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

Synthesis and Decomposition Reactions02:17

Synthesis and Decomposition Reactions

38.4K
Synthesis and decomposition are two types of redox reactions. Synthesis means to make something, whereas decomposition means to break something. The reactions are accompanied by chemical and energy changes. 
38.4K
Dynamic Equilibrium02:20

Dynamic Equilibrium

63.5K
A reversible chemical reaction represents a chemical process that proceeds in both forward (left to right) and reverse (right to left) directions. When the rates of the forward and reverse reactions are equal, the concentrations of the reactant and product species remain constant over time and the system is at equilibrium. A special double arrow is used to emphasize the reversible nature of the reaction. The relative concentrations of reactants and products in equilibrium systems vary greatly;...
63.5K
What is a Mode?01:07

What is a Mode?

26.8K
The mode is one of the commonly used measures of a central tendency. It is defined as the most frequent value in a data set.
There can be more than one mode in a data set if multiple values have the same highest frequency. For instance, suppose that the Statistics exam scores of 20 students are: 50; 53; 59; 59; 63; 63; 72; 72; 72; 72; 72; 76; 78; 81; 83; 84; 84; 84; 90; 93. Here, the mode is 72, as it occurs most frequently, five times.
A data set with two modes is called bimodal. For example,...
26.8K
Ventilatory Modes01:14

Ventilatory Modes

1.7K
Mechanical ventilators are life-saving devices that support or replace spontaneous breathing. They deliver breaths to patients through varying methods known as ventilator modes. Understanding these modes is critical for healthcare providers managing patients with respiratory failure.
There are three ventilatory modes: full support, partial support, and spontaneous. These are described below.
Full Support Modes
Full support modes include controlled mechanical ventilation, continuous mandatory...
1.7K
Modes of Standing Waves - I01:03

Modes of Standing Waves - I

4.1K
A close look at earthquakes provides evidence for the conditions appropriate for resonance, standing waves, and constructive and destructive interference. A building may vibrate for several seconds with a driving frequency matching the building's natural frequency of vibration; this produces a resonance that results in one building collapsing while the neighboring buildings do not. Often, buildings of a certain height are devastated, while other taller buildings remain intact. This...
4.1K
Modes of Standing Waves: II01:04

Modes of Standing Waves: II

1.8K
The starting point for expressing the modes of standing waves is understanding the boundary conditions that the waves must follow. The boundary conditions are derived from the physical understanding of how the standing waves are sustained, that is, how the vibrating particles of the medium behave at the boundaries imposed on them.
For a tube open at one end and closed at the other filled with air, the modes are such that there is always an antinode at the open end and a node at the closed end....
1.8K

You might also read

Related Articles

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

Sort by
Same author

Nonlinear combinatorial analysis of blood transcriptomes identifies PRKAR1A as a regulator of TDP-43 pathophysiology in amyotrophic lateral sclerosis.

Biology methods & protocols·2026
Same author

Data-driven simulator of multi-animal behavior with unknown dynamics via reinforcement learning.

iScience·2026
Same author

An Operator Analysis on Stochastic Differential Equation (SDE)-Based Diffusion Generative Models.

Entropy (Basel, Switzerland)·2026
Same author

Enhancing spectral analysis in nonlinear dynamics with pseudoeigenfunctions from continuous spectra.

Scientific reports·2024
Same author

Fast, accurate, and interpretable decoding of electrocorticographic signals using dynamic mode decomposition.

Communications biology·2024
Same author

Estimating Counterfactual Treatment Outcomes Over Time in Complex Multiagent Scenarios.

IEEE transactions on neural networks and learning systems·2024

Related Experiment Video

Updated: Feb 15, 2026

Measurements of Soil Carbon by Neutron-Gamma Analysis in Static and Scanning Modes
07:51

Measurements of Soil Carbon by Neutron-Gamma Analysis in Static and Scanning Modes

Published on: August 24, 2017

7.8K

Subspace dynamic mode decomposition for stochastic Koopman analysis.

Naoya Takeishi1, Yoshinobu Kawahara2,3, Takehisa Yairi1

  • 1Department of Aeronautics and Astronautics, The University of Tokyo, Bunkyo, Tokyo 113-8656, Japan.

Physical Review. E
|January 20, 2018
PubMed
Summary
This summary is machine-generated.

Subspace Dynamic Mode Decomposition (DMD) improves Koopman spectral analysis for noisy random systems. This new algorithm accurately estimates stochastic Koopman operator spectra, overcoming limitations of existing DMD methods.

More Related Videos

Confocal Microscopy to Measure Three Modes of Fusion Pore Dynamics in Adrenal Chromaffin Cells
12:30

Confocal Microscopy to Measure Three Modes of Fusion Pore Dynamics in Adrenal Chromaffin Cells

Published on: March 16, 2022

2.6K
Stochastic Noise Application for the Assessment of Medial Vestibular Nucleus Neuron Sensitivity In Vitro
06:22

Stochastic Noise Application for the Assessment of Medial Vestibular Nucleus Neuron Sensitivity In Vitro

Published on: August 28, 2019

5.6K

Related Experiment Videos

Last Updated: Feb 15, 2026

Measurements of Soil Carbon by Neutron-Gamma Analysis in Static and Scanning Modes
07:51

Measurements of Soil Carbon by Neutron-Gamma Analysis in Static and Scanning Modes

Published on: August 24, 2017

7.8K
Confocal Microscopy to Measure Three Modes of Fusion Pore Dynamics in Adrenal Chromaffin Cells
12:30

Confocal Microscopy to Measure Three Modes of Fusion Pore Dynamics in Adrenal Chromaffin Cells

Published on: March 16, 2022

2.6K
Stochastic Noise Application for the Assessment of Medial Vestibular Nucleus Neuron Sensitivity In Vitro
06:22

Stochastic Noise Application for the Assessment of Medial Vestibular Nucleus Neuron Sensitivity In Vitro

Published on: August 28, 2019

5.6K

Area of Science:

  • Dynamical Systems and Control Theory
  • Data-Driven Science
  • Nonlinear Dynamics

Background:

  • Koopman operator analysis is crucial for understanding nonlinear dynamical systems.
  • Dynamic Mode Decomposition (DMD) is a popular data-driven method for Koopman spectral analysis.
  • Existing DMD algorithms struggle with observation noise in random dynamical systems, leading to inaccurate spectral estimations.

Purpose of the Study:

  • To introduce subspace DMD, a novel algorithm for Koopman analysis of random dynamical systems with observation noise.
  • To address the inaccuracies in spectral estimation caused by noise in conventional DMD implementations.
  • To provide a robust method for analyzing stochastic Koopman operators.

Main Methods:

  • Subspace DMD computes an orthogonal projection of future data onto the space of past data.
  • It then estimates the spectra of an associated linear model.
  • The method is designed to be robust against observation noise.

Main Results:

  • The output of subspace DMD converges to the true spectra of the stochastic Koopman operator under standard assumptions.
  • Empirical evaluations demonstrate the effectiveness of subspace DMD across various dynamical systems.
  • The algorithm shows significant utility in Koopman analysis of random systems with noise.

Conclusions:

  • Subspace DMD offers a reliable approach for Koopman spectral analysis in the presence of observation noise.
  • This method enhances the accuracy of estimating spectra for stochastic Koopman operators.
  • Subspace DMD is a valuable tool for advancing the study of complex random dynamical systems.