Research | Publications

Research Interests

My general interest is in modeling and analysis of problems from biomathematics. The preferred tools are dynamical systems, differential equations and stochastic processes. Specifically, I have worked and work on

  • mathematical approaches to behavior of zooplankton
  • drug delivery devices for crossing the blood-brain barrier
  • semigroups of operators, dynamics of structured populations
  • dynamics of microtubule growth, collapse and nucleation
  • dynamics of bacterial infections of arthropods
  • cytostatic and cytotoxic chemotherapies of cancer
  • development of resistance to chemotherapy
  • cell migration in structured environments
  • diffusion of nuclear proteins

Publications

  • [31] Copepod manipulation of oil droplet size distribution (with M. Uttieri, A. Nihongi, J. Motschman, H. Jiang, M. Alcaraz and J. R. Strickler), Sci. Rep. 9:547
  • [30] Scaling behavior of drug transport and absorption in in silico cerebral capillary networks (with W. Langhoff and A. Riggs), PLoS One 13:e0200266 (2018) .pdf
  • [29] Olfaction in a viscous environment: The “color” of sexual smells in Temora longicornis (with J. R. Strickler and J. Yen), Sci. Nat. 104 (2017):46 .pdf
  • [28] Chemosensation and potential neuronal mechanism of ratio detection in a copepod (with W. Langhoff, J. R. Strickler and J. Yen),  In “Trends in Copepod Studies – Distribution, Biology and Ecology”, M. Uttieri (ed.), Nova Science Publishers, (2017) .pdf
  • [27] Linear stability of delayed reaction-diffusion systems (with M. Mincheva), Comput. Math. Appl. 73 (2017):226-232 .pdf
  • [26] Ergodicity and loss of capacity for a random family of concave maps (with A. Radunskaya), Discr. Contin. Dyn. Sys. B 21 (2016):2193-2210 .pdf
  • [25] Signaled drug delivery and transport across the blood-brain barrier (with A. Radunskaya, S. M. Mackay, J. N. J. Reynolds, M. Schroeder, E. W. Tan and I. Tucker), J. Liposome Res. 26 (2016):233-245 .pdf
  • [24] Statistical mechanics of zooplankton (with A. Nihongi and J. R. Strickler), PLoS One 10 (2015):e0135258 .pdf
  • [23] Algebraic and topological indices of molecular pathway networks in human cancers (with E. A. Rietman, S. I. Omar and J. A. Tuszyński), Math. Biosci. Eng. 12, (2015):1289-1302 .pdf
  • [22] The Mathematics of Drug Delivery (with A. Radunskaya), In “Mathematical Models of Tumor-Immune Dynamics” (A. Eladdadi, P. Kim, D. Mallet, eds.), Springer Verlag, (2014), p. 109-123 .pdf
  • [21] Swallowing a cellular automaton pill: predicting drug release from a matrix tablet (with E. Buchla, A. Nájera and A. Radunskaya), Simulation 90 (2014):227-237 .pdf
  • [20] A nonsmooth program for jamming hard spheres, Optim. Lett. 8 (2014):13-33 .pdf
  • [19] Kinetics of bile salt binding to liposomes revealed by carboxyfluorescein release and mathematical modeling (with A. Radunskaya, I. Tucker and L. Yang), J. Liposome Res. 22 (2012):237-244 .pdf
  • [18] Pathogen evolution in switching environments: a hybrid dynamical system approach (with J. Z. Farkas and J. Engelstädter), Math. Biosci. 240 (2012):70-75 .pdf, Corrigendum Ibid. 241:147-148 .pdf
  • [17] Steady states in hierarchical structured populations with distributed states at birth (with J. Z. Farkas), Discr. Contin. Dyn. Sys. B 17 (2012):2671-2689 .pdf
  • [16] The ciliate Paramecium shows higher motility in non-uniform chemical landscapes (with C. Giuffre, R. Vogel, T. Ahmed, R. Stocker, T. R. Consi and J. R. Strickler), PLoS One (2011):e15274 .pdf
  • [15] Modeling the effects of drug binding on the dynamic instability of microtubules (with V. Rezania, M. Lopus, M. A. Jordan and J. A. Tuszynski), Phys. Biol. 8 (2011):056004 .pdf
  • [14] Physiologically structured populations with diffusion and dynamic boundary conditions (with J. Z. Farkas), Math. Biosci. Eng. 8 (2011):503-513 .pdf
  • [13] Mathematical analysis of a kinetic model for cell movement in network tissues (with T. Hillen and Z. Wang), Discr. Contin. Dyn. Sys. B 14 (2010):1055-1080 .pdf
  • [12] Semigroup analysis of structured parasite populations (with J. Z. Farkas and D. M. Green), Math. Model. Nat. Phenom. 5 (2010):94-114 .pdf
  • [11] Structured and unstructured continuous models for Wolbachia infections (with J. Z. Farkas), Bull. Math. Biol. 72 (2010):2067-2088 .pdf
  • [10] On a size-structured two-phase population model with infinite states-at-birth (with J. Z. Farkas), Positivity 14 (2010):501-514 .pdf
  • [9] A continuous model for microtubule dynamics with catastrophe, rescue and nucleation processes (with V. Rezania and J. A. Tuszynski), Phys. Rev. E 80 (2009):031904 .pdf
  • [8] Predicting the drug release kinetics of matrix tablets (with B. Baeumer, L. Chatterjee, T. Rades, A. Radunskaya and I. Tucker), Discr. Contin. Dyn. Sys. B 12 (2009):261-277 .pdf
  • [7] A spatial model of tumor-host interaction: application of chemotherapy (with P. Gerlee, L. J. McCawley, V. Quaranta, M. Ciobanu, S. Wang, J. M. Graham, B. P. Ayati, J. Claridge, K. R. Swanson, M. Loveless and A. R. A. Anderson), Math. Biosci. Eng. (2009):521-545 .pdf
  • [6] Analysis of a model for transfer phenomena in biological populations (with F. Le Foll, P. Magal, and G. F. Webb), SIAM J. Appl. Math. 70 (2009):40-62 .pdf
  • [5] A mathematical model quantifies proliferation and motility effects of TGF-β on cancer cells (with S. E. Wang, N. Bryce, A. M. Weaver, L. Estrada, C. L. Arteaga and G. F. Webb), Comput. Math. Methods Med. 10 (2009):71-83 .pdf
  • [4] A mathematical model separates quantitatively the cytostatic and cytotoxic effects of a HER2 tyrosine kinase inhibitor (with S. E. Wang, C. L. Arteaga and G. F. Webb), Theor. Biol. Med. Model. 4 (2007):14 .pdf
  • [3] Molecular seismology: An inverse problem in nanobiology (with E. M. Boczko), J. Theor. Biol. 246 (2006):145-158 .pdf
  • [2] The DNA binding activity of p53 displays reaction-diffusion kinetics. (with C. Rogers, C. E. Barbieri, J. A. Pietenpol, A. K. Kenworthy and E. DiBenedetto), Biophys. J. 91 (2006):330-342 .pdf
  • [1] Moment inequalities and central limit properties of isotropic convex bodies. (with U. Brehm, H. Vogt, and J.Voigt), Math. Z. 240 (2002):37-51 .pdf

Theses, Seminar Papers

  • Partial differential equation models for intranuclear diffusion, inverse problems in nanobiology and cell cycle specific effects of anticancer drugs, Dissertation, Vanderbilt University, 2007 .pdf
  • Moment inequalities and central limit properties of isotropic convex bodies, Diploma Thesis, Dresden University of Technology, 2000 (in German) .ps
  • Set-theoretic study of the initial value problem for first-order ODEs, Seminar paper, 2011 .pdf
  • Schauder’s fixed-point theorem, Seminar paper, 1998 (in German) .ps
  • Deterministic patterns in pseudorandom point sets, (with M. Potužník), Workshop paper, 1997 .pdf

Upcoming conferences of interest to me

Research Talks

  • Tiny giants – Mathematics looks at zooplankton (Georgia Institute of Technology, Atlanta, GA; 2016) .pdf
  • Linear stability of delayed reaction-diffusion systems (11th AIMS DSDEA, Orlando, FL; 2016) .pdf
  • Ergodicity and loss of capacity for a random family of concave maps (Huazhong University of Science and Technology, Wuhan, China; 2016) .pdf
  • A nonsmooth program for jamming hard spheres (Computer Science Colloquium, University of Wisconsin, Milwaukee, WI; 2014) .pdf
  • Pathogen evolution in switching environments (AMS spring meeting, Ames, IA; 2013) .pdf
  • Mathematical modeling of drug release devices (US-Australian Workshop, Sydney, Australia; 2013) .pdf
  • Size-structured populations with distributed states at birth (MMSB 2, Muizenberg, South Africa; 2012) .pdf
  • Continuous models for Wolbachia infections (8th ECMTB, Cracow, Poland; 2011) .pdf
  • Drug binding and dynamic instability of microtubules (3rd AMiTaNS, Albena, Bulgaria; 2011) .pdf
  • A kinetic model for cell movement in network tissues (NCTS, National Tsing Hua University, Hsinchu, ROC Taiwan; 2010) .pdf
  • Semigroup analysis of structured parasite populations (AMS spring meeting, St. Paul, MN; 2010) .pdf
  • Predicting the drug release kinetics of matrix tablets (MMSB 1, Tel Aviv, Israel; 2010) .pdf
  • On a size-structured two-phase population model with infinite states-at-birth (Shanks conference, Vanderbilt University, Nashville, TN; 2009) .pdf
  • A spatial model of tumor-host interaction: Application of chemotherapy (INRIA Rocquencourt, France; 2009) .pdf
  • A continuous model for microtubule dynamics (University of Paris VI “Pierre et Marie Curie”; 2008) .pdf
  • Transfer phenomena in biological populations (CIRM Luminy, Marseille, France; 2008) .pdf
  • Proliferation and motility effects of TGF-β (1st Joint AMS/NZMS meeting, Wellington, New Zealand; 2007) .pdf
  • Cytostatic and cytotoxic effects of a HER2 tyrosine kinase inhibitor (IFIP 23, Cracow, Poland; 2007) .pdf
  • Molecular seismology (ICIAM 2007, Zürich, Switzerland; 2007) .pdf
  • DNA binding activity of p53 (SEARCDE 26, Greensboro, NC; 2006) .pdf

My Former Institutions

Dresden University of Technology
Vanderbilt University
Institute for Mathematics and its Applications
German Mathematical Society