Todd Young
Dynamics in Biology Research Group - Spring 2013. Front: Nathan Breitsch, Xue Gong, Danielle Witt, Kara Finley. Back: Richard Buckalew, Bismark Oduro, Greg Moses, Winfried Just, Philip Miller, Todd Young, Will Clark.	Professor of Mathematics Ohio University My mission: To contribute to transformative progress in biology and numerical analysis through the application of dynamical systems ideas and to give students at all levels exciting and rigorous training in the mathematical sciences that will help them to have productive, rewarding careers.

• Joint Editor-in-Chief of the research journal: Dynamical Systems
• Recipient of the College of Arts and Sciences "Dean's Outstanding Teacher Award"
• Member of the Quantitative Biology Institute
• Member of the Infectious and Tropical Disease Institute

Contact Information Department of Mathematics Ohio University Athens, OH 45701 E-mail: youngt@ohio.edu Office: Morton Hall 547 Office hours: Phone: (740) 593-1277

Education & Professional Experience

Teaching

Materials for the textbook "Introduction to Numerical Methods and Matlab Programming for Engineers" by Young and Mohlenkamp.

Student Course Evaluations

MATLAB for Calculus Homework Assignments

1804 Project - Computational Technology in the Calculus and Beyond

Book: Technology in College Math - A Simple Approach

The Matlab Workbook - A Supplement for Calculus, Differential Equations and Linear Algebra.

Current Students

Gabriel Dooley

PhD candidate in Mathematics; active since summer 2024. Projects: Dynamical modeling of the cell cycle in large ensembles of cells with positive cell-cell feedback.

Brynely Needham

Undergraduate student in Applied Mathematics; active since summer 2024. Projects: Dynamical modeling of the cell cycle in large ensembles of cells with positive cell-cell feedback.

Graham Walther

Undergraduate student in Mathematics; active since summer 2024. Projects: Dynamical modeling of the cell cycle in large ensembles of cells with positive cell-cell feedback and Cardiac cell models.

Camden Kilton

Undergraduate student in Applied Mathematics and Physics; active since summer 2024. Projects: Dynamical modeling of the cell cycle in large ensembles of cells with positive cell-cell feedback and Cardiac cell models.

Past Students

Moayad Odeh

PhD in Mathematics 2025; Dissertaion: Sinc collocation algorithms for some PDEs.

Saad Aldosari

PhD in Mathematics 2024; Dissertation: Dynamics of Extrapolation for Alternating Algorithms. Currently Assistant Professor

Abdalnasar Algoud

PhD in Mathematics 2023; active since summer 2019. Project: Dynamical modeling of the cell cycle in large ensembles of cells with cell-cell feedback.

Daniel Ntiamoah

PhD in Mathematics 2023; Dissertation: The role of Orders in Alternating Algorithms. Currently Assistant Professor at Hamilton University.

Rabi K.C.

PhD Mathematics 2020; Dissertation: Instability of $k$-Cluster Solutions in a Population Model of the Cell Cycle when $k$ is Prime.

Kiattisak Prathom

PhD Mathematics 2019; .Dissertation: Dynamical modeling of the cell cycle in large ensembles of cells with cell-cell feedback. Currently: Assistant Professor of Mathematics at Walailak University in Nakhon Si Thammarat province, Thailand.

Luke Morgan

B.S. Mathematics 2017. Project: Dynamical modeling of the cell cycle in large ensembles of cells with cell-cell feedback. Currently: Data Analyst for Medspace a medical laboratory in Cincinnati, Ohio.

Xue (Shirley) Gong

PhD Mathematics 2016. Dissertation: Dynamical modeling of the cell cycle in large ensembles of cells with cell-cell feedback. Currently: Associate Professor of Mathematics at University of Wisconsin, Stout

Philip Miller

Bachelor of Science in Biology 2016. Projects: Cell Cycle Dynamics and Chagas Disease modeling, with W. Just.

Gregory Moses

PhD Mathematics 2015. Dissertation: Dynamical modeling of the cell cycle in large ensembles of cells with cell-cell feedback. Currently: Associate Professor and Chair of Mathematics at Chadron State College, Chadron, NE.

Kara Finley

B.S. Biology 2014. Projects: Dynamical modeling of the cell cycle in large ensembles of cells with cell-cell feedback and applications in Drosophila embryos. Experiments on related to early detection of ventilator associated pneumonia. Ph.D. in the Cancer and Cell Biology Program at the University of Cincinnati. Currently: Project Manager at PPD Laboratories - Oncology - Scientific Outreach

William Clark

B.S. Mechanical Engineering 2014. Project: Computations of models of epidemiology of Chagas disease, with W. Just. Ph.D. in Applied Mathematics, University of Michigan. Currently: Assistant Professor of Mathematics Ohio Univesity

Richard Bucklew

Ph.D. Mathematics 2014. Dissertation: Dynamical modeling of the cell cycle in large ensembles of cells with cell-cell feedback. Currently:

Danielle Witt

B.S. Math and Physics 2014; active 2012-14. Projects: Computation of random dynamical systems, with A. Neiman and simulation of movement of filaments in axons with P. Jung. Currently: Finished Ph.D. at Bowling Green State and is working as an analyst for the U.S. government.

Nathan Brietch

B.S. HTC Mathematics 2014; active 2011-2014 Project: Dynamical modeling of the cell cycle in large ensembles of cells with cell-cell feedback. Won Outstanding HTC Thesis Award. Currently working for Progressive Insurance as a data scientist specializing in computer vision and deep learning.

Ben Elbert

M.S. Applied Math 2012; active 2010-12. Project: Computation of Lyapunov exponents and conversion between continuous and Boolean dynamical systems, with W. Just. Currently at Alliance Data, Columbus OH.

Neal Burk

B.S. Mathematics 2011; active 2010-2011. Project: Computations of cell cycle systems. Interned with Sherwin Williams. Currently an associate at Ernst and Young in Cleveland.

Mike Smith

M.S. Applied Mathematics 2011; active 2009-2011. Project: Computations of cell cycle systems.

Derrick Sturgill

M.S. Applied Math 2011; active 2009-2011. Project: Computations of cell cycle systems. Currently Assistant Professor of Mathematics at University of Wisconsin, Stout.

Andrew DiLullo

B.S. 2007. Project: Using Potential Functions in binary classification. Finished a PhD Physics at Ohio University. Currently: Postdoctoral Researcher at Argonne National Laboratory

Shannon McDonough

B.S. Actuarial Science 2005. Project: Organization of Matlab learning materials. Currently: Biostatistician at SWOG - leading cancer research.

Hans Kicken

B.S. 2003. Project: Computations of Schelling's model of segregation. Currently: Working in the insurance industry in the Charlottesville, Virginia Area.

Russell Francis

B.S. Chemical Engineering 2003 and M.S. Applied Math 2008. Project: Computation of adiabatic invariants under separatrix crossings in Hamiltonian systems. Currently living in Canandaigua, New York and working as a software engineer for Help Scout.

Kiffany Keyes

B.S. Math and B.A. English 2003. Project: Organization of Matlab learning materials. Currently teaching High School in Cleveland.

Linday Eyink

B.S. Visual Communication 2003. Project: Organization of Matlab learning materials. Currently: Works for Apple making maps for iPhones in Berlin, Germany.

Mohamed Usman

M.S. Applied Math 2001. Project: Computation of adiabatic invariants under separatrix crossings in Hamiltonian systems. Currently: Professor of Mathematics, University of Dayton.

Mike Saum

M.S. Applied Math 1999. Project: Parallel computation of observed rotation numbers in dynamical systems. Currently Associate Professor of Mathematics, Georgia Gwinnett College.

Research

General Interest:

Current Projects and Sample Publications:

Dynamical Systems on Tensor Approximations

This is a project lead by Martin Mohlenkamp and was funded by the NSF DMS grant #1418787

Transient Dynamics of Block Coordinate Descent in a Valley, M. Mohlenkamp, T. Young, B. Barany. Intl~J~Num Anal Modeling 17 (4) 2020, 557-591.

The Optimization Landscape for Fitting a Rank-2 Tensor with a Rank-1 Tensor, M. Mohlenkamp, G. Xue, T. Young, SIAM J Appl Dyn Sys. 17 (2018), 1432-1477. doi: 10.1137/17M112213X.

Cell Cycle Dynamics and Clustering

This is a very broad project including both applied and pure mathematical parts. The project web site has details. It is a joint project with Erik Bozcko formerly of Vanderbilt University School of Medicine and now at Ohio University. It was funded by a Joint DMS/NIGMS Initiative to Support Research in the Area of Mathematical Biology grant NIH-NIGMS R01GM090207.

ODE, RDE and SDE Models of Cell Cycle Dynamics and Clustering in Yeast, Erik M. Boczko, Tomas Gedeon, Chris C. Stowers and T.R. Young, J. Biological Dynamics 4, July 2010, 328–345.

Clustering in Cell Cycle Dynamics with General Responsive/Signaling Feedback, T.R. Young, B. Fernandez, R. Buckalew, G. Moses, E. Boczko, J. Theor. Biology 292 (2012), 103-115.

Cell Cycle Dynamics: Clustering is Universal in Negative Feedback Systems, N. Breitsch, G. Moses, T.R. Young, E. Boczko, J. Math. Biology, 70 (5) (2015), 1151-1175. %50 doi: 10.1007/s00285-014-0786-7.

Instability of the Steady State Solution in Cell Cycle Population Structure Models with Feedback, B. Barany, G. Moses, T. Young, J. Math. Biology. 78 (5) 2019, 1365–1387. doi: 10.1007/s00285-018-1312-0.

Temporal Clustering in Cell Cycle Dynamics, T. Young, K. Prathom, J. Rombouts, Dynamical Systems Magazine, SIAM DSWeb, Jan 2019.

Clusters Tend to be of Equal Size in a Negative Feedback Population Model of Cell Cycle Dynamics, J. Rombouts, K. Prathom, T. Young, SIAM J Appl Dynam Systems, 19 (2) 2020, 1540-1573. doi: 10.1137/19M129070X.

Universality of Stable Multi-Cluster Periodic Solutions in a Population Model of the Cell Cycle with Negative Feedback, J. Biolog. Dynamics 15 (2021), 455-522. doi: 10.1080/17513758.2021.1971781

Instability of $k$-Cluster Solutions in a Cell Cycle Population Model when $k$ is Prime, Rabi K.C., Abdalnaser Algoud, T. Young, J. Appl. Nonlin. Dynamics 11 (1) (2022) 87-138. doi: 10.5890/JAND.2022.03.007

Stability of $p:q$ Temporally Clustered Population Structures in the Cell Cycle with Asymmetric Division, A. Algoud, MJ Mohlenkamp, T Young, accepted 6/26 in SIAM J Applied Dynamical Systems.

Past Projects:

Pulmonary Infection and Immunity

This is joint work with Erik Bozcko and Erin Murphy, Department of Biomedical Sciences in the College of Medicine at Ohio University. We are seeking to develop a new non-invasive monitoring technique, invented by Bozcko, to mitigate ventilator associated pneumonia. We are also seeking to use the monitoring technique as a tool to non-invasively study the human immune system in the lungs.

A Low Dimensional Dynamical Model of the Pulmonary Innate Immune Response to Infection, T.R. Young, R. Buckalew, A.K. May, E.M. Boczko, Math. Biosciences 235 (2012), 189-200. Doi: 10.1016/j.mbs.2011.12.004.

Non-Invasive detection of pulmonary pathogens in ventilator-circuit filters by PCR. R.J. Isaacs, K. Debelak, P.R. Norris, J.M. Jenkins, J.C. Rooks, T.R. Young, A.K. May, E.M. Boczko, Amer. J. Translational Research 4 (1) (2012), 72-82. PMC: 3276378.

Early Treatment Gains for Antibiotic Administration and Within Human Host Time Series Data, E~Boczko, T~Young, Math. Medicine and Biology 35 (2018), 203–224. doi:10.1093/imammb/dqw025

Modularity and other aspects of Neural Networks

This was joint work with the late Valentin Afraimovich, my advisor, Universidad Autónoma de San Luis Potosí and Mikhail Rabinovich at the Institute for Nonlinear Science at UC San Diego.

Nonlinear dynamics of emotion-cognition interaction: When emotion does not destroy cognition?, V. Afraimovich, T.R. Young, M.K. Muezzinoglu, M. Rabinovich, Bulletin Mathematical Biology, 73 (2011), 266-284.

Two dimensional heteroclinic attractor in the generalized Lotka-Volterra system. V. Afraimovich, G. Moses, T. Young, Nonlinearity 29 (2016) 1645-1667. doi:10.1088/0951-7715/29/5/1645

Questions about Random Dynamical Systems and Bifurcations with Bounded Noise

This is a joint project with Ale Jan Homburg in the Department of Mathematics at the University of Amsterdam.

Hard bifurcations in dynamical systems with bounded random perturbations, with A.J. Homburg, Regular & Chaotic Dynamics 11 (2006), 247-258.

The Hopf bifurcation with bounded noise, R.T. Botts, A.J. Homburg, T.R. Young, Discrete Cont. Dynam. Systems - A. 32 (2012), 2997-3007.

Random Questions about Dynamical Systems and Bifurcations

My research started in the area of Global Bifurcation Theory of Smooth Dynamical Systems. I continue to be interested in the general theory of dynamical systems. Some recent publications representing this aspect of my research include:

Topological entropies for equivalent smooth flows, W.X.~Sun, T.R. Young and Y.H.~Zhou, Transactions of the American Mathematical Society 361 (2009), 3071-3082.

Higher Order Birkhoff Averages, Thomas Jordan, Vincent Naudot and T.R. Young, Dynamical Systems 361 (2009), 3071-3082..

Signed Distance Function as a Tool for Binary Classification

This project is a joint effort with Erik Bozcko

Comparison of binary classification based on signed distance functions with support vector machines, E.~Boczko, D.~Wu, M.H.~Xie and T.R. Young, Proc. Ohio Collaborative Conference on Bioinformatics, 2006.