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

Random Variables01:09

Random Variables

16.7K
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...
16.7K
Exponential Equations for Modeling Growth02:33

Exponential Equations for Modeling Growth

74
Exponential models are essential for describing rapid, multiplicative changes in natural systems, such as population growth. When a population doubles at regular intervals, the process can be modeled using a suitable base. For instance, a bacterial culture that doubles every three hours follows the model n(t)=n0⋅2t/3, where n(t) is the population at the time t.A more general model uses the natural base e, especially for continuous growth. This takes the form n(t)=n0⋅ert, where r is...
74
Basic Continuous Time Signals01:22

Basic Continuous Time Signals

550
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...
550
Basic Discrete Time Signals01:16

Basic Discrete Time Signals

504
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...
504
Sampling Continuous Time Signal01:11

Sampling Continuous Time Signal

533
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...
533
Randomized Experiments01:13

Randomized Experiments

8.6K
The randomization process involves assigning study participants randomly to experimental or control groups based on their probability of being equally assigned. Randomization is meant to eliminate selection bias and balance known and unknown confounding factors so that the control group is similar to the treatment group as much as possible. A computer program and a random number generator can be used to assign participants to groups in a way that minimizes bias.
Simple randomization
Simple...
8.6K

You might also read

Related Articles

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

Sort by
Same author

Optimal conditions for first passage of jump processes with resetting.

Chaos (Woodbury, N.Y.)·2025
Same author

Exploring run-and-tumble movement in confined settings through simulation.

The Journal of chemical physics·2024
Same author

Records and Occupation Time Statistics for Area-Preserving Maps.

Entropy (Basel, Switzerland)·2023
Same journal

Research on a Regional Availability Evaluation Model for Road-Area High-Entropy Energy Based on Synergy Factors.

Entropy (Basel, Switzerland)·2026
Same journal

Atmospheric Turbulence Channel Modeling and Performance Analysis of a CO-ZP-OFDM Coherent Optical Communication System for UAV Air-to-Ground Scenarios.

Entropy (Basel, Switzerland)·2026
Same journal

Information Geometry and Asymptotic Theory for SMML Estimators.

Entropy (Basel, Switzerland)·2026
Same journal

Correlation Entropy and Power-Law Kinetics.

Entropy (Basel, Switzerland)·2026
Same journal

Research on the Contagion of Systemic Financial Risk Under the Impact of Climate Risks-From the Perspective of Complex Networks and Machine Learning.

Entropy (Basel, Switzerland)·2026
Same journal

The Statistical-Mechanical Meaning of the Wave Function of Quantum Mechanics.

Entropy (Basel, Switzerland)·2026
See all related articles

Related Experiment Video

Updated: Nov 24, 2025

Generating Acute and Chronic Experimental Models of Motor Tic Expression in Rats
07:38

Generating Acute and Chronic Experimental Models of Motor Tic Expression in Rats

Published on: May 27, 2021

8.4K

A Continuous-Time Random Walk Extension of the Gillis Model.

Gaia Pozzoli1,2, Mattia Radice1,2, Manuele Onofri1,2

  • 1Center for Nonlinear and Complex Systems, Dipartimento di Scienza e Alta Tecnologia, Università degli Studi dell'Insubria, Via Valleggio 11, 22100 Como, Italy.

Entropy (Basel, Switzerland)
|December 23, 2020
PubMed
Summary
This summary is machine-generated.

We introduce a modified Gillis random walk with heavy-tailed waiting times. This process exhibits subdiffusion and ergodicity breaking, altering transport properties compared to normal diffusion.

Keywords:
CTRWGillis modelanomalous diffusionbiased processesergodicityfirst-time events

More Related Videos

Applying the RatWalker System for Gait Analysis in a Genetic Rat Model of Parkinson's Disease
04:08

Applying the RatWalker System for Gait Analysis in a Genetic Rat Model of Parkinson's Disease

Published on: January 18, 2021

3.1K
Quantitative Analysis of Random Migration of Cells Using Time-lapse Video Microscopy
07:27

Quantitative Analysis of Random Migration of Cells Using Time-lapse Video Microscopy

Published on: May 13, 2012

17.1K

Related Experiment Videos

Last Updated: Nov 24, 2025

Generating Acute and Chronic Experimental Models of Motor Tic Expression in Rats
07:38

Generating Acute and Chronic Experimental Models of Motor Tic Expression in Rats

Published on: May 27, 2021

8.4K
Applying the RatWalker System for Gait Analysis in a Genetic Rat Model of Parkinson's Disease
04:08

Applying the RatWalker System for Gait Analysis in a Genetic Rat Model of Parkinson's Disease

Published on: January 18, 2021

3.1K
Quantitative Analysis of Random Migration of Cells Using Time-lapse Video Microscopy
07:27

Quantitative Analysis of Random Migration of Cells Using Time-lapse Video Microscopy

Published on: May 13, 2012

17.1K

Area of Science:

  • Stochastic Processes
  • Mathematical Physics
  • Statistical Mechanics

Background:

  • The Gillis random walk is a known mathematical model for non-homogeneous random walks.
  • Standard random walks often assume finite waiting times, which limits their applicability to systems with anomalous diffusion.

Purpose of the Study:

  • To generalize the Gillis random walk by incorporating heavy-tailed waiting-time distributions.
  • To investigate the impact of these distributions on the process's properties, including diffusion and ergodicity.

Main Methods:

  • Mathematical analysis of a continuous-time random walk with position-dependent drift and heavy-tailed waiting times.
  • Derivation of exact results for various statistical quantities.
  • Numerical simulations to validate theoretical predictions.

Main Results:

  • Normal diffusion transitions to subdiffusion.
  • Ergodicity is broken due to the heavy-tailed waiting times.
  • Exact results obtained for hitting times, survival probabilities, occupation times, and record statistics.

Conclusions:

  • The modified Gillis random walk provides a framework for studying anomalous transport phenomena.
  • Heavy-tailed waiting times fundamentally alter the dynamics and statistical properties of random walks.
  • The findings have implications for understanding complex systems exhibiting subdiffusion and non-ergodic behavior.