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1 Elements and Their PropertiesProperties of SDPS modules are1.
We introduce an algorithmic method, termed modular decomposition, that defines the organization of protein-interaction networks as a hierarchy of nested modules. A useful design heuristic holds that a module is small enough if it could be discarded and begun again if the programmer(s) assigned to implement it left the project. 3 Element Interfaces[omitted][10][10] For examples of interface specifications, see Chapter 7. To distinguish the case of unobserved interactions we flag the proteins in the network as well as in the tree differently for baits and non-baits. 1 Primary Presentation1.
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Some important combinatorial optimization problems on graphs can be solved using a similar strategy (Möhring, 85). Restricting interpretation to the simplest model (top right), the series module reads as a logical AND between its members.
The first polynomial algorithm to compute the modular decomposition tree of a graph was published in 1972 (James, Stanton Cowan 1972) and now linear algorithms are available (McConnell Spinrad 1999, Tedder et al. The program which solves the entire problem is a collection of such functions. The whole tree provides a comprehensive representation of the logical organization of the network into modules.
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Indeed, if M is a module of finite length, then, by induction on length, it has a finite indecomposable decomposition
M
=
i
=
1
n
M
i
{\textstyle M=\bigoplus _{i=1}^{n}M_{i}}
, which is a decomposition with local endomorphism rings. The three polymerases involve a total company website 31 proteins (Figure 5b). Subsystems are both a package and a classifier. Application to experimental interaction data of the TNF-α/NFκB pro-inflammatory pathway requires appropriate distinction of bait proteins and retrieved interactors. Cographs are the graphs that only have parallel or series nodes in their modular decomposition tree.
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If [math]\displaystyle{ X }[/math] and [math]\displaystyle{ browse around these guys }[/math] are disjoint modules, then it is easy to see that either every member of [math]\displaystyle{ X }[/math] is a neighbor of every element of [math]\displaystyle{ Y }[/math], or no member of [math]\displaystyle{ X }[/math] is adjacent to any member of [math]\displaystyle{ Y }[/math]. As a classifier, they encapsulate their contents and can provide an explicit interface. They therefore induce the quotient [math]\displaystyle{ G[X]/P }[/math] in [math]\displaystyle{ G[X] }[/math]. In graph theory, a module is a set of nodes that have the same neighbors outside the module (Figure 1).
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It contains annotations of the modules with the names of their common interactors and reference to the modules described in [21]. The modules of a graph are therefore of great algorithmic interest.
M
{\displaystyle M}
is a strong module of a graph
G
{\displaystyle G}
if it does not overlap any other module of
G
{\displaystyle G}
:
M
{\displaystyle \forall M’}
module of
{\displaystyle G}
, either
M
M
=
{\displaystyle M\cap M’=\emptyset }
or
M
M
{\displaystyle M\subseteq M’}
or
M
M
{\displaystyle M’\subseteq M}
. .