155 citations · 542 across the 36 of their papers we have counts for
7 papers · 1 filter
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…
Discretization strategies for computing Conley indices and Morse decompositions of flows
Konstantin Mischaikow, Marian Mrozek, Frank Weilandt
Conley indices and Morse decompositions of flows can be found by using algorithms which rigorously analyze discrete dynamical systems. This usually involves integrating a time disc…
Structure of force networks in tapped particulate systems of disks and pentagons (Part 2): Persistence analysis
L. Kondic, M. Kramar, L. A. Pangolin +2
In the companion paper~\cite{paper1}, we use classical measures based on force probability density functions (PDFs), as well as Betti numbers (quantifying the number of components,…
Structure of force networks in tapped particulate systems of disks and pentagons (Part 1): Clusters and Loops
L. A. Pugnaloni, C. M. Carlevaro, M. Kramar +2
The force network of a granular assembly, defined by the contact network and the corresponding contact forces, carries valuable information about the state of the packing. Simple a…
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…
Analysis of Kolmogorov Flow and Rayleigh-Bénard Convection using Persistent Homology
Miroslav Kramar, Rachel Levanger, Jeffrey Tithof +5
We use persistent homology to build a quantitative understanding of large complex systems that are driven far-from-equilibrium; in particular, we analyze image time series of flow…