## 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.