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

Weighted Mean00:57

Weighted Mean

5.2K
While taking the arithmetic, geometric, or harmonic mean of a sample data set, equal importance is assigned to all the data points. However, all the values may not always be equally important in some data sets. An intrinsic bias might make it more important to give more weightage to specific values over others.
For example, consider the number of goals scored in the matches of a tournament. While computing the average number of goals scored in the tournament, it may be more important to...
5.2K
Vector Algebra: Graphical Method01:10

Vector Algebra: Graphical Method

12.2K
Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. The vector sum of two (or more) vectors is called the resultant vector or, for short, the resultant.
We use the laws of geometry to construct resultant vectors, followed by trigonometry to find vector magnitudes and directions. For a geometric construction of the sum of two vectors in a plane, we follow the parallelogram rule. Suppose two vectors are at arbitrary positions. Translate either one of...
12.2K
Graphical and Analytic Representation of Sinusoids01:20

Graphical and Analytic Representation of Sinusoids

404
Analyzing two sinusoidal voltages with equal amplitude and period but different phases on an oscilloscope, an instrument used to display and analyze waveforms, involves a three-step process.
The first step is measuring the peak-to-peak value, which is twice the amplitude of the sinusoid. This provides information about the maximum voltage swing of the waveform.
Secondly, the period and angular frequency are determined. The period is the time taken for one complete cycle of the waveform, while...
404
Routh-Hurwitz Criterion I01:15

Routh-Hurwitz Criterion I

252
Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
252
Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

257
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...
257
Vector Representation of Complex Numbers01:16

Vector Representation of Complex Numbers

126
Complex numbers, represented in Cartesian coordinates, can also be visualized as vectors. These vectors can be expressed in polar form, emphasizing their magnitude and angle. When a complex number is input into a function, the output is another complex number, highlighting the function's zero point from which the vector representation can originate.
Consider a function defined as the product of the complex factors in the numerator divided by the product of the complex factors in the...
126

You might also read

Related Articles

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

Sort by
Same author

Programmable Lipid Functionalization of Nucleic Acid Nanoparticles Modulates Liver Cell-Type Targeting.

ACS applied materials & interfaces·2026
Same author

Interpretable Deep Learning for Single-Molecule Nanopore Fingerprinting Using Physics-Guided Preprocessing.

ACS sensors·2026
Same author

Enabling global-scale nucleic acid repositories through versatile, scalable biochemical selection from room-temperature archives.

Nature communications·2026
Same author

DNA origami vaccines program antigen-focused germinal centers.

Science (New York, N.Y.)·2026
Same author

CellUntangler: Separating distinct biological signals in single-cell data with deep generative models.

Cell genomics·2025
Same author

Transport of Delocalized Excitons through DNA-Based Molecular Photonic Wires.

ACS nano·2025

Related Experiment Video

Updated: Jul 10, 2025

Electroencephalography Network Indices as Biomarkers of Upper Limb Impairment in Chronic Stroke
06:37

Electroencephalography Network Indices as Biomarkers of Upper Limb Impairment in Chronic Stroke

Published on: July 14, 2023

915

Isometric Hamming embeddings of weighted graphs.

Joseph Berleant1, Kristin Sheridan2, Anne Condon3

  • 1Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA, United States of America.

Discrete Applied Mathematics (Amsterdam, Netherlands : 1988)
|November 20, 2023
PubMed
Summary

This study introduces Hamming embeddings for weighted graphs into Hamming graphs. It shows that a graph can be Hamming embedded if and only if its canonical isometric representation factors can be embedded, simplifying complex graph embedding problems.

Keywords:
Graph embeddingsGraph factorizationHamming graphsIsometric embeddingsMetric spacesWeighted graphs

More Related Videos

Generating Strictly Controlled Stimuli for Figure Recognition Experiments
05:39

Generating Strictly Controlled Stimuli for Figure Recognition Experiments

Published on: March 18, 2019

5.3K
Network Analysis of Foramen Ovale Electrode Recordings in Drug-resistant Temporal Lobe Epilepsy Patients
09:32

Network Analysis of Foramen Ovale Electrode Recordings in Drug-resistant Temporal Lobe Epilepsy Patients

Published on: December 18, 2016

12.4K

Related Experiment Videos

Last Updated: Jul 10, 2025

Electroencephalography Network Indices as Biomarkers of Upper Limb Impairment in Chronic Stroke
06:37

Electroencephalography Network Indices as Biomarkers of Upper Limb Impairment in Chronic Stroke

Published on: July 14, 2023

915
Generating Strictly Controlled Stimuli for Figure Recognition Experiments
05:39

Generating Strictly Controlled Stimuli for Figure Recognition Experiments

Published on: March 18, 2019

5.3K
Network Analysis of Foramen Ovale Electrode Recordings in Drug-resistant Temporal Lobe Epilepsy Patients
09:32

Network Analysis of Foramen Ovale Electrode Recordings in Drug-resistant Temporal Lobe Epilepsy Patients

Published on: December 18, 2016

12.4K

Area of Science:

  • Graph Theory
  • Combinatorial Optimization
  • Discrete Mathematics

Background:

  • Isometric embeddings preserve shortest path distances between graph vertices.
  • Hamming graphs are unweighted graphs relevant to coding theory and computer science.
  • Prior work focused on Hamming embeddings of unweighted graphs into complete graphs.

Purpose of the Study:

  • To investigate isometric embeddings of weighted graphs into unweighted Hamming graphs (Hamming embeddings).
  • To leverage the canonical isometric representation of graphs for analyzing Hamming embeddings.
  • To establish conditions for the existence of Hamming embeddings for weighted graphs.

Main Methods:

  • Definition of Hamming embeddings for weighted graphs into unweighted Hamming graphs.
  • Utilizing the Cartesian product decomposition of a graph, known as its canonical isometric representation.
  • Introducing the concept of a canonical partition for Hamming embeddings.

Main Results:

  • Every Hamming embedding of a graph can be partitioned into a canonical partition.
  • The parts of the canonical partition provide Hamming embeddings for each factor of the graph's canonical isometric representation.
  • A graph permits a Hamming embedding if and only if each factor in its canonical isometric representation is Hamming embeddable.

Conclusions:

  • The study extends previous results on unweighted graphs to weighted graphs.
  • The existence of a Hamming embedding for a graph is determined by the embeddability of its canonical isometric representation factors.
  • For graphs with nontrivial isometric representations, determining Hamming embeddability can be simplified by analyzing smaller component graphs.