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Related Concept Videos

Vector Algebra: Graphical Method01:10

Vector Algebra: Graphical Method

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...
Graphical Representation of Inequalities01:28

Graphical Representation of Inequalities

The graph of the equation where y equals x squared forms a curve known as a parabola. This curve acts as a boundary in the coordinate plane, dividing it into distinct regions based on the relative position of points.When the equality sign in the equation is replaced with an inequality—such as greater than, less than, greater than or equal to, or less than or equal to—the graphical representation changes from a single curve into a broader shaded area that signifies the set of all points...
Graphs of Two-Variable Functions01:27

Graphs of Two-Variable Functions

A weather map provides a practical example of a function of two variables. Across a wide region such as the United States, temperatures vary from one location to another. Each location can be identified by two geographic coordinates: longitude and latitude. Since a single temperature value is assigned to each coordinate pair, the situation can be represented mathematically as a function with two inputs and one output.In mathematical notation, longitude and latitude can be labeled as x and y,...
Graphs of Functions01:30

Graphs of Functions

Graphs of functions provide a visual representation of how output values change in response to varying inputs. Each point on the graph corresponds to an ordered pair, where the x-coordinate (independent variable) determines the horizontal position and the y-coordinate (dependent variable) determines the vertical position. Linear functions like y = x give a straight line, indicating a constant rate of change.Nonlinear functions display more complex behaviors. Even power functions generate...
Extended Versions of Green’s Theorem01:27

Extended Versions of Green’s Theorem

Green’s Theorem connects the circulation of a vector field around a closed curve with the behavior of the field across the region enclosed by that curve. It provides a way to replace a line integral around a boundary with a double integral over the interior region, making it especially useful in plane geometry, fluid flow, and vector calculus.Although Green’s Theorem is often introduced using simple regions without gaps, it can also be applied to regions made from several simple parts. This...
Block Diagram Reduction01:22

Block Diagram Reduction

The process of deriving the transfer function of a control system often involves reducing its block diagram to a single block. This simplification can be achieved through a series of strategic operations, including relocating branch points and comparators. These operations preserve the overall function of the system while allowing for easier manipulation and combination of blocks.
The first step in this process is the identification and relocation of a branch point. A branch point, where a...

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Related Experiment Video

Updated: Jun 8, 2026

ExCYT: A Graphical User Interface for Streamlining Analysis of High-Dimensional Cytometry Data
05:12

ExCYT: A Graphical User Interface for Streamlining Analysis of High-Dimensional Cytometry Data

Published on: January 16, 2019

ODES: an overlapping dense sub-graph algorithm.

James Long1, Chris Hartman

  • 1International Arctic Research Center and Department of Computer Science, University of Alaska-Fairbanks, AK 99775, USA. jlong@alaska.edu

Bioinformatics (Oxford, England)
|September 11, 2010
PubMed
Summary
This summary is machine-generated.

This study introduces Overlapping Dense Sub-graphs (ODES) software for identifying dense graph communities. ODES efficiently extracts overlapping maximal sub-graphs meeting density criteria, aiding community discovery.

Related Experiment Videos

Last Updated: Jun 8, 2026

ExCYT: A Graphical User Interface for Streamlining Analysis of High-Dimensional Cytometry Data
05:12

ExCYT: A Graphical User Interface for Streamlining Analysis of High-Dimensional Cytometry Data

Published on: January 16, 2019

Area of Science:

  • Graph theory
  • Computer science
  • Network analysis

Background:

  • Dense sub-graphs are crucial for community discovery in networks.
  • Identifying overlapping dense sub-graphs presents computational challenges.

Purpose of the Study:

  • To present ODES, a novel software for extracting overlapping dense sub-graphs.
  • To enable efficient identification of dense communities within graphs.

Main Methods:

  • Development of pthreads parallelized software named ODES.
  • Implementation of algorithms to extract maximal sub-graphs based on density.

Main Results:

  • ODES successfully enumerates overlapping maximal sub-graphs.
  • The software handles graphs with densities greater than or equal to 1/2.

Conclusions:

  • ODES provides an efficient solution for dense sub-graph enumeration.
  • The software facilitates advanced community discovery and membership analysis.