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

Separable Differential Equations01:20

Separable Differential Equations

A separable differential equation is a type of first-order differential equation where the derivative dy/dx can be expressed as a product of two functions: one that depends only on x and another that depends only on y. This allows for the rearrangement of the equation so that all terms involving y are on one side, and all terms involving x are on the other. This process, known as the separation of variables, simplifies the process of solving the equation by enabling the integration of both...
Linear Differential Equations01:27

Linear Differential Equations

The integrating factor method provides a systematic way to solve first-order linear differential equations, especially those that cannot be handled by separation of variables. This method is particularly useful in modeling time-dependent physical systems influenced by both constant inputs and resistive forces. A common example is the motion of a car subjected to a constant engine force while experiencing air resistance proportional to its velocity.In such scenarios, Newton’s second law yields a...
Differential Equations: Problem Solving01:21

Differential Equations: Problem Solving

When analyzing the motion of falling objects, it is essential to consider not only the force of gravity but also the opposing force of air resistance. A practical example involves releasing a heavy test weight during a safety check on a ship. As the weight falls from rest, gravity accelerates it downward while air resistance exerts an upward force that increases with velocity. This dynamic interplay of forces is well described by differential equations, which provide a mathematical framework...
Introduction to Differential Equations01:20

Introduction to Differential Equations

A differential equation is a mathematical expression that establishes a relationship between a function and its derivatives. These equations are fundamental in modeling dynamic systems across various fields of science and engineering. The order of a differential equation is defined by the highest order derivative present in the equation. A first-order differential equation includes only the first derivative, while a second-order differential equation includes up to the second derivative of the...
Modeling with Differential Equations01:25

Modeling with Differential Equations

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from the...

You might also read

Related Articles

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

Sort by
Same author

Sorafenib Restores Pentose Phosphate Pathway-Related Redox Homeostasis via the c-Raf/HSP90/G6PD Axis in Hepatic Ischemia-Reperfusion Injury.

MedComm·2026
Same author

The dissemination of a broad-host-range ARG-carrying plasmid to putative pathogens across agricultural soils.

Environmental pollution (Barking, Essex : 1987)·2026
Same author

Cadmium Stress Favours Biofilm Cooperation and Polysaccharide-Enriched Matrix Remodelling in Bacterial Consortia.

Environmental microbiology·2026
Same author

Developing an Oxygen-17 Isotope-Coupled WRF-Chem Model for Elucidating Sulfate Formation Mechanisms in China Haze and Beyond: Part I. Model Description and Initial Assessments.

Environmental science & technology·2026
Same author

Variable selection in functional linear Cox model.

Biometrics·2026
Same author

Impact of donor-recipient sex-matching patterns on liver transplantation outcomes: a cohort study based on United Network of Organ Sharing data.

Hepatobiliary surgery and nutrition·2025
Same journal

A KL-divergence-based test for elliptical distribution.

Journal of nonparametric statistics·2026
Same journal

Soft Bayesian Additive Regression Trees (SBART) for correlated survey response with non-Gaussian error.

Journal of nonparametric statistics·2026
Same journal

A comparison of causal inference methods for evaluating multiple treatment groups.

Journal of nonparametric statistics·2025
Same journal

Regression analysis of multiplicative hazards model with time-dependent coefficient for sparse longitudinal covariates.

Journal of nonparametric statistics·2025
Same journal

TSSS: A Novel Triangulated Spherical Spline Smoothing for Surface-Based Data.

Journal of nonparametric statistics·2025
Same journal

Nonparametric Density Estimation for Data Scattered on Irregular Spatial Domains: A Likelihood-Based Approach Using Bivariate Penalized Spline Smoothing.

Journal of nonparametric statistics·2025
See all related articles

Related Experiment Video

Updated: Jun 2, 2026

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

An ordinary differential equation based solution path algorithm.

Yichao Wu1

  • 1Department of Statistics, North Carolina State University, 2311 Stinson Drive, Raleigh, NC 27695.

Journal of Nonparametric Statistics
|May 3, 2011
PubMed
Summary
This summary is machine-generated.

This study extends Least Angle Regression (LAR) for generalized linear and quasi-likelihood models. An ordinary differential equation-based algorithm is proposed to compute the entire solution path, advancing statistical modeling techniques.

Related Experiment Videos

Last Updated: Jun 2, 2026

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

Area of Science:

  • Statistics
  • Computational Statistics
  • Machine Learning

Background:

  • Least Angle Regression (LAR) is a solution path algorithm for least squares regression.
  • A modification of LAR yields the LASSO solution path.
  • Extending LAR to generalized linear and quasi-likelihood models remains largely unexplored.

Purpose of the Study:

  • To extend the Least Angle Regression (LAR) algorithm to generalized linear models and quasi-likelihood models.
  • To provide theoretical insights into the propagation of the LAR solution path in these extended models.
  • To develop an ordinary differential equation (ODE)-based algorithm for computing the complete solution path.

Main Methods:

  • The study extends the LAR algorithm for generalized linear models and quasi-likelihood models.
  • It demonstrates that the solution path can be represented by solutions to systems of ordinary differential equations.
  • An ODE-based algorithm is proposed for calculating the entire solution path.

Main Results:

  • The extended LAR algorithm provides a piecewise solution path governed by ODE systems.
  • Theoretical understanding of solution path propagation in generalized linear and quasi-likelihood models is established.
  • A novel ODE-based algorithm is presented for computing the full solution path.

Conclusions:

  • The proposed method successfully extends Least Angle Regression to generalized linear and quasi-likelihood models.
  • The theoretical framework clarifies solution path behavior using ODE systems.
  • The developed algorithm offers an efficient way to obtain the complete solution path for these advanced statistical models.