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

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

45
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
45
Statically Indeterminate Problem Solving01:16

Statically Indeterminate Problem Solving

369
Statically indeterminate problems are those where statics alone can not determine the internal forces or reactions. Consider a structure comprising two cylindrical rods made of steel and brass. These rods are joined at point B and restrained by rigid supports at points A and C. Now, the reactions at points A and C and the deflection at point B are to be determined. This rod structure is classified as statically indeterminate as the structure has more supports than are necessary for maintaining...
369
Alternative Sets of Equilibrium Equations01:31

Alternative Sets of Equilibrium Equations

376
When analyzing the behavior of structures, engineers often rely on the concept of equilibrium. This refers to the state where all forces and moments acting on a system balance each other, resulting in no net movement or rotation. In many cases, equilibrium can be described by a set of standard equations. However, in some situations, alternative sets of equilibrium equations must be used to describe the system's behavior accurately.
One example of such a situation can be observed in a...
376
Castigliano's Theorem: Problem Solving01:14

Castigliano's Theorem: Problem Solving

601
The deflection of a simply supported beam that carries a central point load can be analyzed using structural mechanics principles, particularly by applying Castigliano's theorem. This theorem relates the displacement at the load application point to the partial derivatives of the strain energy in the structure. The simply supported beam with a point load at its center has symmetric reaction forces at the supports, each bearing half of the load. The bending moment at any point along the beam...
601
Theorems of Pappus and Guldinus: Problem Solving01:12

Theorems of Pappus and Guldinus: Problem Solving

711
Pappus and Guldinus's theorems are powerful mathematical principles that are used for finding the surface area and volume of composite shapes. For example, consider a cylindrical storage tank with a conical top. Finding the surface area or volume can be challenging for such complex shapes. These theorems are particularly useful in calculating the volume and surface area of such systems. Here, the cylindrical storage tank with a conical top can be broken down into two simple shapes: a...
711
Trial and Error and Algorithm01:12

Trial and Error and Algorithm

103
A problem-solving strategy is a plan of action used to find a solution. Different strategies have distinct action plans. Trial and error involves trying different solutions until one works. For instance, to fix a broken printer, you might check ink levels, ensure the paper tray isn't jammed, and verify the printer's connection to your laptop. This method can be time-consuming but is commonly used. Thomas Edison, for example, used trial and error to find a suitable filament for the light...
103

You might also read

Related Articles

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

Sort by
Same author

Quasi-synchronization for complex networks with hybrid pinning intermittent control.

Neural networks : the official journal of the International Neural Network Society·2026
Same author

Exponential synchronization of T-S fuzzy complex-valued BAM neural networks with mixed time-varying delays via event-triggered control engineering and applications.

Neural networks : the official journal of the International Neural Network Society·2026
Same author

Relaxed conditions and PSO-based optimization for the problem of Mittag-Leffler synchronization and its application in image restoration for fractional-order octonion-valued two-layer neural networks.

Neural networks : the official journal of the International Neural Network Society·2026
Same author

Real-time sparse signal reconstruction via KKT-conditions-driven analog circuit solver.

Neural networks : the official journal of the International Neural Network Society·2026
Same author

MPQ-DMv2: Flexible Residual Mixed Precision Quantization for Low-Bit Diffusion Models With Temporal Distillation.

IEEE transactions on pattern analysis and machine intelligence·2026
Same author

Stability Switching and Oscillation Regulation Strategies for Large-Scale Fractional-Order Neural Networks With Double Hubs and Multiple Delays.

IEEE transactions on cybernetics·2026
Same journal

Granular Ball-Based Noise-Resistant Fuzzy Multineighborhood Feature Selection via Label Enhancement and Feature Graph.

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

Fighting Evolving Spam With ARTMAP Models: A Noise-Resilient Online Detection Framework.

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

HyperSAT: Unsupervised Hypergraph Neural Networks for Weighted MaxSAT Problems.

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

Negation of Basic Belief Assignment in Multisource Information Fusion on Dempster-Shafer Theory With Applications in Pattern Classification.

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

Intervention Feasible Region and Driver Risk Capacity Aware Human-Machine Collaborative Safe Trajectory Planning.

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

A Unified Differential Denoising Learning Framework With a Pre-Trained Model and Fuzzy Graph Networks for Drug-Drug Interaction Prediction.

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

Related Experiment Video

Updated: Jun 12, 2025

The Modular Design and Production of an Intelligent Robot Based on a Closed-Loop Control Strategy
11:53

The Modular Design and Production of an Intelligent Robot Based on a Closed-Loop Control Strategy

Published on: October 14, 2017

11.6K

Distributed Algorithms for Linear Equations Over General Directed Networks.

Mengke Lian, Zhenyuan Guo, Xiaoxuan Wang

    IEEE Transactions on Neural Networks and Learning Systems
    |September 25, 2024
    PubMed
    Summary
    This summary is machine-generated.

    This study presents new distributed algorithms for solving linear equations $Ax = b$ over communication networks. These methods ensure exponential convergence to solutions or least-squares approximations.

    More Related Videos

    Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
    10:44

    Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

    Published on: December 7, 2021

    2.1K
    Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
    05:30

    Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

    Published on: September 8, 2023

    496

    Related Experiment Videos

    Last Updated: Jun 12, 2025

    The Modular Design and Production of an Intelligent Robot Based on a Closed-Loop Control Strategy
    11:53

    The Modular Design and Production of an Intelligent Robot Based on a Closed-Loop Control Strategy

    Published on: October 14, 2017

    11.6K
    Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
    10:44

    Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

    Published on: December 7, 2021

    2.1K
    Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
    05:30

    Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

    Published on: September 8, 2023

    496

    Area of Science:

    • Distributed Systems
    • Optimization Theory
    • Linear Algebra

    Background:

    • Solving linear equations $Ax = b$ is fundamental in many scientific and engineering fields.
    • Existing distributed methods often require specific network structures or full matrix information.

    Purpose of the Study:

    • To develop novel distributed continuous-time algorithms for solving linear equations over directed graphs.
    • To address challenges posed by weight-unbalanced networks and partial information availability.

    Main Methods:

    • Reformulating the linear equation problem as an unconstrained optimization problem.
    • Developing a gradient-based distributed algorithm for weight-balanced networks.
    • Proposing a distributed algorithm for weight-unbalanced networks using eigenvector estimation.

    Main Results:

    • The proposed algorithms achieve exponential convergence to an equilibrium point for each agent.
    • Convergence rates are explicitly determined.
    • Algorithms provide approximate least-squares solutions for inconsistent linear systems.

    Conclusions:

    • The developed algorithms offer robust and efficient distributed solutions for linear equations.
    • The methods are applicable to dynamic, time-varying communication networks.
    • The study extends distributed optimization techniques to solve fundamental algebraic problems.