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

Temperature Dependence on Reaction Rate

Temperature Dependence on Reaction Rate

The Collision Theory
Atoms, molecules, or ions must collide before they can react with each other. Atoms must be close together to form chemical bonds. This premise is the basis for a theory that explains many observations regarding chemical kinetics, including factors affecting reaction rates.
The collision theory is based on the postulates that (i) the reaction rate is proportional to the rate of reactant collisions, (ii) the reacting species collide in an orientation allowing contact between...

The Integrated Rate Law: The Dependence of Concentration on Time

The Integrated Rate Law: The Dependence of Concentration on Time

While the differential rate law relates the rate and concentrations of reactants, a second form of rate law called the integrated rate law relates concentrations of reactants and time. Integrated rate laws can be used to determine the amount of reactant or product present after a period of time or to estimate the time required for a reaction to proceed to a certain extent. For example, an integrated rate law helps determine the length of time a radioactive material must be stored for its...

Convergent Evolution

Convergent Evolution

Evolution shapes the features of organisms over time, ensuring that they are suited for the environments in which they live. Sometimes, selection pressure leads to the rise of similar but unrelated adaptations in organisms with no recent common ancestors, a process known as convergent evolution.

Punnett Squares

Punnett Squares

Root Mean Square

Root Mean Square

If in an experiment, data values have a probability of being both positive and negative, neither the arithmetic mean, the geometric mean, nor the harmonic mean can be used to calculate the central tendency of the data set. In particular, if the positive and negative values are equally likely, the arithmetic mean is close to zero.
For example, consider the velocity of gas molecules in a container. The gas molecules are moving in different directions, which might impart positive and negative...

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...

You might also read

Related Articles

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

Sort by

Same author

Modulation of sunflower seed protein structure and functionality by chlorogenic acid interaction and stepwise dephenolization.

Food research international (Ottawa, Ont.)·2026

Same author

Parabens exposure in systemic lupus erythematosus: insights from network toxicology and molecular docking.

BMC pharmacology & toxicology·2026

Same author

Cohort profile: Sheyang Mini Birth Cohort Study (SMBCS).

BMJ open·2026

Same author

Platelet-rich plasma facilitates earlier functional recovery and return to sport in traumatic meniscal repair: a retrospective cohort study.

Journal of orthopaedic surgery and research·2026

Same author

Pharmacologic Modulation of ARID3A with Rimegepant Reactivates Type I Interferon Signaling and Sensitizes Triple-Negative Breast Cancer to PD-1 Blockade.

Advanced science (Weinheim, Baden-Wurttemberg, Germany)·2026

Same author

Laparoscopic closure of the fascial defect combined with medial umbilical ligament reinforcement for incarcerated pediatric direct inguinal hernia: a case report with emergency management insights.

Frontiers in medicine·2026

Same journal

The infimum values of two probability functions for the Gamma distribution.

Journal of inequalities and applications·2024

Same journal

The existence of nonnegative solutions for a nonlinear fractional <i>q</i>-differential problem via a different numerical approach.

Journal of inequalities and applications·2021

Same journal

Correction to: On the spectral norms of <i>r</i>-circulant matrices with the bi-periodic Fibonacci and Lucas numbers.

Journal of inequalities and applications·2019

Same journal

Erratum to: General Bahr-Esseen inequalities and their applications.

Journal of inequalities and applications·2019

Same journal

Hermite-Hadamard type inequalities for <i>F</i>-convex function involving fractional integrals.

Journal of inequalities and applications·2019

Same journal

Global maximal inequality to a class of oscillatory integrals.

Journal of inequalities and applications·2019

See all related articles

Search research articles

Related Experiment Video

Updated: Jan 28, 2026

Convergent Polishing: A Simple, Rapid, Full Aperture Polishing Process of High Quality Optical Flats & Spheres

Convergent Polishing: A Simple, Rapid, Full Aperture Polishing Process of High Quality Optical Flats & Spheres

Published on: December 1, 2014

Convergence rate for the moving least-squares learning with dependent sampling.

Qin Guo¹, Peixin Ye¹

¹School of Mathematical Sciences and LPMC, Nankai University, Tianjin, China.

Journal of Inequalities and Applications

|March 7, 2019

Summary

This summary is machine-generated.

This study analyzes the moving least-squares (MLS) method using regression learning, assuming alpha-mixing conditions for dependent samples. Researchers derived optimal learning rates and error bounds for enhanced algorithm performance.

Keywords:

Error bound Mixing sequence Moving least-squares Probability inequality Regression function

More Related Videos

A Flexible Platform for Monitoring Cerebellum-Dependent Sensory Associative Learning

A Flexible Platform for Monitoring Cerebellum-Dependent Sensory Associative Learning

Published on: January 19, 2022

Cooling Rate Dependent Ellipsometry Measurements to Determine the Dynamics of Thin Glassy Films

Cooling Rate Dependent Ellipsometry Measurements to Determine the Dynamics of Thin Glassy Films

Published on: January 26, 2016

Related Experiment Videos

Last Updated: Jan 28, 2026

Convergent Polishing: A Simple, Rapid, Full Aperture Polishing Process of High Quality Optical Flats & Spheres

Convergent Polishing: A Simple, Rapid, Full Aperture Polishing Process of High Quality Optical Flats & Spheres

Published on: December 1, 2014

A Flexible Platform for Monitoring Cerebellum-Dependent Sensory Associative Learning

A Flexible Platform for Monitoring Cerebellum-Dependent Sensory Associative Learning

Published on: January 19, 2022

Cooling Rate Dependent Ellipsometry Measurements to Determine the Dynamics of Thin Glassy Films

Cooling Rate Dependent Ellipsometry Measurements to Determine the Dynamics of Thin Glassy Films

Published on: January 26, 2016

Area of Science:

Statistics
Machine Learning
Data Science

Background:

The moving least-squares (MLS) method is a fundamental technique in regression analysis.
Understanding the behavior of MLS with dependent data is crucial for accurate modeling.
Existing methods often struggle with the complexities of data exhibiting temporal or spatial dependencies.

Purpose of the Study:

To rigorously analyze the moving least-squares (MLS) method within a regression learning framework.
To investigate the impact of the alpha-mixing condition on MLS performance.
To establish theoretical guarantees for MLS algorithms operating on dependent samples.

Main Methods:

Employing a regression learning framework to study the MLS method.
Utilizing probability inequalities specifically designed for dependent samples.
Assuming the sampling process adheres to the alpha-mixing condition.

Main Results:

Derived error estimates for the MLS method under the alpha-mixing assumption.
Established a satisfactory learning rate for the algorithm when samples exhibit exponential alpha-mixing.
Quantified the error bound of the MLS algorithm for dependent data.

Conclusions:

The MLS method, when analyzed through a regression learning framework and assuming alpha-mixing, offers robust performance.
The derived learning rate and error bound provide theoretical support for using MLS with dependent data.
This work contributes to the theoretical understanding of MLS in the context of dependent sampling.