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A biological network is a method of representing systems as complex sets of binary interactions or relations between various biological entities. [1] In general, networks or graphs are used to capture relationships between entities or objects. [1]
A monoidal category where every object has a left and right adjoint is called a rigid category. String diagrams for rigid categories can be defined as non-progressive plane graphs, i.e. the edges can bend backward. In the context of categorical quantum mechanics, this is known as the snake equation.
Topology Analysis analyzes the topology of a network to identify relevant participates and substructures that may be of biological significance. The term encompasses an entire class of techniques such as network motif search, centrality analysis, topological clustering, and shortest paths. These are but a few examples, each of these techniques ...
This is one of the diagrams used in the definition of a monoidal cateogory. It takes care of the case for when there is an instance of an identity between two objects. commutes. A strict monoidal category is one for which the natural isomorphisms α, λ and ρ are identities. Every monoidal category is monoidally equivalent to a strict monoidal ...
such that the pentagon diagram. and the unitor diagram commute. In the above notation, 1 is the identity morphism of M, I is the unit element and α, λ and ρ are respectively the associativity, the left identity and the right identity of the monoidal category C. Dually, a comonoid in a monoidal category C is a monoid in the dual category C op.
Hybrid topology is also known as hybrid network. [19] Hybrid networks combine two or more topologies in such a way that the resulting network does not exhibit one of the standard topologies (e.g., bus, star, ring, etc.). For example, a tree network (or star-bus network) is a hybrid topology in which star networks are interconnected via bus ...
For example, monoids are semigroups with identity. In abstract algebra , a branch of mathematics , a monoid is a set equipped with an associative binary operation and an identity element . For example, the nonnegative integers with addition form a monoid, the identity element being 0 .
Topology of a transmembrane protein refers to locations of N- and C-termini of membrane-spanning polypeptide chain with respect to the inner or outer sides of the biological membrane occupied by the protein. [1] Group I and II transmembrane proteins have opposite final topologies.