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

Network Function of a Circuit01:25

Network Function of a Circuit

285
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.
285
Uniform Distribution01:19

Uniform Distribution

4.9K
The uniform distribution is a continuous probability distribution of events with an equal probability of occurrence. This distribution is rectangular.
Two essential properties of this distribution are
4.9K
Distribution and Dispersion00:54

Distribution and Dispersion

21.7K
To understand intra-specific interactions in populations, scientists measure the spatial arrangement of species individuals. This geographic arrangement is known as the species distribution or dispersion. Highly territorial species exhibit a uniform distribution pattern, in which individuals are spaced at relatively equal distances from one another. Species that are highly tied to particular resources, such as food or shelter, tend to concentrate around those resources, and thus exhibit a...
21.7K
Central Limit Theorem01:14

Central Limit Theorem

14.6K
The central limit theorem, abbreviated as clt, is one of the most powerful and useful ideas in all of statistics. The central limit theorem for sample means says that if you repeatedly draw samples of a given size and calculate their means, and create a histogram of those means, then the resulting histogram will tend to have an approximate normal bell shape. In other words, as sample sizes increase, the distribution of means follows the normal distribution more closely.
The sample size, n, that...
14.6K
Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

681
An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
681
Propagation of Waves01:07

Propagation of Waves

2.3K
When a wave propagates from one medium to another, part of it may get reflected in the first medium, and part of it may get transmitted to the second medium. In such a case, the interface of the two mediums can be considered as a boundary that is neither fixed nor free.
Consider a scenario where a wave propagates from a string of low linear mass density to a string of high linear mass density. In such a case, the reflected wave is out of phase with respect to the incident wave, however the...
2.3K

You might also read

Related Articles

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

Sort by
Same author

Funnel theorems for spreading on networks.

Chaos (Woodbury, N.Y.)·2025
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: Jun 26, 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

1.0K

Universal bounds for spreading on networks.

Gadi Fibich1, Tomer Levin1

  • 1Department of Applied Mathematics, School of Mathematical Sciences, Tel Aviv University, Tel Aviv 6997801, Israel.

Chaos (Woodbury, N.Y.)
|May 8, 2024
PubMed
Summary
This summary is machine-generated.

Innovation diffusion on social networks is influenced by peer effects. This study provides tight lower and upper bounds for adoption rates, even when network structure is unknown, using the Bass model on specific network types.

More Related Videos

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
05:30

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

541
Monitoring Spatial Segregation in Surface Colonizing Microbial Populations
07:40

Monitoring Spatial Segregation in Surface Colonizing Microbial Populations

Published on: October 29, 2016

11.0K

Related Experiment Videos

Last Updated: Jun 26, 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

1.0K
Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
05:30

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

541
Monitoring Spatial Segregation in Surface Colonizing Microbial Populations
07:40

Monitoring Spatial Segregation in Surface Colonizing Microbial Populations

Published on: October 29, 2016

11.0K

Area of Science:

  • Social Network Analysis
  • Innovation Diffusion Theory
  • Stochastic Processes

Background:

  • Innovation diffusion relies on social networks and peer effects (word-of-mouth).
  • Network structure significantly impacts the speed of aggregate adoption over time.
  • Network structure is often unknown in real-world innovation spread scenarios.

Purpose of the Study:

  • To estimate aggregate adoption levels over time for innovations on unknown social networks.
  • To establish theoretical bounds for innovation diffusion rates.
  • To analyze the influence of network structure on adoption probabilities.

Main Methods:

  • Utilizing the Bass model, a standard model for new product adoption.
  • Analyzing diffusion dynamics on two specific network structures: a homogeneous two-node network and a homogeneous infinite complete network.
  • Deriving explicit lower and upper bounds for expected adoption levels and individual adoption probabilities.

Main Results:

  • Minimal and maximal adoption levels are achieved on homogeneous two-node and infinite complete networks, respectively.
  • Explicit, tight lower and upper bounds for expected adoption levels were derived for any network structure.
  • These bounds accurately predict individual adoption probabilities.
  • The gap between bounds widens with increased internal versus external influence rates.

Conclusions:

  • The derived bounds provide a robust method for estimating innovation diffusion on unknown networks.
  • The findings are applicable to understanding word-of-mouth marketing and technology adoption.
  • Network structure's role in diffusion can be bounded even without complete information.