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Dijkstra's algorithm (/ ˈ d aɪ k s t r ə z / DYKE-strəz) is an algorithm for finding the shortest paths between nodes in a weighted graph, which may represent, for example, a road network. It was conceived by computer scientist Edsger W. Dijkstra in 1956 and published three years later.
Springer, T. A. (1977), Invariant Theory, New York: Springer, ISBN 0-387-08242-5 An older but still useful survey. Sturmfels, Bernd (1993), Algorithms in Invariant Theory, New York: Springer, ISBN 0-387-82445-6 A beautiful introduction to the theory of invariants of finite groups and techniques for computing them using Gröbner bases.
The i.i.d. hypothesis allows for a significant reduction in the number of individual cases required in the training sample, simplifying optimization calculations. In optimization problems, the assumption of independent and identical distribution simplifies the calculation of the likelihood function.
In algebra, the first and second fundamental theorems of invariant theory concern the generators and relations of the ring of invariants in the ring of polynomial functions for classical groups (roughly, the first concerns the generators and the second the relations). [1] The theorems are among the most important results of invariant theory.
Since the parameters are constants, reparametrizing a density in terms of different parameters to give a characterization of a different random variable in the family, means simply substituting the new parameter values into the formula in place of the old ones.
Predicate transformer semantics were introduced by Edsger Dijkstra in his seminal paper "Guarded commands, nondeterminacy and formal derivation of programs".They define the semantics of an imperative programming paradigm by assigning to each statement in this language a corresponding predicate transformer: a total function between two predicates on the state space of the statement.
In probability and statistics, the Tweedie distributions are a family of probability distributions which include the purely continuous normal, gamma and inverse Gaussian distributions, the purely discrete scaled Poisson distribution, and the class of compound Poisson–gamma distributions which have positive mass at zero, but are otherwise continuous. [1]
A real tensor in 3D (i.e., one with a 3x3 component matrix) has as many as six independent invariants, three being the invariants of its symmetric part and three characterizing the orientation of the axial vector of the skew-symmetric part relative to the principal directions of the symmetric part.