Sentence examples for discrete metric from inspiring English sources
noun
A metric d such that for any pair of points x and y, d(x,y) = 0 if x = y and d(x,y) = 1 if x \ne y .
Finally, note that we cannot apply Corollary 3 to any of the complete metrics p S, p M, and p 0, since it is clear that these metrics coincide with the discrete metric on X, and for x = y = 0, u = 1, and v = 0, we have p S ( u, v ) = 1 = p S ( x, u ) = max { p S ( x, y ), p S ( x, u ), p S ( y, v ) }.
The approximations preserve the discrete metric identities and the Discrete Geometric Conservation Law (DGCL) by construction.
We give exact and approximation algorithms for computing the Gromov hyperbolicity of an n-point discrete metric space.
We write explicitly Ozawa kernels for group extensions, for discrete metric spaces of finite asymptotic dimension, of large enough Hilbert space compression, and for suitable actions of countable groups on metric spaces.
SBP discretizations with curved elements remain accurate, conservative, and entropy stable provided the mapping Jacobian satisfies the discrete metric invariants; polynomial mappings at most one degree higher than the SBP operators automatically satisfy the metric invariants in two dimensions.
Then, the discrete metric on is a -function on.
This space is called a discrete cone metric space.
We present an any-time concurrent probabilistic temporal planner (CPTP) that includes continuous and discrete uncertainties and metric functions.
In case of metric, discrete, or even ordered categorical data, the area under the receiver operating characteristic (ROC) curve (denoted by AUC) is an appropriate overall accuracy measure for the selection, because the AUC is independent of cut-off points.
The developed approach transforms sub-pixel classifications into discrete maps compliant with metric terms and computes and interprets metric results in the context of the region to explain patterns in the extent, distribution, and connectivity of saltcedar in the Rio Grande basin.
In particular, we verify the almost-everywhere convergence of abstract bounded, additive processes, as well as a Banach space approximation result for the spectral distribution function (integrated density of states) for random operators on discrete structures in a metric space.
