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Hilbert's twelfth problem is the extension of the Kronecker–Weber theorem on abelian extensions of the rational numbers, to any base number field.It is one of the 23 mathematical Hilbert problems and asks for analogues of the roots of unity that generate a whole family of further number fields, analogously to the cyclotomic fields and their subfields.
Separately, game theory has played a role in online algorithms; in particular, the k-server problem, which has in the past been referred to as games with moving costs and request-answer games. [125] Yao's principle is a game-theoretic technique for proving lower bounds on the computational complexity of randomized algorithms , especially online ...
Go is an abstract strategy board game for two players in which the aim is to fence off more territory than the opponent. The game was invented in China more than 2,500 years ago and is believed to be the oldest board game continuously played to the present day.
Mafia, also known as Werewolf, is a Russian social deduction game created by Dimitry Davidoff in 1986. [2] The game models a conflict between two groups: an informed minority (the mafiosi or the werewolves) and an uninformed majority (the villagers).
More abstractly, the logistic function is the natural parameter for the Bernoulli distribution, and in this sense is the "simplest" way to convert a real number to a probability. In particular, it maximizes entropy (minimizes added information), and in this sense makes the fewest assumptions of the data being modeled; see § Maximum entropy .
The simplest kind of feedforward neural network (FNN) is a linear network, which consists of a single layer of output nodes with linear activation functions; the inputs are fed directly to the outputs via a series of weights. The sum of the products of the weights and the inputs is calculated at each node.
The simplest exact expressions are the Green–Kubo relations for the linear shear viscosity or the transient time correlation function expressions derived by Evans and Morriss in 1988. [34] Although these expressions are each exact, calculating the viscosity of a dense fluid using these relations currently requires the use of molecular ...