**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**

1^{st}
Madison Workshop on Mathematics of Reaction Networks

2^{nd} 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.