In this paper, we use a latent-response framework to construct a Bayesian hierarchical model to conduct parameter estimation and variable selection for ordinal QR. Using the asymmetric Laplace working likelihood and the horseshoe prior for the regression coefficients, we obtain the posterior samples to be screened by the sequential two-means clustering process to identify …

A Visitation Grid For Complete Coverage Foraging In Robot Swarms, Arturo Gonzalez, Yifeng Gao, Li Zhang, Qi Lu

Computer Science Faculty Publications

The complete collection of sparse resources in large, unknown environments remains a challenging problem for autonomous robot swarms. Previous studies have shown that a substantial portion of total mission time is consumed during the final stage of collection, where only a small fraction of randomly scattered resources remain. Consequently, many existing swarm foraging algorithms (search and collection) focus on collecting most resources within a limited time window, rather than improving end-stage efficiency for collecting all resources. We propose a grid-based stochastic foraging strategy that explicitly reduces redundant visits and accelerates late-stage collection. The unknown search area is partitioned into a …

Environmental Dna For Endangered Freshwater Mussel Monitoring: A Review On Global Synthesis Of Edna Methods, Challenges, And Innovative Strategies, Mizanur Rahman, Md. Saydur Rahman, Richard J. Kline

School of Earth, Environmental, & Marine Sciences Faculty Publications

Freshwater mussels (family Unionidae) are among the most endangered aquatic species worldwide, making effective monitoring vital for their conservation. Traditional surveys are laborious, time-consuming, and often miss rare or low-density populations. Environmental DNA (eDNA) is a highly sensitive, non-invasive approach for freshwater mussel detection and monitoring; however, uncertainties in ecological interpretation continue to limit its broader application in freshwater biodiversity monitoring. We conducted a systematic review of 49 peer-reviewed studies, identified through an extensive literature search, to assess temporal research trends, methodological advancements, ecological contexts, and regulatory readiness of freshwater mussel eDNA monitoring. Findings show that freshwater mussel eDNA research …

Directed Searches For Gravitational Waves From Ultralight Vector Boson Clouds Around Merger Remnant And Galactic Black Holes During The First Part Of The Fourth Ligo-Virgo-Kagra Observing Run, A. G. Abac, I. Abouelfettouh, Teviet Creighton, Mario C. Diaz, Raul Alberto Espinosa Perez, J. Lawrence, Francisco Llamas Villarreal, Soma Mukherjee, Volker Quetschke, Miriam Ramos Arevalo, Wenhui Wang

Physics & Astronomy Faculty Publications

We present the first directed searches for long-transient and continuous gravitational waves from ultralight vector boson clouds around known black holes (BHs). We use LIGO data from the first part of the fourth LIGO-Virgo-KAGRA observing run. The searches target two distinct types of BHs and use two new semicoherent methods: hidden Markov model (HMM) tracking for the remnant BHs of the mergers GW230814_230901 and GW231123_135430 (referred to as GW230814 and GW231123 in this study) and a dedicated method using the Band Sampled Data (BSD) framework for the galactic BH in the Cygnus X-1 binary system. Without finding evidence of a …

A New Likely Pulsar Binary In 47 Tucanae From Continuum Searches, Thomas Maccarone, Alessandro Paduano, Arash Bahramian, Liliana E. Rivera Sandoval, Jay Strader, James C. A. Miller-Jones, Angiraben D. Mahida, Craig O. Heinke, Laura Chomiuk

Physics & Astronomy Faculty Publications

We present evidence that the X-ray source 47 Tuc W41, long considered to be an X-ray source powered by coronal activity, is actually a redback pulsar binary. The source continually shows LX = 3 × 10³¹ erg s⁻¹ (0.5–10 keV), which is well in excess of the coronal saturation limit for active binaries in quiescence, but is consistent with the intrabinary shock observed in redback pulsars, as is its photon index of Γ = 1.4 ± 0.1. In addition, using deep data from the Australia Telescope Compact Array, we show that W41 is a faint (9.8 ± 1.4μJy …

Deep Neural Networks: A Formulation Via Non-Archimedean Analysis, Wilson A. Zuniga-Galindo

School of Mathematical & Statistical Sciences Faculty Publications

We introduce a new class of deep neural networks (DNNs) with multilayered tree-like architectures. The architectures are codified by using numbers in the ring of integers of non-Archimedean local fields. These rings have a natural hierarchical organization as infinite rooted trees. Natural morphisms on these rings allow us to construct finite multilayered architectures. The new DNNs are robust universal approximators of real-valued functions defined on the mentioned rings. We also show that the DNNs are robust universal approximators of real-valued square-integrable functions defined in the unit interval.

A Machine Learning Approach For Water Quality Assessment In The Lower Rio Grande Valley Watershed, Saika Nowshin Nowrin, Chu-Lin Cheng, Jungseok Ho, Jinwoo An, Fatemeh Nazari

Civil Engineering Faculty Publications

Water quality analysis plays an essential role in maintaining the health and sustainability of river ecosystems, especially in semi-arid regions like the Arroyo Colorado Watershed in South Texas. Since the river is a vital source of water supply for local communities, agriculture, and wildlife, it faces significant challenges and pollution from land use changes, climate variation, and agricultural runoff. Continuous monitoring and assessment of water quality parameters and their temporal variability are essential to ensure the drinking water supply and aquatic ecosystem health. However, comprehensive laboratory-based water quality investigations are often constrained by higher costs, logistical complexity, and limited manpower. …

Iron-Decorated Graphene Nanoplatelets Produced By Atmospheric-Pressure Ferrocene Pyrolysis As Nano-Additives For Cement Mortars, Harutyun Gyulasaryan, Manoj Chhetri, Karen S. Martirosyan, Nelli Muradyan, Hovsep Hoveyan, Manuk Barseghyan, Aram Manukyan

Physics & Astronomy Faculty Publications

This study examines iron-based graphene nanoplatelets (Fe-GNPs), synthesized through a modified ferrocene pyrolysis route, as hybrid nano-additives for cement mortars. The nanomaterial was characterized by scanning electron microscopy, X-ray diffraction, Brunauer–Emmett–Teller surface area analysis, and thermogravimetric analysis, confirming a graphitic carbon network decorated with crystalline α-Fe nanoparticles. Mortars containing 0.001, 0.01, 0.05, and 0.1 wt.% Fe-GNPs, with and without surfactant-assisted ultrasonication, were tested in flexure and compression after 7 and 28 days of curing. The results showed a clear concentration-dependent response, with 0.01 wt.% yielding the highest strength gains. At 28 days, this dosage increased flexural strength by 14.5% without …

Search For Planetary-Mass Ultracompact Binaries Using Data From The First Part Of The Ligo–Virgo–Kagra Fourth Observing Run, A. G. Abac, I. Abouelfettouh, Teviet Creighton, Mario C. Diaz, Raul Alberto Espinosa Perez, J. Lawrence, Francisco Llamas Villarreal, Soma Mukherjee, Volker Quetschke, Miriam Ramos Arevalo, Wenhui Wang

Physics & Astronomy Faculty Publications

We present a search for gravitational waves from inspiraling, planetary-mass ultracompact binaries using data from the first part of the fourth observing run of LIGO, Virgo, and KAGRA. Finding no evidence of such systems, we determine the maximum distance reach for such objects and their merger rate densities. Then, we identify classes of primordial black hole mass distributions for which these rate limits can be translated into relevant constraints on the mass distribution of primordial black holes, assuming that they are all composed of dark matter, in the mass range [10−6,10−3]⁢𝑀⊙. Our constraints for the class of primordial black hole …

Using A Cell Flux Model To Investigate Phytoplankton Growth And Macromolecular Allocation Under Iron Limitation, Margaret Bernish, Meng Gao, Jongsun Kim, Benoit Pasquier

School of Earth, Environmental, & Marine Sciences Faculty Publications

Global biogeochemical models are powerful tools used to interpret observations and empirical data, create hypotheses, and make predictions. Many of these models, however, represent marine microbes as static stoichiometric reactions that convert nutrients into biomass. To better constrain the biological processes that control nutrient cycling in the global ocean, we extend the Cell Flux Model of Phytoplankton to explore the impact of dissolved iron concentration on the allocation of macromolecules and elemental ratios within phytoplankton cells. This model is supported by data obtained from a range of incubation experiments conducted with phytoplankton of varying species and size categories. Model output …

Cultural Traits May Replace Human Mobility Data In Forecasting Covid-19 Mortality: A Deep Learning Approach, Saif Abbas, Tamer Oraby, Michael G. Tyshenko, Samit Bhattacharyya

School of Mathematical & Statistical Sciences Faculty Publications

The COVID-19 pandemic highlighted the need for accurate epidemic forecasting to support public health decision-making. Most existing approaches depend heavily on human mobility data, while largely neglecting population behavior shaped by socio-cultural norms. In this study, we analyze daily COVID-19 mortality and Google mobility data from 72 countries during the first 130 d of the pandemic, a period characterized by high uncertainty and behavioral heterogeneity. In particular, we examine whether Hofstede’s country-level cultural dimensions can serve as latent behavioral forecasters of mortality in lieu of dynamic mobility indicators. Using 100 d for training and 30 d for forecasting, we employ …

Tile-Based Knot Assembly With Celtic!, Divya Bajaj, Ryan Knobel, Juan Manuel Perez, Rene Reyes, Ramiro Santos, Tim Wylie

Computer Science Faculty Publications

In this paper we focus on the intersection of tile assembling systems, edge-matching puzzles, combinatorial games, and knot construction and identity. As a basis, we utilize the game Celtic!, which is a 2-player board game where the goal of the game is to construct knots where one knot uses more of a player’s pieces than the other player over all knots. All pieces must build off an existing knot and a valid knot must be closed. We consider three variations: a 0-player self-assembly variation that deterministically places pieces to form a closed knot of some length, a 1-player puzzle variation …