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

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule01:10

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule

1.1K
In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1  triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the...
1.1K
¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

989
Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
989
Fast Fourier Transform01:10

Fast Fourier Transform

256
The Fast Fourier Transform (FFT) is a computational algorithm designed to compute the Discrete Fourier Transform (DFT) efficiently. By breaking down the calculations into smaller, manageable sections, the FFT significantly reduces the computational complexity involved. Direct computation of an N-point DFT requires N2 complex multiplications, whereas the FFT algorithm needs only (N/2)log⁡2N multiplications, offering a much faster performance.
The computational efficiency of the FFT becomes...
256
Properties of Fourier series I01:20

Properties of Fourier series I

187
The Fourier series is a powerful tool in signal processing and communications, allowing periodic signals to be expressed as sums of sine and cosine functions. A foundational property of the Fourier series is linearity. If we consider two periodic signals, their linear combination results in a new signal whose Fourier coefficients are simply the corresponding linear combinations of the original signals' coefficients. This property is crucial in applications like frequency modulation (FM)...
187
¹H NMR: Pople Notation01:09

¹H NMR: Pople Notation

1.7K
The Pople nomenclature system classifies spin systems based on the difference between their chemical shifts. Coupled spins are denoted by capital letters with subscripts indicating the number of equivalent nuclei. When the coupled nuclei have well-separated chemical shifts, they are assigned letters that are far apart in the alphabet, such as A and X. When the difference in chemical shifts is small, coupled nuclei are named using adjacent letters of the alphabet (AB, MN, or XY).
A proton...
1.7K
¹H NMR: Complex Splitting01:13

¹H NMR: Complex Splitting

1.2K
A proton M that is coupled to a proton X results in doublet signals for M. However, NMR-active nuclei can be simultaneously coupled to more than one nonequivalent nucleus. When M is coupled to a second proton A, such as in styrene oxide, each peak in the doublet is split into another doublet.
Splitting diagrams or splitting tree diagrams are routinely used to depict such complex couplings. While drawing splitting diagrams, the splitting with the larger coupling constant is usually applied...
1.2K

You might also read

Related Articles

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

Sort by
Same author

Safe Fairness Guarantees Without Demographics in Classification: Spectral Uncertainty Set Perspective.

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

A network-based model to assess vaccination strategies for the COVID-19 pandemic by using Bayesian optimization.

Chaos, solitons, and fractals·2025
Same author

On the Use of the Doubly Stochastic Matrix Models for the Quadratic Assignment Problem.

Evolutionary computation·2025
Same author

A probabilistic generative model to discover the treatments of coexisting diseases with missing data.

Computer methods and programs in biomedicine·2023
Same author

Neural Improvement Heuristics for Graph Combinatorial Optimization Problems.

IEEE transactions on neural networks and learning systems·2023
Same author

Learning the progression patterns of treatments using a probabilistic generative model.

Journal of biomedical informatics·2022
Same journal

Computing Optimal Populations for Binary Problems using Logic Minimization.

Evolutionary computation·2026
Same journal

Enhancing Generalization and Scalability for Multi-Objective Optimization with Population Pre-Training.

Evolutionary computation·2026
Same journal

XCS for Sequential Perceptual Aliasing in Multi-Step Decision Making.

Evolutionary computation·2026
Same journal

A dynamic multi-objective evolutionary algorithm using dual-space prediction and surrogate-based sampling.

Evolutionary computation·2026
Same journal

Adapting MOEA/D to CMA-ES for Dealing with Ill-conditioned Multiobjective Problems.

Evolutionary computation·2026
Same journal

Editorial of the Special Issue: Parallel Problem Solving from Nature PPSN 2024 Extended Versions of Best Paper Candidates.

Evolutionary computation·2026
See all related articles

Related Experiment Video

Updated: May 27, 2025

Harmonic Nanoparticles for Regenerative Research
09:23

Harmonic Nanoparticles for Regenerative Research

Published on: May 1, 2014

11.4K

P-NP Instance Decomposition Based on the Fourier Transform for Solving the Linear Ordering Problem.

Xabier Benavides1,2, Leticia Hernando3, Josu Ceberio4

  • 1University of the Basque Country UPV/EHU, Donostia-San Sebastian, 20018, Spain.

Evolutionary Computation
|February 20, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces a novel meta-heuristic algorithm, P-Descent Search (PDS), for the Linear Ordering Problem (LOP). PDS utilizes Fourier transforms to simplify complex optimization problems, leading to improved search efficiency.

Keywords:
Fourier transformLinear Ordering Probleminstance decompositionlocal search.

More Related Videos

Characterization of SiN Integrated Optical Phased Arrays on a Wafer-Scale Test Station
05:57

Characterization of SiN Integrated Optical Phased Arrays on a Wafer-Scale Test Station

Published on: April 1, 2020

8.0K
Author Spotlight: Unlocking New Insights in fNIRS Studies - A Novel Framework for Inter-Brain Synchrony Analysis
05:59

Author Spotlight: Unlocking New Insights in fNIRS Studies - A Novel Framework for Inter-Brain Synchrony Analysis

Published on: October 6, 2023

2.3K

Related Experiment Videos

Last Updated: May 27, 2025

Harmonic Nanoparticles for Regenerative Research
09:23

Harmonic Nanoparticles for Regenerative Research

Published on: May 1, 2014

11.4K
Characterization of SiN Integrated Optical Phased Arrays on a Wafer-Scale Test Station
05:57

Characterization of SiN Integrated Optical Phased Arrays on a Wafer-Scale Test Station

Published on: April 1, 2020

8.0K
Author Spotlight: Unlocking New Insights in fNIRS Studies - A Novel Framework for Inter-Brain Synchrony Analysis
05:59

Author Spotlight: Unlocking New Insights in fNIRS Studies - A Novel Framework for Inter-Brain Synchrony Analysis

Published on: October 6, 2023

2.3K

Area of Science:

  • Combinatorial Optimization
  • Computational Complexity Theory
  • Algorithm Design

Background:

  • Fourier transform over finite groups is a valuable tool for analyzing combinatorial optimization problems.
  • Existing heuristic and meta-heuristic algorithms rarely leverage Fourier transform information for search guidance.
  • The Linear Ordering Problem (LOP) serves as a case study to address this research gap.

Purpose of the Study:

  • To propose a novel meta-heuristic algorithm for the Linear Ordering Problem (LOP) by leveraging Fourier transform properties.
  • To address the research gap in heuristic algorithms that utilize Fourier transform for guided search.
  • To develop an optimization strategy that transforms NP-Hard problems into more tractable forms.

Main Methods:

  • Instance decomposition strategy based on Fourier transform, dividing LOP instances into P and NP-Hard components.
  • Linear aggregation of decomposed instances to create artificial instances with adjustable P and NP-Hard proportions.
  • Development of the P-Descent Search (PDS) meta-heuristic algorithm, optimizing surrogate instances with high P-component weight initially.

Main Results:

  • Increasing the P component's weight results in a less rugged fitness landscape, suitable for local search optimization.
  • The P-Descent Search (PDS) algorithm demonstrates promising and predictable performance.
  • Performance of PDS shows a correlation with specific problem characteristics, suggesting potential for automatic hyper-parameter tuning.

Conclusions:

  • The proposed instance decomposition and P-Descent Search offer an effective approach to tackling the Linear Ordering Problem.
  • The method successfully transforms complex optimization landscapes into more manageable ones for heuristic optimization.
  • The findings open avenues for further research into adaptive and automatically tuned meta-heuristic algorithms for combinatorial optimization.