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

Gaussian Elimination: Problem Solving01:30

Gaussian Elimination: Problem Solving

266
Systems of linear equations in several variables are pivotal in modeling complex scenarios involving multiple unknowns and constraints. Such systems are widely used in various fields to represent relationships where several conditions must be simultaneously satisfied. Each variable in the system corresponds to an unknown quantity, while each equation imposes a linear constraint, leading to a structured approach for analyzing and solving real-world problems.A system of three equations with three...
266
Vector Algebra: Method of Components01:08

Vector Algebra: Method of Components

20.4K
It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like addition, subtraction, and multiplication. There are two ways to circumvent this algebraic complexity. One way is to draw the vectors to scale, as in navigation, and read approximate vector lengths and angles (directions) from the graphs. The other way is to use the method of components.
In many applications, the magnitudes and directions of...
20.4K
Multi-input and Multi-variable systems01:22

Multi-input and Multi-variable systems

458
Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence of...
458
Cartesian Form for Vector Formulation01:26

Cartesian Form for Vector Formulation

1.2K
The Cartesian form for vector formulation is a process to calculate  the moment of force using the position and force vectors. The moment of force is defined as the cross-product of these vectors, making it a vector quantity. The Cartesian form of the position and force vectors involves unit vectors, which can be used to express the cross-product in determinant form.
1.2K
Extraction: Partition and Distribution Coefficients01:14

Extraction: Partition and Distribution Coefficients

5.4K
The distribution law or Nernst's distribution law is the law that governs the distribution of a solute between two immiscible solvents. This law, also known as the partition law, states that if a solute is added to the mixture of two immiscible solvents at a constant temperature, the solute is distributed between the two solvents in such a way that the ratio of solute concentrations in the solvents remains constant at equilibrium.
For extracting a solute from an aqueous phase into an...
5.4K
Kinematic Equations for Rotation01:30

Kinematic Equations for Rotation

962
In mechanics, when one observes a rigid body in rotational motion with constant angular acceleration, it is possible to establish equations for its rotational kinematics. This process resembles how linear kinematics are dealt with in simpler motion studies.
For instance, imagine a point A on a rigid body engaged in circular motion. The translational velocity of this particular point can be calculated by taking the time derivatives of the displacement equation, which essentially measures the...
962

You might also read

Related Articles

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

Sort by
Same author

Coexistence of synchronization manifolds in networks of oscillators with rotation symmetry.

Physical review. E·2026
Same author

Impact of mid-life cardiovascular health on cognitive change in a bi-ethnic cohort.

medRxiv : the preprint server for health sciences·2025
Same author

Effects of Leaf Herbivory on Floral Trait Correlations and Scent Composition in Asclepias syriaca.

Journal of chemical ecology·2025
Same author

Improving synchronization with hypernetworks: Master stability function analysis and simulation validation.

Physical review. E·2025
Same author

Corrigendum to "Proteins from SARS-CoV-2 reduce T cell proliferation: A mirror image of sepsis" [Heliyon Volume 6, Issue 12, December 2020, Article e05635].

Heliyon·2025
Same author

Same data, different analysts: variation in effect sizes due to analytical decisions in ecology and evolutionary biology.

BMC biology·2025
Same journal

Erratum: Low-dimensional model for adaptive networks of spiking neurons [Phys. Rev. E 111, 014422 (2025)].

Physical review. E·2026
Same journal

Disentangling the effects of many-body forces on depletion interactions.

Physical review. E·2026
Same journal

Charge transport and mode transition in dual-energy electron beam diodes.

Physical review. E·2026
Same journal

Optimization of multisite reactions in complex compartmentalized media.

Physical review. E·2026
Same journal

Origin of geometric cohesion in nonconvex granular materials: Interplay between interdigitation and rotational constraints enhancing frictional stability.

Physical review. E·2026
Same journal

Interaction of walkers with a standing Faraday wave.

Physical review. E·2026
See all related articles

Related Experiment Video

Updated: Mar 19, 2026

A Multimodal Wide-Field Fourier-Transform Raman Microscope
06:48

A Multimodal Wide-Field Fourier-Transform Raman Microscope

Published on: December 30, 2025

684

Matrix formulation and singular-value decomposition algorithm for structured varimax rotation in multivariate

Leonardo L Portes1, Luis A Aguirre1

  • 1Departamento de Engenharia Eletrônica, Universidade Federal de Minas Gerais-Avenida Antônio Carlos 6627, 31270-901 Belo Horizonte MG, Brazil.

Physical Review. E
|June 15, 2016
PubMed
Summary
This summary is machine-generated.

Structured varimax rotation (SVR) enhances multivariate singular spectrum analysis (M-SSA) for characterizing phase synchronization in chaotic oscillators. This study presents a matrix formulation for SVR, enabling faster computation and improved analysis of complex systems.

More Related Videos

Multiplex Chemical Imaging Based on Broadband Stimulated Raman Scattering Microscopy
09:57

Multiplex Chemical Imaging Based on Broadband Stimulated Raman Scattering Microscopy

Published on: July 25, 2022

4.7K
Basics of Multivariate Analysis in Neuroimaging Data
06:35

Basics of Multivariate Analysis in Neuroimaging Data

Published on: July 24, 2010

17.4K

Related Experiment Videos

Last Updated: Mar 19, 2026

A Multimodal Wide-Field Fourier-Transform Raman Microscope
06:48

A Multimodal Wide-Field Fourier-Transform Raman Microscope

Published on: December 30, 2025

684
Multiplex Chemical Imaging Based on Broadband Stimulated Raman Scattering Microscopy
09:57

Multiplex Chemical Imaging Based on Broadband Stimulated Raman Scattering Microscopy

Published on: July 25, 2022

4.7K
Basics of Multivariate Analysis in Neuroimaging Data
06:35

Basics of Multivariate Analysis in Neuroimaging Data

Published on: July 24, 2010

17.4K

Area of Science:

  • Nonlinear Dynamics
  • Complex Systems Analysis
  • Time Series Analysis

Background:

  • Multivariate Singular Spectrum Analysis (M-SSA) is used to analyze coupled chaotic oscillators.
  • Characterizing phase synchronization in these systems requires specialized techniques.
  • Groth and Ghil (2011) proposed a modified varimax rotation (structured varimax rotation, SVR) to improve M-SSA's capabilities.

Purpose of the Study:

  • To develop a closed matrix formulation for structured orthomax rotation criteria, generalizing SVR.
  • To enable fast computation of M-SSA eigenvector rotation using singular value algorithms.
  • To illustrate the application of the SVR algorithm for analyzing phase synchronization in chaotic systems.

Main Methods:

  • Development of a general matrix formulation for structured orthomax rotations.
  • Application of singular value decomposition algorithms for efficient M-SSA eigenvector rotation.
  • Testing the SVR algorithm on Rössler system benchmark cases (phase-coherent and funnel regimes).

Main Results:

  • The proposed matrix formulation provides a unified approach to structured rotations.
  • The singular value algorithm allows for simultaneous rotation of M-SSA eigenvectors, crucial for large systems.
  • SVR demonstrated superior performance over unstructured varimax rotation (UVR) in analyzing complex chaotic behavior (funnel regime).

Conclusions:

  • The developed matrix formulation and computational approach enhance M-SSA's utility for phase synchronization analysis.
  • Structured varimax rotation is essential for accurately characterizing complex synchronization patterns in chaotic systems.
  • This work offers a valuable tool for theoretical and applied studies in nonlinear dynamics and complex systems.