different between microhomology vs homology
microhomology
English
Etymology
micro- +? homology
Noun
microhomology (countable and uncountable, plural microhomologies)
- (genetics) The presence of the same short sequence of bases in different genes
Related terms
- homology
- microhomologous
microhomology From the web:
- what does microhomology mean
homology
English
Etymology
From homo- +? -logy.
In topology, first used by French polymath Henri Poincaré, in the sense (close to what is now called a bordism) of a relation between manifolds mapped into a reference manifold: that is, the property of such manifolds that they form the boundary of a higher-dimensional manifold inside the reference manifold. Poincaré's version was eventually replaced by the more general singular homology, which is what mathematicians now mean by homology.
Noun
homology (countable and uncountable, plural homologies)
- The relationship of being homologous; a homologous relationship;
(geometry, projective geometry) specifically, such relationship in the context of the geometry of perspective.- 1863, George Salmon, A Treatise on Conic Sections, Longman, Brown, Green, Longman, and Roberts, 4th Edition, page 61,
- Two triangles are said to be homologous, when the intersections of the corresponding sides lie on the same right line called the axis of homology: prove that the lines joining the corresponding vertices meet in a point [called the centre of homology].
- 1885, Charles Leudesdorf (translator), Luigi Cremona, Elements of Projective Geometry, Oxford University Press (Clarendon Press), page 11,
- Two corresponding straight lines therefore always intersect on a fixed straight line, which we may call s; thus the given figures are in homology, O being the centre, and s the axis, of homology.
- 1863, George Salmon, A Treatise on Conic Sections, Longman, Brown, Green, Longman, and Roberts, 4th Edition, page 61,
- (geometry, projective geometry) An automorphism of the projective plane (representing a perspective projection) that leaves all the points of some straight line (the homology axis) fixed and maps all the lines through some single point (the homology centre) onto themselves.
- (topology, algebraic topology) A general way of associating a sequence of algebraic objects, such as abelian groups or modules, to a sequence of topological spaces; also used attributively: see Usage notes below.
- 2000, Sibe Mardeši?, Strong Shape and Homology, Springer, page v,
- One encounters a similar situation in homology theory. Beside singular homology, which is a homotopy invariant, and ?ech homology, which is a shape invariant, there exists strong homology, which is a strong shape invariant. In the special case of metric compacta, this homology was introduced by N.E. Steenrod in 1940 and is often referred to as the Steenrod homology.
- 2002, Nikolai Saveliev, Invariants of Homology 3-Spheres, Springer, page 2,
- Brieskorn homology spheres are a special case of Siefert fibered homology spheres.
- 2000, Sibe Mardeši?, Strong Shape and Homology, Springer, page v,
- (algebra) Given a chain complex {Gn} and its associated set of homomorphisms {Hn}, the rule which explains how each Hn maps Gn into the kernel of Gn+1.
- (chemistry) The relationship, between elements, of being in the same group of the periodic table.
- (organic chemistry) The relationship, between organic compounds, of being in the same homologous series.
- (biology, psychology) The relationship, between characteristics or behaviours, of having a shared evolutionary or developmental origin;
(evolutionary theory) specifically, a correspondence between structures in separate life forms having a common evolutionary origin, such as that between flippers and hands.- 2000, Julie A. Hawkins, Chapter 2: A survey of primary homology assessment, Robert Scotland, R. Toby Pennington (editors), Homology and Systematics, Taylor & Francis, The Systematics Association, page 22,
- The objective of this study is to classify approaches to primary homology assessment, and to quantify the extent to which different approaches are found in the literature by examining variation in the ways characters are defined and coded in a data matrix.
- 2000, Julie A. Hawkins, Chapter 2: A survey of primary homology assessment, Robert Scotland, R. Toby Pennington (editors), Homology and Systematics, Taylor & Francis, The Systematics Association, page 22,
- (genetics) The presence of the same series of bases in different but related genes.
- (anthropology) The relationship, between temporally separated human beliefs, practices or artefacts, of possessing shared characteristics attributed to genetic or historical links to a common ancestor.
Usage notes
- Like many terms that start with a non-silent h but have emphasis on their second syllable, some people precede homology with an, others with a.
- (topology):
- When used attributively with the name of a topological space (such as in the terms homology n-sphere and homology manifold) the reference is to a space whose homology is the same as that of the named space: thus, for example, a homology manifold is a space whose homology is that of some manifold.
- Sometimes used to mean homology group: thus, X did Y by computing the homology of Z means X did Y by computing the homology groups of Z.
- More loosely, the term homology in a space refers to a singular homology group (group of singular homologies).
- (evolutionary theory):
- For a discussion of the use of the term homology (and homologous) in biology, see: 1998 Nov, Colin Patterson, "Homology in Classical and Molecular Biology", Molecular Biology and Evolution, 5, No. 6: 603–625, (accessed 18 Dec 2009; archived 18 Dec 2009).
Derived terms
Related terms
- analogy
- homolog, homologue
- homologation
- homological
Translations
See also
- homothety
- homotopy
Further reading
- (mathematics):
- Perspective (geometry) on Wikipedia.Wikipedia
- Eilenberg–Steenrod axioms on Wikipedia.Wikipedia
- Floer homology on Wikipedia.Wikipedia
- Khovanov homology on Wikipedia.Wikipedia
- Singular homology on Wikipedia.Wikipedia
- Homological algebra on Wikipedia.Wikipedia
- Homological dimension on Wikipedia.Wikipedia
- (other):
- Homology modeling on Wikipedia.Wikipedia
- Sequence homology on Wikipedia.Wikipedia
References
homology From the web:
- what's homology mean
- homology what does it mean
- what is homology in biology
- what is homology modelling
- what is homology directed repair
- what is homology and analogy
- what is homology in evolution
- what are homology arms
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