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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...
Coordination Number and Geometry02:57

Coordination Number and Geometry

For transition metal complexes, the coordination number determines the geometry around the central metal ion. Table 1 compares coordination numbers to molecular geometry. The most common structures of the complexes in coordination compounds are octahedral, tetrahedral, and square planar.
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,...
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...
Lattice Centering and Coordination Number02:33

Lattice Centering and Coordination Number

The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
Types of Unit Cells
Imagine taking a large number of identical...
Graphs of Equations in Two Variables01:30

Graphs of Equations in Two Variables

An equation with two variables, typically written in the form y = f(x) or Ax + By = C, describes a relationship between quantities represented by x and y. Each solution to such an equation is an ordered pair (x, y) that satisfies the equation when substituted. These pairs can be represented graphically to understand the variables' relationship visually.A common technique for constructing the graph of a two-variable equation is to create a value table. Begin by choosing several values for the...

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Related Experiment Videos

Optimal network alignment with graphlet degree vectors.

Tijana Milenković1, Weng Leong Ng, Wayne Hayes

  • 1Department of Computing, Imperial College London SW7 2AZ, UK.

Cancer Informatics
|July 15, 2010
PubMed
Summary
This summary is machine-generated.

We developed a novel network alignment method using the Hungarian algorithm to identify topological similarities in biological networks. This approach reveals conserved network structures, aiding in functional prediction and evolutionary analysis.

Keywords:
biological networksnetwork alignmentnetwork topologyphylogenyprotein function prediction

Related Experiment Videos

Area of Science:

  • Systems Biology
  • Bioinformatics
  • Network Science

Background:

  • Biological networks encode crucial information.
  • Comparative network analysis offers insights into function, disease, and evolution.
  • Existing methods may not fully capture topological similarities.

Purpose of the Study:

  • To introduce a novel network alignment method based on topology.
  • To apply this method to biological networks for functional and evolutionary insights.
  • To demonstrate the method's ability to detect significant topological similarities.

Main Methods:

  • Utilized the Hungarian algorithm for optimal global network alignment.
  • Designed a cost function based exclusively on network topology.
  • Applied the method to protein-protein interaction networks and metabolic networks.

Main Results:

  • Identified large, topologically complex regions of similarity in eukaryotic protein-protein interaction networks.
  • Demonstrated biological validity of alignments, with many aligned proteins sharing functions.
  • Predicted and validated functions of unannotated proteins.
  • Constructed phylogenetic trees from metabolic network alignment scores, showing resemblance to sequence-based trees.
  • Detected statistically significant topological similarities independent of sequence data.

Conclusions:

  • The developed method effectively aligns biological networks based on topology.
  • Network topology analysis provides valuable insights into biological function and evolution.
  • This approach facilitates functional predictions and aids in understanding evolutionary relationships.