4 papers
Boolean models coarsely sample continuous dynamics of regulatory networks
Breschine Cummins, Marcio Gameiro, Tomáš Gedeon +2
Boolean models are widely used to characterize the dynamics of gene regulatory networks. However, their coarse state discretization limits their ability to capture complex continuo…
Data-driven Identification of Attractors Using Machine Learning
Marcio Gameiro, Brittany Gelb, William Kalies +3
In this paper we explore challenges in developing a topological framework in which machine learning can be used to robustly characterize global dynamics. Specifically, we focus on…
Rigorously Characterizing Dynamics with Machine Learning
Marcio Gameiro, Brittany Gelb, Konstantin Mischaikow
The identification of dynamics from time series data is a problem of general interest. It is well established that dynamics on the level of invariant sets, the primary objects of i…
Global Dynamics of Ordinary Differential Equations: Wall Labelings, Conley Complexes, and Ramp Systems
Marcio Gameiro, Tomáš Gedeon, Hiroshi Kokubu +5
We introduce a combinatorial topological framework for characterizing the global dynamics of ordinary differential equations (ODEs). The approach is motivated by the study of gene…