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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.
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
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).
Goldbach’s Conjecture. One of the greatest unsolved mysteries in math is also very easy to write. Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two primes ...
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 ...
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 ...
Visual proof of the Pythagorean identity: for any angle , the point (,) = (, ) lies on the unit circle, which satisfies the equation + =.Thus, + =. In mathematics, an identity is an equality relating one mathematical expression A to another mathematical expression B, such that A and B (which might contain some variables) produce the same value for all values of the variables ...