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The game tree size is the total number of possible games that can be played. This is the number of leaf nodes in the game tree rooted at the game's initial position.. The game tree is typically vastly larger than the state-space because the same positions can occur in many games by making moves in a different order (for example, in a tic-tac-toe game with two X and one O on the board, this ...
The probability generating function of an almost surely constant random variable, i.e. one with (=) = and () = is G ( z ) = z c . {\displaystyle G(z)=z^{c}.} The probability generating function of a binomial random variable , the number of successes in n {\displaystyle n} trials, with probability p {\displaystyle p} of success in each trial, is
If np = 1, then a graph in G(n, p) will almost surely have a largest component whose size is of order n 2/3. If np → c > 1, where c is a constant, then a graph in G(n, p) will almost surely have a unique giant component containing a positive fraction of the vertices. No other component will contain more than O(log(n)) vertices. If < , then ...
In this model, if for any constant >, then with high probability (in the limit as goes to infinity) all connected components of the graph have size O(log n), and there is no giant component. However, for p ≥ 1 + ϵ n {\displaystyle p\geq {\frac {1+\epsilon }{n}}} there is with high probability a single giant component, with all other ...
Similar to the case of graphing problems, the quantum query complexity of a black-box problem is the smallest number of queries to the oracle that are required in order to calculate the function. This makes the quantum query complexity a lower bound on the overall time complexity of a function.
Euler diagram for P, NP, NP-complete, and NP-hard set of problems. Under the assumption that P ≠ NP, the existence of problems within NP but outside both P and NP-complete was established by Ladner. [1] In computational complexity theory, NP (nondeterministic polynomial time) is a complexity class used to classify decision problems.
The concordance correlation coefficient is nearly identical to some of the measures called intra-class correlations.Comparisons of the concordance correlation coefficient with an "ordinary" intraclass correlation on different data sets found only small differences between the two correlations, in one case on the third decimal. [2]
In physics, the C parity or charge parity is a multiplicative quantum number of some particles that describes their behavior under the symmetry operation of charge conjugation. Charge conjugation changes the sign of all quantum charges (that is, additive quantum numbers ), including the electrical charge , baryon number and lepton number , and ...