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

Parametric Survival Analysis: Weibull and Exponential Methods01:14

Parametric Survival Analysis: Weibull and Exponential Methods

1.3K
Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
1.3K
Basic Continuous Time Signals01:22

Basic Continuous Time Signals

902
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...
902
Noncompartmental Analysis: Mean Residence Time01:05

Noncompartmental Analysis: Mean Residence Time

727
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...
727
Modeling with Differential Equations01:25

Modeling with Differential Equations

334
Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
334
Random Variables01:09

Random Variables

14.7K
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...
14.7K
Basic Discrete Time Signals01:16

Basic Discrete Time Signals

966
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...
966

You might also read

Related Articles

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

Sort by
Same author

Antibacterial and Immunomodulatory Coatings for Orthopedic Metal Implants: Biological Rationale, Design Strategies, and Translational Challenges.

Advanced healthcare materials·2026
Same author

Trend and hotspots of progressive hemifacial atrophy: A bibliometric and visualization analysis.

Journal of stomatology, oral and maxillofacial surgery·2026
Same author

[Mechanism of kynurenine 3-monooxygenase inhibitor GSK180 in alleviating trauma-induced sepsis-induced acute kidney injury in rats].

Zhonghua wei zhong bing ji jiu yi xue·2026
Same author

ITMol: a molecular image-text foundation model bridging the semantic gap for property prediction and retrieval.

BMC biology·2026
Same author

Preparation of Biomimetic Shells from Biomass Based on Selective Laser Sintering Technology.

3D printing and additive manufacturing·2026
Same author

High-Performance Hybrid CMS Membranes Development via Synergistic Pore Tailoring and Sulfur-Doping.

Small (Weinheim an der Bergstrasse, Germany)·2026

Related Experiment Video

Updated: Apr 30, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
06:44

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

709

A directed continuous time random walk model with jump length depending on waiting time.

Long Shi1, Zuguo Yu2, Zhi Mao3

  • 1Hunan Key Laboratory for Computation and Simulation in Science and Engineering and Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, Xiangtan University, Xiangtan, Hunan 411105, China ; Institute of Mathematics and Physics, Central South University of Forest and Technology, Changsha, Hunan 410004, China.

Thescientificworldjournal
|April 24, 2014
PubMed
Summary

A new continuous time random walk model links waiting times to jump direction. This model determines the probability density function

More Related Videos

Image-based Lagrangian Particle Tracking in Bed-load Experiments
10:32

Image-based Lagrangian Particle Tracking in Bed-load Experiments

Published on: July 20, 2017

10.4K
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

2.5K

Related Experiment Videos

Last Updated: Apr 30, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
06:44

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

709
Image-based Lagrangian Particle Tracking in Bed-load Experiments
10:32

Image-based Lagrangian Particle Tracking in Bed-load Experiments

Published on: July 20, 2017

10.4K
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

2.5K

Area of Science:

  • Physics
  • Mathematics
  • Statistical Mechanics

Background:

  • Continuous time random walks (CTRWs) are fundamental in modeling stochastic processes.
  • Existing CTRW models often assume independent waiting times between jumps.
  • Understanding the influence of correlated waiting times is crucial for realistic modeling.

Purpose of the Study:

  • To introduce a novel coupled directed continuous time random walk model.
  • To investigate the impact of waiting time on the subsequent jump direction.
  • To analyze the statistical properties of this correlated random walk.

Main Methods:

  • Development of a one-dimensional directed continuous time random walk model.
  • Utilizing Laplace-Laplace transforms to analyze the probability density function.
  • Derivation of the limit distribution and evolving equations based on waiting time properties.

Main Results:

  • The probability density function is fully determined by the waiting time's Laplace transform.
  • A direct relationship is established between waiting time statistics and random process behavior.
  • The model allows for the derivation of the process's limit distribution and governing equations.

Conclusions:

  • The proposed model provides a new framework for understanding correlated random walks.
  • Waiting time dynamics significantly influence the directional movement of the random walker.
  • The derived mathematical framework enables predictions of long-term behavior and system evolution.