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Lastly, since there are many homology theories for topological spaces that produce the same answer, one also often speaks of the homology of a topological space. (This latter notion of homology admits more intuitive descriptions for 1- or 2-dimensional topological spaces, and is sometimes referenced in popular mathematics .)
The term "homology" was first used in biology by the anatomist Richard Owen in 1843 when studying the similarities of vertebrate fins and limbs, defining it as the "same organ in different animals under every variety of form and function", [6] and contrasting it with the matching term "analogy" which he used to describe different structures ...
Sequence homology is the biological homology between DNA, RNA, or protein sequences, defined in terms of shared ancestry in the evolutionary history of life. Two segments of DNA can have shared ancestry because of three phenomena: either a speciation event (orthologs), or a duplication event (paralogs), or else a horizontal (or lateral) gene ...
"The molecular weight of Sulculus myoglobin is 41kD, 2.5 times larger than other myoglobins." Moreover, its amino acid sequence has no homology with other invertebrate myoglobins or with hemoglobins, but is 35% homologous with human indoleamine dioxygenase (IDO), a vertebrate tryptophan-degrading enzyme. It does not share similar function with IDO.
In homological algebra, the mapping cone is a construction on a map of chain complexes inspired by the analogous construction in topology.In the theory of triangulated categories it is a kind of combined kernel and cokernel: if the chain complexes take their terms in an abelian category, so that we can talk about cohomology, then the cone of a map f being acyclic means that the map is a quasi ...
Homology (anthropology), analogy between human beliefs, practices or artifacts owing to genetic or historical connections; Homology (psychology), behavioral characteristics that have common origins in either evolution or development
A result, due to John Milnor, [2] is that if one takes the Eilenberg–Steenrod axioms for homology theory, and replaces excision by the exact sequence of a weak fibration of pairs, then one gets the homotopy analogy of the Eilenberg–Steenrod theorem: there exists a unique sequence of functors : with P the category of all pointed pairs of ...
The notion of chain complex is central in homological algebra. An abstract chain complex is a sequence (,) of abelian groups and group homomorphisms, with the property that the composition of any two consecutive maps is zero: