Parallel computingParallel computing is a type of computation in which many calculations or processes are carried out simultaneously. Large problems can often be divided into smaller ones, which can then be solved at the same time. There are several different forms of parallel computing: bit-level, instruction-level, data, and task parallelism. Parallelism has long been employed in high-performance computing, but has gained broader interest due to the physical constraints preventing frequency scaling.
Mathematical proofA mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference. Proofs are examples of exhaustive deductive reasoning which establish logical certainty, to be distinguished from empirical arguments or non-exhaustive inductive reasoning which establish "reasonable expectation".
Proof (truth)A proof is sufficient evidence or a sufficient argument for the truth of a proposition. The concept applies in a variety of disciplines, with both the nature of the evidence or justification and the criteria for sufficiency being area-dependent. In the area of oral and written communication such as conversation, dialog, rhetoric, etc., a proof is a persuasive perlocutionary speech act, which demonstrates the truth of a proposition.
MySQLMySQL (ˌmaɪˌɛsˌkjuːˈɛl) is an open-source relational database management system (RDBMS). Its name is a combination of "My", the name of co-founder Michael Widenius's daughter My, and "SQL", the acronym for Structured Query Language. A relational database organizes data into one or more data tables in which data may be related to each other; these relations help structure the data. SQL is a language that programmers use to create, modify and extract data from the relational database, as well as control user access to the database.
Embarrassingly parallelIn parallel computing, an embarrassingly parallel workload or problem (also called embarrassingly parallelizable, perfectly parallel, delightfully parallel or pleasingly parallel) is one where little or no effort is needed to separate the problem into a number of parallel tasks. This is often the case where there is little or no dependency or need for communication between those parallel tasks, or for results between them. Thus, these are different from distributed computing problems that need communication between tasks, especially communication of intermediate results.
Proof calculusIn mathematical logic, a proof calculus or a proof system is built to prove statements. A proof system includes the components: Language: The set L of formulas admitted by the system, for example, propositional logic or first-order logic. Rules of inference: List of rules that can be employed to prove theorems from axioms and theorems. Axioms: Formulas in L assumed to be valid. All theorems are derived from axioms. Usually a given proof calculus encompasses more than a single particular formal system, since many proof calculi are under-determined and can be used for radically different logics.
Formal proofIn logic and mathematics, a formal proof or derivation is a finite sequence of sentences (called well-formed formulas in the case of a formal language), each of which is an axiom, an assumption, or follows from the preceding sentences in the sequence by a rule of inference. It differs from a natural language argument in that it is rigorous, unambiguous and mechanically verifiable. If the set of assumptions is empty, then the last sentence in a formal proof is called a theorem of the formal system.
Query optimizationQuery optimization is a feature of many relational database management systems and other databases such as NoSQL and graph databases. The query optimizer attempts to determine the most efficient way to execute a given query by considering the possible query plans. Generally, the query optimizer cannot be accessed directly by users: once queries are submitted to the database server, and parsed by the parser, they are then passed to the query optimizer where optimization occurs.
NoSQLA NoSQL (originally referring to "non-SQL" or "non-relational") database provides a mechanism for storage and retrieval of data that is modeled in means other than the tabular relations used in relational databases. Such databases have existed since the late 1960s, but the name "NoSQL" was only coined in the early 21st century, triggered by the needs of Web 2.0 companies. NoSQL databases are increasingly used in big data and real-time web applications.
MySQL ClusterMySQL Cluster is a technology providing shared-nothing clustering and auto-sharding for the MySQL database management system. It is designed to provide high availability and high throughput with low latency, while allowing for near linear scalability. MySQL Cluster is implemented through the NDB or NDBCLUSTER storage engine for MySQL ("NDB" stands for Network Database). MySQL Cluster is designed around a distributed, multi-master ACID compliant architecture with no single point of failure.
Massively parallelMassively parallel is the term for using a large number of computer processors (or separate computers) to simultaneously perform a set of coordinated computations in parallel. GPUs are massively parallel architecture with tens of thousands of threads. One approach is grid computing, where the processing power of many computers in distributed, diverse administrative domains is opportunistically used whenever a computer is available. An example is BOINC, a volunteer-based, opportunistic grid system, whereby the grid provides power only on a best effort basis.
Category (mathematics)In mathematics, a category (sometimes called an abstract category to distinguish it from a ) is a collection of "objects" that are linked by "arrows". A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object. A simple example is the , whose objects are sets and whose arrows are functions. is a branch of mathematics that seeks to generalize all of mathematics in terms of categories, independent of what their objects and arrows represent.
PriceA price is the (usually not negative) quantity of payment or compensation expected, required, or given by one party to another in return for goods or services. In some situations, the price of production has a different name. If the product is a "good" in the commercial exchange, the payment for this product will likely be called its "price". However, if the product is "service", there will be other possible names for this product's name.
Monoidal categoryIn mathematics, a monoidal category (or tensor category) is a equipped with a bifunctor that is associative up to a natural isomorphism, and an I that is both a left and right identity for ⊗, again up to a natural isomorphism. The associated natural isomorphisms are subject to certain coherence conditions, which ensure that all the relevant s commute. The ordinary tensor product makes vector spaces, abelian groups, R-modules, or R-algebras into monoidal categories. Monoidal categories can be seen as a generalization of these and other examples.
Enriched categoryIn , a branch of mathematics, an enriched category generalizes the idea of a by replacing hom-sets with objects from a general . It is motivated by the observation that, in many practical applications, the hom-set often has additional structure that should be respected, e.g., that of being a vector space of morphisms, or a topological space of morphisms. In an enriched category, the set of morphisms (the hom-set) associated with every pair of objects is replaced by an in some fixed monoidal category of "hom-objects".
Price ceilingA price ceiling is a government- or group-imposed price control, or limit, on how high a price is charged for a product, commodity, or service. Governments use price ceilings to protect consumers from conditions that could make commodities prohibitively expensive. Such conditions can occur during periods of high inflation, in the event of an investment bubble, or in the event of monopoly ownership of a product, all of which can cause problems if imposed for a long period without controlled rationing, leading to shortages.
Preadditive categoryIn mathematics, specifically in , a preadditive category is another name for an Ab-category, i.e., a that is over the , Ab. That is, an Ab-category C is a such that every hom-set Hom(A,B) in C has the structure of an abelian group, and composition of morphisms is bilinear, in the sense that composition of morphisms distributes over the group operation. In formulas: and where + is the group operation. Some authors have used the term additive category for preadditive categories, but here we follow the current trend of reserving this term for certain special preadditive categories (see below).
Price controlsPrice controls are restrictions set in place and enforced by governments, on the prices that can be charged for goods and services in a market. The intent behind implementing such controls can stem from the desire to maintain affordability of goods even during shortages, and to slow inflation, or, alternatively, to ensure a minimum income for providers of certain goods or to try to achieve a living wage. There are two primary forms of price control: a price ceiling, the maximum price that can be charged; and a price floor, the minimum price that can be charged.
Homotopy categoryIn mathematics, the homotopy category is a built from the category of topological spaces which in a sense identifies two spaces that have the same shape. The phrase is in fact used for two different (but related) categories, as discussed below. More generally, instead of starting with the category of topological spaces, one may start with any and define its associated homotopy category, with a construction introduced by Quillen in 1967. In this way, homotopy theory can be applied to many other categories in geometry and algebra.
Price fixingPrice fixing is an anticompetitive agreement between participants on the same side in a market to buy or sell a product, service, or commodity only at a fixed price, or maintain the market conditions such that the price is maintained at a given level by controlling supply and demand. The intent of price fixing may be to push the price of a product as high as possible, generally leading to profits for all sellers but may also have the goal to fix, peg, discount, or stabilize prices.
