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

Random Sampling Method01:09

Random Sampling Method

15.7K
Sampling is a technique to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. Data are the result of sampling from a population. The sampling method ensures that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest. Among the various sampling methods used by...
15.7K
Area Problem01:26

Area Problem

222
Determining the area of a region with straight edges is straightforward, as geometric formulas for rectangles, triangles, and polygons can be applied directly. However, traditional geometric methods are insufficient when a region has a curved boundary, such as the area under a function.fromThe area problem involves finding a systematic way to measure such regions. One approach to solving this problem is through approximation. Instead of attempting to compute the area exactly at the outset, the...
222
Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

2.1K
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...
2.1K
Debye–Huckel–Onsager Conductance Equation01:28

Debye–Huckel–Onsager Conductance Equation

174
The Debye-Hückel-Onsager equation is a cornerstone of physical chemistry, providing a method to determine the molar conductance (Λm) and molar conductance at infinite dilution (Λ°m) for uni-univalent electrolytes.Uni-univalent electrolytes are electrolytes that dissociate in solution to produce one cation with a +1 charge and one anion with a –1 charge per formula unit.This equation addresses two crucial phenomena: the asymmetry effect and the electrophoretic effect.
174
Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

310
Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
The distributed parameter models are specifically designed to account for variations and differences in some drug classes. This model is particularly useful for assessing regional concentrations of anticancer or...
310
Random Error01:04

Random Error

10.1K
Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...
10.1K

You might also read

Related Articles

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

Sort by
Same author

Tracking Dynamics of Superspreading Through Contacts, Exposures, and Transmissions in Edge-Based Network Epidemics.

Bulletin of mathematical biology·2026
Same author

Inferring signed social networks from contact patterns.

Journal of physics. Complexity·2026
Same author

Biomedical open source software: Crucial packages and hidden heroes.

PLoS computational biology·2026
Same author

App-based epidemic game in a university campus reveals how risk perception and behavioral interventions shape disease transmission dynamics.

Scientific reports·2026
Same author

Ethical Frameworks for Conducting Social Challenge Studies.

Journal of empirical research on human research ethics : JERHRE·2026
Same author

Tracking dynamics of superspreading through contacts, exposures, and transmissions in edge-based network epidemics.

ArXiv·2026

Related Experiment Video

Updated: Mar 27, 2026

Three-Dimensional Particle Shape Analysis Using X-ray Computed Tomography: Experimental Procedure and Analysis Algorithms for Metal Powders
10:10

Three-Dimensional Particle Shape Analysis Using X-ray Computed Tomography: Experimental Procedure and Analysis Algorithms for Metal Powders

Published on: December 4, 2020

2.3K

General and exact approach to percolation on random graphs.

Antoine Allard1, Laurent Hébert-Dufresne1, Jean-Gabriel Young1

  • 1Département de physique, de génie physique, et d'optique, Université Laval, Québec, Québec, Canada G1V 0A6.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2016
PubMed
Summary

We developed a versatile framework for analyzing percolation on complex random graphs. This approach accurately models component size and composition, offering insights into phase transitions in clustered and interdependent networks.

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

1.2K
Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

8.5K

Related Experiment Videos

Last Updated: Mar 27, 2026

Three-Dimensional Particle Shape Analysis Using X-ray Computed Tomography: Experimental Procedure and Analysis Algorithms for Metal Powders
10:10

Three-Dimensional Particle Shape Analysis Using X-ray Computed Tomography: Experimental Procedure and Analysis Algorithms for Metal Powders

Published on: December 4, 2020

2.3K
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

1.2K
Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

8.5K

Area of Science:

  • Statistical physics
  • Network science
  • Graph theory

Background:

  • Percolation theory is crucial for understanding connectivity in complex systems.
  • Existing models often struggle with correlated and clustered random graph structures.
  • Analyzing component size and composition in finite and infinite graphs remains a challenge.

Purpose of the Study:

  • To introduce a unified theoretical framework for site and bond percolation on general random graphs.
  • To provide exact solutions for component distributions in finite and infinite graphs.
  • To extend the framework to interdependent and clustered network models.

Main Methods:

  • Development of iterative equations for component distribution analysis.
  • Definition of a general random graph ensemble.
  • Application of probability generating functions for infinite-size limit solutions.
  • Adaptation of the framework for interdependent and clustered graphs.

Main Results:

  • Exact solutions for component size and composition in finite multitype graphs.
  • Precise calculation of percolation thresholds, giant component size, and composition in infinite graphs.
  • Demonstration of continuous and discontinuous phase transitions in interdependent graphs.
  • Evidence that clustering amplifies discontinuity amplitude in phase transitions.

Conclusions:

  • The presented framework offers a versatile and comprehensive approach to percolation studies on diverse graph types.
  • The methods allow for exact analysis of complex network properties, including phase transitions.
  • The framework advances the understanding of structural properties in correlated, clustered, and interdependent networks.