MetagenomicsMetagenomics is the study of genetic material recovered directly from environmental or clinical samples by a method called sequencing. The broad field may also be referred to as environmental genomics, ecogenomics, community genomics or microbiomics. While traditional microbiology and microbial genome sequencing and genomics rely upon cultivated clonal cultures, early environmental gene sequencing cloned specific genes (often the 16S rRNA gene) to produce a profile of diversity in a natural sample.
Expression (mathematics)In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context. Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax. Many authors distinguish an expression from a formula, the former denoting a mathematical object, and the latter denoting a statement about mathematical objects.
Marker-assisted selectionMarker assisted selection or marker aided selection (MAS) is an indirect selection process where a trait of interest is selected based on a marker (morphological, biochemical or DNA/RNA variation) linked to a trait of interest (e.g. productivity, disease resistance, abiotic stress tolerance, and quality), rather than on the trait itself. This process has been extensively researched and proposed for plant- and animal- breeding.
Graded vector spaceIn mathematics, a graded vector space is a vector space that has the extra structure of a grading or gradation, which is a decomposition of the vector space into a direct sum of vector subspaces, generally indexed by the integers. For "pure" vector spaces, the concept has been introduced in homological algebra, and it is widely used for graded algebras, which are graded vector spaces with additional structures. Let be the set of non-negative integers.
Null vectorIn mathematics, given a vector space X with an associated quadratic form q, written (X, q), a null vector or isotropic vector is a non-zero element x of X for which q(x) = 0. In the theory of real bilinear forms, definite quadratic forms and isotropic quadratic forms are distinct. They are distinguished in that only for the latter does there exist a nonzero null vector. A quadratic space (X, q) which has a null vector is called a pseudo-Euclidean space.
OrthonormalityIn linear algebra, two vectors in an inner product space are orthonormal if they are orthogonal (or perpendicular along a line) unit vectors. A set of vectors form an orthonormal set if all vectors in the set are mutually orthogonal and all of unit length. An orthonormal set which forms a basis is called an orthonormal basis. The construction of orthogonality of vectors is motivated by a desire to extend the intuitive notion of perpendicular vectors to higher-dimensional spaces.
