In statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable y is modelled as an nth degree polynomial in x. Polynomial regression fits a nonlinear relationship between the value of x and the corresponding conditional mean of y, denoted E(y |x). Although polynomial regression fits a nonlinear model to the data, as a statistical estimation problem it is linear, in the sense that the regression function E(y | x) is linear in the unknown parameters that are estimated from the data. For this reason...

A model of a charged membrane introduced by Paul Dirac in 1962. Dirac's original motivation was to explain the mass of the muon as an excitation of the ground state corresponding to an electron. Anticipating the birth of string theory by almost a decade, he was the first to introduce what is now called a type of Nambu–Goto action for membranes. In the Dirac membrane model the repulsive electromagnetic forces on the membrane are balanced by the contracting ones coming from the positive tension. In the case of the spherical membrane, classical equations of motion imply that the balance is met for...

Pablo Ruiz Picasso (UK: , US: , Spanish: [ˈpaβlo piˈkaso]; 25 October 1881 – 8 April 1973) was a Spanish painter, sculptor, printmaker, ceramicist, stage designer, poet and playwright who spent most of his adult life in France. Regarded as one of the most influential artists of the 20th century, he is known for co-founding the Cubist movement, the invention of constructed sculpture, the co-invention of collage, and for the wide variety of styles that he helped develop and explore. Among his most famous works are the proto-Cubist Les Demoiselles d'Avignon (1907), and Guernica (1937), a dramatic...

Lovelock's theorem of general relativity says that from a local gravitational action which contains only second derivatives of the four-dimensional spacetime metric, then the only possible equations of motion are the Einstein field equations. The theorem was described by British physicist David Lovelock in 1971. == Statement == In four dimensional space, any tensor A μ ν {\displaystyle A^{\mu \nu }} whose components are function of metric tensor g...

In theoretical physics, a no-go theorem is a theorem that states that a particular situation is not physically possible. Specifically, the term describes results in quantum mechanics like Bell's theorem and the Kochen–Specker theorem that constrain the permissible types of hidden variable theories which try to explain the apparent randomness of quantum mechanics as a deterministic model featuring hidden states. == Examples == The Weinberg–Witten theorem states that massless particles (either composite or elementary) with spin j > ​1⁄2 cannot carry a Lorentz-covariant current, while massle...

In quantum information theory, the no-teleportation theorem states that an arbitrary quantum state cannot be converted into a sequence of classical bits (or even an infinite number of such bits); nor can such bits be used to reconstruct the original state, thus "teleporting" it by merely moving classical bits around. Put another way, it states that the unit of quantum information, the qubit, cannot be exactly, precisely converted into classical information bits. This should not be confused with quantum teleportation, which does allow a quantum state to be destroyed in one location, and an exact...

In physics, the no-cloning theorem states that it is impossible to create an identical copy of an arbitrary unknown quantum state. This no-go theorem of quantum mechanics was articulated by James Park in proving the impossibility of a simple perfect non-disturbing measurement scheme, in 1970 and rediscovered by Wootters and Zurek and by Dieks in 1982. It has profound implications in quantum computing and related fields. The state of one system can be entangled with the state of another system. For instance, one can use the controlled NOT gate and the Walsh–Hadamard gate to entangle two qubits...