Jove
Visualize
Contact Us

Related Concept Videos

Chebyshev's Theorem to Interpret Standard Deviation01:15

Chebyshev's Theorem to Interpret Standard Deviation

4.5K
Chebyshev’s theorem, also known as Chebyshev’s Inequality, states that the proportion of values of a dataset for K standard deviation is calculated using the equation:
4.5K
Bonferroni Test01:10

Bonferroni Test

2.9K
The Bonferroni test is a statistical test named after Carlo Emilio Bonferroni, an Italian mathematician best known for Bonferroni inequalities. This statistical test is a type of multiple comparison test to determine which means are different than the rest. Bonferroni test can minimize the Type 1 error by reducing the significance level alpha, which otherwise increases with sample pairs.
The means of different samples are first paired in all possible combinations.
The null hypothesis of the...
2.9K
Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

424
In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
424
Law of Independent Assortment02:03

Law of Independent Assortment

56.7K
While Mendel’s Law of Segregation states that the two alleles for one gene are separated into different gametes, a different question of how different genes are inherited remains. For example, is the gene for tall plants inherited with the gene for green peas? Mendel asked this question by experimenting with a dihybrid cross; a cross in which both parents are homozygous for two distinct traits resulting in an F1 generation that are heterozygous for both traits.
56.7K
Random Variables01:09

Random Variables

13.4K
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...
13.4K
Unusual Results01:16

Unusual Results

3.3K
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 =...
3.3K

You might also read

Related Articles

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

Sort by
Same author

Efficient Algorithms for Permutation Arrays from Permutation Polynomials.

Entropy (Basel, Switzerland)·2025
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
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 Experiment Video

Updated: Sep 18, 2025

Personalized Peptide Arrays for Detection of HLA Alloantibodies in Organ Transplantation
08:07

Personalized Peptide Arrays for Detection of HLA Alloantibodies in Organ Transplantation

Published on: September 6, 2017

10.2K

Upper Bounds for Chebyshev Permutation Arrays.

Sergey Bereg1, Zevi Miller2, Ivan Hal Sudborough1

  • 1Department of Computer Science, University of Texas at Dallas, Box 830688, Richardson, TX 75083, USA.

Entropy (Basel, Switzerland)
|June 26, 2025
PubMed
Summary
This summary is machine-generated.

This study improves upper bounds for permutation arrays using the Chebyshev distance. New methods establish better estimates for P(n,d) by analyzing separable arrays, enhancing combinatorial understanding.

Keywords:
Chebyshev metricpermutation arraysupper bounds

More Related Videos

Quadruple-Checkerboard: A Modification of the Three-Dimensional Checkerboard for Studying Drug Combinations
11:15

Quadruple-Checkerboard: A Modification of the Three-Dimensional Checkerboard for Studying Drug Combinations

Published on: July 24, 2021

4.9K
A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
07:56

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

8.6K

Related Experiment Videos

Last Updated: Sep 18, 2025

Personalized Peptide Arrays for Detection of HLA Alloantibodies in Organ Transplantation
08:07

Personalized Peptide Arrays for Detection of HLA Alloantibodies in Organ Transplantation

Published on: September 6, 2017

10.2K
Quadruple-Checkerboard: A Modification of the Three-Dimensional Checkerboard for Studying Drug Combinations
11:15

Quadruple-Checkerboard: A Modification of the Three-Dimensional Checkerboard for Studying Drug Combinations

Published on: July 24, 2021

4.9K
A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
07:56

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

8.6K

Area of Science:

  • Combinatorics
  • Discrete Mathematics
  • Information Theory

Background:

  • Permutation arrays are sets of permutations with specific distance properties.
  • The Chebyshev metric defines distance between permutations based on element-wise differences.
  • Existing research has focused on determining the maximum size of permutation arrays, P(n,d), under this metric.

Purpose of the Study:

  • To derive improved upper bounds for the size of permutation arrays under the Chebyshev metric.
  • To introduce and analyze the concept of 'separable' arrays of strings over {0,1,2}.
  • To establish a relationship between separable arrays and permutation arrays to improve existing bounds.

Main Methods:

  • Defining the Chebyshev distance and permutation arrays (n,d)-PA.
  • Introducing separable arrays R(n;a,b) over {0,1,2} with specific symbol counts.
  • Establishing R(n;k,k) as an upper bound for P(n,n-k).
  • Employing recursive and combinatorial techniques to derive bounds for R(n;a,b).

Main Results:

  • Improved upper bounds for P(n,d) are established.
  • The relationship R(n;k,k) ≤ P(n,n-k) is shown to be effective for k ≤ n/2.
  • New bounds for R(n;a,b) were derived using novel combinatorial methods.

Conclusions:

  • The study successfully improves upon known upper bounds for permutation arrays under the Chebyshev metric.
  • The analysis of separable arrays provides a novel approach to bounding P(n,d).
  • The derived bounds offer significant advancements in the field of combinatorial design and coding theory.