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
Math 703
Madison
Math Circle
Madison Putnam
Club
Workshops
1st
Madison Workshop on Mathematics of Reaction Networks
2nd Madison Workshop
on Mathematics of Reaction Networks
Research Interests: Mathematical and Computational
Methods in Biology and Medicine
Publications
- Endotactic Networks and Toric
Differential Inclusions, (with
Abhishek Deshpande), https://arxiv.org/abs/1906.08384
- A reaction network approach to
the theory of acoustic wave turbulence, (with Stanislav Boldyrev, Leslie Smith, Minh Binh Tran), https://arxiv.org/abs/1901.03005
- Convergence to the complex
balanced equilibrium for some chemical reaction-diffusion systems with
boundary equilibria, (with Jiaxin Jin, Casian Pantea, Adrian Tudorascu), , https://arxiv.org/abs/1812.07707
- An efficient characterization
of complex balanced, detailed balanced, and weakly reversible systems, (with Jiaxin Jin, Polly Yu), https://arxiv.org/abs/1812.06214
, to appear in SIAM Journal on Applied Mathematics.
- Realizations of kinetic
differential equations, (with
Matthew Johnston, Gabor Szederkenyi, Elisa Tonello, Janos Toth, Polly Yu), https://arxiv.org/abs/1907.07266
to appear in Mathematical
Biosciences and Engineering.
- A generalization of Birch's
theorem and vertex-balanced steady states for generalized mass-action
systems, (with Stefan Muller, Casian Pantea, Polly Y.
Yu), https://arxiv.org/abs/1802.06919
to appear in Mathematical Biosciences and Engineering.
- Polynomial Dynamical Systems,
Reaction Networks, and Toric Differential
Inclusions, PDF http://arxiv.org/abs/1901.02544
, SIAM Journal on Applied Algebra and Geometry 3(1) 87-106, 2019.
- A reaction network approach to
the convergence to equilibrium of quantum Boltzmann equations for Bose
gases, (with Minh-Binh Tran), https://arxiv.org/abs/1608.05438
- Mathematical analyis of chemical reaction systems, (with Polly Y. Yu), Israel Journal of
Chemistry, 58, 2018, PDF https://arxiv.org/abs/1805.10371
- Toric Differential Inclusions and a Proof of the Global
Attractor Conjecture, http://arxiv.org/abs/1501.02860
- Robust persistence and
permanence of polynomial and power law dynamical systems, (with James Brunner), SIAM
Journal on Applied Mathematics, 78(2):801-825, 2018. https://arxiv.org/abs/1705.06785
- Conditions for Extinction
Events in Chemical Reaction Networks with Discrete State Spaces, (with Matthew Johnston, David Anderson, Robert
Brijder), Journal
of Mathematical Biology 2017, https://doi.org/10.1007/s00285-017-1182-x
, https://arxiv.org/abs/1701.02012
- High Throughput Analyses of
Budding Yeast ARSs Reveal New DNA Elements Capable of Conferring
Centromere-Independent Plasmid Propagation, (with Timothy Hoggard, Ivan Liachko, Cassaundra Burt, Troy Meikle, Katherine
Jiang, Maitreya Dunham, and Catherine A. Fox),
G3: Genes, Genomes, Genetics 6(4):993-1012,
2016. PDF
- Lyapunov functions, stationary
distributions, and non-equilibrium potential for reaction networks, (with David F. Anderson, Manoj Gopalkrishnan, and Carsten Wiuf), Bulletin
of Mathematical Biology, 77(9): 1744-1767, 2015. PDF
- 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.