Hox geneHox genes, a subset of homeobox genes, are a group of related genes that specify regions of the body plan of an embryo along the head-tail axis of animals. Hox proteins encode and specify the characteristics of 'position', ensuring that the correct structures form in the correct places of the body. For example, Hox genes in insects specify which appendages form on a segment (for example, legs, antennae, and wings in fruit flies), and Hox genes in vertebrates specify the types and shape of vertebrae that will form.
HomeoboxA homeobox is a DNA sequence, around 180 base pairs long, that regulates large-scale anatomical features in the early stages of embryonic development. Mutations in a homeobox may change large-scale anatomical features of the full-grown organism. Homeoboxes are found within genes that are involved in the regulation of patterns of anatomical development (morphogenesis) in animals, fungi, plants, and numerous single cell eukaryotes.
Regulation of gene expressionRegulation of gene expression, or gene regulation, includes a wide range of mechanisms that are used by cells to increase or decrease the production of specific gene products (protein or RNA). Sophisticated programs of gene expression are widely observed in biology, for example to trigger developmental pathways, respond to environmental stimuli, or adapt to new food sources. Virtually any step of gene expression can be modulated, from transcriptional initiation, to RNA processing, and to the post-translational modification of a protein.
EpigeneticsIn biology, epigenetics is the study of stable changes in cell function (known as marks) that do not involve alterations in the DNA sequence. The Greek prefix epi- (ἐπι- "over, outside of, around") in epigenetics implies features that are "on top of" or "in addition to" the traditional genetic basis for inheritance. Epigenetics most often involves changes that affect the regulation of gene expression, and that persist through cellular division.
Gene expressionGene expression is the process by which information from a gene is used in the synthesis of a functional gene product that enables it to produce end products, proteins or non-coding RNA, and ultimately affect a phenotype. These products are often proteins, but in non-protein-coding genes such as transfer RNA (tRNA) and small nuclear RNA (snRNA), the product is a functional non-coding RNA.
Polar coordinate systemIn mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. The reference point (analogous to the origin of a Cartesian coordinate system) is called the pole, and the ray from the pole in the reference direction is the polar axis. The distance from the pole is called the radial coordinate, radial distance or simply radius, and the angle is called the angular coordinate, polar angle, or azimuth.
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.
Spherical coordinate systemIn mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin; its polar angle measured from a fixed polar axis or zenith direction; and the azimuthal angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the fixed axis, measured from another fixed reference direction on that plane.
Transformer (machine learning model)A transformer is a deep learning architecture that relies on the parallel multi-head attention mechanism. The modern transformer was proposed in the 2017 paper titled 'Attention Is All You Need' by Ashish Vaswani et al., Google Brain team. It is notable for requiring less training time than previous recurrent neural architectures, such as long short-term memory (LSTM), and its later variation has been prevalently adopted for training large language models on large (language) datasets, such as the Wikipedia corpus and Common Crawl, by virtue of the parallelized processing of input sequence.
Algebraic expressionIn mathematics, an algebraic expression is an expression built up from constant algebraic numbers, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number). For example, 3x2 − 2xy + c is an algebraic expression. Since taking the square root is the same as raising to the power 1/2, the following is also an algebraic expression: An algebraic equation is an equation involving only algebraic expressions.
