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

Wald-Wolfowitz Runs Test I01:17

Wald-Wolfowitz Runs Test I

947
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...
947
Distance Problem01:29

Distance Problem

7
When an object's velocity changes over time, the total distance traveled can be determined by summing small displacement intervals over short increments. This approach approximates the true distance through numerical summation and the use of integral calculus. An estimate of the total displacement can be obtained by measuring velocity at regular intervals and multiplying each value by the corresponding time step.If a runner accelerates over the first three seconds of a race, speed measurements...
7
Properties of DTFT I01:24

Properties of DTFT I

735
In signal processing, Discrete-Time Fourier Transforms (DTFTs) play a critical role in analyzing discrete-time signals in the frequency domain. Various properties of the DTFTs such as linearity, time-shifting, frequency-shifting, time reversal, conjugation, and time scaling help understand and manipulate these signals for different applications.
The linearity property of DTFTs is fundamental. If two discrete-time signals are multiplied by constants a and b respectively, and then combined to...
735
Unusual Results01:16

Unusual Results

3.7K
Unusual results are those that have a very low chance of occurring. Unusual results can be identified using probabilities and the range rule of thumb. In problems involving probability, unusual results can be observed in 2 instances – an unusually high number of successes or an unusually low number of successes.
According to the range rule of thumb, any value above or below two standard deviations, 2σ  from the mean, μ  is considered unusual.
Maximum unusual value =...
3.7K
Wald-Wolfowitz Runs Test II01:17

Wald-Wolfowitz Runs Test II

527
The Wald-Wolfowitz runs test, commonly referred to as the runs test, is a nonparametric test used to assess the randomness of ordered data. The test evaluates the number of runs, which are consecutive sequences of similar elements within the data. If the number of runs is significantly higher or lower than expected, the data is considered non-random, indicating a detectable pattern or structure.
For binary data, runs are identified using symbols such as + and −, or equivalently, 1s and 0s. In...
527
Comparing the Survival Analysis of Two or More Groups01:20

Comparing the Survival Analysis of Two or More Groups

561
Survival analysis is a cornerstone of medical research, used to evaluate the time until an event of interest occurs, such as death, disease recurrence, or recovery. Unlike standard statistical methods, survival analysis is particularly adept at handling censored data—instances where the event has not occurred for some participants by the end of the study or remains unobserved. To address these unique challenges, specialized techniques like the Kaplan-Meier estimator, log-rank test, and...
561

You might also read

Related Articles

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

Sort by
Same author

An Entropy-Based Framework for Hybrid Coalitions in Game Theory-Part I: Human Arbitration.

Entropy (Basel, Switzerland)·2026
Same author

Entropic and algebraic transcript-based tools in time series analysis.

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

Transcript-based estimators for characterizing interactions.

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

Nonlinear Dynamics and Applications.

Entropy (Basel, Switzerland)·2025
Same author

Applications of Entropy in Data Analysis and Machine Learning: A Review.

Entropy (Basel, Switzerland)·2025
Same author

Generalized synchronization in the presence of dynamical noise and its detection via recurrent neural networks.

Chaos (Woodbury, N.Y.)·2024
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: Jan 16, 2026

Author Spotlight: Alignment of Synchronized Time-Series Data Using the Characterizing Loss of Cell Cycle Synchrony Model for Cross-Experiment Comparisons
07:59

Author Spotlight: Alignment of Synchronized Time-Series Data Using the Characterizing Loss of Cell Cycle Synchrony Model for Cross-Experiment Comparisons

Published on: June 9, 2023

1.9K

Permutation-Based Distances for Groups and Group-Valued Time Series.

José M Amigó1, Roberto Dale1

  • 1Centro de Investigación Operativa, Universidad Miguel Hernández, 03202 Elche, Spain.

Entropy (Basel, Switzerland)
|September 27, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces group distances using permutation metrics like Cayley and Kendall tau distances, applicable to time series analysis via symbolic representations.

Keywords:
Cayley and Kendall distancesCayley’s theoremalgebraic representationsedit distancefinite groupsgroup-valued time seriesordinal patternspermutationstime series analysistranscripts

More Related Videos

VDJ-Seq: Deep Sequencing Analysis of Rearranged Immunoglobulin Heavy Chain Gene to Reveal Clonal Evolution Patterns of B Cell Lymphoma
15:07

VDJ-Seq: Deep Sequencing Analysis of Rearranged Immunoglobulin Heavy Chain Gene to Reveal Clonal Evolution Patterns of B Cell Lymphoma

Published on: December 28, 2015

27.2K
Temporal Ordering of Dynamic Expression Data from Detailed Spatial Expression Maps
11:52

Temporal Ordering of Dynamic Expression Data from Detailed Spatial Expression Maps

Published on: February 9, 2017

6.5K

Related Experiment Videos

Last Updated: Jan 16, 2026

Author Spotlight: Alignment of Synchronized Time-Series Data Using the Characterizing Loss of Cell Cycle Synchrony Model for Cross-Experiment Comparisons
07:59

Author Spotlight: Alignment of Synchronized Time-Series Data Using the Characterizing Loss of Cell Cycle Synchrony Model for Cross-Experiment Comparisons

Published on: June 9, 2023

1.9K
VDJ-Seq: Deep Sequencing Analysis of Rearranged Immunoglobulin Heavy Chain Gene to Reveal Clonal Evolution Patterns of B Cell Lymphoma
15:07

VDJ-Seq: Deep Sequencing Analysis of Rearranged Immunoglobulin Heavy Chain Gene to Reveal Clonal Evolution Patterns of B Cell Lymphoma

Published on: December 28, 2015

27.2K
Temporal Ordering of Dynamic Expression Data from Detailed Spatial Expression Maps
11:52

Temporal Ordering of Dynamic Expression Data from Detailed Spatial Expression Maps

Published on: February 9, 2017

6.5K

Area of Science:

  • Group Theory
  • Time Series Analysis
  • Computational Mathematics

Background:

  • Symmetric groups are formed by permutations under function composition.
  • These groups possess algebraic structures and relevant metrics like Cayley and Kendall tau distances.
  • Finite groups are fundamental in symbolic time series representations, particularly ordinal representations.

Purpose of the Study:

  • To introduce a general concept of distance in finite groups.
  • To leverage permutation-based distances (Cayley, Kendall tau) for group analysis.
  • To explore applications of these distances in group-valued time series analysis.

Main Methods:

  • Utilizing Cayley's theorem to establish group isomorphism to symmetric group subgroups.
  • Defining and applying permutation-based distances within finite groups.
  • Extending metric concepts to group-valued time series.

Main Results:

  • A framework for defining distances on general finite groups is presented.
  • Comparison of permutation-based distances against conventional generator-based distances.
  • Demonstration of the utility of these metric tools in time series analysis.

Conclusions:

  • Permutation-based distances offer a novel approach to quantifying relationships within finite groups.
  • The developed methods provide valuable tools for analyzing complex time series data.
  • The study bridges abstract group theory with practical data analysis applications.