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For example, the two embedded circles in a figure-eight shape provide examples of one-dimensional cycles, or 1-cycles, and the 2-torus and 2-sphere represent 2-cycles. Cycles form a group under the operation of formal addition, which refers to adding cycles symbolically rather than combining them geometrically.
From the example above, if the descendant with genes A1 and B underwent another speciation event where gene A1 duplicated, the new species would have genes B, A1a, and A1b. In this example, genes A1a and A1b are symparalogs. [1] Vertebrate Hox genes are organized in sets of paralogs. Each Hox cluster (HoxA, HoxB, etc.) is on a different chromosome.
Syntelog: a special case of gene homology where sets of genes are derived from the same ancestral genomic region. This may arise from speciation events, or through whole or partial genome duplication events (e.g. polyploidy).
The term "ortholog" was coined in 1970 by the molecular evolutionist Walter Fitch. [41] Homologous sequences are paralogous if they were created by a duplication event within the genome. For gene duplication events, if a gene in an organism is duplicated, the two copies are paralogous. They can shape the structure of whole genomes and thus ...
Top: An ancestral gene duplication produces two paralogs (histone H1.1 and 1.2). A speciation event produces orthologs in the two daughter species (human and chimpanzee). Bottom: in a separate species , a gene has a similar function (histone-like nucleoid-structuring protein) but has a separate evolutionary origin and so is an analog.
This page will attempt to list examples in mathematics. To qualify for inclusion, an article should be about a mathematical object with a fair amount of concreteness. Usually a definition of an abstract concept, a theorem, or a proof would not be an "example" as the term should be understood here (an elegant proof of an isolated but particularly striking fact, as opposed to a proof of a ...
Hilbert's fifth problem is the fifth mathematical problem from the problem list publicized in 1900 by mathematician David Hilbert, and concerns the characterization of Lie groups. The theory of Lie groups describes continuous symmetry in mathematics; its importance there and in theoretical physics (for example quark theory ) grew steadily in ...
In mathematics, a structure on a set (or on some sets) refers to providing it (or them) with certain additional features (e.g. an operation, relation, metric, or topology). Τhe additional features are attached or related to the set (or to the sets), so as to provide it (or them) with some additional meaning or significance.