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

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...
Noncompartmental Analysis: Mean Residence Time01:05

Noncompartmental Analysis: Mean Residence Time

According to statistical moment theory, mean residence time (MRT) is an important measure in pharmacokinetics. MRT can be defined as the expected mean of a probability density function distribution. It provides valuable insights into drug disposition in the body.
After the administration of a drug through intravenous bolus injection, the drug molecules are distributed throughout the body and remain there for varying periods. The MRT represents the average time these drug molecules stay in the...
Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
Randomized Experiments01:13

Randomized Experiments

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...
Wald-Wolfowitz Runs Test I01:17

Wald-Wolfowitz Runs Test I

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...
Basic Continuous Time Signals01:22

Basic Continuous Time Signals

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...

You might also read

Related Articles

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

Sort by
Same author

Establishment of an MR-Conditional Porcine Model for Real-Time Assessment of Cerebral Blood Flow During Extracorporeal Circulation.

Journal of cardiovascular development and disease·2026
Same author

Reliability of a nonlinear fluctuation-dissipation relation as a test of Markovianity.

Physical review. E·2026
Same author

Long term results of elective aortic ascendens wrapping technique - single center study.

Journal of cardiothoracic surgery·2026
Same author

Long-term follow-up of the VORTEC technique: A clampless, sutureless technique for supra-aortic debrancing.

Journal of vascular surgery cases and innovative techniques·2026
Same author

Hitting the blinking target under stochastic resetting.

Chaos (Woodbury, N.Y.)·2026
Same author

Cerebral Hemodynamic Changes During Cardiac Surgery: A Feasibility MR Study in Piglets.

NMR in biomedicine·2026

Related Experiment Video

Updated: Jun 18, 2026

Using a Real-Time Locating System to Measure Walking Activity Associated with Wandering Behaviors Among Institutionalized Older Adults
04:13

Using a Real-Time Locating System to Measure Walking Activity Associated with Wandering Behaviors Among Institutionalized Older Adults

Published on: February 8, 2019

Continuous-time random walk with correlated waiting times.

Aleksei V Chechkin1, Michael Hofmann, Igor M Sokolov

  • 1School of Chemistry, Tel Aviv University, Ramat Aviv, 69978 Tel Aviv, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2009
PubMed
Summary

This study explores correlated continuous time random walks (CTRW). Correlated waiting times slow down subdiffusion at short times but lead to standard behavior at long times, with power-law correlations showing persistent subdiffusion.

More Related Videos

Trajectory Data Analyses for Pedestrian Space-time Activity Study
16:14

Trajectory Data Analyses for Pedestrian Space-time Activity Study

Published on: February 25, 2013

Measuring the Switch Cost of Smartphone Use While Walking
07:00

Measuring the Switch Cost of Smartphone Use While Walking

Published on: April 30, 2020

Related Experiment Videos

Last Updated: Jun 18, 2026

Using a Real-Time Locating System to Measure Walking Activity Associated with Wandering Behaviors Among Institutionalized Older Adults
04:13

Using a Real-Time Locating System to Measure Walking Activity Associated with Wandering Behaviors Among Institutionalized Older Adults

Published on: February 8, 2019

Trajectory Data Analyses for Pedestrian Space-time Activity Study
16:14

Trajectory Data Analyses for Pedestrian Space-time Activity Study

Published on: February 25, 2013

Measuring the Switch Cost of Smartphone Use While Walking
07:00

Measuring the Switch Cost of Smartphone Use While Walking

Published on: April 30, 2020

Area of Science:

  • Physics
  • Statistical Mechanics
  • Complex Systems

Background:

  • Continuous Time Random Walks (CTRW) are fundamental models for anomalous diffusion.
  • Standard CTRW assumes independent waiting times between jumps.
  • Correlated waiting times can significantly alter diffusion dynamics.

Purpose of the Study:

  • To generalize CTRW by incorporating correlated waiting times.
  • To investigate the impact of exponential and power-law correlations on diffusion.
  • To analyze the mean squared displacement under these correlated conditions.

Main Methods:

  • Utilizing the Langevin description for CTRW.
  • Analyzing exponential correlations in waiting times.
  • Analyzing slowly decaying power-law correlations in waiting times.

Main Results:

  • Exponential correlations lead to slower subdiffusion at short times, reverting to standard CTRW behavior at long times.
  • Power-law correlations result in time-independent subdiffusion with a smaller exponent than uncorrelated CTRW.
  • A lower bound exists for the subdiffusion exponent even with extremely long power-law correlations.

Conclusions:

  • Correlated waiting times introduce distinct subdiffusion regimes compared to uncorrelated CTRW.
  • The nature of the correlation (exponential vs. power-law) dictates the long-time diffusion behavior.
  • This generalized CTRW model provides a more nuanced understanding of anomalous diffusion in complex systems.