Industrial control systemAn industrial control system (ICS) is an electronic control system and associated instrumentation used for industrial process control. Control systems can range in size from a few modular panel-mounted controllers to large interconnected and interactive distributed control systems (DCSs) with many thousands of field connections. Control systems receive data from remote sensors measuring process variables (PVs), compare the collected data with desired setpoints (SPs), and derive command functions that are used to control a process through the final control elements (FCEs), such as control valves.
Control systemA control system manages, commands, directs, or regulates the behavior of other devices or systems using control loops. It can range from a single home heating controller using a thermostat controlling a domestic boiler to large industrial control systems which are used for controlling processes or machines. The control systems are designed via control engineering process. For continuously modulated control, a feedback controller is used to automatically control a process or operation.
Distributed control systemA distributed control system (DCS) is a computerised control system for a process or plant usually with many control loops, in which autonomous controllers are distributed throughout the system, but there is no central operator supervisory control. This is in contrast to systems that use centralized controllers; either discrete controllers located at a central control room or within a central computer. The DCS concept increases reliability and reduces installation costs by localising control functions near the process plant, with remote monitoring and supervision.
Laplacian matrixIn the mathematical field of graph theory, the Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix or discrete Laplacian, is a matrix representation of a graph. Named after Pierre-Simon Laplace, the graph Laplacian matrix can be viewed as a matrix form of the negative discrete Laplace operator on a graph approximating the negative continuous Laplacian obtained by the finite difference method. The Laplacian matrix relates to many useful properties of a graph.
Graph theoryIn mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called links or lines). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics.
Topological graph theoryIn mathematics, topological graph theory is a branch of graph theory. It studies the embedding of graphs in surfaces, spatial embeddings of graphs, and graphs as topological spaces. It also studies immersions of graphs. Embedding a graph in a surface means that we want to draw the graph on a surface, a sphere for example, without two edges intersecting. A basic embedding problem often presented as a mathematical puzzle is the three utilities problem.
Incidence matrixIn mathematics, an incidence matrix is a logical matrix that shows the relationship between two classes of objects, usually called an incidence relation. If the first class is X and the second is Y, the matrix has one row for each element of X and one column for each element of Y. The entry in row x and column y is 1 if x and y are related (called incident in this context) and 0 if they are not. There are variations; see below. Incidence matrix is a common graph representation in graph theory.
The TimesThe Times is a British daily national newspaper based in London. It began in 1785 under the title The Daily Universal Register, adopting its current name on 1 January 1788. The Times and its sister paper The Sunday Times (founded in 1821) are published by Times Media, since 1981 a subsidiary of News UK, in turn wholly owned by News Corp. The Times and The Sunday Times, which do not share editorial staff, were founded independently and have had common ownership only since 1966.
Discrete Laplace operatorIn mathematics, the discrete Laplace operator is an analog of the continuous Laplace operator, defined so that it has meaning on a graph or a discrete grid. For the case of a finite-dimensional graph (having a finite number of edges and vertices), the discrete Laplace operator is more commonly called the Laplacian matrix. The discrete Laplace operator occurs in physics problems such as the Ising model and loop quantum gravity, as well as in the study of discrete dynamical systems.
Second quantizationSecond quantization, also referred to as occupation number representation, is a formalism used to describe and analyze quantum many-body systems. In quantum field theory, it is known as canonical quantization, in which the fields (typically as the wave functions of matter) are thought of as field operators, in a manner similar to how the physical quantities (position, momentum, etc.) are thought of as operators in first quantization. The key ideas of this method were introduced in 1927 by Paul Dirac, and were later developed, most notably, by Pascual Jordan and Vladimir Fock.
Times SquareTimes Square is a major commercial intersection, tourist destination, entertainment hub, and neighborhood in Midtown Manhattan, New York City, United States. It is formed by the junction of Broadway, Seventh Avenue, and 42nd Street. Together with adjacent Duffy Square, Times Square is a bowtie-shaped plaza five blocks long between 42nd and 47th Streets. Times Square is brightly lit by numerous digital billboards and advertisements as well as businesses offering 24/7 service.
The New York TimesThe New York Times (NYT) is a daily newspaper based in New York City with a worldwide readership reported in 2022 to comprise 740,000 paid print subscribers, and 8.6 million paid digital subscribers. Founded in 1851 as the New-York Daily Times, it is published by The New York Times Company. The Times has won 132 Pulitzer Prizes, the most of any newspaper, and has long been regarded as a national "newspaper of record". For print, it is ranked 17th in the world by circulation and 3rd in the United States.
Canonical quantizationIn physics, canonical quantization is a procedure for quantizing a classical theory, while attempting to preserve the formal structure, such as symmetries, of the classical theory, to the greatest extent possible. Historically, this was not quite Werner Heisenberg's route to obtaining quantum mechanics, but Paul Dirac introduced it in his 1926 doctoral thesis, the "method of classical analogy" for quantization, and detailed it in his classic text Principles of Quantum Mechanics.
Digraph (orthography)A digraph or digram (from the δίς , "double" and γράφω , "to write") is a pair of characters used in the orthography of a language to write either a single phoneme (distinct sound), or a sequence of phonemes that does not correspond to the normal values of the two characters combined. Some digraphs represent phonemes that cannot be represented with a single character in the writing system of a language, like the English sh in ship and fish. Other digraphs represent phonemes that can also be represented by single characters.
Matrix (mathematics)In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, is a matrix with two rows and three columns. This is often referred to as a "two by three matrix", a " matrix", or a matrix of dimension . Without further specifications, matrices represent linear maps, and allow explicit computations in linear algebra.
Ch (digraph)Ch is a digraph in the Latin script. It is treated as a letter of its own in Chamorro, Old Spanish, Czech, Slovak, Igbo, Uzbek, Quechua, Guarani, Welsh, Cornish, Breton, Ukrainian Latynka and Belarusian Łacinka alphabets. Formerly ch was also considered a separate letter for collation purposes in Modern Spanish, Vietnamese, and sometimes in Polish; now the digraph ch in these languages continues to be used, but it is considered as a sequence of letters and sorted as such. The digraph was first used in Latin since the 2nd century B.
IJ (digraph)IJ (lowercase ij; ɛi; also encountered as deprecated codepoints IJ and ij) is a digraph of the letters i and j. Occurring in the Dutch language, it is sometimes considered a ligature, or a letter in itself. In most fonts that have a separate character for ij, the two composing parts are not connected but are separate glyphs, which are sometimes slightly kerned. An ij in written Dutch usually represents the diphthong [ɛi]. In standard Dutch and most Dutch dialects, there are two possible spellings for the diphthong [ɛi]: ij and ei.
Communication protocolA communication protocol is a system of rules that allows two or more entities of a communications system to transmit information via any variation of a physical quantity. The protocol defines the rules, syntax, semantics, and synchronization of communication and possible error recovery methods. Protocols may be implemented by hardware, software, or a combination of both. Communicating systems use well-defined formats for exchanging various messages.
Adjacency matrixIn graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph. In the special case of a finite simple graph, the adjacency matrix is a (0,1)-matrix with zeros on its diagonal. If the graph is undirected (i.e. all of its edges are bidirectional), the adjacency matrix is symmetric. The relationship between a graph and the eigenvalues and eigenvectors of its adjacency matrix is studied in spectral graph theory.
Computable functionComputable functions are the basic objects of study in computability theory. Computable functions are the formalized analogue of the intuitive notion of algorithms, in the sense that a function is computable if there exists an algorithm that can do the job of the function, i.e. given an input of the function domain it can return the corresponding output. Computable functions are used to discuss computability without referring to any concrete model of computation such as Turing machines or register machines.
