Reflexive relationIn mathematics, a binary relation R on a set X is reflexive if it relates every element of X to itself. An example of a reflexive relation is the relation "is equal to" on the set of real numbers, since every real number is equal to itself. A reflexive relation is said to have the reflexive property or is said to possess reflexivity. Along with symmetry and transitivity, reflexivity is one of three properties defining equivalence relations.
Google TranslateGoogle Translate is a multilingual neural machine translation service developed by Google to translate text, documents and websites from one language into another. It offers a website interface, a mobile app for Android and iOS, as well as an API that helps developers build browser extensions and software applications. As of 2022, Google Translate supports languages at various levels; it claimed over 500 million total users , with more than 100 billion words translated daily, after the company stated in May 2013 that it served over 200 million people daily.
Converse relationIn mathematics, the converse relation, or transpose, of a binary relation is the relation that occurs when the order of the elements is switched in the relation. For example, the converse of the relation 'child of' is the relation 'parent of'. In formal terms, if and are sets and is a relation from to then is the relation defined so that if and only if In set-builder notation, The notation is analogous with that for an inverse function. Although many functions do not have an inverse, every relation does have a unique converse.
ChromatinChromatin is a complex of DNA and protein found in eukaryotic cells. The primary function is to package long DNA molecules into more compact, denser structures. This prevents the strands from becoming tangled and also plays important roles in reinforcing the DNA during cell division, preventing DNA damage, and regulating gene expression and DNA replication. During mitosis and meiosis, chromatin facilitates proper segregation of the chromosomes in anaphase; the characteristic shapes of chromosomes visible during this stage are the result of DNA being coiled into highly condensed chromatin.
Ternary relationIn mathematics, a ternary relation or triadic relation is a finitary relation in which the number of places in the relation is three. Ternary relations may also be referred to as 3-adic, 3-ary, 3-dimensional, or 3-place. Just as a binary relation is formally defined as a set of pairs, i.e. a subset of the Cartesian product A × B of some sets A and B, so a ternary relation is a set of triples, forming a subset of the Cartesian product A × B × C of three sets A, B and C.
Connected relationIn mathematics, a relation on a set is called connected or complete or total if it relates (or "compares") all pairs of elements of the set in one direction or the other while it is called strongly connected if it relates pairs of elements. As described in the terminology section below, the terminology for these properties is not uniform. This notion of "total" should not be confused with that of a total relation in the sense that for all there is a so that (see serial relation).
Machine translationMachine translation is use of either rule-based or probabilistic (i.e. statistical and, most recently, neural network-based) machine learning approaches to translation of text or speech from one language to another, including the contextual, idiomatic and pragmatic nuances of both languages. History of machine translation The origins of machine translation can be traced back to the work of Al-Kindi, a ninth-century Arabic cryptographer who developed techniques for systemic language translation, including cryptanalysis, frequency analysis, and probability and statistics, which are used in modern machine translation.
Evo-devo gene toolkitThe evo-devo gene toolkit is the small subset of genes in an organism's genome whose products control the organism's embryonic development. Toolkit genes are central to the synthesis of molecular genetics, palaeontology, evolution and developmental biology in the science of evolutionary developmental biology (evo-devo). Many of them are ancient and highly conserved among animal phyla. Toolkit genes are highly conserved among phyla, meaning that they are ancient, dating back to the last common ancestor of bilaterian animals.
Homogeneous relationIn mathematics, a homogeneous relation (also called endorelation) on a set X is a binary relation between X and itself, i.e. it is a subset of the Cartesian product X × X. This is commonly phrased as "a relation on X" or "a (binary) relation over X". An example of a homogeneous relation is the relation of kinship, where the relation is between people. Common types of endorelations include orders, graphs, and equivalences. Specialized studies of order theory and graph theory have developed understanding of endorelations.
Evolution of mammalsThe evolution of mammals has passed through many stages since the first appearance of their synapsid ancestors in the Pennsylvanian sub-period of the late Carboniferous period. By the mid-Triassic, there were many synapsid species that looked like mammals. The lineage leading to today's mammals split up in the Jurassic; synapsids from this period include Dryolestes, more closely related to extant placentals and marsupials than to monotremes, as well as Ambondro, more closely related to monotremes.
