- On the relationship of steady states of continuous and discrete models arising from biology
University of Nebraska Lincoln, Lincoln, NE 68505, USA
Bull Math Biol 74:2779-92. 2012
..Our results also provide a novel method to analyze certain classes of nonlinear models using discrete mathematics...
- Reduction of Boolean network models
Department of Mathematics, University of Nebraska Lincoln, USA
J Theor Biol 289:167-72. 2011
..In particular, we use the reduction method to study steady states of Boolean networks and apply our results to models of Th-lymphocyte differentiation and the lac operon...
- Identification of control targets in Boolean molecular network models via computational algebra
Department of Mathematics, University of Kentucky, Lexington, 40506 0027, KY, USA
BMC Syst Biol 10:94. 2016
..The mathematical model type considered is that of Boolean networks. The potential control targets can be represented by a set of nodes and edges that can be manipulated to produce a desired effect on the system...
- Steady state analysis of Boolean molecular network models via model reduction and computational algebra
Department of Mathematics, University of Houston, 651 PGH Building, Houston TX, USA
BMC Bioinformatics 15:221. 2014
..While these methods represent a substantial improvement in scalability over exhaustive enumeration, the problem for large networks is still unsolved in general...
- Boolean models can explain bistability in the lac operon
Department of Mathematics, University of Nebraska Lincoln, Lincoln, Nebraska, USA
J Comput Biol 18:783-94. 2011
..This work suggests that the key to model qualitative dynamics of gene systems is the topology of the network and Boolean models are well suited for this purpose...
- The neural ring: an algebraic tool for analyzing the intrinsic structure of neural codes
Department of Mathematics, University of Nebraska Lincoln, Lincoln, NE, USA
Bull Math Biol 75:1571-611. 2013
..This allows us to algorithmically extract the canonical form associated to any neural code, providing the groundwork for inferring stimulus space features from neural activity alone...
- Modeling stochasticity and variability in gene regulatory networks
Department of Mathematics, Virginia Tech, Blacksburg, VA 24061 0123, USA
EURASIP J Bioinform Syst Biol 2012:5. 2012
..We applied our methods to two of the most studied regulatory networks, the outcome of lambda phage infection of bacteria and the p53-mdm2 complex...
- Polynomial algebra of discrete models in systems biology
Virginia Bioinformatics Institute, Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA
Bioinformatics 26:1637-43. 2010
..There is increasing evidence that such models can capture key dynamic features of biological networks and can be used successfully for hypothesis generation...