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

Discrete-time Fourier transform01:26

Discrete-time Fourier transform

1.1K
The Discrete-Time Fourier Transform (DTFT) is an essential mathematical tool for analyzing discrete-time signals, converting them from the time domain to the frequency domain. This transformation allows for examining the frequency components of discrete signals, providing insights into their spectral characteristics. In the DTFT, the continuous integral used in the continuous-time Fourier transform is replaced by a summation to accommodate the discrete nature of the signal.
One of the notable...
1.1K
Basic Discrete Time Signals01:16

Basic Discrete Time Signals

709
The unit step sequence is defined as 1 for zero and positive values of the integer n. This sequence can be graphically displayed using a set of eight sample points, showing a step function starting from n=0 and remaining constant thereafter.
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is the...
709
Discrete-Time Fourier Series01:20

Discrete-Time Fourier Series

680
The Discrete-Time Fourier Series (DTFS) is a fundamental concept in signal processing, serving as the discrete-time counterpart to the continuous-time Fourier series. It allows for the representation and analysis of discrete-time periodic signals in terms of their frequency components. Unlike its continuous counterpart, which utilizes integrals, the calculation of DTFS expansion coefficients involves summations due to the discrete nature of the signal.
For a discrete-time periodic signal x[n]...
680
Setting Time of Cement01:12

Setting Time of Cement

655
The setting time of cement refers to the process of cement paste transitioning from a plastic state to a solid state. This process is crucial in construction as it dictates the timeframe for concrete placement, compaction, and finishing. The onset of this solidification is termed the initial set, indicating when the paste becomes unworkable. The final set is when the paste has solidified completely, and further handling or manipulation can no longer affect its shape. The cement strength is...
655
BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

918
System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
918
The Z-Scheme of Electron Transport in Photosynthesis01:34

The Z-Scheme of Electron Transport in Photosynthesis

13.7K
The light reactions of photosynthesis assume a linear flow of electrons from water to NADP+. During this process, light energy drives the splitting of water molecules to produce oxygen. However, oxidation of water molecules is a thermodynamically unfavorable reaction and requires a strong oxidizing agent. This is accomplished by the first product of light reactions: oxidized P680 (or P680+), the most powerful oxidizing agent known in biology. The oxidized P680 that acquires an electron from the...
13.7K

You might also read

Related Articles

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

Sort by
Same author

Atomically Precise Bismuth Oxido Nanoclusters as Hosts for Ln<sup>3+</sup>: Effects of Doping on Optical and Magnetic Properties of a Soluble Metal Oxide.

Inorganic chemistry·2026
Same author

A Generalized NMF-Based Method for Analyzing Time-Resolved Spectroscopic Data.

The journal of physical chemistry. A·2026
Same author

Revealing the Atomistic Mechanism of Rare Events in Molecular Dynamics.

Journal of chemical theory and computation·2026
Same author

Topological Analysis Reveals Multiple Pathways in Molecular Dynamics.

Journal of chemical theory and computation·2025
Same author

Pentraxin-3, MyD88, GLP-1, and PD-L1: Performance assessment and composite algorithmic analysis for sepsis identification.

The Journal of infection·2025
Same author

Atomically precise bismuth oxido nanoclusters: cerium doping for optical modification and supramolecular self-assembly on Au(111).

Nanoscale·2025

Related Experiment Video

Updated: Jan 30, 2026

The Synthesis of [Sn10SiSiMe334]2- Using a Metastable SnI Halide Solution Synthesized via a Co-condensation Technique
12:43

The Synthesis of [Sn10SiSiMe334]2- Using a Metastable SnI Halide Solution Synthesized via a Co-condensation Technique

Published on: November 28, 2016

9.1K

From metastable to coherent sets- Time-discretization schemes.

Konstantin Fackeldey1, Péter Koltai2, Peter Névir3

  • 1Institut für Mathematik, TU Berlin, Straße des 17, Juni 136, 10623 Berlin, Germany.

Chaos (Woodbury, N.Y.)
|February 3, 2019
PubMed
Summary
This summary is machine-generated.

This study shows that spectral algorithms, used for identifying metastable sets, can also find coherent sets in dynamical systems. This extends the analysis of complex systems by linking time-dependent processes to metastability concepts.

More Related Videos

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

9.7K
Optical Coherence Tomography Based Biomechanical Fluid-Structure Interaction Analysis of Coronary Atherosclerosis Progression
13:07

Optical Coherence Tomography Based Biomechanical Fluid-Structure Interaction Analysis of Coronary Atherosclerosis Progression

Published on: January 15, 2022

4.5K

Related Experiment Videos

Last Updated: Jan 30, 2026

The Synthesis of [Sn10SiSiMe334]2- Using a Metastable SnI Halide Solution Synthesized via a Co-condensation Technique
12:43

The Synthesis of [Sn10SiSiMe334]2- Using a Metastable SnI Halide Solution Synthesized via a Co-condensation Technique

Published on: November 28, 2016

9.1K
Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

9.7K
Optical Coherence Tomography Based Biomechanical Fluid-Structure Interaction Analysis of Coronary Atherosclerosis Progression
13:07

Optical Coherence Tomography Based Biomechanical Fluid-Structure Interaction Analysis of Coronary Atherosclerosis Progression

Published on: January 15, 2022

4.5K

Area of Science:

  • Dynamical Systems Theory
  • Stochastic Processes
  • Computational Physics
  • Data Analysis

Background:

  • Time-dependent stochastic processes exhibit complex behaviors, including metastability and coherence.
  • Metastable sets are defined in space, while coherent sets are defined in space-time.
  • Existing spectral algorithms effectively identify metastable sets in dynamical systems.

Purpose of the Study:

  • To demonstrate that established spectral algorithms can identify coherent sets in non-autonomous dynamical systems.
  • To leverage the relationship between coherent sets and metastable sets for analyzing complex processes.
  • To provide an overview of time-discretization schemes for computing transfer operator discretizations.

Main Methods:

  • Utilized spectral algorithms, such as Perron Cluster Cluster Analysis (PCCA+), for identifying metastable sets.
  • Computed space-time discretizations (transfer operator matrix T) of the underlying stochastic process.
  • Applied various time-discretization schemes to analyze the transfer operator.

Main Results:

  • Established that spectral algorithms for metastable sets successfully identify coherent sets in non-autonomous systems.
  • Demonstrated the applicability of these methods across different fields through two case studies.
  • Provided a practical framework for analyzing space-time coherent structures in complex systems.

Conclusions:

  • Spectral algorithms are versatile tools for analyzing both metastability and coherence in dynamical systems.
  • The connection between coherent and metastable sets offers a powerful approach for understanding complex system dynamics.
  • The presented time-discretization schemes are effective for identifying coherent sets in various applications.