Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Region of Convergence of Laplace Tarnsform01:20

Region of Convergence of Laplace Tarnsform

750
The Region of Convergence (ROC) is a fundamental concept in signal processing and system analysis, particularly associated with the Laplace transform. The ROC represents an area in the complex plane where the Laplace transform of a given signal converges, determining the transform's applicability and utility.
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This...
750
Lattice Centering and Coordination Number02:33

Lattice Centering and Coordination Number

10.2K
The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
Types of Unit Cells
Imagine taking a large number of identical...
10.2K
Second Derivatives and Laplace Operator01:22

Second Derivatives and Laplace Operator

1.8K
The first order operators using the del operator include the gradient, divergence and curl. Certain combinations of first order operators on a scalar or vector function yield second order expressions. Second-order expressions play a very important role in mathematics and physics. Some second order expressions include the divergence and curl of a gradient function, the divergence and curl of a curl function, and the gradient of a divergence function.
Consider a scalar function. The curl of its...
1.8K
Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

452
In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
452
Routh-Hurwitz Criterion I01:15

Routh-Hurwitz Criterion I

353
Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
353
Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

3.5K
The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
3.5K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Introduction to Focus Issue: Symmetry and optimization in the synchronization and collective behavior of complex systems.

Chaos (Woodbury, N.Y.)·2020
Same author

Machine learning for the New York City power grid.

IEEE transactions on pattern analysis and machine intelligence·2011
Same journal

Exploring mechanisms for reversal of flow in tunicate hearts.

Chaos (Woodbury, N.Y.)·2026
Same journal

State estimation in spatiotemporal chaos via low-rank StatFEM.

Chaos (Woodbury, N.Y.)·2026
Same journal

Universal response functions in driven dissipative tunneling dynamics.

Chaos (Woodbury, N.Y.)·2026
Same journal

A network-based approach to characterize the dynamics of the coupling field of thermoacoustic oscillators in annular geometry.

Chaos (Woodbury, N.Y.)·2026
Same journal

Data-driven soliton manifold approximations for dark and bright waves: Some prototypical 1D case examples.

Chaos (Woodbury, N.Y.)·2026
Same journal

Gap junction architecture and synchronization clusters in the thalamic reticular nuclei.

Chaos (Woodbury, N.Y.)·2026
See all related articles

Related Experiment Video

Updated: Oct 1, 2025

Optimization of Synthetic Proteins: Identification of Interpositional Dependencies Indicating Structurally and/or Functionally Linked Residues
07:08

Optimization of Synthetic Proteins: Identification of Interpositional Dependencies Indicating Structurally and/or Functionally Linked Residues

Published on: July 14, 2015

7.4K

Balanced Hodge Laplacians optimize consensus dynamics over simplicial complexes.

Cameron Ziegler1, Per Sebastian Skardal2, Haimonti Dutta3

  • 1Department of Mathematics, University at Buffalo, State University of New York, Buffalo, New York 14260, USA.

Chaos (Woodbury, N.Y.)
|March 2, 2022
PubMed
Summary
This summary is machine-generated.

We studied consensus dynamics on edges within simplicial complexes, finding that balancing higher- and lower-order interactions accelerates collective behavior. Network topology, specifically the dispersion of triangles, also impacts consensus speed.

More Related Videos

Convergent Polishing: A Simple, Rapid, Full Aperture Polishing Process of High Quality Optical Flats & Spheres
13:07

Convergent Polishing: A Simple, Rapid, Full Aperture Polishing Process of High Quality Optical Flats & Spheres

Published on: December 1, 2014

11.3K
Author Spotlight: Advancing Cell Membrane Biophysics - Exploring Interactions and Challenges Through Experimental and Computational Approaches
07:31

Author Spotlight: Advancing Cell Membrane Biophysics - Exploring Interactions and Challenges Through Experimental and Computational Approaches

Published on: September 1, 2023

2.6K

Related Experiment Videos

Last Updated: Oct 1, 2025

Optimization of Synthetic Proteins: Identification of Interpositional Dependencies Indicating Structurally and/or Functionally Linked Residues
07:08

Optimization of Synthetic Proteins: Identification of Interpositional Dependencies Indicating Structurally and/or Functionally Linked Residues

Published on: July 14, 2015

7.4K
Convergent Polishing: A Simple, Rapid, Full Aperture Polishing Process of High Quality Optical Flats & Spheres
13:07

Convergent Polishing: A Simple, Rapid, Full Aperture Polishing Process of High Quality Optical Flats & Spheres

Published on: December 1, 2014

11.3K
Author Spotlight: Advancing Cell Membrane Biophysics - Exploring Interactions and Challenges Through Experimental and Computational Approaches
07:31

Author Spotlight: Advancing Cell Membrane Biophysics - Exploring Interactions and Challenges Through Experimental and Computational Approaches

Published on: September 1, 2023

2.6K

Area of Science:

  • Network science
  • Algebraic topology
  • Computational neuroscience

Background:

  • Understanding network dynamics on higher-order structures (simplices) is crucial but underexplored.
  • Neuroscience suggests neural computations may arise from groups of neurons, highlighting the importance of higher-order interactions.
  • Existing models often focus on pairwise interactions, neglecting complex network structures.

Purpose of the Study:

  • To investigate consensus dynamics on edges within simplicial complexes.
  • To analyze the influence of higher- and lower-order interactions on convergence speed.
  • To explore the role of network topology in collective dynamics.

Main Methods:

  • Utilized a generalized Hodge Laplacian for simplicial complexes.
  • Applied techniques from algebraic topology to analyze dynamics.
  • Employed Hodge decomposition to study interaction balancing and convergence acceleration.

Main Results:

  • Collective dynamics converge to a subspace corresponding to the simplicial complex's homology space.
  • Optimal balancing of higher- and lower-order interactions maximally accelerates convergence, aligning with curl and gradient subspace dynamics.
  • Consensus over edges is faster when two-simplices (triangles) are dispersed rather than clustered.

Conclusions:

  • Higher-order interactions significantly influence network dynamics, particularly consensus processes.
  • The Hodge Laplacian and algebraic topology provide powerful tools for analyzing complex network dynamics.
  • Optimizing interaction strengths and considering network topology are key to controlling and accelerating collective behavior in higher-order networks.