Weight (representation theory)In the mathematical field of representation theory, a weight of an algebra A over a field F is an algebra homomorphism from A to F, or equivalently, a one-dimensional representation of A over F. It is the algebra analogue of a multiplicative character of a group. The importance of the concept, however, stems from its application to representations of Lie algebras and hence also to representations of algebraic and Lie groups. In this context, a weight of a representation is a generalization of the notion of an eigenvalue, and the corresponding eigenspace is called a weight space.
DictionaryA dictionary is a listing of lexemes from the lexicon of one or more specific languages, often arranged alphabetically (or by consonantal root for Semitic languages or radical and stroke for logographic languages), which may include information on definitions, usage, etymologies, pronunciations, translation, etc. It is a lexicographical reference that shows inter-relationships among the data. A broad distinction is made between general and specialized dictionaries.
Natural languageIn neuropsychology, linguistics, and philosophy of language, a natural language or ordinary language is any language that occurs naturally in a human community by a process of use, repetition, and change without conscious planning or premeditation. It can take different forms, namely either a spoken language or a sign language. Natural languages are distinguished from constructed and formal languages such as those used to program computers or to study logic. Natural language can be broadly defined as different from artificial and constructed languages, e.
Representation theoryRepresentation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrices and their algebraic operations (for example, matrix addition, matrix multiplication).
Group representationIn the mathematical field of representation theory, group representations describe abstract groups in terms of bijective linear transformations of a vector space to itself (i.e. vector space automorphisms); in particular, they can be used to represent group elements as invertible matrices so that the group operation can be represented by matrix multiplication. In chemistry, a group representation can relate mathematical group elements to symmetric rotations and reflections of molecules.
Artificial neural networkArtificial neural networks (ANNs, also shortened to neural networks (NNs) or neural nets) are a branch of machine learning models that are built using principles of neuronal organization discovered by connectionism in the biological neural networks constituting animal brains. An ANN is based on a collection of connected units or nodes called artificial neurons, which loosely model the neurons in a biological brain. Each connection, like the synapses in a biological brain, can transmit a signal to other neurons.
Simultaneous bilingualismSimultaneous bilingualism is a form of bilingualism that takes place when a child becomes bilingual by learning two languages from birth. According to Annick De Houwer, in an article in The Handbook of Child Language, simultaneous bilingualism takes place in "children who are regularly addressed in two spoken languages from before the age of two and who continue to be regularly addressed in those languages up until the final stages" of language development. Both languages are acquired as first languages.
Semantic role labelingIn natural language processing, semantic role labeling (also called shallow semantic parsing or slot-filling) is the process that assigns labels to words or phrases in a sentence that indicates their semantic role in the sentence, such as that of an agent, goal, or result. It serves to find the meaning of the sentence. To do this, it detects the arguments associated with the predicate or verb of a sentence and how they are classified into their specific roles. A common example is the sentence "Mary sold the book to John.
Topic modelIn statistics and natural language processing, a topic model is a type of statistical model for discovering the abstract "topics" that occur in a collection of documents. Topic modeling is a frequently used text-mining tool for discovery of hidden semantic structures in a text body. Intuitively, given that a document is about a particular topic, one would expect particular words to appear in the document more or less frequently: "dog" and "bone" will appear more often in documents about dogs, "cat" and "meow" will appear in documents about cats, and "the" and "is" will appear approximately equally in both.
Static program analysisIn computer science, static program analysis (or static analysis) is the analysis of computer programs performed without executing them, in contrast with dynamic program analysis, which is performed on programs during their execution. The term is usually applied to analysis performed by an automated tool, with human analysis typically being called "program understanding", program comprehension, or code review. In the last of these, software inspection and software walkthroughs are also used.
