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

Circles01:18

Circles

108
A circle in the coordinate plane is defined as the set of all points that lie at a constant distance, known as the radius, from a fixed point called the center. This relationship is captured using the distance formula. For a point (x, y) on the circle and a center (h, k), the distance between them equals the radius r. By squaring both sides of the distance formula, the equation of the circle is written in standard form:Constructing the Equation from Geometric InformationIf the center and the...
108
Frost Circles for Different Conjugated Systems01:18

Frost Circles for Different Conjugated Systems

3.4K
The inscribed polygon method is consistent with Hückel’s 4n + 2 rule and helps to learn whether the given cyclic compound is aromatic or not. The compound is stable and aromatic if every bonding molecular orbital (MO) is completely filled with a pair of electrons. However, if the non-bonding or antibonding orbitals are filled with electrons, the compound is unstable and not aromatic. Consider the Frost circle diagrams for cycloalkenes containing 4 to 8 carbons.
3.4K
Degree of Curvature and Radius of Curvature01:19

Degree of Curvature and Radius of Curvature

382
The degree of curvature and the radius of curvature are fundamental concepts in determining the sharpness or smoothness of a curve. The degree of curvature is a measure of how steeply a curve bends and can be determined using the chord basis or the arc basis. In the chord basis method, the degree of curvature is defined as the central angle subtended by a chord of 30.48 meters, helping in the calculation of the radius of the curve. The arc basis method defines the degree of...
382
Stereoisomerism of Cyclic Compounds02:33

Stereoisomerism of Cyclic Compounds

10.7K
In this lesson, we delve into the role of ring conformation and its stability, which determines the spatial arrangement and, consequently, the molecular symmetry and stereoisomerism of cyclic compounds. 1,2-Dimethylcyclohexane is used as a case study to evaluate the possible number of stereoisomers. Here, given the multiple (n = 2) chiral centers, there are 2n = 4 possible configurations that lack a plane of symmetry, as the ring skeleton exists in a non-planar chair conformation. In addition,...
10.7K
Torsion of Noncircular Members01:16

Torsion of Noncircular Members

416
Circular shafts undergoing torsional stress maintain their cross-sectional integrity due to their axisymmetric nature. This symmetry ensures an even distribution of stress, allowing the shaft to withstand torsion without distorting. In contrast, square bars, lacking this axial symmetry, experience significant distortion across their cross-sections when subjected to torsion, with the exception of along their diagonals and at lines connecting midpoints. A detailed examination of a cubic element...
416
Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

740
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...
740

You might also read

Related Articles

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

Sort by
Same author

Construction of Dinucleotide Circular Codes Based on Nucleotide Probabilities.

Acta biotheoretica·2025
Same author

Isomorphisms of Maximal Self-complementary [Formula: see text]-codes.

Acta biotheoretica·2025
Same author

Codes across (life)sciences.

Bio Systems·2025
Same author

Enhancing FAIRdata by providing digital workflows from data generation to the publication of data: an open source approach described for cyclic voltammetry.

Chemical science·2025
Same author

Forbidden codon combinations in error-detecting circular codes.

Theory in biosciences = Theorie in den Biowissenschaften·2024
Same author

Genome Galaxy Identified by the Circular Code Theory.

Bulletin of mathematical biology·2024
Same journal

Effects of Seasonal Births and Predation on Disease Spread.

Bulletin of mathematical biology·2026
Same journal

Identifiability, Sensitivity, and Genetic Algorithms in Bacterial Biofilm Selection Models.

Bulletin of mathematical biology·2026
Same journal

Slow Evolution Towards Generalism in a Model of Variable Dietary Range.

Bulletin of mathematical biology·2026
Same journal

CBINN: Cancer Biology-Informed Neural Network for Unknown Parameter Estimation and Missing Physics Identification.

Bulletin of mathematical biology·2026
Same journal

A Cost-Sensitive Behavioral Modeling Analysis of the Early Identification and Control of Infectious Diseases.

Bulletin of mathematical biology·2026
Same journal

Tracking Dynamics of Superspreading Through Contacts, Exposures, and Transmissions in Edge-Based Network Epidemics.

Bulletin of mathematical biology·2026
See all related articles

Related Experiment Video

Updated: Dec 13, 2025

Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules
09:32

Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules

Published on: April 12, 2019

6.9K

The Relation Between k-Circularity and Circularity of Codes.

Elena Fimmel1, Christian J Michel2, François Pirot3,4

  • 1Institute of Mathematical Biology, Faculty for Computer Sciences, Mannheim University of Applied Sciences, 68163, Mannheim, Germany.

Bulletin of Mathematical Biology
|August 6, 2020
PubMed
Summary
This summary is machine-generated.

Researchers identified the minimum integer k, ensuring k-circular codes become circular codes for any alphabet size and code length. This advances understanding of circular codes and their relation to genetic code evolution.

Keywords:
Circular codeCode evolutionGenetic codek-circular code

More Related Videos

CD Spectroscopy to Study DNA-Protein Interactions
06:48

CD Spectroscopy to Study DNA-Protein Interactions

Published on: February 10, 2022

7.4K
Identification of Circular RNAs using RNA Sequencing
08:25

Identification of Circular RNAs using RNA Sequencing

Published on: November 14, 2019

12.6K

Related Experiment Videos

Last Updated: Dec 13, 2025

Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules
09:32

Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules

Published on: April 12, 2019

6.9K
CD Spectroscopy to Study DNA-Protein Interactions
06:48

CD Spectroscopy to Study DNA-Protein Interactions

Published on: February 10, 2022

7.4K
Identification of Circular RNAs using RNA Sequencing
08:25

Identification of Circular RNAs using RNA Sequencing

Published on: November 14, 2019

12.6K

Area of Science:

  • Theoretical Computer Science
  • Information Theory
  • Combinatorics on Words

Background:

  • Circular codes are fundamental in areas like data compression and bioinformatics.
  • The relationship between k-circular codes and fully circular codes requires deeper investigation.
  • Understanding these code properties is crucial for applications in coding theory.

Purpose of the Study:

  • To determine the minimum integer k for which k-circular codes become circular codes.
  • To analyze the transition from k-circular to circular codes for varying alphabet sizes (n) and code lengths (m).
  • To establish a theoretical foundation for k-circular codes as an intermediate step towards circular codes.

Main Methods:

  • Formal language theory and combinatorial analysis were employed.
  • The study involved analyzing word concatenations on a circle.
  • Mathematical proofs were used to establish the existence and value of k.

Main Results:

  • For every pair (n, m), a specific integer k exists such that all k-circular m-letter codes over an n-letter alphabet are circular.
  • The minimum such integer k was determined for all n and m.
  • This k represents the threshold for the evolutionary step from k-circular to circular codes.

Conclusions:

  • The study provides a precise condition for k-circular codes to be classified as circular.
  • The findings offer insights into the structure and properties of codes relevant to biological systems.
  • k-circular codes serve as a crucial link between simpler codes and complex systems like the genetic code.