## Research

My background is in application-oriented mathematics, and I am especially interested in applications to medicine, biology, and
biochemistry. My past and current projects involve: cardiac electrophysiology, biochemical reaction kinetics, wound healing and the
acute inflammatory response, and the emergence of

* de novo * genes. For a list of some of my research articles, either refer to
my

curriculum vitae or follow some of the article links appearing below.

## Research with undergraduates

I love to mentor qualified undergraduates in substantive research projects, usually involving applications of mathematics but occasionally
involving theory-oriented mathematics. If you are a student interested in mathematics
research, please e-mail me at:

## Selected publications and presentations

51. J.W. Cain, Controlling Alternans in Spatially-Extended Cardiac Tissue Via Locally-Applied Stimuli,
in preparation, 2015.

50. M. Lindsay and J.W. Cain, Improved Lower Bounds on the Classical Ramsey Numbers R(4,22) and R(4,25).
http://arxiv.org/abs/1510.06102

49. D.G. Schaeffer and J.W. Cain, Ordinary Differential Equations: Basics and Beyond.
Springer, 2016.

48. J.W. Cain,
Chemical Reaction Kinetics: Mathematical Underpinnings, In: * Molecular Life Sciences: An Encyclopedic Reference*,
Springer, 2014.

47. J.W. Cain,
Equilibria and Bifurcations in the Molecular Biosciences, In: * Molecular Life Sciences: An Encyclopedic Reference*,
Springer, 2014.

46. J.W. Cain,
Mathematical Models in the Sciences, In: * Molecular Life Sciences: An Encyclopedic Reference*, Springer, 2014.

45. J.W. Cain,
Mathematics of Fitting Scientific Data, In: * Molecular Life Sciences: An Encyclopedic Reference*, Springer, 2014.

44. K.G. Workman, S. Zhao, and J.W. Cain,
Restricted Feedback Control in Discrete-Time Dynamical Systems with Memory, Physical Review E, Vol. 89, 2014, 042903.

43. J.W. Cain,
Stability of Impulsively-Forced Excitable Fibers to Perturbations of the Forcing Period, SIAM Journal on Applied Mathematics, Vol. 74,
2014, pp. 191--207.

42. J.W. Cain,
Chaos Control in Cardiac Tissue: Some Mathematics Behind Terminating Cardiac Arrhythmias, Springer Proceedings in Mathematics
and Statistics (B. Toni, ed.), Vol. 37, 2014.

41. J.W. Cain,
Using Local Control to Stabilize Global Behavior in Excitable Media, Proceedings of the Fifth International Conference
on Applied Mathematics and Informatics, Cambridge, MA, January 2014.

40. J.W. Cain, To Make Free or Not to Make Free?---That is the Question, Joint Mathematics Meetings, special session on open source
publishing,
Baltimore, MD, January 2014.

39. J.W. Cain, Restricted Feedback Control and Discrete-Time Dynamical Systems, Joint Mathematics Meetings, special session on difference
equations and applications,
Baltimore, MD, January 2014.

38. J.W. Cain, Chaos Control in Cardiac Tissue: Local Stimulation versus Far-Field Pacing, Joint Mathematics Meetings,
San Diego, CA, January 9--12, 2013.

37. J.W. Cain, Controlling Cardiac Alternans via Point Stimulation versus Far-Field Pacing, Proceedings of the
13th International conference on Mathematics and Computers in Biology and Chemistry (MCBC 2012), Iasi, Romania,
June 2012.

36. J.W. Cain, Controlling Nonlinear Systems with Memory: An
Example from Cardiac Dynamics, Dynamics Days 2012, Baltimore, MD, January 4--7, 2012.

35. J.W. Cain, CardioMathematics, * Notes * of the Canadian Mathematical
Society, Vol. 44, No. 1, Feb. 2012.

34. Keeping the Beat, a podcast interview with the American
Mathematical Society, edited by Mike Breen, 2011. See also the Math
Moments poster

33. J.W. Cain, Mathematics, Cardiac Phenomena, and the Diagnosis of
Pathology, Future Cardiology, Vol. 7, No. 5, Sept. 2011, pp. 587--590.

32. Q&A: Taking Mathematics to Heart
, an interview with * Science Careers * (from the journal
* Science *), edited by Kate Travis, April 29, 2011.

31. J.W. Cain and A.M. Reynolds,
Ordinary and Partial Differential Equations: An Introduction to Dynamical
Systems , ISBN#: 978-0-9824062-3-6, published August 2010, 418 pages,
hardback. If you want a free electronic copy of this book, e-mail me!

30. J.W. Cain, Feedback Control of Cardiac Alternans, SIAM Annual
Meeting/SIAM Conference on the Life Sciences, Pittsburgh, PA, July 12,
2010.

29. J.W. Cain, Taking Math to
Heart: Mathematical Challenges in Cardiac Electrophysiology,
Notices of the American Mathematical Society, Vol. 58., No. 4 (April 2011), pp. 542--549.

28. N.B. Menke, J.W. Cain, A.M. Reynolds, D.M. Chan, R.A. Segal, T.M. Witten,
D.G. Bonchev, R.F. Diegelmann, and K.R. Ward,
An In Silico Approach to the
Analysis of Acute Wound Healing , Wound Repair and Regeneration,
Vol. 18 (2010), pp. 105--113.

27. D.T. Taylor, J.W. Cain, D.G. Bonchev, S.S. Fong, A.A. Apte, and L.E.
Pace,
Toward a Classification of Isodynamic Feed-Forward Motifs ,
Journal of Biological Dynamics, Vol. 4 (2010), pp. 196--211.

26. J.W. Cain, Local Asymptotic Stability and Difference Equations of
Arbitrary Finite Order, Joint Mathematics Meetings,
Washington, DC, January 5--8, 2009.

25. J.W. Cain,
A Kinematic Model of Wave Propagation ,
International Journal of Pure and Applied Mathematics, Vol. 49 (2008), pp.
599--605.

24. J.W. Cain, A Kinematic Model of Wave Propagation, invited address,
International Conference of Applied Mathematics and Computing,
Plovdiv, Bulgaria, August 12--18, 2008.

23. J.W. Cain, A Kinematic Model of Wave Propagation in an Excitable Medium,
AMS Spring Eastern Meeting, New York, NY, March 15--16, 2008.

22. S.V. Narayanan and J.W. Cain, Mathematical Investigation of a
Feedback Control Algorithm for Suppressing Electrical Alternans in
Cardiac Tissue, TIMBER 2007: Undergraduate Research Conference in
Quantitative Biology, November 2-3, 2007, Appalachian State University,
Boone, NC.

21. A.A. Apte, J.W. Cain, D.G. Bonchev and S.S. Fong,
Cellular Automata Simulation of Topological
Effects on the Dynamics of Feed-Forward Motifs , Journal of Biological
Engineering, 2:2 (2008)

20. H. Sedaghat, M.A. Wood, J.W. Cain, C.K. Cheng, C.M. Baumgarten
and D.M. Chan,
Complex Temporal Patterns of Spontaneous Initiation and
Termination of Reentry in a Loop of Cardiac Tissue , Journal of
Theoretical Biology, Vol. 254 (2008), pp. 14--26.

19. J.W. Cain and D.G. Schaeffer,
Shortening of Cardiac Action Potential Duration Near an Insulating
Boundary , Mathematical Medicine and Biology, Vol. 25 (2008), pp.
21--36.

18. J.W. Cain, Analysis of Transient Alternans in a Paced Cardiac Fiber,
Applications of Analysis to Mathematical Biology,
Durham, NC, May 21--23, 2007.

17. C.M. Berger, J.W. Cain, J.E.S. Socolar, and D.J. Gauthier,
Control of Electrical Alternans in Paced Myocardium Using Extended
Time-Delay Autosynchronization , Physical Review E, Vol. 76 (2007), pp.
041917. (Selected to appear in the Virtual Journal of Biological Physics
Research, Volume 14, Issue 9, November 1, 2007) .

16. S.V. Narayanan and J.W. Cain,
Analysis of a Modified Feedback Control
Technique for Suppressing Electrical Alternans in Cardiac Tissue ,
MEJAM undergraduate research journal, Vol. 5 (2007),
pp. 1--17.

15. J.W. Cain,
Criterion for Stable Reentry in a Ring of Cardiac Tissue ,
Journal of Mathematical Biology, Vol. 55 (2007), pp. 433--448.

14. D.G. Schaeffer, J.W. Cain, D.J. Gauthier, S.S. Kalb, W. Krassowska,
R.A. Oliver, E.G. Tolkacheva and W. Ying,
An ionically based mapping model with memory for cardiac restitution ,
Bulletin of Mathematical Biology, Vol. 69 (2007), pp. 459--482.

13. H. Sedaghat, C.M. Baumgarten, J.W. Cain, D.M. Chan, C. Cheng, C.M.
Kent and M.A. Wood, Modeling Spontaneous Initiation and Termination of
Reentry in Cardiac Tissue, Dynamics Days 2007: International Conference on
Chaos and Nonlinear Dynamics, Boston, MA, January 2007.

12. J.W. Cain, C.M. Berger and D.J. Gauthier,
Controlling Electrical Alternans in Paced Myocardium Using
Extended Time-Delay Autosynchronization, Dynamics Days 2007:
International Conference on Chaos and Nonlinear Dynamics, Boston, MA,
January 2007.

11. J.W. Cain and D.G. Schaeffer, Shortening of Cardiac Action Potential
Duration Near a Non-Conducting Boundary, Dynamics Days 2007:
International Conference on Chaos and Nonlinear Dynamics, Boston, MA,
January 2007.

10. J.W. Cain.
Review of R.C. Robinson's, "An Introduction to Dynamical
Systems: Continuous and Discrete."
J. Difference Equations and Applications, Vol. 12 (2006), No. 9, pp. 957--958.

9. J.W. Cain, C.M. Berger and D.J. Gauthier, Adaptive Control of Abnormal
Rhythms in a Patch of Cardiac Tissue, Joint SIAM/SMB Conference on the
Life Sciences, Raleigh, NC, August 2, 2006.

8. J.W. Cain, Criterion for Stable Reentrant Excitation in a Ring of
Cardiac Tissue, Dynamics Days 2006: International Conference on Chaos and
Nonlinear Dynamics, Bethesda, MD, January 2006.

7. J.W. Cain,
Dynamic behavior of a paced cardiac fiber ,
SIAM J. Applied Mathematics, Vol. 66 (2006), No. 5, pp. 1776--1792.

6. J.W. Cain and D.G. Schaeffer,
Two-term asymptotic approximation of a cardiac restitution curve ,
SIAM Review, Vol. 48 (2006), No. 3, pp. 537--546.

5. J.W. Cain, Issues in the one-dimensional dynamics of a paced cardiac
fiber, Ph.D. Dissertation, Duke University (2005) .

4. D.G. Schaeffer, J.W. Cain, D.J. Gauthier, S.S. Kalb, W. Krassowska,
R.A. Oliver, E.G. Tolkacheva and W. Ying, An ionically based mapping
model with memory for cardiac restitution, Gordon Research Conference on
Cardiac Arrhythmia Mechanisms, Buellton, CA, February 2005.

3. J.W. Cain, E.G. Tolkacheva, D.G. Schaeffer, and D.J. Gauthier,
Rate-dependent propagation of cardiac action potentials in a
one-dimensional fiber , Phys. Rev. E., vol. 70 no. 6 (2004), pp. 061906
(Selected to appear in the Virtual Journal of Biological Physics
Research, Volume 8, Issue 12, December 15, 2004) .

2. J.W. Cain, E.G. Tolkacheva, D.G. Schaeffer, and D.J. Gauthier,
Rate-dependent waveback velocity of cardiac action potentials in a
one-dimensional cable, International Conference for Mathematics in
Biology and Medicine: Annual Meeting for the Society for Mathematical
Biology, July, 2004.

1. J.W. Cain, Simulating discordant alternans with a two-current model,
International School on Biomathematics, Bioengineering and Clinical
Aspects of Blood Flow, MSRI, August, 2002.