What is a cycle in homology?
Loosely speaking, a cycle is a closed submanifold, a boundary is a cycle which is also the boundary of a submanifold, and a homology class (which represents a hole) is an equivalence class of cycles modulo boundaries. …
What is Computer homologous?
The homology groups of a space characterize the number and type of holes in that space and therefore give a fundamental description of its structure. In many applications knowledge of the entire group structure is unnecessary — all that is needed is the rank of the homology group, i.e., the Betti number.
What are orthologous sequences?
Homologous sequences are orthologous if they are inferred to be descended from the same ancestral sequence separated by a speciation event: when a species diverges into two separate species, the copies of a single gene in the two resulting species are said to be orthologous.
How is singular homology calculated?
I would say the easiest way in general is Morse theory. If possible, divide the space into simplices (homeomorphic multidimensional tetrahedron). Obtain a simplicial complex (it is also called a simplicial scheme), consisting of the simplices.
What is homology used for math?
homology, in mathematics, a basic notion of algebraic topology. Intuitively, two curves in a plane or other two-dimensional surface are homologous if together they bound a region—thereby distinguishing between an inside and an outside.
How can an ortholog become a Paralog?
Orthologous are homologous genes where a gene diverges after a speciation event, but the gene and its main function are conserved. If a gene is duplicated in a species, the resulting duplicated genes are paralogs of each other, even though over time they might become different in sequence composition and function.
How do you get orthologous genes?
To find orthologs enter a gene symbol (e.g. RAG1) or a gene symbol combined with a taxonomic group (e.g. primate RAG1). Select the matching entry from the suggestions menu or you can select the orthologs option (e.g. Rag1 orthologs) to see all orthologs.
What is simplicial homology?
In algebraic topology, simplicial homology is the sequence of homology groups of a simplicial complex. It formalizes the idea of the number of holes of a given dimension in the complex.
What is a simplicial map?
A simplicial map f from S to T is a function from the vertex set of S to the vertex set of T such that the image of each simplex in S (viewed as a set of vertices) is a simplex in T. A simplicial map f: S → T determines a homomorphism of homology groups Hk ( S) → Hk ( T) for each integer k.
Is the 1 cycle homologous to the sum of the 2-simplex?
, the 1-cycle at right-middle is homologous to its sum with the boundary of the 2-simplex at left. A key concept in defining simplicial homology is the notion of an orientation of a simplex.
Is the sum of trivial 1-cycles homologous to its sum?
Because trivial 1-cycles are equivalent to 0 in , the 1-cycle at right-middle is homologous to its sum with the boundary of the 2-simplex at left. A key concept in defining simplicial homology is the notion of an orientation of a simplex.