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.

  • 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
  • Rob Davis, A polyhedral proof of a wreath product identity
    With B. Sagan
    Journal of Combinatorics
  • 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

 

  • 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

 

  • 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

 

 

  • 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

 

 

  • 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


 

 

  • 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

 

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
    To appear in Experimental Mathematics
  • 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 and abstracts are listed below.
 

  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)