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

Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

165
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....
165
Network Function of a Circuit01:25

Network Function of a Circuit

424
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.
424
Region of Convergence of Laplace Tarnsform01:20

Region of Convergence of Laplace Tarnsform

770
The Region of Convergence (ROC) is a fundamental concept in signal processing and system analysis, particularly associated with the Laplace transform. The ROC represents an area in the complex plane where the Laplace transform of a given signal converges, determining the transform's applicability and utility.
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This...
770
SFG Algebra01:16

SFG Algebra

187
In Signal Flow Graph (SFG) algebra, the value a node represents is determined by the sum of all signals entering that node. This summed value is then transmitted through every branch leaving the node, making the SFG a powerful tool for visualizing and analyzing control systems.
Each node in an SFG corresponds to a variable, and the interactions between nodes are represented by branches with associated gains. When multiple branches lead into a node, the value at that node is the sum of the...
187
Region of Convergence01:17

Region of Convergence

613
The z-transform is a powerful mathematical tool used in the analysis of discrete-time signals and systems. It is a crucial tool in the analysis of discrete-time systems, but its convergence is limited to specific values of the complex variable z. This range of values, known as the Region of Convergence (ROC), is fundamental in determining the behavior and stability of a system or signal. The ROC defines the region in the complex plane where the z-transform converges, which can take various...
613
Convergence of Fourier Series01:21

Convergence of Fourier Series

229
The Fourier series is a powerful mathematical tool for representing periodic signals as an infinite sum of complex exponentials. In practice, this infinite series is truncated to a finite number of terms, yielding a partial sum. This truncation makes the approximation of the signal feasible but introduces certain challenges, particularly near discontinuities, known as the Gibbs phenomenon.
The Gibbs phenomenon refers to the persistent oscillations and overshoots that occur near discontinuities...
229

You might also read

Related Articles

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

Sort by
Same author

Multimodal deep learning for predicting WHO/ISUP grading in renal tumors on CT using a self-attention-based model: variable Vision Transformer (vViT).

European journal of radiology open·2026
Same author

Transformer-based Deep Learning Models with Shape Guidance for Predicting Breast Cancer in Mammography Images.

Journal of imaging informatics in medicine·2025
Same author

Bilateral Information-Guided Diagnosis of Breast Masses in Mammography Using Vision Transformer.

IEEE journal of biomedical and health informatics·2025
Same author

Deep learning-based dual-energy subtraction synthesis from single-energy kV x-ray fluoroscopy for markerless tumor tracking.

Medical & biological engineering & computing·2025
Same author

Reproducible Machine Learning-Based Voice Pathology Detection: Introducing the Pitch Difference Feature.

Journal of voice : official journal of the Voice Foundation·2025
Same author

Noise-related inaccuracies in the quantitative evaluation of CT artifacts.

Radiological physics and technology·2025

Related Experiment Video

Updated: Oct 13, 2025

Network Analysis of Foramen Ovale Electrode Recordings in Drug-resistant Temporal Lobe Epilepsy Patients
09:32

Network Analysis of Foramen Ovale Electrode Recordings in Drug-resistant Temporal Lobe Epilepsy Patients

Published on: December 18, 2016

12.6K

Comments on "Convergence Analysis of Adaptive Exponential Functional Link Network".

Ivo Bukovsky, Gejza Dohnal, Noriyasu Homma

    IEEE Transactions on Neural Networks and Learning Systems
    |November 11, 2021
    PubMed
    Summary

    This paper comments on the weight-update stability derivation for in-parameter-linear nonlinear learning systems using gradient descent. It highlights issues in the original article to ensure accurate understanding of learning system stability.

    More Related Videos

    An Experimental Platform to Study the Closed-loop Performance of Brain-machine Interfaces
    10:51

    An Experimental Platform to Study the Closed-loop Performance of Brain-machine Interfaces

    Published on: March 10, 2011

    13.9K
    Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
    06:45

    Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

    Published on: October 28, 2022

    1.8K

    Related Experiment Videos

    Last Updated: Oct 13, 2025

    Network Analysis of Foramen Ovale Electrode Recordings in Drug-resistant Temporal Lobe Epilepsy Patients
    09:32

    Network Analysis of Foramen Ovale Electrode Recordings in Drug-resistant Temporal Lobe Epilepsy Patients

    Published on: December 18, 2016

    12.6K
    An Experimental Platform to Study the Closed-loop Performance of Brain-machine Interfaces
    10:51

    An Experimental Platform to Study the Closed-loop Performance of Brain-machine Interfaces

    Published on: March 10, 2011

    13.9K
    Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
    06:45

    Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

    Published on: October 28, 2022

    1.8K

    Area of Science:

    • Machine Learning
    • Artificial Intelligence
    • System Dynamics

    Background:

    • Nonlinear learning systems are crucial in AI.
    • Gradient descent is a common learning rule.
    • Weight-update stability is a key performance metric.

    Purpose of the Study:

    • To critically evaluate the derivation of weight-update stability.
    • To address specific issues in a previously published article.
    • To prevent the spread of potential inaccuracies in learning system analysis.

    Main Methods:

    • Commentary on existing mathematical derivations.
    • Analysis of gradient descent application.
    • Review of stability conditions in nonlinear systems.

    Main Results:

    • Identification of potential flaws in the weight-update stability derivation.
    • Specific issues are detailed for clarity.
    • The comments aim to refine understanding, not invalidate the entire contribution.

    Conclusions:

    • The analysis highlights areas needing careful consideration in nonlinear learning systems.
    • Accurate derivation of weight-update stability is essential for reliable AI.
    • Further scrutiny of stability proofs is recommended for gradient descent-based systems.