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

Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

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.
Modeling with Differential Equations01:25

Modeling with Differential Equations

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from the...
Multimachine Stability01:25

Multimachine Stability

Multimachine stability analysis is crucial for understanding the dynamics and stability of power systems with multiple synchronous machines. The objective is to solve the swing equations for a network of M machines connected to an N-bus power system.
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

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...
Nonlinear Pharmacokinetics: Michaelis-Menten Equation01:18

Nonlinear Pharmacokinetics: Michaelis-Menten Equation

The Michaelis–Menten equation is a fundamental model for describing capacity-limited kinetics in drug metabolism. It offers insights into the rate of decline of plasma drug concentration Cp over time, with Vmax and KM as pivotal parameters.
Vmax represents the maximum achievable process rate, while KM, known as the Michaelis constant, signifies the drug concentration at which the process rate reaches half its maximum. This relationship between Vmax, KM, and Cp gives rise to three distinct...

You might also read

Related Articles

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

Sort by
Same author

Temporal self-similarity reveals percolation universality classes in complex networks.

Nature communications·2026
Same author

Unifying network connectivity from geodesics to random walks via the random cluster model.

Nature communications·2026
Same author

Temporal heterogeneity shapes diffusion dynamics in complex networks.

Nature communications·2026
Same author

Bounded-confidence opinion models with random-time interactions.

Physical review. E·2026
Same author

Unifying Summary Statistic Selection for Approximate Bayesian Computation.

Statistics and computing·2026
Same author

Clustering-induced localization of quantum walks on networks.

Physical review. E·2026

Related Experiment Video

Updated: May 16, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Generalized master equations for non-Poisson dynamics on networks.

Till Hoffmann1, Mason A Porter, Renaud Lambiotte

  • 1Department of Physics, University of Oxford, Oxford, United Kingdom.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 11, 2012
PubMed
Summary

This study explores non-Poisson edge dynamics in temporal networks. We introduce a generalized master equation for continuous-time random walks, offering new insights into network behavior beyond traditional methods.

More Related Videos

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

Related Experiment Videos

Last Updated: May 16, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

Area of Science:

  • Network Science
  • Statistical Physics
  • Complex Systems

Background:

  • Traditional temporal network analysis often aggregates edge dynamics into static weighted networks.
  • This aggregation assumes Poisson processes for edge events, which is frequently inaccurate for real-world temporal networks.

Purpose of the Study:

  • To investigate the impact of non-Poisson inter-event time statistics on temporal network dynamics.
  • To apply a generalized master equation framework to continuous-time random walks on networks.

Main Methods:

  • Developed a generalized master equation applicable to non-Poisson processes in temporal networks.
  • Analyzed the equation's reduction to standard rate equations under Poissonian assumptions.
  • Derived analytical and numerical solutions for the stationary state, particularly for networks with uniform waiting-time distributions.

Main Results:

  • The generalized master equation accurately models non-Poisson edge dynamics.
  • The stationary solution is governed by an easily calculable effective transition matrix.
  • Demonstrated the utility of the framework through simulations and analytical derivations.

Conclusions:

  • Non-Poisson statistics significantly influence temporal network dynamics.
  • The generalized master equation provides a robust tool for analyzing complex temporal networks.
  • Findings have implications for understanding dynamical processes and developing network diagnostics for stochastic temporal networks.