Both students and faculty members in Colgate’s Department of Mathematics engage in research at the forefront of the field. View recent publications by department faculty members as well as theses from students majoring in mathematics.

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## Faculty Publications

This is a continuously updated list of the most recent publications from mathematics departmental faculty members.

- Joe P. Chen, Spectral decimation of the magnetic Laplacian on the Sierpinski gasket: Solving the Hofstadter-Sierpinski butterfly

With Ruoyu Guo*Communications in Mathematical Physics* - Silvia Jiménez Bolaños, On the Dimension Reduction in Prestrained Elasticity
*Advances in Mathematical Sciences: AWM Research Symposium* - Rob Davis, Further combinatorics and applications of two-toned tilings

With Greg Simay*Fibonacci Quarterly* - Will Cipolli, Economic inequality shapes the relationship between globalization and prejudice

With N. Caluori and J. Brown-Iannuzzi*Social Psychological and Personality Science* - Aaron Robertson, Down the large rabbit hole
*Rocky Mountain Journal of Mathematics* - Jens Christensen, New Atomic Decompositions of Bergman Spaces on Bounded Symmetric Domains

With G. Ólafsson*Journal of Geometric Analysis* - Joe P. Chen, Laplacian growth and sandpiles on the Sierpinski gasket: limit shape universality and exact solutions

With Jonah Kudler-Flam*Annales de l’Institut Henri Poincaré (D) Combinatorics, Physics and their Interactions* - Aaron Robertson, Zero-sum analogues of van der Waerden's theorem on arithmetic progressions
*Journal of Combinatorics* - Joe P. Chen, Internal DLA on Sierpinski gasket graphs

With Wilfried Huss, Ecaterina Sava-Huss, and Alexander Teplyaev

in*Analysis and Geometry on Graphs and Manifolds*, M. Keller et al. (Eds.),*London Mathematical Society Lecture Notes* - Silvia Jiménez Bolaños, Relative bending energy for weakly prestrained shells

With Anna Zemlyanova*Rocky Mountain Journal of Mathematics* - Joe P. Chen, Fractal AC circuits and propagating waves on fractals

With Eric Akkermans, Gerald Dunne, Luke G. Rogers, and Alexander Teplyaev

in*Analysis, Probability, and Mathematical Physics on Fractals*, P. Alonso-Ruiz et al. (Eds.) - Tom Tucker, Asymmetrizing trees of maximum valence 2
^{ℵ0}

With I. Imrich*Monatshefte fur Mathematik* - Tom Tucker, Recurrences for genus polynomials of linear sequences of graphs

With Y. Chen, J. Gross, and T. Mansour*Mathematica Slovaca*

- Dan Saracino, On criteria for rook equivalence of Ferrers boards

With J. Bloom*European Journal of Combinatorics* - Rob Davis, Descents and des-Wilf equivalence of permutations avoiding certain non-classical patterns

With C. Bielawa, D. Greeson, and Q. Zhou*Involve* - Jens Christensen, Coorbits for projective representations with an application to Bergman spaces

With A. Darweesh and G. Olafsson*Monatshefte für Mathematik* - Will Cipolli, We are all Broncos: Hockey, tragedy, and the formation of Canadian identity

With L. Kennedy, D. silva, and M. Coelho*Sociology of Sport Journal* - Rob Davis, A polyhedral proof of a wreath product identity

With B. Sagan*Journal of Combinatorics* - Will Cipolli, Racial biases in officers’ decisions to frisk are amplified for Black people stopped among groups leading to similar biases in searches, arrests, and use of force

With E. Cooley, N. Hester, L. Rivera, K. Abrams, J. Pagan, S. Sommers, and K. Payne*Social Psychological and Personality Science* - Rob Davis, A product formula for the normalized volume of free sums of lattice polytopes

With T. Chen*Advances in Algebra: Proceedings of the Southern Regional Algebra Conference 2017* - Will Cipolli, Complex intersections of race and class: Among social liberals, learning about White Privilege reduces sympathy, increases blame, and decreases external

attributions for White people struggling with poverty

With E. Cooley, J. Brown-Iannuzzi, and R. Lei*Journal of Experimental Psychology: General*

- Tom Tucker, Partial duality for ribbon graphs: Distributions

With J. Gross and T. Mansour*European Journal of Combinatorics* - Tom Tucker, The distinguishing index of maps

With M. Pilsniak*European Journal of Combinatorics* - Tom Tucker, Distinguishing graphs with maximum valence 3

With W. Imrich, S. Huning, J. Kloas, and H. Schreiber*Electronic Journal of Combinatorics* - Tom Tucker, Finite groups acting on all but finitely many closed surfaces: Kulkarni revisited
*Acta Mathematica Universitatis Comeniana*

- Aaron Robertson, The Determination of 2-Color Zero-Sum Generalized Schur Numbers

With B. Roy and S. Sarkar*Integers* - Aaron Robertson, Zero-Sum Generalized Schur Numbers
*Journal of Combinatorics and Number Theory* - Jens Christensen, Atomic decompositions of mixed norm Bergman spaces on tube type domains
*Contemporary Mathematics* - Joe P. Chen, From non-symmetric particle systems to non-linear PDEs on fractals

With M. Hinz and A. Teplyaev*Stochastic Partial Differential Equations and Related Fields* - Ahmet Ay, Noise in the Vertebrate Segmentation Clock Is Boosted by Time Delays but Tamed by Notch Signaling

With S. Keskin, G. Devakanmalai, S. Kwon, H. Vu, Q. Hong, Y. Lee, M. Soltani, A. Singh, and E. Özbudak*Cell Reports* - Dan Saracino, Rook and Wilf equivalence of integer partitions

With J. Bloom*European Journal of Combinatorics* - Will Cipolli, Cellular metabolism and oxidative stress as a possible determinant for longevity in small breed and large breed dogs

With A. Jimenez, J. Winward, and U. Beattle*PLoS ONE* - Joe P. Chen, Regularized Laplacian determinants of self-similar fractals

With A. Teplyaev and K. Tsougkas*Letters in Mathematical Physics* - Gunog Seo, Sensitivity of the dynamics of the general Rosenzweig–MacArthur model to the mathematical form of the functional response: a bifurcation theory approach

With G. Wolkowicz*Journal of Mathematical Biology* - Gunog Seo, Bifurcations and global dynamics in a toxin-dependent aquatic population model

With Q. Huang and C. Shan*Mathematical Biosciences* - Ahmet Ay, Modeling Strengthens Molecular Link between Circadian Polymorphisms and Major Mood Disorders

With A. Liberman, L. Halitjaha, and K. Ingram*Journal of Biological Rhythms* - Will Cipolli, A copula approach for testing independence between Poisson distributed variables

With R. Bower, J. Hussey, J. Zhang, J. Quattro, and J. Hardin*Communications in Statistics: Case Studies, Data Analysis, and Applications* - Tom Tucker, Calculating genus polynomials with string operations and matrices

With J. Gross, I. Khan, and T. Mansour*Ars Mathematica Contemporanea* - Tom Tucker, Graphical Frobenius representations

With K. Doyle and M. Watkins*Journal of Algebraic Combinatorics*

- Will Cipolli, The paradox of group mind: 'People in a group' have more mind than 'a group of people'

With E. Cooley, B. Payne, C. Cameron, A. Berger, and K. Gray*Journal of Experimental Psychology: General* - Evelyn Hart, The equivalence of two methods: finding representatives of non-empty Nielsen classes

With H. Vu*Bulletin of the Belgian Mathematical Society-Simon Stevin* - Joe P. Chen, The moving particle lemma for the exclusion process on a weighted graph

Electronic Communications in Probability - Ahmet Ay, Construction of signaling pathways with RNAi data and multiple reference networks

With M. Alim, M. Hasan, M. Thai, and T. Kahveci*IEEE/ACM Transactions on Computational Biology and Bioinformatics* - Joe P. Chen, Wave Equation on One-Dimensional Fractals with Spectral Decimation and the Complex Dynamics of Polynomials

With U. Andrews, G. Bonik, R. Martin, and A. Teplyaev*Journal of Fourier Analysis and Applications* - Will Cipolli, In search of a five-star: The centrality of body discourses in the scouting of high school football players

With D. Silva and R. Bower*Sociology of Sport Journal* - Ahmet Ay, Shifts in bird migration timing in North American long-distance and short-distance migrants are associated with climate change

With J. Zaifman, D. Shan, and A. Jimenez*International Journal of Zoology* - Joe P. Chen, Stabilization by noise of a ℂ2-valued coupled system

With L. Ford, D. Kielty, R. Majumdar, H. McCain, D. O'Connell, and F. Shum*Stochastics & Dynamics* - Jens Christensen, New atomic decompositions for Bergman spaces on the unit ball

With K. Grochenig and G. Olafsson*Indiana University Mathematics Journal* - Ahmet Ay, Circadian clock model supports molecular link between PER3 and human anxiety

With A. Liberman, S. Kwon, H. Vu, A. Filipowicz, and K. Ingram*Nature Scientific Reports* - Silvia Jiménez Bolaños, Derivation of the Navier slip and slip length for viscous flows over a rough boundary

With B. Vernescu*Physics of Fluids* - Ahmet Ay, Differential DNA level regulation by alternatively designed molecular mechanisms: A mathematical modeling approach

With N. Yildirim, M. Aktas, S. Ozcan, and E. Akbas*In Silico Biology* - Jens Christensen, Surjectivity of mean value operators on noncompact symmetric spaces

With F. Gonzalez and T. Kakehi*Journal of Functional Analysis* - Ahmet Ay, WORMSPREAD: An Individual-based Model of Invasive Earthworm Population Dynamics

With G. Armstrong, A. Mahmood, A. Nugent, S. Dexter, E. Hutto, and T. McCay*Computational Ecology and Software* - Dan Schult, Synchronization dynamics on the picosecond timescale in coupled Josephson junction neurons

With K. Segall, M. LeGro, S. Kaplan, O. Svitelskiy, S. Khadka, P. Crotty*Physical Review E* - Tom Tucker, Bipartite polyhedral maps on closed surfaces are 3-distinguishable with few exceptions

With S. Negami*Graphs and Combinatorics* - Tom Tucker, Valence partitioned genus polynomials and their application to generalized dipoles

With J. Gross and T. Mansour*Australasian Journal of Combinatorics* - Tom Tucker, Distinguishing Cartesian products of countable graphs

With E. Estaji, W. Imrich, R. Kalinowski, and M. Pilsniak*Discussiones Mathematicae Graph Theory*

- Dan Saracino, The 2-color Rado number of x1 + x2+ · · · + xn = y1 + y2 + · · · + yk
*Ars Combinatoria* - Ahmet Ay, Molecular basis for chronotype and time-of-day effects on decision-making

With K. Ingram, S. Kwon, K. Woods, S. Escobar, M. Gordon, I. Smith, I. Bearden, A. Filipowicz, and K. Jain*Nature Scientific Reports* - Will Cipolli, Computationally tractable approximate and smoothed Polya trees

With T. Hanson*Statistics and Computing* - Dan Saracino, Pattern avoidance for set partitions à la Klazar

With Jonathan Bloom*Discrete Mathematics and Theoretical Computer Science* - Evelyn Hart, Algorithms for Nielsen type periodic numbers of maps with remnant on surfaces with boundary and on bouquets of circles II

With P. Heath and E. Keppelmann*Fundamenta Mathematicae* - Will Cipolli, Bayesian nonparametric multiple testing

With T. Hanson and A. McLain*Computational Statistics and Data Analysis* - Ahmet Ay, Mutant screen report: microarray analysis of gene expression in S. cerevisiae kap108delta mutants upon addition of oxidative stress

With K. Belanger, N. Larson, J. Kahn, and D. Tkachev*G3: Genes | Genomes | Genetics* - Joe P. Chen, Singularly continuous spectrum of a self-similar Laplacian on the half-line

With A. Teplyaev*Journal of Mathematical Physics* - Dan Saracino, Proofs and generalizations of a homomesy conjecture of J. Propp and T. Roby

With J. Bloom and O. Pechenik*Discrete Mathematics* - Aaron Robertson, A probabilistic threshold for monochromatic arithmetic progressions
*Journal of Combinatorial Theory Series A* - Jens Christensen, Sampling in Euclidean and non-Euclidean domains: a unified approach

Chapter in*Sampling Theory, a Renaissance*(Birkhauser) - Ahmet Ay, Identifying the topology of signaling networks from partial RNAi data

With R. Yuanfang, Q. Wang, M. Hasan, and T. Kahveci*BMC Systems Biology* - Will Cipolli, A comparison of three diagnostic tests for diagnosis of carpal tunnel syndrome using latent class analysis

With J. Fowler and T. Hanson*Journal of Bone and Joint Surgery* - Aaron Robertson, Intermingled ascending wave m-sets

With C. Cremin, W. Daniel, and Q. Xiang*Discrete Mathematics* - Tom Tucker, Iterated claws Have real-rooted genus polynomials

With J. Gross, T. Mansour, and D. Wang*Ars Mathematica Contemporanea* - Tom Tucker, Root geometry of polynomial sequences II: Type (1,0)

With J. Gross, T. Mansour, and D. Wang*Journal of Mathematical Analysis and Applications* - Tom Tucker, Cyclic complements and skew morphisms of groups

With M. Conder and R. Jajcay*Journal of Algebra* - Tom Tucker, Euclidean symmetry of closed surfaces immersed in 3-space

With U. Leopold*Topology and Its Applications* - Tom Tucker, Combinatorial conjectures that imply log-concavity of graph genus polynomials

With J. Gross, T. Mansour, and D. Wang*European Journal of Combinatorics* - Tom Tucker, Root geometry of polynomial sequences I: type (0,1)

With J. Gross, T. Mansour, and D. Wang*Journal of Mathematical Analysis and Applications*

- Silvia Jiménez Bolaños, Nonlinear neutral inclusions: assemblages of coated ellipsoids

With B. Vernescu*Royal Society Open Science* - Ahmet Ay, Hierarchical decomposition of dynamically evolving regulatory networks

With D. Gong and T. Kahveci*BMC Bioinformatics* - Ahmet Ay, Genome-wide errant targeting by Hairy

With K. Kok, L. Li, and D. Arnosti*eLife* - Joe P. Chen, Spectral dimension and Bohr's formula for Schrodinger operators on unbounded fractal spaces

With S. Molchanov and A. Teplyaev*Journal of Physics A: Mathematical and Theoretical* - Ahmet Ay, Construction of signaling networks with incomplete RNAi data

With Q. Wang, Y. Ren, M. Hasan, and T. Kahveci*Bioinformatics and Biomedicine* - Gunog Seo, Existence of multiple limit cycles in a predator–prey model with arctan(ax) as functional response

With G. Wolkowicz*Communications in Mathematical Analysis* - Ahmet Ay, Multiple reference networks improve accuracy of signaling network construction

With M. Alim, M. Hasan, M. Thai, and T. Kahveci*Computational Biology and Health Informatics* - Dan Saracino, The 2-color Rado number of x1+x2+· · ·+xm-1 = axm, II
*Ars Combinatoria* - Ahmet Ay, Diurnal preference predicts phase differences in expression of human peripheral circadian clock genes

With A. Ferrante, D. Gellerman, K. Woods, A. Filipowicz, K. Jain, N. Bearden, and K. Ingram*Journal of Circadian Rhythms* - Joe P. Chen, Entropic repulsion of Gaussian free field on high-dimensional Sierpinski carpet graphs

With B. Ugurcan*Stochastic Processes and their Applications* - Ahmet Ay, Mathematical modeling deciphers the benefits of alternatively-designed conserved activatory and inhibitory gene circuits

With N. Wilner and N. Yildirim*Molecular BioSystems* - Tom Tucker, Log-concavity of the genus polynomials for Ringel ladders

With J. Gross and T. Mansour*Electronic Journal of Graph Theory and Its Applications* - Tom Tucker, Log-concavity of combinations of sequences and applications to genus distributions

With J. Gross and T. Mansour*Siam Journal of Discrete Mathematics* - Tom Tucker, Infinite motion and 2-distinguishability of graphs and groups

With W. Imrich, S. Smith, and M. Watkins*Journal of Algebraic Combinatorics*

- Dan Saracino, A simple bijective proof of the shape-Wilf-equivalence of the patterns 231 and 312

With J. Bloom*Journal of Combinatorial Mathematics and Combinatorial Computing* - Ahmet Ay, Dynamics matter: differences and similarities between alternatively designed regulatory mechanisms

With N. Yildirim*Molecular BioSystems* - Dan Saracino, The 2-color Rado number of x1+x2+· · ·+xm-1 = axm
*Ars Combinatoria* - Aaron Robertson, Ramsey Theory on the Integers, Second edition

With B. Landman*American Mathematical Society* - Ahmet Ay, Spatial gradients of protein-level time delays set the pace of the traveling segmentation clock waves

With J. Holland, A. Sperlea, G. Devakanmalai, S. Knierer, S. Sangervasi, A. Stevenson, and E. Ozbudak*Development* - Dan Schult, Phase-flip bifurcation in a coupled Josephson junction neuron system

With K. Segall, S. Guo, P. Crotty, and M. Miller*Physica B: Condensed Matter* - Gunog Seo, Spatial dynamics of an age-structured population model of Asian Clams

With J. Fang, K. Lan, and J. Wu*SIAM Journal on Applied Mathematics* - Jens Christensen, Multi-window Gabor frames in amalgam spaces

With R. Balan, I. Krishtal, K. Okoudjou, and J. Romero*Mathematical Research Letters* - Ahmet Ay, Network-based prediction of cancer under genetic storm

With D. Gong and T. Kahveci*Cancer Inform* - Joe P. Chen, Periodic billiard orbits of self-similar Sierpinski carpets

With R. Niemeyer*Journal of Mathematical Analysis and Applications* - Tom Tucker, Log-concavity of genus distributions for ring-like families of graphs

With J. Gross and T. Mansour*European Journal of Combinatorics* - Tom Tucker, Log-concavity of the genus polynomials for a sequence of cubic Halin graphs

With J. Gross and T. Mansour*Journal of Combinatorics* - Tom Tucker, On the maximum number of independent elements in configurations of points and lines

With T. Pisanski*Discrete Computational Geometry* - Tom Tucker, Two notes on surface symmetry

in*Rigidity and Symmetry,*editors: R. Connelly, A. Weiss, and W. Whiteley*Fields Institute Communications,*Springer - Tom Tucker, Regular Cayley maps for cyclic groups

With M. Conder*Transactions of the American Mathematical Society* - Tom Tucker, Representativity for Cayley maps

With C. Stevens and X. Zha*European Journal of Combinatorics*

## Student Publications

Undergraduate research assistants at Colgate are often granted coauthor credits on the publications resulting from their research. See below for a sample of recent publications with undergraduate coauthors. Students are marked in bold.

- On the distribution of monochromatic complete subgraphs and arithmetic progression

Aaron Robertson, William Cipolli, and**Maria Dascalu***Experimental Mathematics,*2021

- Spectral decimation of the magnetic Laplacian on the Sierpinski gasket: Solving the Hofstadter-Sierpinski butterfly, Joe P. Chen and
**Ruoyu Guo***Communications in Mathematical Physics,*2020 - Laplacian growth and sandpiles on the Sierpinski gasket: limit shape universality and exact solutions, Joe P. Chen and
**Jonah Kudler-Flam***Annales de l’Institut Henri Poincaré (D) Combinatorics, Physics and their Interactions,*2020 - Noise in the Vertebrate Segmentation Clock Is Boosted by Time Delays but Tamed by Notch Signaling

S. Keskin, G. S. Devakanmalai,**Son Bin Kwon**,**Ha Vu**, Q. Hong, Q., …, Ahmet Ay and E. M. Özbudak, E. M.*Cell Reports*, 2018 - Modeling Strengthens Molecular Link between Circadian Polymorphisms and Major Mood Disorders
**Amanda Liberman**,**Lumi Halitjaha**, Ahmet Ay, and K. K. Ingram*Journal of Biological Rhythms*, 2018 - Synchronization dynamics on the picosecond time scale in coupled Josephson junction neurons

K. Segall,**M. LeGro**, S. Kaplan, O. Svitelskiy, S. Khadka, P. Crotty, and D. Schult,*Physical Review E*, 2017 - Circadian clock model supports molecular link between PER3 and human anxiety
**Amanda Liberman**,**Son Bin Kwon**,**Ha Vu**, A. Filipowicz, Ahmet Ay, and K. K. Ingram*Scientific Reports*, 2017 - WORMSPREAD: an individual-based model of invasive earthworm population dynamics.
**George Armstrong**,**Ahsan Mahmood**, A. Nugent, A. Dexter, E. Hutto, T.S. McCay, and Ahmet Ay*Computational Ecology and Software*, 2017 - Shifts in bird migration timing in North American long-distance and short-distance migrants are associated with climate change.
**Jay Zaifman**,**Daoyang Shan**, Ahmet Ay, and A. Jimenez*International Journal of Zoology,*2017 - The equivalence of two methods: finding representatives of non--empty Nielsen classes

Evelyn Hart and**Ha Vu***Bulletin of the Belgian Mathematical Society-Simon Stevin*, 2017 - Molecular insights into chronotype and time-of-day effects on decision-making

K. K. Ingram, Ahmet Ay,**Son Bin Kwon**, K. Woods, et al*Scientific Reports*, 2016 - Mutant Screen Report: Microarray Analysis of Gene Expression in S. cerevisiae kap108Δ Mutants Upon Addition of Oxidative Stress

K. D. Belanger,**Nate Larson**,**Jonathan Kahn**, D. Tkachev, and Ahmet Ay*G3: Genes, Genomes, Genetics*, 2016 - Intermingled ascending wave m-sets

Aaron Robertson,**Caitlin Cremin**,**Will Daniel**, and**Quer Xiang***Discrete Mathematics*, 2016 - Mathematical modeling deciphers the benefits of alternatively-designed conserved activatory and inhibitory gene circuits.

Ahmet Ay,**Natalie Wilner**, and N. Yildirim*Molecular BioSystems*, 2015 - Spatial gradients of protein-level time delays set the pace of the traveling segmentation clock waves.

Ahmet Ay,**Jack Holland**,**Adriana Sperlea**, G. S. Devakanmalai, S. Knierer, S. Sangervasi, ... and E. M. Özbudak, E. M.*Development*, 2014 - Phase-flip bifurcation in a coupled Josephson junction neuron system

Kenneth Segall,**Siyang Guo**, Patrick Crotty, Dan Schult, and**Max Miller**,*Physica B: Condensed Matter*, 2014 - Short-lived Her proteins drive robust synchronized oscillations in the zebrafish segmentation clock

Ahmet Ay, S. Knierer,**Adrian Sperlea**,**Jack Holland**, and E. M. Özbudak*Development*, 2013 - A primer on thermodynamic-based models for deciphering transcriptional regulatory logic.

J. M. Dresch,**Megan Richards**, and Ahmet Ay*Biochimica et Biophysica Acta (BBA)-Gene Regulatory Mechanisms*, 2013

## Student Theses

To be eligible for graduation with a major from the Department of Mathematics, each student must submit a thesis stemming from a semester in one of the department’s research seminars. Samples of recent thesis titles are listed below.

*Maximal Distance Sets in 2-dimensional Euclidean Space*by Elżbieta Bołdyriew**(Faculty Advisor:**Aaron Robertson)*An Application of Page Rank*by Matt Chistolini**(Faculty Advisor:**Silvia Jimenez Bolanos)*The Modernization of Search Engines and Social Network Influence*by Samantha Gould**(Faculty Advisor:**Silvia Jimenez Bolanos)*Exploring the GCD of the Entries of a Matrix and Corresponding Actions, Orbits, and Stabilizers in R*by Amogh Gupta^{3}**(Faculty Advisor:**Rob Davis)*Clusterings in Analyzing Top Female Tennis Ranking*by Candice He**(Faculty Advisor:**Silvia Jimenez Bolanos)*1/3 - 2/3 Conjecture*by Ruiting Hu**(Faculty Advisor:**Rob Davis)*Word Recognition With a Neural Network*by Noah Jackson**(Faculty Advisor:**Silvia Jimenez Bolanos)*3*x*3 Magic Squares and the Existence of Magic Triangles*by Nicole Joyal**(Faculty Advisor:**Aaron Robertson)*Distribution of the Average Shortest Path Length in Random Graphs*by Jack Koefoed**(Faculty Advisor:**Aaron Robertson)*Investigation of Standard Young Tableaux*by Rishi Lohar**(Faculty Advisor:**Rob Davis)*Multivariate Ehrhart Theory: Dilating Polytopes With Separate Variables*by Sean Mandrick**(Faculty Advisor:**Rob Davis)*Exploring Multiples of a Real Number*by Sydney Maxson**(Faculty Advisor:**Aaron Robertson)*Sums of Powers: Divisibility, Formulation, and a Matrix Method*by Mohammad Omair**(Faculty Advisor:**Aaron Robertson)*Genetic Algorithms for Cluster Analysis: A Comparison With K-means and Guassian Mixture Models*by Delaney Scheiern**(Faculty Advisor:**Silvia Jimenez Bolanos)*The m-distance Chromatic Number and Graph Colorings*by Michael Shea**(Faculty Advisor:**Rob Davis)*Tetration on Real Numbers*by Xiyu (Cici) Wu**(Faculty Advisor:**Rob Davis)*Compartmental Model for Covid-19 With Sojourn Time Cycle*by Yang Ye**(Faculty Advisor:**Silvia Jimenez Bolanos)*Knight's Tour on a Torus*by Yuxuan Zhang**(Faculty Advisor:**Rob Davis)

*The Non-uniqueness of Entropy of Probability Distributions*by Ethan Ackerman**(Faculty Advisor:**Aaron Robertson)*Solving a Generalization of a Putnam Problem*by Hannah Bailey**(Faculty Advisor:**Aaron Robertson)*Modeling a Social Network for Music Recommendation*by Jacob Berkofsky**(Faculty Advisor:**Dan Schult)*Eigenvalues of a Path, Its Complement, and the Associated Adjacency Matrices*by Julia Blackwell**(Faculty Advisor:**Aaron Robertson)*Predicting Retweets on Twitter Via Linear Modeling*by Lucy Bonin**(Faculty Advisor:**Dan Schult)*Evaluating MLB Single Season Accolades via Batter vs. Pitcher Interactions*by Robbie Chalker**(Faculty Advisor:**Dan Schult)*SealNet: Harbor Seal Face Recognition*by Ryan Dunham and Daniel Gathogo**(Faculty Advisor:**Ahmet Ay)*Finding Derivatives Without the Use of Limits*by Katherine Ellsworth**(Faculty Advisor:**Aaron Robertson)*An Analysis of k-Path Centrality*by TianShu Fan**(Faculty Advisor:**Dan Schult)*The Propagation and Clustering of Laughter - An Agent-Based Model*by Sarah Gans**(Faculty Advisor:**Dan Schult)*Analyzing NBA Player Value Through Network Analysis*by Matt Gentile**(Faculty Advisor:**Dan Schult)*The Louvain Method of Community Detection: Implementation and Application*by Yanjun Gong**(Faculty Advisor:**Dan Schult)*Using Contour Integration for Infinite Sums*by Kelly Goodwin**(Faculty Advisor:**Aaron Robertson)*Constructing Derivative Rules for Positive Integers*by Malachi Jones**(Faculty Advisor:**Aaron Robertson)*The Louvain Method for Community Detection in Python*by Yuanrun Li**(Faculty Advisor:**Dan Schult)*Using Markov Chains to Imitate Authors' Styles*by Kayla Logar**(Faculty Advisor:**Aaron Robertson)*The Score Test for Independence of Zero-Inflated Bivariate Poisson Variables*by Megan Maloney**(Faculty Advisor:**Dan Schult)*Optimizing the Determination of a Rectangle's Coordinates*by Philip Matos**(Faculty Advisor:**Aaron Robertson)*Modeling the Circadian Clock to Display Link Between SNPs and Seasonal Affective Disorder*by Meghan Minturn**(Faculty Advisor:**Ahmet Ay)*Finding Solutions to Initial Conditions of a 5*x*5 Gameboard With Tiles Linked by Adjacency*by Tyler Nelson**(Faculty Advisor:**Aaron Robertson)*Graph and SubGraph Isomorphism Checking - VF2++*by Alexandra Newlon**(Faculty Advisor:**Dan Schult)*Exploring a Set of Matrices*by Brooke Perisho**(Faculty Advisor:**Aaron Robertson)*A Support Vector Machine (SVM) Model for Predicting Mood Disorders with Improved Accuracy and Uncovering Epistatic Interactions*by Arda Berk Sagir (joint with Connor Madalo)**(Faculty Advisor:**Ahmet Ay)*Exploring the Impacts of More Complex Reactions on Smoldering Combustion*by Carly Schwartz**(Faculty Advisor:**Dan Schult)*WORMMIGRATE: Invasive earthworm population dynamics and migration modeled using MATLAB and Leslie Matrices*by Jordan Tockstein (joint with Kelly Goodwin)**(Faculty Advisor:**Ahmet Ay)*Network Analysis on the 4,000-foot Mountains in the Adirondack State Park and White Mountain National Forest*by Cortland Troutman**(Faculty Advisor:**Dan Schult)*Dynamics of Non-adiabatic Smolder Waves near Extinction*by Casey White**(Faculty Advisor:**Dan Schult)

*Distribution of Minimum Path Lengths*by Patrick Beljan**(Faculty Advisor:**Aaron Robertson)*Hierarchical Linear Modeling of Hitters in Baseball*by Jake Bensky (**Faculty Adviser**: Dan Schult)*Computerized Proofs of Hypergeometric Identities*by Nicole Brower**(Faculty Advisor:**Aaron Robertson)*The Black-Scholes Option Pricing Model with Time-dependent Volatility and Stochastic Risk-free Rate*by Darren Chen (**Faculty Adviser**: Dan Schult)*Transition from Smoldering to Flaming*by Sheng Chen (**Faculty Adviser**: Dan Schult)*Exploring Equi-Colored Arithmetic Progressions on Equi-Colored Two-Colorings*by Jackson French**(Faculty Advisor:**Aaron Robertson)*Spectral Decimation of the Magnetic Laplacian on the Sierpinski Gasket*by Ruoyu (Tony) Guo (**Faculty Advisor**: Joe Chen)*A Non-trivial Lower Bound for a Van der Waerden-like Function*by Lumbardh Halitjaha**(Faculty Advisor:**Aaron Robertson)*Computational Modeling of Combustion Reactions*by Mingrui Hong (**Faculty Adviser**: Dan Schult)*Mathematics and Music*by Carter Hunt (**Faculty Adviser**: Dan Schult)*Investigating Feynman's Integration Technique*by Sang Kyung (Kathy) Lee**(Faculty Advisor:**Aaron Robertson)*Fingering in Flames*by Liam Moran (**Faculty Adviser**: Dan Schult)*Determining Knight-distance Between Squares on an n x n Chessboard*by Ruchit Shrestha**(Faculty Advisor:**Aaron Robertson)*Discrete Dynamical System Modeling to Solve a Card Trick*by Maddie Srivastava**(Faculty Advisor:**Aaron Robertson)*Fast Inverse Square Root Algorithm*by Serena Sutaria**(Faculty Advisor:**Aaron Robertson)*Lattice Points on the Surface of n-Spheres for Small n*by Ruiyun Tang**(Faculty Advisor:**Aaron Robertson)*Mathematical Model of Tumor Growth and Treatment*by Caroline Zaworski (**Faculty Adviser**: Dan Schult)*Monte Carlo and Quasi-Monte Carlo Integration*by Saiyang Zhang**(Faculty Advisor:**Aaron Robertson)

*Emulating Neuron Synapses in the Brain*by William J. Boyd (**Faculty Adviser:**Daniel Schult)*Modeling The Influenza Virus on Colgate University’s Campus***Faculty Adviser:**Daniel Schult)*Bursting Patterns of Josephson Junction Neurons*by Ruiyan Tang (**Faculty Adviser:**Daniel Schult)*Josephson Junction Modeling of Neuron Bursting Behavior*by Noah Campbell (**Faculty Adviser:**Daniel Schult)*Using a Small-World Network to Investigate Convergence Patterns in a Mimura-Murray System***Faculty Adviser:**Daniel Schult)*Modeling Language Differentiation Over Social Networks***Faculty Adviser:**Daniel Schult)*STEM persistence in college - An agent-based model*by Julie Nguyen (**Faculty Adviser:**Daniel Schult)*Network Analysis of Persistence of Women in STEM***Faculty Adviser:**Daniel Schult)*Impacts of extracellular potassium and intracellular chloride concentration on epileptic neuronal activity*by Alexandra Krez (**Faculty Adviser:**Daniel Schult)*A Tool for the Visualization of Data Mining Through Coupled Oscillators*by Armando Belardo (**Faculty Adviser:**Daniel Schult)*Voronoi Modeling of Tissue Structure and Cell Regeneration: Perimeter Approach*by Maria Chen, Emily Derozier, and Alexandre Lauretti (**Faculty Adviser:**Silvia Jimenez Bolanos)*Voronoi Modeling of Tissue Structure and Cell Regeneration: Area Approach*by Katie Bushee, Adib Chowdhury, and Emily Gu (**Faculty Adviser:**Silvia Jimenez Bolanos)*Machine Learning: Automated scoring system for short answer responses*by Saw Lin (**Faculty Advisers:**Silvia Jimenez Bolanos and Will Cipolli)*Cancer Classification with Probabilistic Networks*by Ahsan Mahmood and Boris Shou (**Faculty Adviser:**Ahmet Ay)*Pan Cancer Analysis of Ectopic Germline Gene Expression*by Ben Harris (**Faculty Adviser:**Ahmet Ay)*GPU Acceleration in Large Computational Models*by Carlton Yang (**Faculty Adviser:**Ahmet Ay)*Shifts in Bird Migration Timing in North American Long-Distance and Short-Distance Migrants Are Associated with Climate Change*by Jay Zaifman and Daoyang Shan (**Faculty Adviser:**Ahmet Ay)*Modeling Strengthens Molecular Link between Circadian Polymorphisms and Major Mood Disorders*by Amanda Liberman (**Faculty Adviser:**Ahmet Ay)*Regulatory network of the scoliosis-associated genes establishes rostrocaudal patterning of somites in zebrafish*by Ha Vu (**Faculty Adviser:**Ahmet Ay)

*An Investigation of the Abundancy Index of Ten*by Adam Buys**(Faculty Advisor:**Aaron Robertson)*Finding a Class of 4x4 Matrices on which the Rule of Sarrus can be Applied*by Jordan Chervin**(Faculty Advisor:**Aaron Robertson)*Elliptic Curve Cryptography*by Robert Galante**(Faculty Advisor:**Aaron Robertson)*Analysis of a Puck Puzzle*by Kil Hyun Kim**(Faculty Advisor:**Aaron Robertson)*Van der Waerden’s Theorem on Sequences With Interchanging Gap Sizes*by Daoyang Shan**(Faculty Advisor:**Aaron Robertson)*Change-Making Problems In The World of Even Value*by Limin Tang**(Faculty Advisor:**Aaron Robertson)*Schur’s Theorem Over Finite Fields*by Caroline Wardlow**(Faculty Advisor:**Aaron Robertson)*Algorithmic Solution to Rado’s Columns Condition*by Dylan Giustra**(Faculty Advisor:**Aaron Robertson)*Some New Difference Ramsey Numbers*by Jiayang Li**(Faculty Advisor:**Aaron Robertson)*A Classification of Exponents that Form Triangles*by Dan Pucci**(Faculty Advisor:**Aaron Robertson)*On the Non-Uniqueness of Entropy*by Skylar Weber**(Faculty Advisor:**Aaron Robertson)*Looking at Discrete Derivatives for Monomials*by Ames Tardio**(Faculty Advisor:**Aaron Robertson)