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

Basic Continuous Time Signals01:22

Basic Continuous Time Signals

194
Basic continuous-time signals include the unit step function, unit impulse function, and unit ramp function, collectively referred to as singularity functions. Singularity functions are characterized by discontinuities or discontinuous derivatives.
The unit step function, denoted u(t), is zero for negative time values and one for positive time values, exhibiting a discontinuity at t=0. This function often represents abrupt changes, such as the step voltage introduced when turning a car's...
194
BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

353
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....
353
Sampling Continuous Time Signal01:11

Sampling Continuous Time Signal

211
In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
In the...
211
Random Variables01:09

Random Variables

11.4K
A random variable is a single numerical value that indicates the outcome of a procedure. The concept of random variables is fundamental to the probability theory and was introduced by a Russian mathematician, Pafnuty Chebyshev, in the mid-nineteenth century.
Uppercase letters such as X or Y denote a random variable. Lowercase letters like x or y denote the value of a random variable. If X is a random variable, then X is written in words, and x is given as a number.
For example, let X = the...
11.4K
Wald-Wolfowitz Runs Test I01:17

Wald-Wolfowitz Runs Test I

611
The Wald-Wolfowitz test, also known as the runs test, is a nonparametric statistical test used to assess the randomness of a sequence of two different types of elements (e.g., positive/negative values, successes/failures). It examines whether the order of the elements in a sequence is random or if there is a pattern or trend present. This nonparametric test applies to any ordered data despite the population and sample data distribution, even if a higher sample size is available.
The test works...
611
Basic Discrete Time Signals01:16

Basic Discrete Time Signals

200
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...
200

You might also read

Related Articles

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

Sort by
Same author

The role and therapeutic potential of nanotechnology-mediated ferroptosis regulation in myelodysplastic syndromes.

Frontiers in oncology·2026
Same author

Longitudinal drug response assessment of tumor organoids based on optical attenuation coefficient and multi-dimensional morphological characterization.

Biomedical optics express·2026
Same author

Dynamic epigenetic and transcriptional regulatory network in pepper fruit development and ripening.

The Plant cell·2026
Same author

Heptametallic high‑entropy nanozyme‑based biosensors for detecting bacterial pathogens in food and infected wound.

Mikrochimica acta·2026
Same author

The Pt-Al Cooperative Effect Improves the Wettability of Sn-Zn Solder via Oxide Film Structure Optimization and Solid-Liquid Interfacial Tension Reduction.

ACS applied materials & interfaces·2026
Same author

Statistics of a large number of renewals in equilibrium and ordinary renewal processes at the short time limit.

Chaos (Woodbury, N.Y.)·2026

Related Experiment Video

Updated: Jun 10, 2025

Asymmetric Walkway: A Novel Behavioral Assay for Studying Asymmetric Locomotion
08:19

Asymmetric Walkway: A Novel Behavioral Assay for Studying Asymmetric Locomotion

Published on: January 15, 2016

8.8K

Simulation of the continuous time random walk using subordination schemes.

Danhua Jiang1, Yuanze Hong1, Wanli Wang1

  • 1School of Mathematical Sciences, <a href="https://ror.org/02djqfd08">Zhejiang University of Technology</a>, Hangzhou 310023, China.

Physical Review. E
|October 19, 2024
PubMed
Summary

We developed an algorithm using a subordinate formula to generate continuous time random walk data in the long time limit. This method accurately reproduces key statistical properties and fluctuations, validating its effectiveness.

More Related Videos

Structure-Based Simulation and Sampling of Transcription Factor Protein Movements along DNA from Atomic-Scale Stepping to Coarse-Grained Diffusion
09:17

Structure-Based Simulation and Sampling of Transcription Factor Protein Movements along DNA from Atomic-Scale Stepping to Coarse-Grained Diffusion

Published on: March 1, 2022

3.1K
Bouncing Ball with a Uniformly Varying Velocity in a Metronome Synchronization Task
05:04

Bouncing Ball with a Uniformly Varying Velocity in a Metronome Synchronization Task

Published on: September 21, 2017

5.9K

Related Experiment Videos

Last Updated: Jun 10, 2025

Asymmetric Walkway: A Novel Behavioral Assay for Studying Asymmetric Locomotion
08:19

Asymmetric Walkway: A Novel Behavioral Assay for Studying Asymmetric Locomotion

Published on: January 15, 2016

8.8K
Structure-Based Simulation and Sampling of Transcription Factor Protein Movements along DNA from Atomic-Scale Stepping to Coarse-Grained Diffusion
09:17

Structure-Based Simulation and Sampling of Transcription Factor Protein Movements along DNA from Atomic-Scale Stepping to Coarse-Grained Diffusion

Published on: March 1, 2022

3.1K
Bouncing Ball with a Uniformly Varying Velocity in a Metronome Synchronization Task
05:04

Bouncing Ball with a Uniformly Varying Velocity in a Metronome Synchronization Task

Published on: September 21, 2017

5.9K

Area of Science:

  • Complex Systems
  • Statistical Physics
  • Computational Modeling

Background:

  • The continuous time random walk (CTRW) model is a fundamental tool for describing anomalous diffusion and transport phenomena.
  • CTRW finds applications across diverse scientific disciplines, including physics, biology, chemistry, finance, and social sciences.
  • Generating accurate CTRW data, especially in the long-time limit, is crucial for theoretical validation and practical applications.

Purpose of the Study:

  • To introduce a novel algorithm for generating CTRW data.
  • To specifically address data generation in the long-time limit of the CTRW model.
  • To validate the algorithm's performance against established CTRW observables.

Main Methods:

  • Development of a new algorithm based on a subordinate formula.
  • Generation of CTRW data using the proposed algorithm.
  • Validation through analysis of positional distribution fluctuations (typical and rare), mean, variance, and breakthrough curves.

Main Results:

  • The algorithm successfully generates CTRW data in the long-time limit.
  • Validated results show a perfect match with commonly employed observables.
  • Demonstrated accuracy in reproducing typical and rare fluctuations, as well as statistical moments.

Conclusions:

  • The presented algorithm provides a reliable method for simulating CTRW processes.
  • The algorithm's ability to match key observables confirms its validity for long-time limit simulations.
  • This work offers a valuable tool for researchers studying anomalous diffusion and related phenomena.