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Example graph with the state variables s(v) indicated A possible finite firing sequence, with the vertex to be fired in red – the game ends as each vertex has s smaller than its degree. The chip-firing game is a one-player game on a graph which was invented around 1983 and since has become an important part of the study of structural ...
The Rankine scale is used in engineering systems where heat computations are done using degrees Fahrenheit. [3] The symbol for degrees Rankine is °R [2] (or °Ra if necessary to distinguish it from the Rømer and Réaumur scales). By analogy with the SI unit kelvin, some authors term the unit Rankine, omitting the degree symbol. [4] [5]
(For a graph with n vertices and r terminals, they use t = n − r − 1 added vertices per tree.) Then, they ask for the k -minimum spanning tree in this augmented graph with k = rt . The only way to include this many vertices in a k -spanning tree is to use at least one vertex from each added tree, for there are not enough vertices remaining ...
A common example is picking the tile that lies right under the cursor when a user clicks. One such method is using the same rotation matrices that originally produced the isometric view in reverse to turn a point in screen coordinates into a point that would lie on the game board surface before it was rotated. Then, the world x and y values can ...
Today, the game is used by math and physics teachers around the world when teaching vectors and kinematics. However, the game has a certain charm of its own, and may be played as a pure recreation. Martin Gardner noted that the game was "virtually unknown" in the United States, and called it "a truly remarkable simulation of automobile racing".
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The size of G is bounded above by the Moore bound; for 1 < k and 2 < d, only the Petersen graph, the Hoffman-Singleton graph, and possibly graphs (not yet proven to exist) of diameter k = 2 and degree d = 57 attain the Moore bound. In general, the largest degree-diameter graphs are much smaller in size than the Moore bound.
The quadratic scoring rule is a strictly proper scoring rule (,) = = =where is the probability assigned to the correct answer and is the number of classes.. The Brier score, originally proposed by Glenn W. Brier in 1950, [4] can be obtained by an affine transform from the quadratic scoring rule.