Published Papers:
Numerical semigroups, polyhedra, and posets II: locating certain families of semigroups. Jackson Autry, Abigail Ezell, Tara Gomes, Christopher O'Neill, Christopher Preuss, Tarang Saluja, Eduardo Torres Davila. Advances in Geometry 22 (1) 2022, pp. 33-48.
Compementary Numerical Sets. Matthew Guhl, Jazmine Juarez, Vadim Ponomarenko, Rebecca Rechkin, Deepesh Singhal. INTEGERS: The Electronic Journal of Number Theory (#A17) 2022, pp. 1-13.
Squarefree Divisor Complexes of Certain Numerical Semigroup Elements. Jackson Autry, Paige Graves, Jessie Loucks, Christopher O'Neill, Vadim Ponomarenko, Sam Yih, Involve 14 (1) 2021, pp. 1-9.
On Numerical Semigroups with Almost-Maximal Genus Joshua Arroyo, Jackson Autry, Charlotte Crandall, Jessica Lefler, Vadim Ponomarenko, The PUMP Journal of Undergraduate Research (3) 2020, pp. 62-67.
Elasticity in Apery Sets. Jackson Autry, Tara Gomes, Christopher O'Neill, Vadim Ponomarenko, American Mathematical Monthly 127 (8) 2020, pp. 744-749.
Membership and Elasticity in Certain Affine Monoids. Jackson Autry, Vadim Ponomarenko, Pi Mu Epsilon journal 15 (1) 2019, pp. 1-8.
Augmented Hilbert Series of Numerical Semigroups. Jeske Glenn, Christopher O'Neill, Vadim Ponomarenko, Ben Sepanski, INTEGERS: The Electronic Journal of Number Theory (19) 2019, #A32.
Interaction of a Free Surface with a Vortex Patch. Christopher Curtis, Henrik Kalisch, Wave Motion 90 August 2019, pp. 32-50.
Detection of moving objects through turbulent media. Decomposition of Oscillatory vs Non-Oscillatory spatio-temporal vector fields. J.Gilles, F.Alvarez, N.B.Ferrante, M.Fortman, L.Tahir, A.Tarter, A.von Seeger, Image and Vision Computing Journal 73 May 2018, pp. 40-55.
Open Turbulent Image Set (OTIS). J. Gilles, N.B. Ferrante, Pattern Recognition Letters 86 2017, pp. 38-41.
On the Set of Catenary Degrees of Finitely Generated Cancellative Commutative Monoids. Christopher O'Neill, Vadim Ponomarenko, Reuben Tate, Gautam Webb, International Journal of Algebra and Computation 26 (3) 2016, pp. 565-576.
Numerical Semigroups on Compound Sequences. Christopher O'Neill, Vadim Ponomarenko, Claire (Spychalla) Kiers, Communications in Algebra 44 (9) 2016, pp. 3842-3852.
Arithmetic of Congruence Monoids. Arielle Fujiwara, Joseph Gibson, Matthew O. Jenssen, Daniel Montealagre, Vadim Ponomarenko, Ari Tenzer, Communications in Algebra 44 (8) 2016, pp. 3407-3421.
Accepted Elasticity in Local Arithmetic Congruence Monoids. Lorin Crawford, Vadim Ponomarenko, Jason Steinberg, Marla Williams, Results in Mathematics 66 (1) 2014, pp. 227-245.
Diagnosing teachers' Understandings of Rational Numbers: Building a Multidimensional Test Within the Diagnostic Classification Framework. Laine Bradshaw, Andrew Iszak, Jonathan Templin, Erik Jacobson, Educational Measurement: Issues and Practice 33 (1) 2014, pp. 2-14.
Irreducible Factorization Lengths and the Elasticity Problem within N. Matthew Jenssen, Daniel Montealegre, Vadim Ponomarenko, American Mathematical Monthly 120 (4) 2013, pp. 322-328.
Multivariate Analysis of Functional Metagenomes. Elizabeth A. Dinsdale, Robert A. Edwards, Barbara Bailey, Imre Tuba, Sajia Akhter, Katelyn McNair, Robert Schmieder, Naneh Apkarian, Michelle Creek, Eric Guan, Mayra Hernandez, Catherine Isaacs, Chris Peterson, Todd Regh, Vadim Ponomarenko, Frontiers in Statistical Genetics and Methodology 41 (4) 2013.
Number Theory of Matrix Semigroups. Donald Adams, Rene Ardila, Nick Baeth, David Hannasch, Audra Kosh, Hanah McCarthy, Vadim Ponomarenko, Ryan Rosenbaum, Journal of Linear Algebra and its Applications (434) 2011, pp. 694-711.
Bifurcus Semigroups and Rings. Donald Adams, Rene Ardila, David Hannasch, Audra Kosh, Hanah McCarthy, Vadim Ponomarenko, Ryan Rosenbaum, Involve 2 (3) 2009, pp. 351-356.
The Geometry and Motion of Nematode Sperm Cells. Evgeny Demekhin, Nicole Haugen, Brian Ibanez, Jerome Lederman, Kaitlyn Murphy, Diana Verzi, and Debra Witczak. Cell Motility and the Cytoskeleton 66 (6) June 2009, pp. 317-327.
2023 Final Reports:
On the t-Elasticity of Numerical Semigroups. Karina Behera, Rachael Combes, James Howard, Christopher O'Neill, Shawn Perry, Vadim Ponomarenko, Brianna Worms.
Generalized Factorization Lenghts in Atomic Monoids. Spencer Chapman, Eli Dugan, Shadi Gaskari, Ron Lycan II, Sarah Mendoza De La Cruz.
t-Delta Sets of Numerical Semigroups. Sogol Cyrusian, Alex Domat, Eric Ren, Mayla Ward.
2022 Final Reports:
Comparing and Examining Different Methods of Determining Structural and Practical Identifiability of a Vector-Host Model. Joel Nathe, Kevin Phan, Alyssa Sharma.
Investigating the Structural and Practical Identifiability of Adult-Child Compartment Epidemic Models. Zander Memon, Charlotte Moser, Zoe Plzak.
Characteristics of glued numerical semigroups and the Kunz cone. Isidora Bailly-Hall, Ethan Bogle.
REU Summer 2022 Final Report. Lily Natasha Wartman, Anastasia Brooks, Geourge Tsoukalas, Austin Pineau.
2019 Final Reports:
A Bunch of Tilde's and Squares. Matthew Guhl, Rebecca Rechkin, Jazmine Juarez.
An Investigation of Single Small Atom Numerical Semigroups. Joshua Arroyo, Jackson Autry, Charlotte Crandall, Jess Lefler, Vadim Ponomarenko.
On The Preimage of Associated Semigroups. April Chen, Liam Lawson, Deepesh Singhal.
Seizing the Numerical Semigroups of Kuntz Polyhedra. Abigail Ezell, Tara Gomes, Christopher Preuss, Tarang Saluja.
2018 Final Reports:
Mathematical Models for Linking Within-Host and Between-Host Viral Dynamics. Aidan Backus, Angelica Bloomquist, Carlos Villanueva-Chavez, J Montgomery Maxwell, Elyssa Sliheet, Yuanming Tang.
Predicting Zeros of the Riemann Zeta Function Using Machine Learning. Jennifer Kampe, Artem Vysogorets.
LASSO With Centralized Kernel. Jennifer Kampe, Maya Brody, Sophia Friesenhahn, Adrina Garrett, Marissa Hegy.
2017 Final Reports:
Generating Functions of Invariants in Numerical Semigroups. Jeske Glenn, Benjamin Sepanski.
Question 0.4. Jackson Autry, Paige Graves, Jessie Loucks, Samuel Yih.
Study of Vortex Dynamics with Free Surface in a Shallow Water Regime Christopher Curtis, Robert Insley, Eunji Yoo, Hannah Barta, Phoebe Coy, Thomas Pecha, Thomas Retzloff, Alec Todd.
2016 Final Reports:
Image Processing and Restoration under Atmospheric Turbulence. Francis Alvarez, Nicholas Ferrante, Margaret Fortman, Lena Tahir, Alex Tarter, Anneke von Seeger.
Analysis of Markov Chain Monte Carlo Algorithms for Bayesian Statistical Models. Long Zhao, Connor Kennedy, Shane Lubold, Ethan Gwaltney, Patrick Dejesus, Bethany Faz.
2014 Final Reports:
Extremal Arithmetic in Numerical Semigroups. Andy Fry, Sarah McConnell, Claire Spychalla, Zofia Stanley, Brandon Van Over.
Invariants of Generalized Arithmetic Numerical Semigroups. Josiah Banks, Casey Fu, Julia Getsos, Rebecca Heinen, Sarah Hillier, Daniel Montealegre.
The Catenary Degrees of Elements in Numerical Monoids of Embedding Dimension Three. Christopher O'Neill, Reuben Tate, Gautam Webb.
See also the relevant Sage package, written mostly by Christopher O'Neill. (mirror)
2013 Final Reports:
Finding Hadamard Difference Sets. Alec Biehl, Kevin Halasz, Rachael Keller, Maryna Longnickel, Dylan Peifer, Ken Smith, Jason Steinberg.
An Investigation of d-Separable and d-Disjunct Binary Matrices. Greg Balint, Melanie Bloch, Robert Ellis, Gregory Monson, Abraham Schulte, Allie Schultz, Micky Soule, David Vaden.
2012 Final Reports:
Factorization Properties of Congruence Monoids. Arielle Fujiwara, Joseph Gibson, Matthew Jenssen, Daniel Montealegre, Ari Tenzer.
On the Accepted Elasticity of Arithmetic Congruence Monoids. Lorin Crawford, Jason Steinberg, Marla Williams.
Full Elasticity of Local Singular Arithmetic Congruence Monoids. Cody Allen, Whitney Radil, Rachel Rankin, Helen Williams.
2009 Final Reports:
A Large-Scale Statistical Survey of Environmental Metagenomes. Naneh Apkarian, Michelle Creek, Eric Guan, Mayra Hernandez, Kate Isaacs, Chris Peterson, Todd Regh.
Diagnosing Teacher Knowledge: A New Model. Bridget Druken, Laura Giberson, Cynthia Lopez, Jessica McCreary, Caitlyn O'Connor, Amanda Paganin, Lauren Susoeff.
2008 Final Reports:
The Geometry and Motion of Nematode Sperm Cells, Evgeny Demekhin, Nicole Haugen, Brian Ibanez, Jerome Lederman, Kaitlyn Murphy, Diana Verzi, Debra Witczak.
Matrix Number Theory: Factorization in Integral Matrix Semigroups, Donald Adams, Rene Ardila, David Hannasch, Audra Kosh, Hanah McCarthy, Vadim Ponomarenko, Ryan Rosenbaum.
2007 Final Reports:
Using Category Theory to Justify EvoHop, David Aaby.
Eigenvector Centrality for Decomposable Markov Chains, Kristen Mecadon, Megan Schneck, Annalinda Arroyo, Karl Heinz Hoffman, Jim Nulton, Peter Salamon.
PHACCS III: A Tool for Predicting Environmental Characteristics of Bacteriophage, Justin Domes, Bridget Druken, Peter Salamon.
Evolutionary Protein Distances to Phage Evolution Model, Andrew Detzel.
Towards a Phylogeny of Bacteriophage via Protein Importance Ranking, Kevin Manley.
Weighting for Coverage Bias in Internet Surveys, Zachary Boboth, Alisha Zimmer, Mark Scott, Eloise Hilarides, Donovan Gromet, Craig Massey.
