53 citations · 137 across the 21 of their papers we have counts for
23 papers
Characterizing High-dimensional Dynamics by Combinatorial-Topological Methods on a Latent Space
Patrick Bailon, Marcio Gameiro, Brittany Gelb +5
Combinatorial-topological methods for characterizing dynamics are rigorous, generalizable, computable, and they only require approximations, but the dimension of the phase space is…
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…
Inferring Long-term Dynamics of Ecological Communities Using Combinatorics
William S. Cuello, Marcio Gameiro, Juan A. Bonachela +1
In an increasingly changing world, predicting the fate of species across the globe has become a major concern. Understanding how the population dynamics of various species and comm…
A framework for rigorous computational methods using Haar wavelets for differential equations
Guilherme Nakassima, Marcio Gameiro
This work presents a framework for a-posteriori error-estimating algorithms for differential equations which combines the radii polynomial approach with Haar wavelets. By using Haa…
A yeast cell cycle pulse generator model shows consistency with multiple oscillatory and checkpoint mutant datasets
Julian Fox, Breschine Cummins, Robert C. Moseley +2
The regulatory mechanisms driving progression of the yeast cell cycle appears to be comprised of an interacting network of transcription factors (TFs), cyclin-dependent kinases (CD…
Data-Efficient Characterization of the Global Dynamics of Robot Controllers with Confidence Guarantees
Ewerton R. Vieira, Aravind Sivaramakrishnan, Yao Song +5
This paper proposes an integration of surrogate modeling and topology to significantly reduce the amount of data required to describe the underlying global dynamics of robot contro…
Identifying Nonlinear Dynamics with High Confidence from Sparse Data
Bogdan Batko, Marcio Gameiro, Ying Hung +3
We introduce a novel procedure that, given sparse data generated from a stationary deterministic nonlinear dynamical system, can characterize specific local and/or global dynamic b…
Towards computational Morse-Floer homology: forcing results for connecting orbits by computing relative indices of critical points
Jan Bouwe van den Berg, Marcio Gameiro, Jean-Philippe Lessard +1
To make progress towards better computability of Morse-Floer homology, and thus enhance the applicability of Floer theory, it is essential to have tools to determine the relative i…
Morse Graphs: Topological Tools for Analyzing the Global Dynamics of Robot Controllers
Ewerton R. Vieira, Edgar Granados, Aravind Sivaramakrishnan +3
Understanding the global dynamics of a robot controller, such as identifying attractors and their regions of attraction (RoA), is important for safe deployment and synthesizing mor…
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…
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…
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…
On the feasibility and convergence of the inexact Newton method under minor conditions on the error terms
Eduardo Ramos, Marcio Gameiro, Victor Nolasco
In this paper we introduce a semi-local theorem for the feasibility and convergence of the inexact Newton method, regarding the sequence ,…
Rigorous Enclosures of Solutions of Neumann Boundary Value Problems
Eduardo Ramos, Victor Nolasco, Marcio Gameiro
This paper is dedicated to the problem of isolating and validating zeros of non-linear two point boundary value problems. We present a method for such purpose based on the Newton-K…
Interaction network analysis in shear thickening suspensions
Marcio Gameiro, Abhinendra Singh, Lou Kondic +2
Dense, stabilized, frictional particulate suspensions in a viscous liquid undergo increasingly strong continuous shear thickening (CST) as the solid packing fraction, , increase…
A Framework for the Numerical Computation and a Posteriori Verification of Invariant Objects of Evolution Equations
Jordi-Lluís Figueras, Marcio Gameiro, Jean Philippe Lessard +1
We develop a theoretical framework for computer-assisted proofs of the existence of invariant objects in semilinear PDEs. The invariant objects considered in this paper are equilib…
Rigorous numerics for ill-posed PDEs: periodic orbits in the Boussinesq equation
R. Castelli, M. Gameiro, J. -P. Lessard
In this paper, we develop computer-assisted techniques for the analysis of periodic orbits of ill-posed partial differential equations. As a case study, our proposed method is appl…
Continuation of Point Clouds via Persistence Diagrams
Marcio Gameiro, Yasuaki Hiraoka, Ippei Obayashi
In this paper, we present a mathematical and algorithmic framework for the continuation of point clouds by persistence diagrams. A key property used in the method is that the persi…
Homological Characterizations of Spiral Defect Chaos in Rayleigh-Benard Convection
Kapilanjan Krishan, Marcio Gameiro, Konstantin Mischaikow +1
We use a quantitative topological characterization of complex dynamics to measure geometric structures. This approach is used to analyze the weakly turbulent state of spiral defect…
Homology and symmetry breaking in Rayleigh-Benard convection: Experiments and simulations
Kapilanjan Krishan, Huseyin Kurtuldu, Michael F. Schatz +2
Algebraic topology (homology) is used to analyze the weakly turbulent state of spiral defect chaos in both laboratory experiments and numerical simulations of Rayleigh-Benard conve…