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

Divergence and Stokes' Theorems01:06

Divergence and Stokes' Theorems

2.0K
The divergence and Stokes' theorems are a variation of Green's theorem in a higher dimension. They are also a generalization of the fundamental theorem of calculus. The divergence theorem and Stokes' theorem are in a way similar to each other; The divergence theorem relates to the dot product of a vector, while Stokes' theorem relates to the curl of a vector. Many applications in physics and engineering make use of the divergence and Stokes' theorems, enabling us to write...
2.0K
Network Function of a Circuit01:25

Network Function of a Circuit

392
Frequency response analysis in electrical circuits provides vital insights into a circuit's behavior as the frequency of the input signal changes. The transfer function, a mathematical tool, is instrumental in understanding this behavior. It defines the relationship between phasor output and input and comes in four types: voltage gain, current gain, transfer impedance, and transfer admittance. The critical components of the transfer function are the poles and zeros.
392
Reynolds Transport Theorem01:24

Reynolds Transport Theorem

1.4K
The Reynolds transport theorem provides a framework to relate the time rate of change of an extensive property within a system to that in a control volume, which is crucial for analyzing fluid dynamics. Extensive properties, such as mass, velocity, acceleration, temperature, and momentum, can be expressed in terms of the mass of a fluid portion. These properties are called extensive because they depend on the system's size, while intensive properties are their corresponding values per unit...
1.4K
Vector Algebra: Graphical Method01:10

Vector Algebra: Graphical Method

14.0K
Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. The vector sum of two (or more) vectors is called the resultant vector or, for short, the resultant.
We use the laws of geometry to construct resultant vectors, followed by trigonometry to find vector magnitudes and directions. For a geometric construction of the sum of two vectors in a plane, we follow the parallelogram rule. Suppose two vectors are at arbitrary positions. Translate either one of...
14.0K
Signal Flow Graphs01:18

Signal Flow Graphs

321
Signal-flow graphs offer a streamlined and intuitive approach to representing control systems, providing an alternative to traditional block diagrams. These graphs use branches to symbolize systems and nodes to represent signals, effectively illustrating the relationships and interactions within the system.
In a signal-flow graph, branches denote the system's transfer functions, while nodes represent the signals. The direction of signal flow is indicated by arrows, with the corresponding...
321
SFG Algebra01:16

SFG Algebra

176
In Signal Flow Graph (SFG) algebra, the value a node represents is determined by the sum of all signals entering that node. This summed value is then transmitted through every branch leaving the node, making the SFG a powerful tool for visualizing and analyzing control systems.
Each node in an SFG corresponds to a variable, and the interactions between nodes are represented by branches with associated gains. When multiple branches lead into a node, the value at that node is the sum of the...
176

You might also read

Related Articles

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

Sort by
Same author

Universal bounds for spreading on networks.

Chaos (Woodbury, N.Y.)·2024
Same journal

Topological dependence of viral mutation spread in complex host-interaction networks.

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

Multifractal signatures of Hamiltonian chaos in Hyperion's rotational dynamics.

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

Related Experiment Video

Updated: Sep 16, 2025

Modeling the Functional Network for Spatial Navigation in the Human Brain
05:55

Modeling the Functional Network for Spatial Navigation in the Human Brain

Published on: October 13, 2023

1.2K

Funnel theorems for spreading on networks.

Gadi Fibich1, Tomer Levin1, Steven Schochet1

  • 1Department of Applied Mathematics, Tel Aviv University, Tel Aviv, Israel.

Chaos (Woodbury, N.Y.)
|July 7, 2025
PubMed
Summary
This summary is machine-generated.

New funnel theorems bound susceptibility probabilities in Bass and susceptible-infected models on networks. These theorems offer precise calculations for adoption and infection levels in various network structures.

More Related Videos

The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

8.7K
Network Analysis of Foramen Ovale Electrode Recordings in Drug-resistant Temporal Lobe Epilepsy Patients
09:32

Network Analysis of Foramen Ovale Electrode Recordings in Drug-resistant Temporal Lobe Epilepsy Patients

Published on: December 18, 2016

12.5K

Related Experiment Videos

Last Updated: Sep 16, 2025

Modeling the Functional Network for Spatial Navigation in the Human Brain
05:55

Modeling the Functional Network for Spatial Navigation in the Human Brain

Published on: October 13, 2023

1.2K
The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

8.7K
Network Analysis of Foramen Ovale Electrode Recordings in Drug-resistant Temporal Lobe Epilepsy Patients
09:32

Network Analysis of Foramen Ovale Electrode Recordings in Drug-resistant Temporal Lobe Epilepsy Patients

Published on: December 18, 2016

12.5K

Area of Science:

  • Network Science
  • Mathematical Modeling
  • Epidemiology

Background:

  • Understanding information and disease propagation on networks is crucial.
  • Existing models often lack precise analytical solutions for complex network structures.

Purpose of the Study:

  • To derive and present novel funnel theorems for Bass and susceptible-infected models.
  • To provide bounds for susceptibility probabilities on modified networks.
  • To enable exact expressions for adoption/infection probabilities and levels.

Main Methods:

  • Derivation of funnel theorems for network models.
  • Analysis of susceptibility probabilities on modified networks with restricted incoming edges.
  • Application to networks with and without cycles.

Main Results:

  • Funnel theorems establish lower and upper bounds for susceptibility differences.
  • The theorems allow for simplification by considering single-edge influence.
  • Exact explicit expressions for adoption/infection probabilities are obtained.

Conclusions:

  • The derived funnel theorems offer a powerful analytical tool for network models.
  • These theorems facilitate precise calculations of adoption and infection dynamics.
  • The approach is applicable to diverse network types, enhancing predictive capabilities.