#### 8,939 Citations

Empirical Dynamic Modeling

- 2020

Empirical dynamic modeling (EDM) is an emerging non-parametric framework for modeling nonlinear dynamic systems. EDM is based on the mathematical theory of reconstructing attractor manifolds from… Expand

Persistent Homology of Complex Networks for Dynamic State Detection

- Computer Science, Physics
- Physical review. E
- 2019

It is shown how persistent homology, a tool from TDA, can be used to yield a compressed, multi-scale representation of the graph that can distinguish between dynamic states such as periodic and chaotic behavior. Expand

Analysis of Flow Dynamics in the High-Flux Gas-Solid Riser Using Trajectory Distances across Attractors Reconstructed from Solid Concentration Signals

- Engineering
- 2018

The study of the entrance and wall dynamics of a high-flux gas-solid riser was conducted using trajectory distances of the reconstructed attractors from solid concentration signals collected from a… Expand

Complex Systems Research in Educational Psychology: Aligning Theory and Method

- Psychology, Medicine
- Educational psychologist
- 2018

A philosophically and theoretically sourced definition of complex systems research organized around complex, dynamic, and emergent ontological characteristics that is useful and appropriate for educational psychology is outlined. Expand

Quantitatively Characterizing Drug-Induced Arrhythmic Contractile Motions of Human Stem Cell-Derived Cardiomyocytes.

- Medicine
- Biotechnology and bioengineering
- 2018

This paper generated contractile motion data from beating hiPSC-CMs using motion tracking software based on optical flow analysis, and implemented a computational algorithm, phase space reconstruction (PSR), to derive parameters (embedding, regularity, and fractal dimensions) to further characterize the dynamic nature of the cardiac contractile motions. Expand

Data Analysis Methods using Persistence Diagrams

- Computer Science
- 2017

A new distance is introduced on the space of persistence diagrams, and it is shown that it is useful in detecting changes in geometry and topology, which is essential for the supervised learning problem. Expand

Selección de Características Mediante un Algoritmo Genético para el Diagnóstico de Caoticidad en Series de Tiempo Usando un Clasificador con Redes Neuronales

- Philosophy
- 2017

En este trabajo presentamos una metodologia para el diagnostico de caos en series de tiempo basada en el calculo de 118 caracteristicas sobre la serie de tiempo y un clasificador construido con una… Expand

Physiological Signal Analysis: A Topo-Geometric Perspective.

- Physics
- 2016

EMRANI, SABA. Physiological Signal Analysis: A Topo-Geometric Perspective. (Under the direction of Dr. Hamid Krim.) The first goal of this dissertation is to find evidence of periodicity in data with… Expand

Development of new analytical techniques for chaotic time series

- Mathematics
- 2015

In the present thesis two main results are presented. The first is a study of the statistical properties of the finite-time maximum Lyapunov exponent determined out of a time series by using the… Expand

Analog Forecasting with Dynamics-Adapted Kernels

- Physics, Mathematics
- 2014

Analog forecasting is a nonparametric technique introduced by Lorenz in 1969 which predicts the evolution of states of a dynamical system (or observables defined on the states) by following the… Expand

#### References

SHOWING 1-10 OF 21 REFERENCES

GENERIC OBSERVABILITY OF DIFFERENTIABLE SYSTEMS

- Mathematics
- 1981

A dynamical system consists of a smooth vectorfield defined on a differentiable manifold, and a smooth mapping from the manifold to the real numbers. The vectorfield represents the dynamics of a… Expand

2[he pre-turbutent transitions and flows of a viscous fluid between concentric rotating cylinders

- 2[he pre-turbutent transitions and flows of a viscous fluid between concentric rotating cylinders
- 1980

Xhe dimension of the strange attractor for a class of difference systems, preprint

- Xhe dimension of the strange attractor for a class of difference systems, preprint
- 1980

Dynamical instabilities and the transition to chaotic Taylor vortex flow

- Physics
- 1979

We have used the technique of laser-Doppler velocimetry to study the transition to turbulence in a fluid contained between concentric cylinders with the inner cylinder rotating. The experiment was… Expand

Geometry from the time series, preprint

- Geometry from the time series, preprint
- 1979

Ergodic Theory on Compact Spaces

- Mathematics
- 1976

Measure-theoretic dynamical systems.- Measures on compact metric spaces.- Invariant measures for continuous tranformations.- Time averages.- Ergodicity.- Mixing and transitivity.- Shifts and… Expand

The Hopf Bifurcation and Its Applications

- Mathematics
- 1976

The goal of these notes is to give a reasonably complete, although not exhaustive, discussion of what is commonly referred to as the Hopf bifurcation with applications to specific problems, including… Expand