Research and Publications

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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.

  • Ahmet Ay, Sex- and substance-specific associations of circadian-related genes with addiction in the UK Biobank cohort implicate neuroplasticity pathways
    With A. Khan, M. Minbay, Z. Attia, and K. Ingram
    Brain Sciences
  • Ahmet Ay, Site fidelity of harbor seals in Casco Bay, ME, USA using facial recognition technology: a pilot study
    With L. Horstmyer, H. Do, and K. Ingram
    Biodiversity and Conservation
  • Ahmet Ay, Sex-specific associations between circadian-related genes and depression in UK Biobank participants highlight links to glucose metabolism, inflammation and neuroplasticity pathways
    With M. Minbay, A. Khan, A. Ghasemi, and K. Ingram
    Psychiatry Research
  • Ahmet Ay, Analysis of the gut microbiome in sled dogs reveals glucosamine- and activity-related effects on gut microbial composition
    With D. Wang, W. Russel,  K. De Leon, and K. Belanger
    Frontiers in Veterinary Science
  • Jens Christensen, The snapshot problem for the wave equation
    With F. Gonzalez, T. Kakehi, and J. Wang
    Advances in Mathematics
  • Will Cipolli,  White Americans who perceive themselves to be “last place” in the racial status hierarchy are most drawn to alt-right extremism
    With E. Cooley, J. L. Brown-Iannuzzi, N. Caluori, and N. Elacqua
    Communications Psychology
  • Will Cipolli, Is discrimination widespread or concentrated? Evaluating the distribution of anti-Black discrimination in judicial, hiring, and housing decisions
    With M. J Galvan, G. M. Alvarez, E. Cooley, K. A. Muscatell, and B. K. Payne
    Social Psychology Bulletin
  • Will Cipolli, Cellular metabolic pathways of aging in dogs: Could p53 and SIRT1 be at play?
    With A. G. Jimenez, K. D. Paul, M. Benson, and S. Lalwani
    GeroScience
  • Will Cipolli, Perceptions of falling behind “most White people”: Within-group status comparisons predict fewer positive emotions and worse health over time among White (but not Black) Americans
    With N. Caluori, E. Cooley, J. L. Brown-Iannuzzi, E. Klein, R.F. Lei, and L. E. Philbrook
    Psychological Science
  • Robert Davis, Normalized volumes of type-PQ adjacency polytopes for certain classes of graphs
    With J. Jakovlesk and Q. Pan
    Involve
  • Robert Davis, The integer decomposition property and weighted projective space simplices
    With B. Braun, D. Hanely, M. Lane, and L. Solus
    Integers
  • Robert Davis, Weighted Ehrhart theory: extending Stanley's nonnegativity theorem
    With E. Bajo, J. De Loera, A. Garber, S. Mora, K. Jochemko, and J. Yu
    Advances in Mathematics
  • Robert Davis, Perfectly matchable set polynomials and  h* -polynomials for stable set polytopes of complements of graphs
    With F. Kohl
    Discrete Mathematics
  • Kelly Isham, Expanding the Scalability Horizon of Diameter-3 Networks
    With K. Lahotia, L. Monroe, M. Besta, N. Blach, T. Hoefler, and F. Petrini
    Proceedings of the 36th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA ’24)
  • Zichen Ma Multi-omics integrative analysis for incomplete data using weighted p-value adjustment approaches
    With Z. Zhang, Y.-Y. Ho, S. Yang, J. Habiger, H.-H. Huang, and Y. Huang
    Journal of Agricultural, Biological and Environmental Statistics
  • Zichen Ma An epidemiological modeling framework to inform institutional‑level response to infectious disease outbreaks: a Covid‑19 case study
    With L. Rennert
    Scientific Reports
  • Nicholas Moore, Large-scale circulation reversals explained by pendulum correspondence
    With J. M. Huang
    Journal of Fluid Mechanics
  • Nicholas Moore, A computational framework for the administration of 5-aminovulinic acid before glioblastoma surgery
    With J. Zeng
    Bulletin of Mathematical Biology
  • Aaron Robertson, On the minimum number of monochromatic 2-dimensional Schur triples
    Integers
  • Dan Saracino, Strictly increasing and decreasing sequences in subintervals of words and a conjecture of Guo and Poznanovic
    With J. Bloom
    European Journal of Combinatorics
  • Dan Saracino, Transitive generalized toggle groups containing a cycle
    With J. Bloom 
    Journal of Algebraic Combinatorics
  • Ahmet Ay, Risk for seasonal affective disorder (SAD) Linked to circadian clock gene variants
    With T. Dang, W. Russel, T. Saad, L. Dhawka, and K. Ingram
    Biology
  • Ahmet Ay, Machine learning analyses reveal circadian clock features predictive of anxiety among UK biobank participants
    With C. Ventresca, W. Mohamed, W. Russel, and K. Ingram
    Nature Scientific Reports
  • Ahmet Ay, Feature selection and association rule learning identify risk factors of malnutrition among Ethiopian schoolchildren
    With W. Russell, J. Perry, C. Bonzani, A. Dontino, and B. Taye
    Frontiers in Epidemiology
  • Ahmet Ay, Machine learning and network analysis of the gut microbiome from patients with schizophrenia and non-psychiatric subject controls reveal behavioral risk factors and bacterial interactions
    With D. Wang, W. Russel, Y. Sun, and K. Belanger
    Schizophrenia Research
  • Jens Christensen, Uncertainty principles and differential operators on the weighted Bergman space
    With C. Deng
    Complex Analysis and Operator Theory
  • Will Cipolli, Cellular metabolic pathways of aging in dogs: could p53 and SIRT1 be at play?
    With A.G. Jiménez, K.D. Paul, M. Benson, and S. Lalwani,
    GeroScience
  • Will Cipolli, Racialized sexism: Nonverbal displays of power in workplace settings are evaluated as more masculine when displayed by white (vs. black) women with implications for the expression of ambivalent sexism
    With Q.A.N. Tran, E. Cooley, J.A. Lisnek, and J.L. Brown-Iannuzzi
    Personality and Social Psychology Bulletin
  • Will Cipolli, Fracking Twitter: Utilizing machine learning and natural language processing tools for identifying coalition and causal narratives With A. Pattison, J. Marichal, and C. Cherniakov
    Politics & Policy
  • Will Cipolli, Repurposing a peer-reviewed publication to engage students in statistics: An illustration of study design, data collection, and analysis
    With C. Evans, Z.A. Draper, and J.T. Binfet
    Journal of Statistics and Data Science Education
  • Will Cipolli, Groups amplify the perceived threat and justification for using force against black people protesting for racial equality—especially among social conservatives
    With E. Cooley, J.L. Brown-Iannuzzi, B.K. Payne, and J. Steele
    Group Processes & Intergroup Relations
  • Kelly Isham, Is the number of subrings in Zn of index pe a polynomial in p?
    Communications in Algebra
  • Kelly Isham, In-network Allreduce with multiple spanning trees on PolarFly
    With Kartik Lakhotia, Laura Monroe, Maciej Besta, Torsten Hoefler, and Fabrizio Petrini
    Proceedings of the 35th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA ’23)
  • Silvia Jiménez-Bolaños, Homogenization of a non-linear strongly coupled model of magnetorheological fluids
    With T. Dang, Y. Gorb
    SIAM Journal on Mathematical Analysis
  • Silvia Jiménez-Bolaños, Homogenization for a variational problem with a slip interface condition With Y. Ou SIAM Journal on Applied Mathematics
  • Zichen Ma Genome-wide search algorithms for identifying dynamic gene co-expression via Bayesian variable selection
    With W. Zhang, L. Wang, J. Fan, and Y.-Y. Ho
    Statistics in Medicine
  • Zichen Ma Bayesian variable selection for linear regression with the k-G priors
    With E.P. Fokoue
    Mathematics for Applications
  • Nicholas Moore, Generalization of waving-plate theory to multiple interacting swimmers
    With P.J. Baddoo, A.U. Oza, D.G. Crowdy,
    Communications on Pure and Applied Mathematics
  • Nicholas Moore, Parameter estimation for the truncated KdV model through a direct filter method
    With Hui Su, Feng Bao
    Journal of Machine Learning for Modeling and Computing
  • Nicholas Moore, Stokes flow solutions in infinite and semi-infinite porous channels
    With Francesca Bernardi, Shankararaman Chellam, N.G. Cogan
    Studies in Applied Mathematics
  • Nicholas Moore, How fluid-mechanical erosion creates anisotropic porous media
    With Jake Cherry, Shang-Huan Chiu, Bryan D. Quaife
    Physica D
  • Nicholas Moore, On normal and non-normal wave statistics implied by a canonical–microcanonical Gibbs ensemble of the truncated KdV system
    With H. Sun
    Journal of Statistical Physics
  • Aaron Robertson, Ramsey properties for integer sequences with restricted gaps
    With B. Landman and Q. Robertson
    Moscow J. of Combinatorics and Number Theory
  • Aaron Robertson, Arithmetic progressions, quasi progressions, and Gallai-Ramsey colorings
    with Y. Mao, K. Ozeki, and Z. Wang
    J. Combinatorial Theory, Series A
  • Aaron Robertson, Monochromatic strictly ascending waves and permutation pattern waves
    with B. Landman
    Adv. in Applied Math
  • Dan Schult, A Superconducting synapse exhibiting spike-timing dependent plasticity
    With Ken Segall, Cheranjeev Purmessur, Anthony D’Addario
    Applied Physics Letters
  • Dan Schult, Biologically realistic behaviors from a superconducting neuron model
    With Patrick Crotty, Ken Segall
    IEEE Transactions on Applied Superconductivity
  • Ahmet Ay, Gene copy number and negative feedback differentially regulate transcriptional variability of segmentation clock genes.
    With O. Q. Zinani, K. Keseroğlu, S. Dey, A. Singh, and E. M. Özbudak
    iScience
  • Will Cipolli, ‘Essential for the soul’?: leisure as a flashpoint during COVID-19 lockdowns in Ontario, Canada.
    With M. Norman, D. Silva, and L. Kennedy
    Annals of Leisure Research
  • Will Cipolli, Race, Ambivalent Sexism, and Perceptions of Situations When Police Shoot Black Women.
    With J.L. Brown-Iannuzzi, E. Cooley, and S. Mehta
    Social Psychological and Personality Science
  • Will Cipolli, Beliefs That White People Are Poor, Above and Beyond Beliefs That Black People Are Poor, Predict White (But Not Black) Americans’ Attitudes Toward Welfare Recipients and Policy.
    With E. Cooley, J. L. Brown-Iannuzzi, R. F. Lei, and L. E. Philbrook
    Personality and Social Psychology Bulletin
  • Robert Davis, Facets and facet subgraphs of adjacency polytopes.
    With Tianran Chen and Evgeniia Korchevskaia
    Discrete Applied Mathematics
  • Robert Davis, State Polytopes Related to Two Classes of Combinatorial Neural Codes.
    Advances in Applied Mathematics
  • Robert Davis, A toric deformation method for solving Kuramoto equations. 
    With Tianran Chen
    Nonlinear Dynamics
  • Robert Davis, Computing Volumes of Adjacency Polytopes via Draconian Sequences.
    With Tianran Chen
    The Electronic Journal of Combinatorics
  • Kelly Isham, An algorithm for counting arcs in higher-dimensional projective space.
    Finite Fields and Their Applications
  • Kelly Isham, PolarFly: A Cost-Effective and Flexible Low-Diameter Topology.
    With K. Lakhotia, M. Besta, L. Monroe, P. Iff, T. Hoefler, F. Petrini
    International Conference for High Performance Computing, Networking, Storage and Analysis (Supercomputing '22)
  • Silvia Jiménez-Bolaños, Bloch waves in high contrast electromagnetic crystals
    With R. Lipton, R. Viator, and A. Adili
    ESAIM: M2AN, 2022
  • Silvia Jiménez-Bolaños, Global Gradient Estimate for a Divergence Problem and Its Application to the Homogenization of a Magnetic Suspension
    With T. Dang and Y. Gorb
    Research in Mathematics of Materials Science. Association for Women in Mathematics Series, 2022
  • Zichen Ma, Flexible copula model for integrating correlated multi-omics data from single-cell experiments. 
    With S. W. Davis and Y.-Y. Ho
    Biometrics
  • Zichen Ma, Effectiveness and protection duration of Covid-19 vaccines and previous infection against any SARS-CoV-2 infection in young adults. 
    With L. Rennert, C. McMahan, and D. Dean
    Nature Communications
  • Zichen Ma, Covid-19 vaccine effectiveness against general SARS-CoV-2 infection from the omicron variant: A retrospective cohort study.
    With L. Rennert, L., C. McMahan, and D. Dean
    PLoS Global Public Health
  • Nicholas Moore, Morphological attractors in natural convective dissolution.
    With J.M. Huang
    Physical Review Letters
  • Nicholas Moore, Predicting convection configurations in coupled fluid–porous systems.
    With M. McCurdy and X. Wang
    Journal of Fluid Mechanics
  • Nicholas Moore, On Normal and Non-Normal Wave Statistics Implied by a Canonical–Microcanonical Gibbs Ensemble of the Truncated KdV System.
    With H. Sun
    Journal of Statistical Physics
  • Nicholas Moore, How fluid-mechanical erosion creates anisotropic porous media.
    With Jake Cherry, Shang-Huan Chiu, and Bryan D. Quaife
    Physica D
  • Gabriel Sosa Castillo, MultiRees Algebras of Strongly Stable Ideals.
    With Selvi Kara and Kuei-Nuan Lin
    Collectanea Mathematica
  • Tom Tucker, Asymmetrizing cost and density for vertex-transitive cubic graphs
    With W. Imrich, T. Lachman, and G. M. Wiegel
    Art of Discrete and Applied Mathematics (ADAM)
  • Tom Tucker, The GFR problem and a theorem of Godsil
    With M.D.E. Conder
    Art of Discrete and Applied Mathematics (ADAM)
  • Ahmet Ay, Pattern discovery in multilayer networks
    With Y. Ren, A. Sarkar, P. Veltri, A. Dobra and T. Kahveci
    IEEE/ACM Transactions on Computational Biology and Bioinformatics
  • Ahmet Ay, Pairing of segmentation clock genes drives robust pattern formation
    With O. Q. Zinani, K. Keseroğlu and E. M. Özbudak, E. M.
    Nature
  • Aaron Robertson,  Fundamentals of Ramsey Theory
    CRC Press
  • Silvia Jiménez Bolaños, Homogenization of Nondilute Suspension of Viscous Fluid with Magnetic Particles
    With T. Dang and Y. Gorb
    SIAM Journal on Applied Mathematics
  • Joe P. Chen, Higher order hydrodynamics and equilibrium fluctuations of interacting particle
    With F. Sau
    Markov Processes and Related Fields
  • Will Cipolli, The Instagram/Facebook ban on graphic self‐harm imagery: A sentiment analysis and topic modeling approach
    With H. Smith
    Policy & Internet
  • Will Cipolli, Using Metacognitive Training with Kinesiology Students 
    With C. Davlin-Pater, L.S. Dunn, R. Bower, and S. Biddle
    Journal of Occupational Therapy Education
  • Joe P. Chen, Asymptotic behavior of density in the boundary-driven exclusion process on the Sierpinski gasket
    With P. Gonçalves
    Mathematical Physics, Analysis, and Geometry
  • Will Cipolli, The devil we know and the angel that did not fly: An examination of devil/angel shift in Twitter fracking “debates” in NY 2008–2018
    With A. Pattison and J. Marichal
    Review of Policy Research
  • Jens Christensen, New Atomic Decompositions of Bergman Spaces on Bounded Symmetric Domains
    With G. Ólafsson

    Journal of Geometric Analysis
  • Will Cipolli, Cellular metabolism and IL-6 concentrations during stimulated inflammation in small and large dog breeds’ primary fibroblasts cells, as they age
    With A. G. Jimenez,  C. J. Downs, and S. Lalwani
    Journal of Experimental Biology
  • Silvia Jiménez Bolaños, Dimension reduction for thin films prestrained by shallow curvature
    With M. Lewicka
    Proceedings of the Royal Society A
  • Will Cipolli, Investigating the health consequences for White Americans who believe White Americans are wealthy
    With E. Cooley, J. L. Brown-Iannuzzi, R. F. Lei, L. E. Philbrook, and S. E. McKee
    Social Psychological and Personality Science
  • Will Cipolli, The policy implications of feeling relatively low versus high status within a privileged group
    With E. Cooley, J. L. Brown-Iannuzzi, R. F. Lei, and L. E. Philbrook
    Journal of Experimental Psychology: General
  • Tom Tucker, Groups acting with almost all signatures
    With M. Carvacho, J. Paulus and A. Wootton
    Journal of Pure and Applied Algebra
  • Tom Tucker, Enumerating graph embeddings and partial-duals by genus and euler genus
    With J.  Gross
    Enumerative Combinatorics and Applications
  • Tom Tucker, Partial duality for ribbon graphs, II Partial-twuality polynomials, monodromy, and computations
    With J.  Gross and T. Mansour
    European Journal Combinatorics
  • Tom Tucker, Partial duality for ribbon graphs, III a Gray code algorithm for enumeration
    With J.L. Gross and T. Mansour
    Journal of Algebraic Combinatorics
  • Tom Tucker, Orientation-reversing Euclidean symmetry of closed  surfaces immersed in 3-space
    With Undine Leopold
    Polytopes and Discrete Geometry
  • Tom Tucker, Genera of polyhedral embeddings of cubic graphs
    With G. Brinkman and N. van  Cleemput
    Discrete Math and Theoretical Computer Science
  • 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
  • Will Cipolli, Who gets to vote? Racialized mental images of legitimate and illegitimate voters
    With J.L. Brown-Iannuzzi, E. Cooley, and B. K. Payne
    Social Psychological and Personality Science
  • Aaron Robertson,  Down the large rabbit hole
    Rocky Mountain Journal of Mathematics
  • 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 2ℵ0
    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
  • Tom Tucker, Genus polynomials for ladder-like sequences of graphs
    With J.  Gross and T. Mansour
    Journal of Algebraic Combinatorics
  • Tom Tucker, Observations and answers to questions about edge-transitive maps
    With Marston Conder and Isabel Holm
    Art of Discrete and Applied Mathematics
  • Ahmet Ay, Characterizing building blocks of resource constrained biological networks
    With Y. Ren, A. Dobra, and T. Kahveci  
    BMC Bioinformatics
  • 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
  • Will Cipolli, Supervised learning via smoothed Polya trees
    With T. Hanson
    Advances in Data Analysis and Classification
  • 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
  • Gabriel Sosa Castillo, MultiRees Algebras and Toric Dynamical Systems
    With David Cox and Kuei-Nuan Lin
    Proceeding of the American Mathematical Society
  • 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
  • Will Cipolli, The score test for independence of two marginal Poisson variables
    With R. Bower, J.R. Hussey, J. Zhang, J. Quattro, B. Muhling, and J. W. Hardin
    Communications in Statistics: Case Studies, Data Analysis and Applications
  • 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

 

Faculty Grants

This is a continuously updated list of current and recent grants awarded to members of the mathematics department.

  • Nicholas Moore, New Models to Characterize and Predict Rare Events in Complex Physical Systems
    Office of Naval Research
  • Kelly Isham, Exploring the Mathematics of Large-scale Computer Network Design: Toward Zettascale
    With K. Lakhotia (Intel) and L. Monroe (Los Alamos National Lab)
    Colgate Picker Interdisciplinary Science Institute
  • Dan Schult, Sparse Arrays for Scientific Python.
    With Stéfan van der Walt and Jarrod Millman
    Chan Zuckerberg Initiative
  • Kelly Isham, Mathematical Aspects of Network Design for Post-Exascale Systems.
    With PI Laura Monroe
    Los Alamos National Lab LDRD reserve grant
  • Nicholas Moore, Erosion, Transport, and Dispersion in Granular and Porous Media.
    With Bryan Quaife
    National Science Foundation
  • Rob Davis, Collaborative Research: A convex geometry and homotopy approach for power-flow equations
    National Science Foundation
  • Silvia Jiménez Bolaños, RUI: Multiscale Methods, Singular Limits, and Spectral Problems Related to Materials Science
    National Science Foundation
  • Joe P. Chen, Stochastic Dynamics on Large-Scale Networks
    National Science Foundation
  • Will Cipolli, How radicalization became the dominant framework for understanding terrorism
    With D. Silva
    Social Science and Humanities Research Council of Canada
  • Dan Schult, Sustained Code and Community Development for NetworkX
    With S. Mridul and J. Millman
    Chan Zuckerberg Institute
  • Will Cipolli, Why does rich = White and poor = Black in the minds of United States' citizens? Race-based class assumptions and their consequences for increasing racial resentment and race-related health disparities in the United States
    With E. Cooley, L. Philbrook,  J. Brown-Iannuzzi, and R. Lei
    Colgate Picker Interdisciplinary Science Institute
  • Will Cipolli, The Data Analysis + Consultation Network
    With J. Finnell
    Central New York Library Resources Council

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.
 

  • Uncertainty principles and differential operators on the weighted Bergman space
    J. Christensen and C. Deng
    Complex Analysis and Operator Theory, 2023
  • Fracking Twitter: Utilizing machine learning and natural language processing tools for identifying coalition and causal narratives
    W. Cipolli, A. Pattison, J. Marichal, and C. Cherniakov
    Politics & Policy, 2023
  • Groups amplify the perceived threat and justification for using force against black people protesting for racial equality—especially among social conservatives
    W. Cipolli, E. Cooley, J.L. Brown-Iannuzzi, B.K. Payne, and J. Steele
    Group Processes & Intergroup Relations, 2023
  • A Superconducting synapse exhibiting spike-timing dependent plasticity
    D. Schult, K. Segall, C. Purmessur, and A. D’Addario
    Applied Physics Letters, 2023
  • Effect of different masses, ages, and coats on the thermoregulation of dogs before and after exercise across different seasons
    A. G. Jimenez, K. Paul, A. Zafar, and Ahmet Ay
    Veterinary Research Communications, 2022
  • Machine Learning Analyses Reveal Circadian Features Predictive of Risk for Sleep Disturbance
    R. Overton, A. Zafar, Z. Attia, Ahmet Ay, and K. K. Ingram
    Nature and Science of Sleep, 2022
  • Low circadian amplitude and delayed phase are linked to Seasonal Affective Disorder (SAD)
    L. Dhawka, Y. Cha, Ahmet Ay, K. K. Ingram
    Journal of Affective Disorders Reports, 2022
  • Helicobacter pylori (H. pylori) risk factor analysis and prevalence prediction: a machine learning-based approach
    V. Tran, T. Saad, M. Tesfaye, S. Walelign, M. Wordofa, D. Abera, K. Desta, A. Tsegaye, Ahmet Ay, and B. Taye
    BMC Infectious Diseases, 2022
  • Machine learning-based risk factor analysis and prevalence prediction of intestinal parasitic infections using epidemiological survey data
    A. Zafar, Z. Attia, M. Tesfaye, S. Walelign, M. Wordofa, D. Abera, K. Desta, A. Tsegaye, Ahmet Ay, and B. Taye, 
    PLoS Neglected Tropical Diseases, 2022
  • SEALNET: Facial recognition software for ecological studies of harbor seals
    Z. Birenbaum, H. Do, L. Horstmyer, H. Orff, K. Ingram, and Ahmet Ay 
    Ecology and Evolution, 2022
  • Machine learning and expression analyses reveal circadian clock features predictive of anxiety. 
    A. Zafar, R. Overton, Z. Attia, Ahmet Ay and K. Ingram
    Scientific Reports, 2022
  • Why Every Leader Needs to Worry About Toxic Culture
    D. Sull, C. Sull, Will Cipolli, and C. Brighenti
    MIT Sloan Management Review, 2022
  • Scaling with body mass and age in glycolytic enzymes of domestic dogs With M. R. Wynkoop, S. Lalwani, Will Cipolli, and A.G. Jimenez
    Veterinary Research Communications, 2022
  • A Case for Nonparametrics
    R. Bower, J. Hager, C. Cherniakov, S. Gupta, and Will Cipolli
    The American Statistician, 2022
  • Effects of metformin, rapamycin, and resveratrol on cellular metabolism of canine primary fibroblast cells isolated from large and small breeds as they age
    A. G. Jimenez, S. Lalwani, and Will Cipolli
    GeroScience, 2021
  • Surface boulder banding indicates Martian debris-covered glaciers formed over multiple glaciations
    J. S. Levy, C. I. Fassett, J. W. Holt, R. Parsons, Will Cipolli, T. A. Goudge, M. Tebolt, L. Kuentz, J. Johnson, F. Ishraque, B. Cvijanovich, and Ian Armstrong
    Proceedings of the National Academy of Sciences, 2021
  • 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
  • ANCA: Alignment-Based Network Construction Algorithm
    K. Chow, A. Sarkar, R. Elhesha, P. Cinaglia, Ahmet Ay and T. Kahveci
    IEEE/ACM Transactions on Computational Biology and Bioinformatics, 2019
  • Regulatory network of the scoliosis-associated genes establishes rostrocaudal patterning of somites in zebrafish
    S. Keskin, M. F. Simsek, H. T. Vu, C. Yang, S. H. Devoto, Ahmet Ay, and E. M. Özbudak
    iScience, 2019
  • 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. Recent thesis titles and student authors are listed below.
 

  1. Optimizing Vocabulary Retention: Analyzing Repeated Learning and Its Impact on Memory Curves by Jiaying Bai (Faculty Advisor: Gunog Seo)
  2. The Hilbert Series of Toric Ideals Associated to Principally Generated Borel Ideals by Dennis Belotserkovskiy (Faculty Advisor: Kelly Isham)
  3. Numerical Methods for the LWR Traffic Model by Jackson Carter (Faculty Advisor: Nick Moore)
  4. Edge-disjoint Spanning Trees of Product Graphs by Sophia Child (Faculty Advisor: Kelly Isham)
  5. Mathematically Modeling Circadian Rhythms: Exploring the Potential Effects of Light by Caroline Devine (Faculty Advisor: Gunog Seo)
  6. Optimal Control Theory and Applications to Jet Plane Landing Trajectories by Carter Gordon (Faculty Advisor: Nick Moore)
  7. Centrality Measures for the Richardson Arms Race Model by PJ Horoszewski (Faculty Advisor: Nick Moore)
  8. Mathematics in Motion: Exploring Butterfly Wing Patterns Through Reaction-Diffusion Models by Amy Jasso (Faculty Advisor: Gunog Seo)
  9. Herd Behavior and the Dynamics of Financial Bubbles: Understanding Market Instability by Avery Johnson (Faculty Advisor: Gunog Seo)
  10. Mathematical Modeling of Drug Synergy and Resistance Evolution in Cancer Growth by Jenna Lacy (Faculty Advisor: Gunog Seo)
  11. Extending a Fishery Model with Nonlinear Demand to Include Maximum Sustainable Yield by Kyle LeClair (Faculty Advisor: Gunog Seo)
  12. Analysis of Overdrafting and Finite Difference Modeling of Subsidence in Confined Aquifer Systems by Pierce Leclerc (Faculty Advisor: Gunog Seo)
  13. A Markov-LSTM Neural Network Model for Stock Price Prediction by Zhuoyuan (Justin) Li (Faculty Advisor: Gunog Seo)
  14. A Dynamical Systems Approach to Public Opinion Dynamics by Sam Mikesell (Faculty Advisor: Nick Moore)
  15. Comparing Ranking Methods for Soccer Teams: Markov Chains vs. Neural Networks by James Njoroge (Faculty Advisor: Nick Moore)
  16. Modeling the Behavior of Animals in Groups: Flocking by Molly Pritchard (Faculty Advisor: Nick Moore)
  17. Astrological Prediction Conducted by Hybridized Naïve Bayesian and Logistic Regression Models for STEM/non-STEM Job Prediction by Jing (Yvette) Qian (Faculty Advisor: Gunog Seo)
  18. Maximizing Crossword Grids by Abigail Schnitzer (Faculty Advisor: Kelly Isham)
  19. An Exceedingly Brief Overview of Infinitesimal Calculus by Paul Schulze (Faculty Advisor: Kelly Isham)
  20. Linked In: An Investigation Into the Importance and Thrill of Network Analysis by Michael Senehi (Faculty Advisor: Kelly Isham)
  21. An Exploration of Discrete Dynamical Systems in Elementary and Chaotic Dynamics by Tajveer Singh Dhesi (Faculty Advisor: Kelly Isham)
  22. An Exploration of Strict Pandigital Numbers by Sophie Smyth (Faculty Advisor: Kelly Isham)
  23. Critical Groups: Exploring the Algebra of Chip-Firing Games on Graphs by Marisa Zarcone (Faculty Advisor: Kelly Isham)
  1. Hair Animation Using the Follow the Leader Method by Kahyla Cocchia (Faculty Advisor: Silvia Jimenez Bolanos)
  2. Novel Algorithms to Sample the TKdV Gibbs Measure in Search of Rogue Waves by Brendan Foerster (Faculty Advisor: Nick Moore)
  3. An Exploration of Generating Functions by Samay Gupta (Faculty Advisor: Joe Chen)
  4. Understanding the Sensitivity Theorem by Dean Kardas (Faculty Advisor: Joe Chen)
  5. Bayesian Statistics, Copulas, and Survival Analysis by Chang Liu (Faculty Advisor: Silvia Jimenez Bolanos)
  6. The Random Harmonic Series: Distribution and Density by Jenna Mapley (Faculty Advisor: Joe Chen)
  7. Attempting to Accurately Rank MMA Fighters with the PageRank Algorithm by Gannon Odierno (Faculty Advisor: Silvia Jimenez Bolanos)
  8. The Algebraic Magic behind Sampling Algorithms for Independence Models by Aranya Pal (Faculty Advisor: Joe Chen)
  9. Understanding the Mathematics of Cloaking by Ryan Ruan (Faculty Advisor: Silvia Jimenez Bolanos)
  10. Derived Voltage Graphs by Omshi Samal (Faculty Advisor: Joe Chen)
  11. Network Analysis of United States Metropolitan Internal Migration by Alina Vu (Faculty Advisor: Silvia Jimenez Bolanos)
  1. Cracking the Code of Addiction: Revealing Risk through Machine Learning and Network Analysis of Polymorphisms in HPAAxis and Circadian Rhythm Genes by Ziad Attia (Faculty Advisor: Ahmet Ay)
  2. Enumerating Possible Lattice Paths by Brian Buys (Faculty Advisor: Rob Davis)
  3. A Non-Homogeneous Markov Chain Model for NBA Games by Kartik Devpura (Faculty Advisor: Silvia Jimenez Bolanos)
  4. Properties of Matrices with Constant Diagonals Above and Below the Main Diagonal by Joel Diaz (Faculty Advisor: Rob Davis)
  5. Modeling and Forecasting on Day-Ahead Electricity Market Using ARIMA-GARCH and LSTM by Yvonne Ding (Faculty Advisor: Silvia Jimenez Bolanos)
  6. Neural Networks and the Blues: Using Deep Learning to Investigate the Association between Circadian SNPs and Depression by Hieu Do (Faculty Advisor: Ahmet Ay)
  7. Modeling Passenger Rail Ridership on Intercity Routes by Mitch Duerr (Faculty Advisor: Silvia Jimenez Bolanos)
  8. Modeling the Term Structure in a Negative Interest Rate Environment by Partait Kabore (Faculty Advisor: Silvia Jimenez Bolanos)
  9. Game Theory: Investigating Winnable Sets by Stephanie Skura (Faculty Advisor: Rob Davis)
  10. Total Difference Chromatic Numbers of Graphs and its Relation to Other Labeling Types by Gunes Tiryaki (Faculty Advisor: Rob Davis)
  11. Pattern Avoidance in Lattice Path Enumeration by Tedi Totojani  (Faculty Advisor: Rob Davis)
  12. Computational Algebraic Geometry by Wayne Wang  (Faculty Advisor: Rob Davis)
  13. Romantic Mathematical Model by Dominique Yozzi (Faculty Advisor: Silvia Jimenez Bolanos)
  14. Subconcussive Brain Injuries Sustained During American Football Alter Gut Microbiome Diversity and Composition by Aziz Zafar (Faculty Advisor: Ahmet Ay)
  15. A Mathematical Model For 5-ALA Transport and Distribution in Glioblastoma by Emma Zeng (Faculty Advisor: Nick Moore)
  1. Expected Length of the Cop-Robber Game with Added Random Movement by Giancarlo Arcese (Faculty Advisor: Gabe Sosa Castillo)
  2. Wavelet Analysis of the Labor Market by Austin Beers (Faculty Advisor: Jens Christensen)
  3. Predicting Stunting and Thinness in Ethiopian Schoolchildren Using Machine Learning Classification by Claire Bonzani (Faculty Advisor: Ahmet Ay)
  4. Individual-Based Modeling of COVID-19 at Colgate University by Emily Carter (Faculty Advisor: Jens Christensen)
  5. A SEICR model for COVID-19 in China by Lihui Chen (Faculty Advisor: Jens Christensen)
  6. Some Properties of the Convolution of Fibonacci Numbers by Tarik Cigeroglu (Faculty Advisor: Gabe Sosa Castillo)
  7. Network Analysis on Machine Learning-Discovered Significant Genes Associated with Colorectal Cancer and KLF4 by Emily Clark (Faculty Advisor: Ahmet Ay)
  8. Asymmetric Hales-Jewett Numbers by Nathan Conlon (Faculty Advisor:  Aaron Robertson)
  9. Analysis of Directional Grids by Nicholas Coeytaux (Faculty Advisor: Aaron Robertson)
  10. Generating Uncertainty Principles by Christoper Deng  (Faculty Advisor: Jens Christensen)
  11. The Stochastic Evolution of Open Quantum Systems by Nick DiBrita (Faculty Advisor: Dan Schult)
  12. Modular Applications of Fourier Analysis by Greta Ferdinand (Faculty Advisor: Aaron Robertson)
  13. An Exposition of Modern Cryptography: A Tough Subject to Crack by Andrew Ferrante (Faculty Advisor: Gabe Sosa Castillo)
  14. Pursuit Trajectory for a Fox Chasing a Rabbit Moving in a Straight, Parabolic and Circular Motion by Federico Aguilera Gonzalez (Faculty Advisor: Gabe Sosa Castillo)
  15. Applications of Dynamic Mode Decomposition and Modern Portfolio Theory in Financial Markets by John Gunnin (Faculty Advisor: Dan Schult)
  16. A Three Step Reaction Model of Smoldering and Flaming Combustion by Emma Hart (Faculty Advisor: Dan Schult)
  17. Investigating Atmospheric Tracers with Dynamic Mode Decomposition by Fairuz Ishraque (Faculty Advisor: Dan Schult
  18. Representations of the Natural Numbers Using Box Arrangements of Lengths at Most 3 by Joakim Jakovleski (Faculty Advisor: Gabe Sosa Castillo)
  19. Content-Based Book Recommendation Systems: Comparing TF-IDF, Word Vectors, Paragraph Vectors and Transformers by Vani Kanoria (Faculty Advisor: Dan Schult)
  20. ARIMA Model for Forecasting the Wage Differential Associated with Education by Dipesh Khati (Faculty Advisor: Jens Christensen)
  21. Broadcast Domination in Rectangular Grids by Miya Kim (Faculty Advisor: Gabe Sosa Castillo)
  22. Smoldering and Flaming Model by Elena Larocco (Faculty Advisor: Dan Schult)
  23. Modeling Extinction for Non-Adiabatic Opposed-Flow Smolder by Chloe Malinowski (Faculty Advisor: Dan Schult)
  24. The Quantum Bit and Quantum Key Exchange by Nam Nguyen (Faculty Advisor: Aaron Robertson)
  25. Elementary Properties of Some Integer Sequences by Qizhe Pan (Faculty Advisor: Aaron Robertson)
  26. Eventown and Oddtown with Even and Odd Intersections by Jayvion Queen (Faculty Advisor: Aaron Robertson)
  27. Modeling Sectarianism:  Analyzing the Dynamics of the Arab Spring in Syria by Akshara Ramaseshan (Faculty Advisor: Dan Schult)
  28. Vermilion: Efficient Simulation of Delayed Stochastic Systems by Taz Saad (Faculty Advisor: Ahmet Ay)
  29. Machine Learning Algorithms with Application to Green Energy Economics by Isabelle Sapountzis (Faculty Advisor: Dan Schult)
  30. Optimus Prime: The Circle Method and Infinite Three-Term Arithmetic Progressions of Primes by Rachel Schaaf (Faculty Advisor:  Aaron Robertson)
  31. Welfare Under Excess Supply and Demand in a Ride-Hailing Market by Ayush Sinha (Faculty Advisor: Dan Schult)
  32. Homogenizing a Grid of Lightbulbs: A Dive into an Interesting Coloring Problem by Joseph Smith (Faculty Advisor: Gabe Sosa Castillo)
  33. Deciphering the Perception of Charisma as a Cognitive Mechanism through Analysis of EEG Data with Machine Learning Techniques by Cole Ventresca (Faculty Advisor: Ahmet Ay)
  34. Predicting Schizophrenia from Human Gut Microbiome by Dong Wang (Faculty Advisor: Ahmet Ay)
  35. Predicting Stock Market Trends Using Random Forests by Jessica Zhao (Faculty Advisor: Jens Christensen)
  1. Maximal Distance Sets in 2-dimensional Euclidean Space by Elżbieta Bołdyriew (Faculty Advisor: Aaron Robertson)
  2. An Application of Page Rank by Matt Chistolini (Faculty Advisor: Silvia Jimenez Bolanos)
  3. Decoding and Predicting Charismatic and Non-charismatic Perceptions Using Machine Learning on EEG Data by Isabel Gephart (Faculty Advisor: Ahmet Ay)
  4. The Modernization of Search Engines and Social Network Influence by Samantha Gould (Faculty Advisor: Silvia Jimenez Bolanos)
  5. Exploring the GCD of the Entries of a Matrix and Corresponding Actions, Orbits, and Stabilizers in R3 by Amogh Gupta (Faculty Advisor: Rob Davis)
  6. Clusterings in Analyzing Top Female Tennis Ranking by Candice He (Faculty Advisor: Silvia Jimenez Bolanos)
  7. 1/3 - 2/3 Conjecture by Ruiting Hu (Faculty Advisor: Rob Davis)
  8. Word Recognition With a Neural Network by Noah Jackson (Faculty Advisor: Silvia Jimenez Bolanos)
  9. 3 x 3 Magic Squares and the Existence of Magic Triangles by Nicole Joyal  (Faculty Advisor: Aaron Robertson)
  10. Distribution of the Average Shortest Path Length in Random Graphs by Jack Koefoed (Faculty Advisor: Aaron Robertson)
  11. Investigation of Standard Young Tableaux by Rishi Lohar (Faculty Advisor: Rob Davis)
  12. Multivariate Ehrhart Theory: Dilating Polytopes With Separate Variables by Sean Mandrick (Faculty Advisor: Rob Davis)
  13. Exploring Multiples of a Real Number by Sydney Maxson  (Faculty Advisor: Aaron Robertson)
  14. Sums of Powers: Divisibility, Formulation, and a Matrix Method by Mohammad Omair  (Faculty Advisor: Aaron Robertson)
  15. Genetic Algorithms for Cluster Analysis: A Comparison With K-means and Guassian Mixture Models by Delaney Scheiern (Faculty Advisor: Silvia Jimenez Bolanos)
  16. The m-distance Chromatic Number and Graph Colorings by Michael Shea (Faculty Advisor: Rob Davis)
  17. Tetration on Real Numbers by Xiyu (Cici) Wu (Faculty Advisor: Rob Davis)
  18. Compartmental Model for Covid-19 With Sojourn Time Cycle by Yang Ye (Faculty Advisor: Silvia Jimenez Bolanos)
  19. Knight's Tour on a Torus by Yuxuan Zhang (Faculty Advisor: Rob Davis)
  1. The Non-uniqueness of Entropy of Probability Distributions by Ethan Ackerman (Faculty Advisor: Aaron Robertson)
  2. Solving a Generalization of a Putnam Problem by Hannah Bailey  (Faculty Advisor: Aaron Robertson)
  3. Modeling a Social Network for Music Recommendation by Jacob Berkofsky (Faculty Advisor: Dan Schult)
  4. Eigenvalues of a Path, Its Complement, and the Associated Adjacency Matrices by Julia Blackwell  (Faculty Advisor: Aaron Robertson)
  5. Predicting Retweets on Twitter Via Linear Modeling by Lucy Bonin (Faculty Advisor: Dan Schult)
  6. Evaluating MLB Single Season Accolades via Batter vs. Pitcher Interactions by Robbie Chalker (Faculty Advisor: Dan Schult)
  7. SealNet: Harbor Seal Face Recognition by Ryan Dunham and Daniel Gathogo (Faculty Advisor: Ahmet Ay)
  8. Finding Derivatives Without the Use of Limits by Katherine Ellsworth  (Faculty Advisor: Aaron Robertson)
  9. An Analysis of k-Path Centrality by TianShu Fan (Faculty Advisor: Dan Schult)
  10. The Propagation and Clustering of Laughter - An Agent-Based Model by Sarah Gans (Faculty Advisor: Dan Schult)
  11. Analyzing NBA Player Value Through Network Analysis by Matt Gentile (Faculty Advisor: Dan Schult)
  12. The Louvain Method of Community Detection: Implementation and Application by Yanjun Gong (Faculty Advisor: Dan Schult)
  13. Using Contour Integration for Infinite Sums by Kelly Goodwin  (Faculty Advisor: Aaron Robertson)
  14. Constructing Derivative Rules for Positive Integers by Malachi Jones (Faculty Advisor: Aaron Robertson)
  15. The Louvain Method for Community Detection in Python by Yuanrun Li (Faculty Advisor: Dan Schult)
  16. Using Markov Chains to Imitate Authors' Styles by Kayla Logar (Faculty Advisor: Aaron Robertson)
  17. The Score Test for Independence of Zero-Inflated Bivariate Poisson Variables by Megan Maloney (Faculty Advisor: Dan Schult)
  18. Optimizing the Determination of a Rectangle's Coordinates by Philip Matos (Faculty Advisor: Aaron Robertson)
  19. Modeling the Circadian Clock to Display Link Between SNPs and Seasonal Affective Disorder by Meghan Minturn (Faculty Advisor: Ahmet Ay)
  20. Finding Solutions to Initial Conditions of a 5 x 5 Gameboard With Tiles Linked by Adjacency by Tyler Nelson (Faculty Advisor: Aaron Robertson)
  21. Graph and SubGraph Isomorphism Checking - VF2++ by Alexandra Newlon (Faculty Advisor: Dan Schult)
  22. Exploring a Set of Matrices by Brooke Perisho (Faculty Advisor: Aaron Robertson)
  23. 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)
  24. Exploring the Impacts of More Complex Reactions on Smoldering Combustion by Carly Schwartz (Faculty Advisor: Dan Schult)
  25. WORMMIGRATE: Invasive earthworm population dynamics and migration modeled using MATLAB and Leslie Matrices  by Jordan Tockstein (joint with Kelly Goodwin) (Faculty Advisor: Ahmet Ay)
  26. 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)
  27. Dynamics of Non-adiabatic Smolder Waves near Extinction by Casey White (Faculty Advisor: Dan Schult)

 

  1. Distribution of Minimum Path Lengths by Patrick Beljan (Faculty Advisor: Aaron Robertson)
  2. Hierarchical Linear Modeling of Hitters in Baseball by Jake Bensky (Faculty Adviser: Dan Schult)
  3. Computerized Proofs of Hypergeometric Identities by Nicole Brower  (Faculty Advisor: Aaron Robertson)
  4. The Black-Scholes Option Pricing Model with Time-dependent Volatility and Stochastic Risk-free Rate by Darren Chen (Faculty Adviser: Dan Schult)
  5. Transition from Smoldering to Flaming by Sheng Chen (Faculty Adviser: Dan Schult)
  6. Exploring Equi-Colored Arithmetic Progressions on Equi-Colored Two-Colorings by Jackson French  (Faculty Advisor: Aaron Robertson)
  7. Spectral Decimation of the Magnetic Laplacian on the Sierpinski Gasket by Ruoyu (Tony) Guo (Faculty Advisor: Joe Chen)
  8. A Non-trivial Lower Bound for a Van der Waerden-like Function by Lumbardh Halitjaha (Faculty Advisor: Aaron Robertson)
  9. Computational Modeling of Combustion Reactions by Mingrui Hong (Faculty Adviser: Dan Schult)
  10. Mathematics and Music by Carter Hunt (Faculty Adviser: Dan Schult)
  11. Investigating Feynman's Integration Technique by Sang Kyung (Kathy) Lee (Faculty Advisor: Aaron Robertson)
  12. Fingering in Flames by Liam Moran (Faculty Adviser: Dan Schult)
  13. Determining Knight-distance Between Squares on an n x n Chessboard by Ruchit Shrestha (Faculty Advisor: Aaron Robertson)
  14. Discrete Dynamical System Modeling to Solve a Card Trick by Maddie Srivastava (Faculty Advisor: Aaron Robertson)
  15. Fast Inverse Square Root Algorithm by Serena Sutaria (Faculty Advisor: Aaron Robertson)
  16. Lattice Points on the Surface of n-Spheres for Small n by Ruiyun Tang (Faculty Advisor: Aaron Robertson)
  17. Mathematical Model of Tumor Growth and Treatment by Caroline Zaworski (Faculty Adviser: Dan Schult)
  18. Monte Carlo and Quasi-Monte Carlo Integration by Saiyang Zhang (Faculty Advisor: Aaron Robertson)
  1. Emulating Neuron Synapses in the Brain by William J. Boyd (Faculty Adviser: Daniel Schult)
  2. Modeling The Influenza Virus on Colgate University’s Campus by Thomas Fretz (Faculty Adviser: Daniel Schult)
  3. Bursting Patterns of Josephson Junction Neurons by Ruiyan Tang (Faculty Adviser: Daniel Schult)
  4. Josephson Junction Modeling of Neuron Bursting Behavior by Noah Campbell (Faculty Adviser: Daniel Schult)
  5. Using a Small-World Network to Investigate Convergence Patterns in a Mimura-Murray System by Maria Cesarini (Faculty Adviser: Daniel Schult)
  6. Modeling Language Differentiation Over Social Networks by Jice Kunfeng Zheng (Faculty Adviser: Daniel Schult)
  7. STEM persistence in college - An agent-based model by Julie Nguyen (Faculty Adviser: Daniel Schult)
  8. Network Analysis of Persistence of Women in STEM by Emmie McCaffery (Faculty Adviser: Daniel Schult)
  9. Impacts of extracellular potassium and intracellular chloride concentration on epileptic neuronal activity by Alexandra Krez (Faculty Adviser: Daniel Schult)
  10. A Tool for the Visualization of Data Mining Through Coupled Oscillators by Armando Belardo (Faculty Adviser: Daniel Schult)
  11. Voronoi Modeling of Tissue Structure and Cell Regeneration: Perimeter Approach by Maria Chen, Emily Derozier, and Alexandre Lauretti (Faculty Adviser: Silvia Jimenez Bolanos)
  12. Voronoi Modeling of Tissue Structure and Cell Regeneration: Area Approach by Katie Bushee, Adib Chowdhury, and Emily Gu (Faculty Adviser: Silvia Jimenez Bolanos)
  13. Machine Learning: Automated scoring system for short answer responses by Saw Lin (Faculty Advisers: Silvia Jimenez Bolanos and Will Cipolli)
  14. Cancer Classification with Probabilistic Networks by Ahsan Mahmood and Boris Shou (Faculty Adviser: Ahmet Ay)
  15. Pan Cancer Analysis of Ectopic Germline Gene Expression by Ben Harris (Faculty Adviser: Ahmet Ay)
  16. GPU Acceleration in Large Computational Models by Carlton Yang (Faculty Adviser: Ahmet Ay)
  17. 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)
  18. Modeling Strengthens Molecular Link between Circadian Polymorphisms and Major Mood Disorders by Amanda Liberman (Faculty Adviser: Ahmet Ay)
  19. Regulatory network of the scoliosis-associated genes establishes rostrocaudal patterning of somites in zebrafish by Ha Vu (Faculty Adviser: Ahmet Ay)
  1. An Investigation of the Abundancy Index of Ten by Adam Buys (Faculty Advisor: Aaron Robertson)
  2. Finding a Class of 4x4 Matrices on which the Rule of Sarrus can be Applied by Jordan Chervin (Faculty Advisor: Aaron Robertson)
  3. Elliptic Curve Cryptography by Robert Galante (Faculty Advisor: Aaron Robertson)
  4. Analysis of a Puck Puzzle by Kil Hyun Kim (Faculty Advisor: Aaron Robertson)
  5. Van der Waerden’s Theorem on Sequences With Interchanging Gap Sizes by Daoyang Shan (Faculty Advisor: Aaron Robertson)
  6. Change-Making Problems In The World of Even Value by Limin Tang (Faculty Advisor: Aaron Robertson)
  7. Schur’s Theorem Over Finite Fields by Caroline Wardlow (Faculty Advisor: Aaron Robertson)
  8. Algorithmic Solution to Rado’s Columns Condition by Dylan Giustra (Faculty Advisor: Aaron Robertson)
  9. Some New Difference Ramsey Numbers by Jiayang Li (Faculty Advisor: Aaron Robertson)
  10. A Classification of Exponents that Form Triangles by Dan Pucci (Faculty Advisor: Aaron Robertson)
  11. On the Non-Uniqueness of Entropy by Skylar Weber (Faculty Advisor: Aaron Robertson)
  12. Looking at Discrete Derivatives for Monomials by Ames Tardio (Faculty Advisor: Aaron Robertson)