My Research Interests
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 SturmLiouville problems and singular
techniques. In biological applications, eigenvalues often represent growth
rate information. We use capturemarkrecapture 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.
I am also interested in the
recruitment and retention of women faculty in science at rural institutions
like Murray State. In conjunction with Paula Waddill,
Robin Zhang, Echo Wu and Steve Cobb, I work on the MSU ADVANCE project www.murraystate.edu/advance
which is a National Science Foundation funded project to study recruitment
and retention of women in STEM.


Research Publications
 Carrie Diaz Eaton,
Maeve L. McCarthy, M. Drew LaMar, Progress in the Quantitative
Preparation of Biologists in the United States of America,
submitted.
 M.L. McCarthy, D.
Wallace, H. H. Whiteman, E. T. Rheingold, A. M. Dunham, O. Prosper, M.
Chen and E. HuWang, Modeling the
population dynamics and community impacts of Ambystoma tigrinum; a case study of phenotype plasticity, Mathematical
Biosciences 2017 June; 288: 3545. http://doi.org/10.1016/j.mbs.2017.02.011
 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); 199204 http://dx.doi.org/10.1137/15M1008002
 Maeve McCarthy,
Howard Whiteman, A model of
intercohort cannibalism and paedomorphosis in
Arizona Tiger Salamanders, Ambystoma tigrinum nebulosum,
International Journal of Biomathematics, 9 (2016), DOI: 10.1142/S1793524516500303.
 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. 3742.
6.
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. 122. (Abstract,
PDF)
7.
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):20112. doi:
10.1016/j.mbs.2013.05.008 (PDF)
 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. 113. (Abstract)
(PDF)
 Erwin, S., Huckaba, A., He, K.S., McCarthy, M. 2012. Matrix Analysis to Model the Invasion
of Alligatorweed (Alternanthera
philoxeroides) on Kentucky Lakes. Journal
of Plant Ecology (2012), doi: 10.1093/jpe/rts024. First published online: September 1,
2012. (Abstract,
Full
Paper)
 McCarthy, M.,
Fister, R. (2010). BioMapS: A
Roadmap to Success. CBE Life Sciences Education, 9, 175180. www.lifescied.org/cgi/reprint/9/3/175.pdf
 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.
215232. DOI:10.1093/imammb/dqn015 ).(Abstract)
(PDF)
 K. Renee Fister
and Maeve L. McCarthy, Mathematics
instruction and the tablet PC, International Journal of Mathematical
Education in Science and Technology, to appear (DOI:
10.1080/00207390701690303).(Abstract)
(PDF)
 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. 207226. (Abstract)
(PDF)
 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. 14071423. (Abstract)
(PDF)
 Brandon M. Hale
and Maeve L. McCarthy, An Introduction to Population Ecology, Journal of
Online Mathematics.
 Robert Butera, Maeve L. McCarthy, Analysis of realtime numerical integration methods applied to
dynamic clamp experiments, Journal of Neural Engineering 1 (2004) pp. 187194. (Abstract)
(PDF)
 Ian W. Knowles,
Maeve L. McCarthy, Isospectral
membranes: a connection between shape and density, J. Phys. A: Math.
Gen. 37 (2004) pp. 81038109.
(Abstract)
(PDF)
 C. Maeve
McCarthy, William Rundell, The
inverse eigenparameter dependent SturmLiouville problem, Numerical Functional Analysis
and Optimization, 24 no. 12
(2003) pp. 85106. (Abstract)
(PDF)
 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. 217230. (Abstract)
(PDF)
 K. Renee Fister,
C. Maeve McCarthy, Optimal control
of a chemotaxis problem, Quarterly of Applied Mathematics, 61 (2003), pp. 193211. (Abstract)
(PDF)
 C. Maeve
McCarthy, Reconstruction of an
impedance in twodimensions from spectral data, Applicable Analysis,
81 (2002), pp. 11611177. (Abstract)
(PDF)
 C. Maeve
McCarthy, The inverse eigenvalue
problem for a weighted Helmholtz equation, Applicable Analysis, 77 no. 12 (2001), pp. 7796. (Abstract)
(PDF)
 C. Maeve
McCarthy, The Optimal Design of
Tubular Structures, Journal of Computational and Applied
Mathematics, 114 no. 1 (2000). (Abstract)
(PDF)
 S. Lenhart, C. M. McCarthy (Editors), Control of Partial Differential
Equations, Special Issue, Journal of Computational and Applied
Mathematics, 114 no. 1 (2000).
 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 1318, 1999, Port
Ludlow, Washington. (Abstract)
(PDF)
 C. Maeve
McCarthy, The Tallest Column  Optimality
Revisited, Journal of Computational and Applied Mathematics, 101 no. 12 (1999), pp 2737. (Abstract)
(PDF)
 Steven J. Cox, C. Maeve McCarthy, The shape of the tallest column,
SIAM Journal on Mathematical Analysis, 29 no. 3 (1998). pp. 547554. (Abstract)
(PDF1,
PDF2)
NonResearch
Publications
 Teaching Excellence: Sharing Part of
Yourself,
MSU Teaching Chronicles, Fall 2005, no. 1. http://racernet.murraystate.edu/mstc/

