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

53
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...
53
Deconvolution01:20

Deconvolution

159
Deconvolution, also known as inverse filtering, is the process of extracting the impulse response from known input and output signals. This technique is vital in scenarios where the system's characteristics are unknown, and they must be inferred from the observable signals.
Deconvolution involves several mathematical techniques to derive the impulse response. One common approach is polynomial division. In this method, the input and output sequences are treated as coefficients of...
159
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

89
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....
89
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

81
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,...
81
Inverse z-Transform by Partial Fraction Expansion01:20

Inverse z-Transform by Partial Fraction Expansion

325
The inverse z-transform is a crucial technique for converting a function from its z-domain representation back to the time domain. One effective method for finding the inverse z-transform is the Partial Fraction Method, which involves decomposing a function into simpler fractions with distinct coefficients. These fractions correspond to known z-transform pairs, facilitating the inverse transformation process.
To begin the process, the poles of the function are identified and the function is...
325
Convolution: Math, Graphics, and Discrete Signals01:24

Convolution: Math, Graphics, and Discrete Signals

249
In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time.
To simplify the convolution integral, it is assumed that both the input signal and impulse response are zero for negative time values. The graphical convolution process...
249

You might also read

Related Articles

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

Sort by
Same author

Deciphering the cluster-to-spinel transformation pathway of CoMn<sub>2</sub> precursors toward efficient bifunctional electrocatalysis.

Journal of colloid and interface science·2026
Same author

Wavelet spectral-aware Kolmogorov-Arnold Network for organ and tumor segmentation.

Computerized medical imaging and graphics : the official journal of the Computerized Medical Imaging Society·2026
Same author

Data and knowledge-driven imaging biomarkers for lumbar aging and degenerative risk stratification monitoring.

NPJ digital medicine·2026
Same author

PEG-Dependent Tunable Degradation and Curcumin Release from Curcumin-Based Biomedical Polyurethanes.

Biomolecules·2026
Same author

Scale-Aware Prompting With Optimal Transport for Remote Sensing Image Captioning.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·2026
Same author

Elastic Multi-Gradient Descent for Parallel Continual Learning.

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

Hidden Data Recovery and Forecasting via Next-Generation Reservoir Computing With Multiscale Delay Selection.

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

CAFF-CIL: Causality-Aware Freedom Forgetting Approach for Class-Incremental Learning.

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

Harmonic Autoencoding Framework for Multiple Tasks in Magnetic Particle Imaging Reconstruction.

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

A Survey on Human-Centric Voice-Face Multimodal Learning.

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

Vision-Assisted Foundation Model for Solving Multitask Vehicle Routing Problems.

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

FP3O: Enabling Proximal Policy Optimization in Multiagent Cooperation With Parameter-Sharing Versatility.

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

Related Experiment Video

Updated: Jun 28, 2025

Author Spotlight: Advancing Alzheimer's Research &#8211; Exploring Early Detection and Multi-Omics Approaches
09:47

Author Spotlight: Advancing Alzheimer's Research – Exploring Early Detection and Multi-Omics Approaches

Published on: December 15, 2023

1.0K

DEs-Inspired Accelerated Unfolded Linearized ADMM Networks for Inverse Problems.

Weixin An, Yuanyuan Liu, Fanhua Shang

    IEEE Transactions on Neural Networks and Learning Systems
    |April 16, 2024
    PubMed
    Summary
    This summary is machine-generated.

    This study connects unfolded linearized alternating direction multiplier methods (ADMMs) to differential equations (DEs). New Trapezoid ADMM schemes offer improved accuracy and efficiency for inverse problems using deep networks.

    More Related Videos

    Deep Neural Networks for Image-Based Dietary Assessment
    13:19

    Deep Neural Networks for Image-Based Dietary Assessment

    Published on: March 13, 2021

    9.1K
    Swin-PSAxialNet: An Efficient Multi-Organ Segmentation Technique
    04:48

    Swin-PSAxialNet: An Efficient Multi-Organ Segmentation Technique

    Published on: July 5, 2024

    394

    Related Experiment Videos

    Last Updated: Jun 28, 2025

    Author Spotlight: Advancing Alzheimer's Research &#8211; Exploring Early Detection and Multi-Omics Approaches
    09:47

    Author Spotlight: Advancing Alzheimer's Research – Exploring Early Detection and Multi-Omics Approaches

    Published on: December 15, 2023

    1.0K
    Deep Neural Networks for Image-Based Dietary Assessment
    13:19

    Deep Neural Networks for Image-Based Dietary Assessment

    Published on: March 13, 2021

    9.1K
    Swin-PSAxialNet: An Efficient Multi-Organ Segmentation Technique
    04:48

    Swin-PSAxialNet: An Efficient Multi-Organ Segmentation Technique

    Published on: July 5, 2024

    394

    Area of Science:

    • Optimization Algorithms
    • Deep Learning
    • Applied Mathematics

    Background:

    • Traditional alternating direction multiplier methods (ADMMs) are increasingly understood through continuous-time differential equations (DEs).
    • Unfolded deep networks inherit ADMM iterations but lack clear structural insights.
    • Existing unfolded methods show practical performance gains but limited theoretical understanding.

    Purpose of the Study:

    • To explore unfolded linearized ADMM (LADMM) from a differential equation (DE) perspective.
    • To design novel, more efficient unfolded deep networks based on DE insights.
    • To establish theoretical guarantees connecting unfolded ADMMs with DEs.

    Main Methods:

    • Proposed an unfolded Euler LADMM scheme and a more accurate Trapezoid LADMM scheme based on trapezoid discretization.
    • Developed explicit versions of the Trapezoid LADMM scheme using a prediction-correction strategy.
    • Designed accelerated Euler and Trapezoid LADMM variants, interpretable as second-order DEs, to expand network representation capabilities.
    • Implemented schemes as (A-)ELADMM and (A-)TLADMM with proximal operators and (A-)ELADMM-Net and (A-)TLADMM-Net with convolutional neural networks (CNNs).

    Main Results:

    • Demonstrated a comprehensive connection between unfolded ADMMs and first- (second-) order DEs with theoretical guarantees.
    • The proposed Trapezoid LADMM schemes (A-TLADMM) showed superior performance in extensive inverse problem experiments compared to existing methods.
    • Accelerated schemes expanded the representation space of unfolded networks, enhancing capability.

    Conclusions:

    • The study provides the first theoretical framework linking unfolded ADMMs to DEs, offering insights into network structures.
    • The novel Trapezoid LADMM schemes and their accelerated variants significantly improve performance in inverse problems.
    • This work paves the way for designing more efficient and interpretable deep learning models for optimization tasks.