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
Undergraduate Chair
Department of Mathematics

My mission: To contribute to transformative progress in biology and medicine 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.


New Professor Lecture, April 2011

Contact Information

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  • Department of Mathematics
    Ohio University
    Athens, OH 45701
  • E-mail: youngt@ohio.edu
  • Office: Morton Hall 547
  • Office hours: MR 11:10-12:00
  • Phone: (740) 593-1277

Education & Professional Experience


Teaching

Introduction to Numerical Math and Matlab Programming

Ohio University's MATLAB Homework Page

MATH 344 Page

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

Richard Bucklew
PhD Mathematics; active since Winter 2010. Project: Dynamical modeling of the cell cycle in large ensembles of cells with cell-cell feedback.
Gregory Moses
PhD Mathematics; active since Summer 2010. Project: Dynamical modeling of the cell cycle in large ensembles of cells with cell-cell feedback.
Xue (Shirley) Gong
PhD Mathematics; active since Fall 2010. Project: Dynamical modeling of the cell cycle in large ensembles of cells with cell-cell feedback.
Nathan Brietch
HTC Mathematics; active since Spring 2011. Project: Dynamical modeling of the cell cycle in large ensembles of cells with cell-cell feedback.
Kara Finley
Bachelors Biology; active since Spring 2012. Project: Dynamical modeling of the cell cycle in large ensembles of cells with cell-cell feedback.
Philip Miller
Bachelors Biology expected 2015; active 2012-13. Project: Cell cycle dynamics and Chagas Disease modeling, with W. Just..
Danielle Witt
Bachelors Math and Physics; active since Fall 2012. Project: Computation of random dynamical systems, with A. Neiman.
William Clark
Bachelors Math and Mechanical Engineering; active since Spring 2013. Project: Computations of models of epidemiology of Chagas disease, with W. Just.


Past Students

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. Currently interning with Sherwin Williams.
Mike Smith
M.S. Applied Mathematics 2011; active 2009-2011. Currently studying for doctorate in Math Ed at Ohio U.
Derrick Sturgill
M.S. Applied Math 2011; active 2009-2011. Currently studying for doctorate in Math Ed at Ohio U.
Andrew DiLullo
B.S. 2007. Project: Using Potential Function in binary classification. Currently: Graduate student in Physics at Ohio University.
Hans Kicken
B.S. 2003. Project: Computations of Schelling's model of segregation. Currently: .
Russell Francis
B.S. Chemical Engineering and M.S. Applied Math. Project: Computation of adiabatic invariants under separatrix crossings in Hamiltonian systems. Currently .
Kiffany Keyes
B.S. Math ; . Currently .
Mike Suam
M.S. Applied Math 1999. Project: Parallel computation of observed rotation numbers in dynamical systems. Currently Assistant Professor of Mathematics, Georgia Gwinnett College.
Mohamed Usman
M.S. Applied Math 2000. Project: Computation of adiabatic invariants under separatrix crossings in Hamiltonian systems. Currently Associate Professor of Mathematics, University of Dayton.


Research

General Interest:

Differential Equations and Dynamical Systems. Especially: Global Bifurcation Theory, Random Dynamical Systems and Applications to Biological Systems

Publications and Preprints

Seminar Talks

Current Projects and Sample Publications

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 of Vanderbilt University School of Medicine. It is funded by a Joint DMS/NIGMS Initiative to Support Research in the Area of Mathematical Biology grant NIH-NIGMS R01GM090207 that includes opportunities for partial support for Graduate and Undergraduate Research Assistants.

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

Clustering in Cell Cycle Dynamics with General Responsive/Signaling Feedback, T. 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.~Young, E.~Boczko, J. Math. Biology, to appear.


Pulmonary Infection and Immunity
This is joint work with Erik Bozcko at Vanderbilt University School of Medicine. 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.


Modularity and other aspects of Neural Networks
This is joint work with 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? , by V. Afraimovich, T. Young, M.K. Muezzinoglu, M. Rabinovich, Bulletin Mathematical Biology, 73 (2011), 266-284.


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, with W.X.~Sun, T.Y. and Y.H.~Zhou, Transactions of the American Mathematical Society 361 (2009), 3071-3082.

Higher Order Birkhoff Averages, Thomas Jordan, Vincent Naudot and T.Y., 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, with E.~Boczko, D.~Wu and M.H.~Xie, Proc. Ohio Collaborative Conference on Bioinformatics, 2006.


Some Past Conferences:


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