32 citations · 33 across the 7 of their papers we have counts for
6 papers · 1 filter
Extracting Global Dynamics of Loss Landscape in Deep Learning Models
Mohammed Eslami, Hamed Eramian, Marcio Gameiro +2
Deep learning models evolve through training to learn the manifold in which the data exists to satisfy an objective. It is well known that evolution leads to different final states…
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…
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…
Lattice Structures for Attractors III
William D. Kalies, Konstantin Mischaikow, Robert C. A. M. Vandervorst
The theory of bounded, distributive lattices provides the appropriate language for describing directionality and asymptotics in dynamical systems. For bounded, distributive lattice…
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…
Stability and Uniqueness of Slowly Oscillating Periodic Solutions to Wright's Equation
Jonathan Jaquette, Jean-Philippe Lessard, Konstantin Mischaikow
In this paper, we prove that Wright's equation has a unique slowly oscillating periodic solution (SOPS) for all parameter values ,…