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

Inverse z-Transform by Partial Fraction Expansion01:20

Inverse z-Transform by Partial Fraction Expansion

379
The inverse z-transform is a crucial technique for converting a function from its z-domain representation back to the time domain. One effective method for finding the inverse z-transform is the Partial Fraction Method, which involves decomposing a function into simpler fractions with distinct coefficients. These fractions correspond to known z-transform pairs, facilitating the inverse transformation process.
To begin the process, the poles of the function are identified and the function is...
379
Compacting Factor test01:22

Compacting Factor test

199
The compacting factor test is a method used to assess the workability of concrete. It is  especially suitable for concrete mixes containing aggregates up to one and a half inches in size. This test involves specialized equipment consisting of two truncated cone-shaped hoppers and a cylinder, all with polished interior surfaces to minimize friction.
The procedure begins by placing concrete into the upper hopper without any compaction. Once filled, the bottom door of this hopper is opened,...
199
Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

306
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...
306
Factorial Design02:01

Factorial Design

13.1K
Factorial Analysis is an experimental design that applies Analysis of Variance (ANOVA) statistical procedures to examine a change in a dependent variable due to more than one independent variable, also known as factors. Changes in worker productivity can be reasoned, for example, to be influenced by salary and other conditions, such as skill level. One way to test this hypothesis is by categorizing salary into three levels (low, moderate, and high) and skills sets into two levels (entry level...
13.1K
Theorems of Pappus and Guldinus: Problem Solving01:12

Theorems of Pappus and Guldinus: Problem Solving

772
Pappus and Guldinus's theorems are powerful mathematical principles that are used for finding the surface area and volume of composite shapes. For example, consider a cylindrical storage tank with a conical top. Finding the surface area or volume can be challenging for such complex shapes. These theorems are particularly useful in calculating the volume and surface area of such systems. Here, the cylindrical storage tank with a conical top can be broken down into two simple shapes: a...
772
Vector Algebra: Graphical Method01:10

Vector Algebra: Graphical Method

12.5K
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...
12.5K

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
Same journal

Corrigendum to: "On Ramsey and star-critical Ramsey numbers for generalized fans versus <i>nK</i> <sub><i>m</i></sub> " [Discrete Appl. Math. 305 (2021) 64-70].

Discrete applied mathematics (Amsterdam, Netherlands : 1988)·2026
Same journal

Enumeration of rooted binary perfect phylogenies.

Discrete applied mathematics (Amsterdam, Netherlands : 1988)·2025
Same journal

A lattice structure for ancestral configurations arising from the relationship between gene trees and species trees.

Discrete applied mathematics (Amsterdam, Netherlands : 1988)·2023
Same journal

Isometric Hamming embeddings of weighted graphs.

Discrete applied mathematics (Amsterdam, Netherlands : 1988)·2023
Same journal

On Ramsey and star-critical Ramsey numbers for generalized fans versus <i>nK</i> <sub><i>m</i></sub>.

Discrete applied mathematics (Amsterdam, Netherlands : 1988)·2021
Same journal

On the Colijn-Plazzotta numbering scheme for unlabeled binary rooted trees.

Discrete applied mathematics (Amsterdam, Netherlands : 1988)·2020
See all related articles

Related Experiment Video

Updated: Jul 29, 2025

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

Factorization and pseudofactorization of weighted graphs.

Kristin Sheridan1, Joseph Berleant2, Mark Bathe2

  • 1Department of of Computer Science, University of Texas, Austin, TX.

Discrete Applied Mathematics (Amsterdam, Netherlands : 1988)
|May 22, 2023
PubMed
Summary
This summary is machine-generated.

This study extends graph factorization and pseudofactorization to weighted graphs, enabling canonical isometric embeddings. Efficient algorithms are developed for minimal weighted graphs, improving metric space analysis.

More Related Videos

Divergence of Root Microbiota in Different Habitats based on Weighted Correlation Networks
09:49

Divergence of Root Microbiota in Different Habitats based on Weighted Correlation Networks

Published on: September 25, 2021

4.4K
Generalized Psychophysiological Interaction PPI Analysis of Memory Related Connectivity in Individuals at Genetic Risk for Alzheimer's Disease
09:38

Generalized Psychophysiological Interaction PPI Analysis of Memory Related Connectivity in Individuals at Genetic Risk for Alzheimer's Disease

Published on: November 14, 2017

15.0K

Related Experiment Videos

Last Updated: Jul 29, 2025

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
Divergence of Root Microbiota in Different Habitats based on Weighted Correlation Networks
09:49

Divergence of Root Microbiota in Different Habitats based on Weighted Correlation Networks

Published on: September 25, 2021

4.4K
Generalized Psychophysiological Interaction PPI Analysis of Memory Related Connectivity in Individuals at Genetic Risk for Alzheimer's Disease
09:38

Generalized Psychophysiological Interaction PPI Analysis of Memory Related Connectivity in Individuals at Genetic Risk for Alzheimer's Disease

Published on: November 14, 2017

15.0K

Area of Science:

  • Graph theory
  • Metric geometry
  • Combinatorial optimization

Background:

  • Isometric embeddings and graph decompositions are crucial for understanding graph structures.
  • Prior work focused on unweighted graphs, leaving weighted graphs largely unexplored.
  • Factorization and pseudofactorization concepts were limited to unweighted graphs.

Purpose of the Study:

  • To generalize factorization and pseudofactorization to weighted graphs.
  • To develop efficient algorithms for finding these structures in minimal weighted graphs.
  • To enable canonical isometric embeddings for weighted graphs.

Main Methods:

  • Generalizing factorization and pseudofactorization definitions to minimal weighted graphs.
  • Developing novel proof techniques extending existing algorithms for unweighted graphs.
  • Analyzing algorithmic complexity for factorization and pseudofactorization.

Main Results:

  • Efficient algorithms for factorization and pseudofactorization of minimal weighted graphs are presented.
  • Factorization of an N-vertex, M-edge graph with positive integer weights runs in O(M^2) time plus All-Pairs Shortest Paths (APSP) time.
  • Pseudofactorization runs in O(M) time plus APSP time.

Conclusions:

  • The developed methods provide a significant advancement in the analysis of weighted graphs as metric spaces.
  • These findings pave the way for broader applications of graph embeddings in various scientific domains.
  • The efficient algorithms offer practical tools for researchers working with complex network structures.