Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Network Function of a Circuit

Network Function of a Circuit

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.

Relationship Formation

Relationship Formation

What do you think is the single most influential factor in determining with whom you become friends and whom you form romantic relationships? You might be surprised to learn that the answer is simple: the people with whom you have the most contact. This most important factor is proximity. You are more likely to be friends with people you have regular contact with. For example, there are decades of research that shows that you are more likely to become friends with people who live in your dorm,...

Entropy Change in Reversible Processes

Entropy Change in Reversible Processes

In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.

Net Change Theorem

Net Change Theorem

The Net Change Theorem is a fundamental principle in calculus that establishes a direct relationship between a function’s rate of change and its accumulated change over an interval. Mathematically, it states that the definite integral of a function's derivative over a given interval [a,b] yields the net change in the original function:This theorem has significant applications in various real-world scenarios, including physics, economics, and engineering. A particularly useful application...

Multimachine Stability

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:

Classification of Systems-I

Classification of Systems-I

Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:

You might also read

Related Articles

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

Sort by

Same author

Network-driven discovery of repurposable drugs targeting hallmarks of aging.

Nature aging·2026

Same author

The aging genome exhibits organized vulnerability to somatic mutations.

bioRxiv : the preprint server for biology·2026

Same author

Hungary's chance to rebuild science.

Science (New York, N.Y.)·2026

Same author

Human mobility in the metaverse mirrors patterns in the physical world.

Scientific reports·2026

Same author

Surface optimization governs the local design of physical networks.

Nature·2026

Same author

Observing network dynamics through sentinel nodes.

Nature communications·2025

Same journal

Simple input-output dependencies explain neuronal activity.

Nature physics·2026

Same journal

Scaling and self-similarity in the formation of the embryonic epigenome.

Nature physics·2026

Same journal

Adhesion-driven rigidity transition decoupled from density-driven jamming triggers epithelial organization in embryonic tissues.

Nature physics·2026

Same journal

The local mechanostructural properties of protein cargoes regulate nucleocytoplasmic transport.

Nature physics·2026

Same journal

Squeezing, trisqueezing and quadsqueezing in a hybrid oscillator-spin system.

Nature physics·2026

Same journal

Noise-induced shallow circuits and the absence of barren plateaus.

Nature physics·2026

See all related articles

Search research articles

Related Experiment Video

Updated: May 5, 2026

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

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

Published on: December 7, 2021

Universality in network dynamics.

Baruch Barzel¹, Albert-László Barabási

¹Center for Complex Network Research and Departments of Physics, Computer Science and Biology, Northeastern University, Boston, Massachusetts 02115, USA ; Center for Cancer Systems Biology, Dana-Farber Cancer Institute, Harvard Medical School, Boston, Massachusetts 02115, USA.

|December 10, 2013

Summary

This summary is machine-generated.

Researchers developed a new theory to separate network topology and dynamics in complex systems. This framework predicts universality classes for system behavior and validates findings across various real-world systems.

More Related Videos

Soft Pneumatic Robot Modulates Graph Theory Metrics of Brain Network for Hand Rehabilitation After Stroke

Soft Pneumatic Robot Modulates Graph Theory Metrics of Brain Network for Hand Rehabilitation After Stroke

Published on: October 10, 2025

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

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

Published on: September 8, 2023

Related Experiment Videos

Last Updated: May 5, 2026

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

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

Published on: December 7, 2021

Soft Pneumatic Robot Modulates Graph Theory Metrics of Brain Network for Hand Rehabilitation After Stroke

Soft Pneumatic Robot Modulates Graph Theory Metrics of Brain Network for Hand Rehabilitation After Stroke

Published on: October 10, 2025

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

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

Published on: September 8, 2023

Area of Science:

Complex Systems Science
Network Theory
Mathematical Modeling

Background:

Characterizing complex networks is advancing, but a unified mathematical framework for network topology and dynamics is lacking.
Understanding the interplay between structure and function in complex systems is crucial for diverse scientific fields.

Purpose of the Study:

To develop a self-consistent theory for dynamical perturbations in complex systems.
To systematically separate the contributions of network topology and system dynamics.
To identify universal properties and predict system behavior.

Main Methods:

Developed a novel mathematical framework for analyzing dynamical perturbations.
Formulated a theory applicable to steady-state dynamical processes.
Derived predictions for system response and correlation development.

Main Results:

The theory predicts distinct universality classes based on system dynamics.
Validated predictions on canonical network models (biochemical, epidemic spreading).
Successfully identified universality classes in real-world social and biological systems without prior continuum theories.

Conclusions:

The developed theory provides a unified mathematical framework for complex systems.
It enables accurate prediction and classification of system behavior based on topology and dynamics.
The approach is broadly applicable to diverse empirical systems.