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Python sets are very much like mathematical sets, and support operations like set intersection and union. Python also features a frozenset class for immutable sets, see Collection types. Dictionaries (class dict) are mutable mappings tying keys and corresponding values. Python has special syntax to create dictionaries ({key: value})
For example, suppose P(L = red) = 0.2, P(L = yellow) = 0.1, and P(L = green) = 0.7. Multiplying each column in the conditional distribution by the probability of that column occurring results in the joint probability distribution of H and L, given in the central 2×3 block of entries. (Note that the cells in this 2×3 block add up to 1).
The following example written in Eiffel sets the value of a class attribute hour based on a caller-provided argument a_hour.The postcondition follows the keyword ensure.In this example, the postcondition guarantees, in cases in which the precondition holds (i.e., when a_hour represents a valid hour of the day), that after the execution of set_hour, the class attribute hour will have the same ...
In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements.For example, in the conditional statement: "If P then Q", Q is necessary for P, because the truth of Q is guaranteed by the truth of P.
Inequality i) is known as the Armijo rule [4] and ii) as the curvature condition; i) ensures that the step length decreases 'sufficiently', and ii) ensures that the slope has been reduced sufficiently. Conditions i) and ii) can be interpreted as respectively providing an upper and lower bound on the admissible step length values.
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The Frank–Wolfe algorithm is an iterative first-order optimization algorithm for constrained convex optimization.Also known as the conditional gradient method, [1] reduced gradient algorithm and the convex combination algorithm, the method was originally proposed by Marguerite Frank and Philip Wolfe in 1956. [2]