The resulting ranks, if not specified explicitly, correspond to pessimistic ranks, where the worst rank is reported in the case where the correct candidate has the same score as other candidates.
Rotation terms (nonlinear trigonometric functions) are integrated explicitly and correspond to a change in the reference configuration.
In the ideal case (what is not always possible, especially for nondifferentiable DC programs) an optimal solution of ((P_{k})) is explicitly determined, which corresponds to the explicit computation of a subgradient of (g^.) Otherwise one should find efficient convex optimization algorithms suitably adapted to ((P_{k}))'s specific structures in order to save computation time.
Even though the inhibitory unit is modeled explicitly, this network corresponds to a network with self-exciting units that mutually inhibit each other, 53 except for the delayed inhibition caused by the inhibitory unit.
It is explicitly shown that this corresponds to the maximum area development of the flame front and to minimum net work losses (including heat transfer, mechanical frictions and working fluid internal irreversibilities).
This seems needlessly strong, and it is not easy to find real-life correspondence theorists who explicitly embrace part (b): Why shouldn't different truths correspond to the same fact, as long as they are not too different?
A well specified SketchEl file is shown in (d), which uses the inline abbreviation form to explicitly include the fragment to which "Ph" corresponds, i.e. the phenyl ring itself, and the attachment point.
Our complementary but generative approach here explicitly pursues energetically coherent substates clusters which correspond intuitively to separated energy wells.
17 For instance, Halpern and Pearl explicitly state that "events" on their account correspond to sets of possible worlds rather than changes in states.
Within the above-mentioned terminology, space time separable receptive fields correspond to spatio-temporal scale-space kernels without velocity adaptation, whereas inseparable receptive fields correspond to kernels that are explicitly adapted to nonzero velocities.
