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

Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

1.6K
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...
1.6K
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

287
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
287
Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

1.2K
The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...
1.2K
Second Order systems II01:18

Second Order systems II

340
In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
340
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

314
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
314
Second Order systems I01:20

Second Order systems I

505
A servo system exemplifies a second-order system, featuring a proportional controller and load elements that ensure the output position aligns with the input position. The relationship between these components is described by a second-order differential equation. Applying the Laplace transform under zero initial conditions yields the transfer function, showing how inputs are converted to outputs in the system.
By reinterpreting the system, one can derive the closed-loop transfer function, which...
505

You might also read

Related Articles

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

Sort by
Same author

Patronin facilitates neurite remodeling via epithelial-to-neuronal signaling.

Cell communication and signaling : CCS·2026
Same author

Targeting STAT3 in systemic lupus erythematosus and lupus nephritis: mechanisms, therapeutic advances, and structure-informed perspectives.

Frontiers in pharmacology·2026
Same author

Deep learning prediction of pathological complete response in breast cancer using Mamba architecture.

NPJ digital medicine·2026
Same author

Multimodal Deep Learning with Routine Clinical Data for Recurrence Risk Stratification in HR<sup>+</sup>/HER2<sup>-</sup> Early Breast Cancer.

Research (Washington, D.C.)·2026
Same author

Cold-water immersion alleviates intestinal damage induced by exertional heat stroke via modulation of gut microbiota in rats.

Frontiers in microbiomes·2026
Same author

Byzantine-Robust and Communication-Efficient Distributed Learning via Compressed Momentum Filtering.

IEEE transactions on neural networks and learning systems·2026

Related Experiment Video

Updated: Dec 29, 2025

Author Spotlight: Unlocking New Insights in fNIRS Studies - A Novel Framework for Inter-Brain Synchrony Analysis
05:59

Author Spotlight: Unlocking New Insights in fNIRS Studies - A Novel Framework for Inter-Brain Synchrony Analysis

Published on: October 6, 2023

3.1K

Fast Approximation of Coherence for Second-Order Noisy Consensus Networks.

Zuobai Zhang, Wanyue Xu, Yuhao Yi

    IEEE Transactions on Cybernetics
    |February 4, 2020
    PubMed
    Summary

    This study introduces a fast algorithm to approximate biharmonic distances in large networks, crucial for understanding network coherence in consensus dynamics. The method offers a scalable solution for analyzing complex systems.

    More Related Videos

    Statistical Modelling of Cortical Connectivity Using Non-invasive Electroencephalograms
    08:51

    Statistical Modelling of Cortical Connectivity Using Non-invasive Electroencephalograms

    Published on: November 1, 2019

    6.0K
    Conducting Hyperscanning Experiments with Functional Near-Infrared Spectroscopy
    06:42

    Conducting Hyperscanning Experiments with Functional Near-Infrared Spectroscopy

    Published on: January 19, 2019

    10.9K

    Related Experiment Videos

    Last Updated: Dec 29, 2025

    Author Spotlight: Unlocking New Insights in fNIRS Studies - A Novel Framework for Inter-Brain Synchrony Analysis
    05:59

    Author Spotlight: Unlocking New Insights in fNIRS Studies - A Novel Framework for Inter-Brain Synchrony Analysis

    Published on: October 6, 2023

    3.1K
    Statistical Modelling of Cortical Connectivity Using Non-invasive Electroencephalograms
    08:51

    Statistical Modelling of Cortical Connectivity Using Non-invasive Electroencephalograms

    Published on: November 1, 2019

    6.0K
    Conducting Hyperscanning Experiments with Functional Near-Infrared Spectroscopy
    06:42

    Conducting Hyperscanning Experiments with Functional Near-Infrared Spectroscopy

    Published on: January 19, 2019

    10.9K

    Area of Science:

    • Network Science
    • Control Theory
    • Computational Mathematics

    Background:

    • Second-order consensus dynamics with noise exhibit performance measures (vertex and network coherence) linked to biharmonic distances.
    • Calculating biharmonic distances is computationally prohibitive for large-scale networks.

    Purpose of the Study:

    • To develop an efficient and scalable algorithm for approximating biharmonic distances in massive networks.
    • To enable accurate estimation of network coherence measures for large systems.

    Main Methods:

    • Leveraging the relationship between coherence measures and the pseudoinverse of the graph Laplacian squared (L^2†).
    • Developing a nearly linear-time approximation algorithm for diagonal entries of L^2†.
    • Integrating the Johnson-Lindenstrauss lemma with Laplacian solvers.

    Main Results:

    • A theoretically guaranteed approximation algorithm for the diagonal entries of L^2†.
    • Demonstrated efficiency, accuracy, and scalability through extensive numerical experiments.
    • The algorithm successfully handles networks with millions of vertices.

    Conclusions:

    • The proposed algorithm provides a computationally feasible approach to analyze network coherence in large-scale systems.
    • This method overcomes the limitations of direct biharmonic distance computation for massive networks.
    • The findings are applicable to various fields involving distributed systems and network analysis.