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

Convergence of Sequences

Convergence of Sequences

A sequence is a function defined on the natural numbers that assigns a value to each index. It can be understood as an ordered list of terms generated one after another. In mathematical analysis, an important question is whether the terms of a sequence approach a single real number as the index becomes very large. When this happens, the sequence is said to converge, and the value approached is called the limit. From a graphical perspective, convergence means that the plotted terms approach a...

Region of Convergence of Laplace Tarnsform

Region of Convergence of Laplace Tarnsform

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 substitution...

Region of Convergence

Region of Convergence

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...

Convergence of Taylor Series

Convergence of Taylor Series

The Taylor series provides a systematic method for approximating a smooth function by a polynomial that closely matches the function near a chosen point. This approach is particularly valuable in scientific and engineering contexts where functions may be difficult to evaluate directly, such as oscillatory voltages in alternating current (AC) circuits. Replacing complex functions with polynomial expressions simplifies computation while preserving essential local behavior. Taylor’s Theorem...

Application of Linearization and Approximation

Application of Linearization and Approximation

A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during...

Convergence of Fourier Series

Convergence of Fourier Series

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...

You might also read

Related Articles

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

Sort by

Same author

Development of advanced photon calibrator for Kamioka gravitational wave detector (KAGRA).

The Review of scientific instruments·2023

Same author

Scintillation light detection in the 6-m drift-length ProtoDUNE Dual Phase liquid argon TPC.

The European physical journal. C, Particles and fields·2022

Same author

[Effects of direct antiviral agent on the frequency of peripheral blood mononuclear cells and their activating factors sCD14s and CD163 in patients with chronic hepatitis C].

Zhonghua gan zang bing za zhi = Zhonghua ganzangbing zazhi = Chinese journal of hepatology·2021

Same author

Prospects for beyond the Standard Model physics searches at the Deep Underground Neutrino Experiment: DUNE Collaboration.

The European physical journal. C, Particles and fields·2021

Same author

Severe myocardial bridge presenting as paroxysmal atrioventricular block.

Journal of postgraduate medicine·2021

Same author

Isolated intracardiac recurrence of diffuse large B-cell lymphoma successfully treated with rituximab and bendamustine chemotherapy regimen.

Journal of postgraduate medicine·2020

Search research articles

Related Experiment Videos

Learning convergence of CMAC technique.

C S Lin¹, C T Chiang

¹Dept. of Electr. Eng., Missouri Univ., Columbia, MO.

IEEE Transactions on Neural Networks

|January 1, 1997

Summary

This summary is machine-generated.

Cerebellar Model Articulation Controller (CMAC) learning behavior is analyzed using mathematical formulation. This study investigates CMAC convergence properties and learning rules, providing a foundation for future research.

Related Experiment Videos

Area of Science:

Artificial Intelligence
Machine Learning
Computational Neuroscience

Background:

The Cerebellar Model Articulation Controller (CMAC) is a widely used learning technique lacking a robust theoretical foundation.
Previous research primarily focused on algorithmic development, structural improvements, and applications, neglecting theoretical analysis of CMAC learning behavior.

Purpose of the Study:

To establish a theoretical foundation for CMAC by developing a mathematical formulation.
To analyze CMAC convergence characteristics and learning behaviors, including the impact of hash mapping and memory size.

Main Methods:

Developed a mathematical formulation for CMAC, expressing information retrieval and learning rules in matrix form.
Utilized the matrix formulation and eigenvalue analysis to investigate CMAC convergence properties.
Examined the effects of hash mapping on CMAC learning behavior.

Main Results:

The mathematical formulation provides a basis for analyzing CMAC convergence and learning dynamics.
Eigenvalue analysis reveals insights into the convergence characteristics of CMAC with and without hash mapping.
The study quantifies the impact of hash mapping on CMAC performance.

Conclusions:

The developed mathematical framework offers a theoretical foundation for understanding CMAC.
Results provide a basis for predicting CMAC learning behavior and optimizing its parameters.
This work facilitates further theoretical investigations into CMAC and related adaptive learning systems.