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

Multi-input and Multi-variable systems01:22

Multi-input and Multi-variable systems

138
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...
138
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

122
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....
122
Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

337
In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
337
Routh-Hurwitz Criterion I01:15

Routh-Hurwitz Criterion I

307
Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
307
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

114
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,...
114
One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation

642
This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
642

You might also read

Related Articles

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

Sort by
Same author

Richards's curve induced Banach space valued ordinary and fractional neural network approximation.

Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A, Matematicas·2022
Same author

Application of artificial intelligence neural network modeling to predict the generation of domestic, commercial and construction wastes.

Waste management & research : the journal of the International Solid Wastes and Public Cleansing Association, ISWA·2020
Same author

Multivariate sigmoidal neural network approximation.

Neural networks : the official journal of the International Neural Network Society·2011
See all related articles

Related Experiment Video

Updated: Aug 16, 2025

Basics of Multivariate Analysis in Neuroimaging Data
06:35

Basics of Multivariate Analysis in Neuroimaging Data

Published on: July 24, 2010

16.9K

Richards's curve induced Banach space valued multivariate neural network approximation.

George A Anastassiou1, Seda Karateke2

  • 1Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152 USA.

Arabian Journal of Mathematics
|December 19, 2022
PubMed
Summary

This study introduces novel neural network operators for approximating complex functions in Banach spaces. These methods offer precise, uniform, and pointwise approximations using generalized logistic functions.

Keywords:
41A1741A2541A3041A36

More Related Videos

Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data
14:27

Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data

Published on: June 26, 2013

15.7K
A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
08:12

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

2.6K

Related Experiment Videos

Last Updated: Aug 16, 2025

Basics of Multivariate Analysis in Neuroimaging Data
06:35

Basics of Multivariate Analysis in Neuroimaging Data

Published on: July 24, 2010

16.9K
Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data
14:27

Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data

Published on: June 26, 2013

15.7K
A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
08:12

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

2.6K

Area of Science:

  • Numerical Analysis
  • Functional Analysis
  • Machine Learning

Background:

  • Approximation theory deals with approximating complex functions using simpler ones.
  • Neural networks are increasingly used in approximation tasks.
  • Banach spaces provide a framework for studying function spaces.

Purpose of the Study:

  • To develop and analyze new multivariate neural network operators for function approximation.
  • To investigate the approximation capabilities of normalized, quasi-interpolation, Kantorovich-type, and quadrature-type operators.
  • To examine the effect of iterated operators on approximation quality.

Main Methods:

  • Utilizing multivariate normalized, quasi-interpolation, Kantorovich-type, and quadrature-type neural network operators.
  • Establishing multidimensional Jackson type inequalities.
  • Employing a multidimensional density function based on the Richards's curve (a generalized logistic function).
  • Analyzing pointwise and uniform approximation errors.

Main Results:

  • Quantitative approximations of continuous multivariate functions in Banach spaces were achieved.
  • The effectiveness of iterated operators in enhancing approximation was demonstrated.
  • Multidimensional Jackson type inequalities provided error bounds based on continuity moduli and derivatives.
  • The feed-forward neural network architecture involved one hidden layer.

Conclusions:

  • The proposed neural network operators provide effective tools for approximating continuous multivariate functions.
  • The theoretical framework, based on Jackson type inequalities, validates the approximation quality.
  • The use of Richards's curve-based density functions offers a novel approach in this domain.