DefinitionA definition is a statement of the meaning of a term (a word, phrase, or other set of symbols). Definitions can be classified into two large categories: intensional definitions (which try to give the sense of a term), and extensional definitions (which try to list the objects that a term describes). Another important category of definitions is the class of ostensive definitions, which convey the meaning of a term by pointing out examples. A term may have many different senses and multiple meanings, and thus require multiple definitions.
Outer measureIn the mathematical field of measure theory, an outer measure or exterior measure is a function defined on all subsets of a given set with values in the extended real numbers satisfying some additional technical conditions. The theory of outer measures was first introduced by Constantin Carathéodory to provide an abstract basis for the theory of measurable sets and countably additive measures.
Measure (mathematics)In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as magnitude, mass, and probability of events. These seemingly distinct concepts have many similarities and can often be treated together in a single mathematical context. Measures are foundational in probability theory, integration theory, and can be generalized to assume negative values, as with electrical charge.
Suffix treeIn computer science, a suffix tree (also called PAT tree or, in an earlier form, position tree) is a compressed trie containing all the suffixes of the given text as their keys and positions in the text as their values. Suffix trees allow particularly fast implementations of many important string operations. The construction of such a tree for the string takes time and space linear in the length of .
GenomeIn the fields of molecular biology and genetics, a genome is all the genetic information of an organism. It consists of nucleotide sequences of DNA (or RNA in RNA viruses). The nuclear genome includes protein-coding genes and non-coding genes, other functional regions of the genome such as regulatory sequences (see non-coding DNA), and often a substantial fraction of junk DNA with no evident function. Almost all eukaryotes have mitochondria and a small mitochondrial genome.
Genome projectGenome projects are scientific endeavours that ultimately aim to determine the complete genome sequence of an organism (be it an animal, a plant, a fungus, a bacterium, an archaean, a protist or a virus) and to annotate protein-coding genes and other important genome-encoded features. The genome sequence of an organism includes the collective DNA sequences of each chromosome in the organism. For a bacterium containing a single chromosome, a genome project will aim to map the sequence of that chromosome.
SubstringIn formal language theory and computer science, a substring is a contiguous sequence of characters within a string. For instance, "the best of" is a substring of "It was the best of times". In contrast, "Itwastimes" is a subsequence of "It was the best of times", but not a substring. Prefixes and suffixes are special cases of substrings. A prefix of a string is a substring of that occurs at the beginning of ; likewise, a suffix of a string is a substring that occurs at the end of .
Population dynamicsPopulation dynamics is the type of mathematics used to model and study the size and age composition of populations as dynamical systems. Population dynamics has traditionally been the dominant branch of mathematical biology, which has a history of more than 220 years, although over the last century the scope of mathematical biology has greatly expanded. The beginning of population dynamics is widely regarded as the work of Malthus, formulated as the Malthusian growth model.
Population geneticsPopulation genetics is a subfield of genetics that deals with genetic differences within and among populations, and is a part of evolutionary biology. Studies in this branch of biology examine such phenomena as adaptation, speciation, and population structure. Population genetics was a vital ingredient in the emergence of the modern evolutionary synthesis. Its primary founders were Sewall Wright, J. B. S. Haldane and Ronald Fisher, who also laid the foundations for the related discipline of quantitative genetics.
Whole genome sequencingWhole genome sequencing (WGS), also known as full genome sequencing, complete genome sequencing, or entire genome sequencing, is the process of determining the entirety, or nearly the entirety, of the DNA sequence of an organism's genome at a single time. This entails sequencing all of an organism's chromosomal DNA as well as DNA contained in the mitochondria and, for plants, in the chloroplast. Whole genome sequencing has largely been used as a research tool, but was being introduced to clinics in 2014.
Lexical definitionThe lexical definition of a term, also known as the dictionary definition, is the definition closely matching the meaning of the term in common usage. As its other name implies, this is the sort of definition one is likely to find in the dictionary. A lexical definition is usually the type expected from a request for definition, and it is generally expected that such a definition will be stated as simply as possible in order to convey information to the widest audience.
Variable (computer science)In computer programming, a variable is an abstract storage location paired with an associated symbolic name, which contains some known or unknown quantity of data or object referred to as a value; or in simpler terms, a variable is a named container for a particular set of bits or type of data (like integer, float, string etc...). A variable can eventually be associated with or identified by a memory address. The variable name is the usual way to reference the stored value, in addition to referring to the variable itself, depending on the context.
Random variableA random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. The term 'random variable' can be misleading as it is not actually random nor a variable, but rather it is a function from possible outcomes (e.g., the possible upper sides of a flipped coin such as heads and tails ) in a sample space (e.g., the set ) to a measurable space (e.g., in which 1 corresponding to and −1 corresponding to ), often to the real numbers.
Lebesgue measureIn measure theory, a branch of mathematics, the Lebesgue measure, named after French mathematician Henri Lebesgue, is the standard way of assigning a measure to subsets of n-dimensional Euclidean space. For n = 1, 2, or 3, it coincides with the standard measure of length, area, or volume. In general, it is also called n-dimensional volume, n''-volume, or simply volume. It is used throughout real analysis, in particular to define Lebesgue integration.
Finite-state machineA finite-state machine (FSM) or finite-state automaton (FSA, plural: automata), finite automaton, or simply a state machine, is a mathematical model of computation. It is an abstract machine that can be in exactly one of a finite number of states at any given time. The FSM can change from one state to another in response to some inputs; the change from one state to another is called a transition. An FSM is defined by a list of its states, its initial state, and the inputs that trigger each transition.
EvolutionIn biology, evolution is the change in heritable characteristics of biological populations over successive generations. Evolution occurs when evolutionary processes such as natural selection (including sexual selection) and genetic drift act on genetic variation, resulting in certain characteristics becoming more or less common within a population over successive generations. The process of evolution has given rise to biodiversity at every level of biological organisation.
Alphabet (formal languages)In formal language theory, an alphabet, sometimes called a vocabulary, is a non-empty set of indivisible symbols/glyphs, typically thought of as representing letters, characters, digits, phonemes, or even words. Alphabets in this technical sense of a set are used in a diverse range of fields including logic, mathematics, computer science, and linguistics. An alphabet may have any cardinality ("size") and depending on its purpose maybe be finite (e.g., the alphabet of letters "a" through "z"), countable (e.
Σ-finite measureIn mathematics, a positive (or signed) measure μ defined on a σ-algebra Σ of subsets of a set X is called a finite measure if μ(X) is a finite real number (rather than ∞), and a set A in Σ is of finite measure if μ(A) < ∞. The measure μ is called σ-finite if X is a countable union of measurable sets each with finite measure. A set in a measure space is said to have σ-finite measure if it is a countable union of measurable sets with finite measure. A measure being σ-finite is a weaker condition than being finite, i.
Evolutionary biologyEvolutionary biology is the subfield of biology that studies the evolutionary processes (natural selection, common descent, speciation) that produced the diversity of life on Earth. It is also defined as the study of the history of life forms on Earth. Evolution holds that all species are related and gradually change over generations. In a population, the genetic variations affect the phenotypes (physical characteristics) of an organism. These changes in the phenotypes will be an advantage to some organisms, which will then be passed onto their offspring.
Deterministic finite automatonIn the theory of computation, a branch of theoretical computer science, a deterministic finite automaton (DFA)—also known as deterministic finite acceptor (DFA), deterministic finite-state machine (DFSM), or deterministic finite-state automaton (DFSA)—is a finite-state machine that accepts or rejects a given string of symbols, by running through a state sequence uniquely determined by the string. Deterministic refers to the uniqueness of the computation run.
