Dynamical systems theoryDynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems. From a physical point of view, continuous dynamical systems is a generalization of classical mechanics, a generalization where the equations of motion are postulated directly and are not constrained to be Euler–Lagrange equations of a least action principle.
Blade RunnerBlade Runner is a 1982 science fiction film directed by Ridley Scott, and written by Hampton Fancher and David Peoples. Starring Harrison Ford, Rutger Hauer, Sean Young, and Edward James Olmos, it is an adaptation of Philip K. Dick's 1968 novel Do Androids Dream of Electric Sheep? The film is set in a dystopian future Los Angeles of 2019, in which synthetic humans known as replicants are bio-engineered by the powerful Tyrell Corporation to work on space colonies.
Dynamical systemIn mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured.
Pelton wheelThe Pelton wheel or Pelton Turbine is an impulse-type water turbine invented by American inventor Lester Allan Pelton in the 1870s. The Pelton wheel extracts energy from the impulse of moving water, as opposed to water's dead weight like the traditional overshot water wheel. Many earlier variations of impulse turbines existed, but they were less efficient than Pelton's design. Water leaving those wheels typically still had high speed, carrying away much of the dynamic energy brought to the wheels.
Blade Runner 2049Blade Runner 2049 is a 2017 American epic neo-noir science fiction film directed by Denis Villeneuve and written by Hampton Fancher and Michael Green. A sequel to the 1982 film Blade Runner, the film stars Ryan Gosling and Harrison Ford, with Ana de Armas, Sylvia Hoeks, Robin Wright, Mackenzie Davis, Dave Bautista, and Jared Leto in supporting roles. Ford and Edward James Olmos reprise their roles from the original film. Gosling plays K, a Nexus-9 replicant "blade runner" who uncovers a secret that threatens to destabilize society and the course of civilization.
Gold standard (test)In medicine and statistics, a gold standard test is usually the diagnostic test or benchmark that is the best available under reasonable conditions. In other words, a gold standard is the most accurate test possible without restrictions. The meanings may differ in the two fields, because in medicine with some conditions only an autopsy guarantees diagnostic certainty, thus the gold standard test would be the best one that keeps the patient alive instead of the autopsy.
ReproducibilityReproducibility, closely related to replicability and repeatability, is a major principle underpinning the scientific method. For the findings of a study to be reproducible means that results obtained by an experiment or an observational study or in a statistical analysis of a data set should be achieved again with a high degree of reliability when the study is replicated. There are different kinds of replication but typically replication studies involve different researchers using the same methodology.
Complete latticeIn mathematics, a complete lattice is a partially ordered set in which all subsets have both a supremum (join) and an infimum (meet). A lattice which satisfies at least one of these properties is known as a conditionally complete lattice. Specifically, every non-empty finite lattice is complete. Complete lattices appear in many applications in mathematics and computer science. Being a special instance of lattices, they are studied both in order theory and universal algebra.
Complete partial orderIn mathematics, the phrase complete partial order is variously used to refer to at least three similar, but distinct, classes of partially ordered sets, characterized by particular completeness properties. Complete partial orders play a central role in theoretical computer science: in denotational semantics and domain theory. A complete partial order, abbreviated cpo, can refer to any of the following concepts depending on context. A partially ordered set is a directed-complete partial order (dcpo) if each of its directed subsets has a supremum.
Completeness (order theory)In the mathematical area of order theory, completeness properties assert the existence of certain infima or suprema of a given partially ordered set (poset). The most familiar example is the completeness of the real numbers. A special use of the term refers to complete partial orders or complete lattices. However, many other interesting notions of completeness exist. The motivation for considering completeness properties derives from the great importance of suprema (least upper bounds, joins, "") and infima (greatest lower bounds, meets, "") to the theory of partial orders.
