ar X iv : n lin / 0 40 40 32 v 1 [ nl in . A O ] 1 6 A pr 2 00 4 Metrics for more than two points at once
نویسنده
چکیده
The conventional definition of a topological metric over a space specifies properties that must be obeyed by any measure of “how separated” two points in that space are. Here it is shown how to extend that definition, and in particular the triangle inequality, to concern arbitrary numbers of points. Such a measure of how separated the points within a collection are can be bootstrapped, to measure “how separated” from each other are two (or more) collections. The measure presented here also allows fractional membership of an element in a collection. This means it directly concerns measures of “how spread out” a probability distribution over a space is. When such a measure is bootstrapped to compare two collections, it allows us to measure how separated two probability distributions are, or more generally, how separated a distribution of distributions is.
منابع مشابه
ar X iv : n lin / 0 00 40 13 v 1 [ nl in . S I ] 9 A pr 2 00 0 The critical A ( 1 ) n − 1 chain
(1) n−1 chain Abstract We study the A (1) n−1 spin chain at the critical regime |q| = 1. We give the free boson realizations of the type-I vertex operators and their duals. Using these free boson realizations, we give the integral representations for the correlation functions.
متن کاملar X iv : n lin / 0 60 40 34 v 1 [ nl in . S I ] 1 7 A pr 2 00 6 Integrable inhomogeneous Lakshmanan - Myrzakulov equation
Abstract. The integrable inhomogeneous extension of the Lakshmanan-Myrzakulov equation is constructed by using the prolongation structure theory. The corresponding L-equivalent counterpart is also given, which is the (2+1)-dimensional generalized NLSE. PACS: 02.30.Ik, 02.40.Hw, 75.10.Hk
متن کاملar X iv : m at h - ph / 0 40 40 45 v 1 1 9 A pr 2 00 4 On the refined 3 - enumeration of alternating sign matrices
An explicit expression for the numbers A(n, r; 3) describing the refined 3-enumeration of alternating sign matrices is given. The derivation is based on the recent results of Stroganov for the corresponding generating function. As a result, A(n, r; 3)'s are represented as 1-fold sums which can also be written in terms of terminating 4 F 3 series of argument 1/4.
متن کاملar X iv : g r - qc / 0 40 40 40 v 1 9 A pr 2 00 4 Could the Gravitons Have Rest Masses ?
If the cosmological constant Λ can not be neglected, we will show in this short report, that graviton should have a rest mass mg = √ 2Λ = √ 2Λh̄c−1 different from zero.
متن کامل