Gheorghe Craciun
Professor
Department of Mathematics and
Department of Biomolecular
Chemistry
University of Wisconsin-Madison
Contact Information:
405 Van Vleck Hall
480 Lincoln Dr
Madison, WI 53706-1388
Phone: (608) 265-3391
Fax: (608) 263-8891
E-mail: craciun at math dot wisc dot edu
Teaching
Research Interests: Mathematical and Computational
Methods in Biology and Medicine
Publications
- Toric Differential Inclusions and a Proof of the Global
Attractor Conjecture, http://arxiv.org/abs/1501.02860
- The QSSA in chemical kinetics:
As taught and as practiced,
(with Casian Pantea,
Ankur Gupta, and James B. Rawlings), in Discrete and Topological Models in
Molecular Biology, edited by N. Jonoska
and M. Saito, pages 419-442, Natural Computing Series, Springer 2014. PDF
- Modeling the endocrine control
of vitellogenin production in female rainbow
trout, (with Kaitlin Sundling, Irvin Schultz, Sharon Hook, James Nagler, Tim Cavileer, Joseph Verducci, Yushi Liu, Jonghan Kim, and William Hayton), Mathematical Biosciences and Engineering 11(3): 621-639, 2014.
PDF
- Dynamical properties of
Discrete Reaction Networks,
(with Loïc Paulevé
and Heinz Koeppl), Journal of Mathematical Biology, 69(1): 55-72, 2014. PDF
- Persistence and permanence of
mass-action and power-law dynamical systems, (with Fedor Nazarov and Casian Pantea), SIAM
Journal on Applied Mathematics, 73(1): 305-329, 2013. PDF
- Most homeomorphisms with a
fixed point have a Cantor set of fixed points, Archiv der Mathematik 100(1), 95-100, 2013. PDF
- Graph-theoretic conditions for
zero-eigenvalue Turing instability in general chemical reaction
networks, (with Maya Mincheva), Mathematical Biosciences and Engineering 10(4):1207-1226,
2013.
PDF
- Statistical Model for Biochemical
Networks Inference, (with Jajae Kim, Casian Pantea and Grzegorz A. Rempala), Communications
in Statistics: Simulation and Computation, 42(1) 121-137, 2013. PDF
- Finding invariant sets for
biological systems using monomial domination, (with Elias August and Heinz Koeppl), Proceedings
of the IEEE International Conference on Decision and Control,
3001-3006, 2012.
- Periodic Patterns in
Distributions of Peptide Masses,
(with Shane Hubler), Biosystems 109(2):
179-185, 2012. PDF
- Counting Chemical Compositions using Ehrhart Quasi-Polynomials, (with
Shane Hubler), Journal
of Mathematical Chemistry, 50:9, 2446-2470, 2012. PDF
- Global injectivity
and multiple equilibria in uni-
and bi-molecular reaction networks, (with Casian Pantea
and Heinz Koeppl), Discrete and Continuous Dynamical Systems Series B, 17:6,
2153-2170, 2012. PDF
- Mass distributions of linear
chain polymers, (with Shane Hubler), Journal
of Mathematical Chemistry, 50:6, 1458-1483, 2012. PDF
- Graph-theoretic characterizations
of multistability and monotonicity for
biochemical reaction networks, (with Casian Pantea and Eduardo Sontag), in Koeppl,
H.; Densmore, D.; Setti,
G.; di Bernardo, M. (Eds.), Design
and Analysis of Biomolecular Circuits,
Springer, 2011. PDF
- Computational methods for
analyzing bistability in biochemical reaction
networks, (with Casian Pantea) Proceedings of the IEEE
International Symposium on Circuits and Systems, 549-553, 2010. PDF
- Product-form stationary
distributions for deficiency zero chemical reaction networks, (with David F. Anderson and Thomas G. Kurtz),
Bulletin of Mathematical Biology,
72:8, 1947-1970, 2010. PDF
- Graph theoretic approaches to injectivity in general chemical reaction systems, (with Murad Banaji), Advances
in Applied Mathematics 44 168-184, 2010. PDF
- Some Geometric Aspects of Control
Points for Toric Patches, (with Luis David Garcia-Puente, Frank Sottile), Proceedings of the 7th international
conference on Mathematical Methods for Curves and Surfaces, (M. Daehlen et al. Eds). Lecture Notes in Computer Science
5862, 111-135, Springer Heidelberg, 2010. PDF
- Multiple Equilibria
in Complex Chemical Reaction Networks: Semiopen
Mass Action Systems (with
Martin Feinberg), SIAM Journal on
Applied Mathematics 70(6): 1859-1877, 2010. PDF
- Algebraic methods for inferring
biochemical networks: a maximum likelihood approach, (with Casian Pantea and Grzegorz A. Rempala), Computational
Biology and Chemistry, 33(5):361-367, 2009. PDF
- Graph-theoretic approaches to injectivity and multiple equilibria
in systems of interacting elements, (with Murad Banaji),
Communications in Mathematical Sciences 7:4,
867–900, 2009. PDF
- Time course analysis of
microarray data for the pathway of reproductive development in female
rainbow trout, (with Yushi Liu, Joseph Verducci,
Irvin Schultz, Sharon Hook, James Nagler,
Kaitlin Sundling, and William Hayton), Statistical
Analysis and Data Mining, 2:3, 192-208,
2009. PDF
- Toric Dynamical Systems,
(with Alicia Dickenstein, Anne Shiu, Bernd Sturmfels), Journal of Symbolic Computation 44:11,
1551–1565 , 2009. PDF
- Homotopy methods for counting reaction network equilibria, (with J. William Helton, Ruth J. Williams), Mathematical Biosciences 216:2, 140-149,
2008. PDF
- A lifespan-extending form of
autophagy employs the vacuole-vacuole fusion machinery, (with Fusheng Tang,
Joseph Watkins, Maria Bermudez, Russell Gray, Adam Gaban,
Ken Portie, Stephen Grace, Maurice Kleve), Autophagy 4:7, 874-886, 2008. PDF
- Multigraph conditions for multistability,
oscillations and pattern formation in biochemical reaction networks, (with Maya Mincheva),
Proceedings of IEEE 96:8,
1281-1291, 2008. PDF
- A Combinatorial H4 Tail Library for
Exploring the Histone Code,
(with Adam L. Garske, John M. Denu), Biochemistry
47:31, 8094-8102, 2008. PDF
- Valence Parity Renders z-type ions
Chemically Distinct, (with
Shane Hubler, April Jue,
Jason Keith, Graeme McAlister, Joshua Coon), Journal of the American Chemical Society 130:20, 6388-6394,
2008. PDF
- Identifiability of chemical reaction networks, (with Casian Pantea), Journal
of Mathematical Chemistry 44:1, 244-259, 2008. PDF
- Understanding Bistability
in Complex Enzyme-Driven Reaction Networks, (with Martin Feinberg and Yangzhong
Tang), Proceedings of the
National Academy of Sciences 103:23, 8697-8702, 2006. PDF
- Approximate Traveling Waves in
Linear Reaction-Hyperbolic Equations, (with Avner
Friedman), SIAM Journal on
Mathematical Analysis 38:3, 741-758, 2006. PDF
- Multiple Equilibria
in Complex Chemical Reaction Networks: Extensions to Entrapped Species
Models,
(with Martin Feinberg), IEE
Proceedings Systems Biology 153:4, 179-186, 2006. PDF
- Multiple Equilibria
in Complex Chemical Reaction Networks: II. The Species-Reactions Graph, (with Martin Feinberg), SIAM Journal on Applied Mathematics 66:4, 1321-1338, 2006. PDF
- Multiple Equilibria
in Complex Chemical Reaction Networks: I. The Injectivity
Property,
(with Martin Feinberg), SIAM
Journal on Applied Mathematics 65:5,
1526-1546, 2005. PDF
- A Model of Intracellular Transport
of Particles in an Axon, (with
Avner Friedman), Journal of Mathematical Biology, 51:2, 217-246, 2005. PDF
- A Distributed Parameter
Identification Problem in Neuronal Cable Theory Models, (with Jonathan Bell), Mathematical Biosciences 194:1, 1-19, 2005. PDF
- Data Sources and Computational
Approaches for Generating Models of Gene Regulatory Networks, (with Baltazar Aguda and Rengul Cetin-Atalay), Reviews
in Computational Chemistry, Vol. 21, edited by Kenny Lipkowitz, Raima Larter, and Thomas
R. Cundari, 2005. PDF
- Spatial Domain Wavelet Design for
Feature Preservation in Computational Datasets, (with Ming Jiang, David Thompson, and Raghu Machiraju), accepted by IEEE Transactions on Visualization and Computer Graphics 11:2,
149-159, 2005. PDF
- Controlling Release from the Lipidic Cubic Phase by Selective Alkylation, (with Jeffrey Clogston,
David Hart, and Martin Caffrey), Journal of Controlled Release,
102:2, 441-461, 2005. PDF
- Everybody Else Is: Networks, Power
Laws and Peer Contagion in the Aggressive Recess Behavior, (with Keith Warren and Dawn Anderson-Butcher),
Nonlinear Dynamics, Psychology,
and Life Sciences, 9:2, 155-173, 2005.
- Mathematical Analysis of a Modular
Network Coordinating the Cell Cycle and Apoptosis, (with Baltazar Aguda and Avner Friedman),
Mathematical Biosciences and
Engineering, 2:3, 473-485, 2005. PDF
- Mathematical Models of the Cell
Cycle and Apoptosis, (with
David Goulet, Namyong
Lee, Taras Odushkin,
Galen Cook Wiens), MBI Technical Report, 2004.
- Image Segmentation using Neuronal
Oscillators, (with Talia Konkle, Ning Jiang, Jie Zhang, Fatma Gurel, Christopher Scheper),
MBI Technical Report, 2003.
- Physics-based feature mining for
large data exploration, (with
D.S. Thompson, R.K. Machiraju, M. Jiang, J.S. Nair, S.S.D. Venkata),
Computing in Science and Engineering 4:4, 22-30, 2002. PDF
- The Output of Chemical Reactors Is
Almost Always Unique. Why ?, Proceedings of the 14th Annual Edward F.
Hayes Research Forum, p. 184-189, 2001.
- A Framework for Filter Design
Emphasizing Multiscale Feature Preservation, (with David Thompson, Raghu Machiraju and Ming Jiang), Proceedings of the AHPCRC
and CASC/LLNL Third Workshop on Mining Scientific Datasets
, p. 105-111, 2001.
- The Dimension Print of Most Convex
Surfaces, (with Tudor Zamfirescu), Monatshefte
fur Mathematik 123:3, 203-207, 1997. PDF
- Most Homeomorphisms of the Circle
are Semiperiodic, (with Paul Horja, Mihai Prunescu, Tudor Zamfirescu), Archiv der Mathematik 64:5, 452-458, 1995. PDF
- Generic Properties of the
Homeomorphisms of Spheres, Archiv der Mathematik
62:4, 349-353, 1994.
- On a Covering Theorem, Mathematical
Reports 44:2, 109-112, 1992.