Research

My main mathematical research interests are inverse problems in differential equations and the development of mathematical models for biological phenomena.

Inverse Problems involve the use of optimization techniques to determine model parameters from available data. I am particularly interested in applications involving eigenvalues. In mechanical problems, eigenvalues represent vibrational information. The mathematics involves Sturm-Liouville problems and singular techniques. In biological applications, eigenvalues often represent growth rate information. We use capture-mark-recapture methods, projection matrix models  and linear algebra to estimate biological properties like fecundity.

I’m also interested in the behavior of invasive species, mosquitoes and cells that are being affected by chemotaxis. Mathematically, all of these are modeled by nonlinear partial differential equations. I have developed methods to identify the unknown parameters in the PDE models, and in some cases to control certain phenomena. Recently, I have become interested in the Arizona Tiger Salamander which displays facultative paedomorphosis in certain populations. One morph eats the juveniles, while the other does not. I am currently developing mathematical models to describe this phenomenon.

1.       Bordieri MJ, Waddill PJ, Zhang Q, McCarthy ML, Fuller C, Balthrop D (2024), Exploring the stability of the gender gap in faculty perceptions of gender climate at a rural regional university. PLoS ONE 19(4): e0301285. https://doi.org/10.1371/journal.pone.0301285

2.       Maeve L. McCarthy, Dorothy I. Wallace. Optimal control of a tick population with a view to control of Rocky Mountain Spotted Fever. Mathematical Biosciences and Engineering, 2023, 20(10): 18916-18938. doi: 10.3934/mbe.2023837

3.       Maeve L. McCarthy, Reigh Kemp, Spring Break Camp to the Rescue, AWIS Magazine, Fall 2023, 46-47.

4.       Maeve L. McCarthy, Karoline Pershell, Jennifer J. Quinn, The Evolution of the AWM Executive Director Position: 2005—2020, Fifty Years of Women in Mathematics, Janet L. Beery, Sarah J. Greenwald, Cathy Kessel, editors,. Springer, 2022.

5.       Carrie Diaz Eaton, Maeve L. McCarthy, M. Drew LaMar, 21st Century Reform Efforts in Undergraduate Quantitative Biology Education; Conversations, Initiatives, and Curriculum Change in the United States of America, Letters in Biomathematics, 2020.

6.       K. Renee Fister, Maeve McCarthy, Seth Oppenheimer, Diffusing Wild Type and Sterile Mosquitoes in an Optimal Control Setting, Mathematical Biosciences (2018) https://doi.org/10.1016/j.mbs.2018.05.015

7.   Maeve L. McCarthy, A Letter to My Daughters, Journal of Humanistic Mathematics, Volume 8 Issue 2 (July 2018), pages 103-105, DOI: 10.5642/jhummath.201802.10.

8.   ** M.L. McCarthy, D. Wallace, H. H. Whiteman, E. T. Rheingold, A. M. Dunham, O. Prosper, M. Chen and E. Hu-Wang, Modeling the population dynamics and community impacts of  Ambystoma tigrinum; a case study of phenotype plasticity, Mathematical Biosciences 2017 June; 288: 35-45. http://doi.org/10.1016/j.mbs.2017.02.011

9.   Rachel Levy, Edmond Chow, Byong Kwon, Katherine Socha, Maeve McCarthy, and Peter Turner, SIAM Education Subcommittee Report on Undergraduate Degree Programs in Applied Mathematics, SIAM Review, 2017; 59 (1); 199-204 http://dx.doi.org/10.1137/15M1008002

10.   Maeve McCarthy, Howard Whiteman, A model of inter-cohort cannibalism and paedomorphosis in Arizona Tiger Salamanders, Ambystoma tigrinum nebulosum, International Journal of Biomathematics, 9 (2016), DOI: 10.1142/S1793524516500303.

11.   ** Donald Adongo, Maeve L. McCarthy, Ryan Walls, An Integer Programming Model of Fire Station Allocation in Murray, Kentucky, Journal of the Kentucky Academy of Sciences, 74   (2013), pp. 37-42.

12.    Don Hinton, Maeve Lewis McCarthy, Bounds and optimization of the minimum eigenvalue for a vibrating system, Electronic Journal of Qualitative Theory of Differential Equations, No. 48 (2013), pp. 1-22.

13.   K. Renee Fister, Maeve McCarthy, Seth Oppenheimer, Craig Collins, Optimal control of insects through sterile insect release and habitat modification. Mathematical Biosciences 2013 Aug; 244(2):201-12. doi: 10.1016/j.mbs.2013.05.008

14.   ** Erwin, S., Huckaba, A., He, K.S., McCarthy, M. Matrix Analysis to Model the Invasion of Alligatorweed (Alternanthera philoxeroides) on Kentucky Lakes. Journal of Plant Ecology (2013), 6(2):150-157. doi: 10.1093/jpe/rts024.

15.   Boris P. Belinskiy, James W. Hiestand, Maeve L. McCarthy, Optimal design of a bar with an attached mass. Electronic Journal of Differential Equations. Vol. 2012 (2012), No. 181, pp. 1-13.

16.   McCarthy, M., Fister, R. (2010). BioMapS: A Roadmap to Success. CBE Life Sciences Education, 9, 175-180. www.lifescied.org/cgi/reprint/9/3/175.pdf.

17.   K. Renee Fister and Maeve L. McCarthy, Identification of a chemotactic sensitivity in a coupled system, Mathematical Medicine and Biology, 25 no. 3 (2008), pp. 215-232. DOI:10.1093/imammb/dqn015

18.   K. Renee Fister and Maeve L. McCarthy, Mathematics instruction and the tablet PC, International Journal of Mathematical Education in Science and Technology, 39 no. 3 (2008), pp. 285-292. DOI: 10.1080/00207390701690303.

19.   Don Hinton, Maeve L. McCarthy, Optimization of the minimum eigenvalue for a class of second order differential operators, Recent Advances in Differential Equations and Mathematical Physics, Nikolai Chernov, Yulia Karpeshina, Ian W. Knowles, Roger T. Lewis, and Rudi Weikard, University of Alabama at Birmingham, Editors - AMS, 2006, pp. 207-226.

20.   K. Renee Fister, Maeve L. McCarthy and Seth F. Oppenheimer, The identification of a time dependent parameter from a soil column experiment, SIAM Journal on Applied Mathematics, 66 no. 4 (2006) pp. 1407-1423.

21.   ** Brandon M. Hale, Maeve L. McCarthy, An Introduction to Population Ecology Using Maplets, Journal of Online Mathematics and its Applications, 5 (2005)  http://www.joma.org/mathDL/4/?pa=content&sa=viewDocument&nodeId=634

22.   Robert Butera, Maeve L. McCarthy, Analysis of real-time numerical integration methods 0applied to dynamic clamp experiments, Journal of Neural Engineering 1 (2004) pp. 187-194.

23.   Ian W. Knowles, Maeve L. McCarthy, Isospectral membranes: a connection between shape and density, Journal of Physics A: Mathematical & General, 37 (2004) pp. 8103-8109.

24.   C. Maeve McCarthy, William Rundell,  Eigenparameter Dependent Inverse Sturm-Liouville problem, Numerical Functional Analysis and Optimization, 24 no. 1-2 (2003) pp. 85-106.

25.   Boris P. Belinskiy, C. Maeve McCarthy, Terry J. Walters, Optimal turbines in the absence of an attached mass, European Series in Applied and Industrial Mathematics: Control, Optimisation and Calculus of Variations, 9 (2003), pp. 217-230.

26.   K. Renee Fister, C. Maeve McCarthy, Optimal control of a chemotaxis system, Quarterly of Applied Mathematics, 61 (2003), pp. 193-211.

27.   C. Maeve McCarthy, Reconstruction of an impedance in two-dimensions from spectral data, Applicable Analysis, 81 (2002), pp. 1161-1177.

28.   C. Maeve McCarthy, The inverse eigenvalue problem for a weighted Helmholtz equation, Applicable Analysis, 77 no. 1-2 (2001), pp. 77-96.

29.   C. Maeve McCarthy, The Optimal Design of Tubular Structures, Journal of Computational and Applied Mathematics, 114  no. 1 (2000).

30.   C. Maeve McCarthy, Recovery of a density from the eigenvalues of a nonhomogeneous membrane, Proceedings of Inverse Problems in Engineering: Theory and Practice, 3rd International Conference on Inverse Problems in Engineering, June 13-18, 1999, Port Ludlow, Washington.

31.   C. Maeve McCarthy, The Tallest Column -- Optimality Revisited, Journal of Computational and Applied Mathematics, 101 no. 1-2 (1999), pp 27-37.

32.   Steven J. Cox, C. Maeve McCarthy, The shape of the tallest column, SIAM Journal on Mathematical Analysis, 29 no. 3 (1998), pp. 547-554; The shape of the tallest column: Corrected, SIAM Journal on Mathematical Analysis, 31 no. 4 (2000), p. 940.

33.   E.F. Fallon, P.G. Nallen, C.M. McCarthy, M.E.J. O'Kelly, The use of Monte Carlo simulation in workstation design, Proceedings of the 12th Triennial Congress of the International Ergonomics Association, 1994.

** with students