17 citations · 51 across the 13 of their papers we have counts for
11 papers · 1 filter
A smooth Riemannian metric on an arbitrary product of spheres with Bernoulli geodesic flow
Keith Burns, Tomas Gedeon, Yuping Ruan
We construct a smooth Riemannian metric on an arbitrary product of spheres whose geodesic flow is Bernoulli with respect to the Liouville measure.
A Nonlinear Delay Model for Metabolic Oscillations in Yeast Cells
Max M. Chumley, Firas A. Khasawneh, Andreas Otto +1
We introduce two time-delay models of metabolic oscillations in yeast cells. Our model tests a hypothesis that the oscillations occur as multiple pathways share a limited resource…
Extending combinatorial regulatory network modeling to include activity control and decay modulation
Bree Cummins, Marcio Gameiro, Tomas Gedeon +3
Understanding how the structure of within-system interactions affects the dynamics of the system is important in many areas of science. We extend a network dynamics modeling platfo…
Operon Dynamics with State Dependent Transcription and/or Translation Delays
Tomas Gedeon, Antony R. Humphries, Michael C. Mackey +3
Transcription and translation retrieve and operationalize gene encoded information in cells. These processes are not instantaneous and incur significant delays. In this paper we st…
Equilibria and their Stability in Networks with Steep Sigmoidal Nonlinearities
William Duncan, Tomas Gedeon, Hiroshi Kokubu +2
In this paper we investigate equilibria of continuous differential equation models of network dynamics. The motivation comes from gene regulatory networks where each directed edge…
Joint Realizability of Monotone Boolean functions
Peter Crawford-Kahrl, Bree Cummins, Tomas Gedeon
The study of monotone Boolean functions (MBFs) has a long history. We explore a connection between MBFs and ordinary differential equation (ODE) models of gene regulation, and, in…
Rational design of complex phenotype via network models
Marcio Gameiro, Tomas Gedeon, Shane Kepley +1
We demonstrate a modeling and computational framework that allows for rapid screening of thousands of potential network designs for particular dynamic behavior. To illustrate this…
Comparison of two combinatorial models of global network dynamics
Peter Crawford-Kahrl, Bree Cummins, Tomas Gedeon
Modeling the dynamics of biological networks introduces many challenges, among them the lack of first principle models, the size of the networks, and difficulties with parameteriza…
Model rejection and parameter reduction via time series
Bree Cummins, Tomas Gedeon, Shaun Harker +1
We show how a graph algorithm for finding matching labeled paths in pairs of labeled directed graphs can be used to perform model validation for a class of dynamical systems includ…
Combinatorial Representation of Parameter Space for Switching Systems
Bree Cummins, Tomas Gedeon, Shaun Harker +2
We describe the theoretical and computational framework for the Dynamic Signatures for Genetic Regulatory Network (DSGRN) database. The motivation stems from urgent need to underst…
Global Dynamics for Steep Sigmoidal Nonlinearities in Two Dimensions
Tomas Gedeon, Shaun Harker, Hiroshi Kokubu +2
We introduce a novel approach to obtaining mathematically rigorous results on the global dynamics of ordinary differential equations. Motivated by models of regulatory networks, we…