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 Time Domain01:21

Linear Approximation in Time Domain

234
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,...
234
Improving Translational Accuracy02:07

Improving Translational Accuracy

13.1K
Base complementarity between the three base pairs of mRNA codon and the tRNA anticodon is not a failsafe mechanism. Inaccuracies can range from a single mismatch to no correct base pairing at all. The free energy difference between the correct and nearly correct base pairs can be as small as 3 kcal/ mol. With complementarity being the only proofreading step, the estimated error frequency would be one wrong amino acid in every 100 amino acids incorporated. However, error frequencies observed in...
13.1K
Improving Translational Accuracy02:07

Improving Translational Accuracy

3.4K
3.4K
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

280
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....
280
Multi-input and Multi-variable systems01:22

Multi-input and Multi-variable systems

295
Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence of...
295
Linear time-invariant Systems01:23

Linear time-invariant Systems

725
A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
725

You might also read

Related Articles

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

Sort by
Same author

The rise of <i>Candidozyma auris</i> in Czechia: three clades, prosthetic joint infection and fluconazole resistance development, 2022 to 2024.

Euro surveillance : bulletin Europeen sur les maladies transmissibles = European communicable disease bulletin·2025
Same author

Approximation of classifiers by deep perceptron networks.

Neural networks : the official journal of the International Neural Network Society·2023
Same author

Exploratory drilling: how to set up, carry out, and evaluate a seroprevalence study.

Casopis lekaru ceskych·2020
Same author

Kolmogorov's Theorem Is Relevant.

Neural computation·2019
Same author

Some insights from high-dimensional spheres: Comment on "The unreasonable effectiveness of small neural ensembles in high-dimensional brain" by Alexander N. Gorban et al.

Physics of life reviews·2019
Same author

Classification by Sparse Neural Networks.

IEEE transactions on neural networks and learning systems·2019
Same journal

Hidden Data Recovery and Forecasting via Next-Generation Reservoir Computing With Multiscale Delay Selection.

IEEE transactions on neural networks and learning systems·2026
Same journal

CAFF-CIL: Causality-Aware Freedom Forgetting Approach for Class-Incremental Learning.

IEEE transactions on neural networks and learning systems·2026
Same journal

Harmonic Autoencoding Framework for Multiple Tasks in Magnetic Particle Imaging Reconstruction.

IEEE transactions on neural networks and learning systems·2026
Same journal

A Survey on Human-Centric Voice-Face Multimodal Learning.

IEEE transactions on neural networks and learning systems·2026
Same journal

Vision-Assisted Foundation Model for Solving Multitask Vehicle Routing Problems.

IEEE transactions on neural networks and learning systems·2026
Same journal

FP3O: Enabling Proximal Policy Optimization in Multiagent Cooperation With Parameter-Sharing Versatility.

IEEE transactions on neural networks and learning systems·2026
See all related articles

Related Experiment Video

Updated: Dec 6, 2025

Cross-Modal Multivariate Pattern Analysis
13:51

Cross-Modal Multivariate Pattern Analysis

Published on: November 9, 2011

20.3K

Translation-Invariant Kernels for Multivariable Approximation.

Vera Kurkova, David Coufal

    IEEE Transactions on Neural Networks and Learning Systems
    |October 12, 2020
    PubMed
    Summary
    This summary is machine-generated.

    Shallow neural networks with translation-invariant kernels are suitable for approximation and classification. Kernel Fourier transforms determine network capabilities, with different properties needed for approximation versus maximal margin classification.

    More Related Videos

    Basics of Multivariate Analysis in Neuroimaging Data
    06:35

    Basics of Multivariate Analysis in Neuroimaging Data

    Published on: July 24, 2010

    17.2K
    Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
    13:44

    Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

    Published on: August 30, 2013

    43.4K

    Related Experiment Videos

    Last Updated: Dec 6, 2025

    Cross-Modal Multivariate Pattern Analysis
    13:51

    Cross-Modal Multivariate Pattern Analysis

    Published on: November 9, 2011

    20.3K
    Basics of Multivariate Analysis in Neuroimaging Data
    06:35

    Basics of Multivariate Analysis in Neuroimaging Data

    Published on: July 24, 2010

    17.2K
    Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
    13:44

    Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

    Published on: August 30, 2013

    43.4K

    Area of Science:

    • Machine Learning
    • Applied Mathematics
    • Signal Processing

    Background:

    • Shallow neural networks with translation-invariant kernels are widely used for function approximation and classification.
    • Understanding the theoretical underpinnings of these networks is crucial for optimizing their performance.

    Purpose of the Study:

    • To investigate the suitability of shallow networks with translation-invariant kernel units for function approximation and classification.
    • To identify critical properties of kernel functions that influence network capabilities.

    Main Methods:

    • Analysis of the convergence behavior of Fourier transforms of kernel functions.
    • Utilizing the Hankel transform to analyze multivariable kernels.
    • Illustrating general results with examples of univariable and multivariable kernels (Gaussian, Laplace, rectangle, sinc, cut power).

    Main Results:

    • A critical property influencing kernel network capabilities is how kernel Fourier transforms converge to zero.
    • Kernels for multivariable approximation require Fourier transforms that can be negative but are almost everywhere nonzero.
    • Kernels for maximal margin classification require nonnegative Fourier transforms that can be zero over large sets.

    Conclusions:

    • The behavior of kernel Fourier transforms dictates suitability for specific tasks.
    • Distinct properties of kernel Fourier transforms are necessary for effective function approximation and maximal margin classification.