A family of connected graphs G is said to be a family with constant metric dimension if its metric dimension is finite and does not depend upon the choice of G in G. In this paper, we study the metric dimension of the generalized Petersen graphs P (n, m) for n = 2m + 1 and m ≥ 1 and give partial answer of the question raised in [9]: Is P (n, m) for n ≥ 7 and 3 ≤ m ≤ bn−1 2 c, a family of graphs...

equality of -curvatures of the berwald and cartan connections leads to a new class of finsler metrics, so-called bc-generalized landsberg metrics. here, we prove that every bc-generalized landsberg metric of scalar flag curvature with dimension greater than two is of constant flag curvature.

Measuring the transmitted information in metric-based clustering has become something of a standard test for the performance of a spike train metric. In this comment, the recently proposed Lp VictorPurpura metric is used to cluster spiking responses to zebra finch songs, recorded from field L of anesthetized zebra finch. It is found that for these data the Lp metrics with p > 1 modestly outperf...

Measuring the transmitted information in metric-based clustering has become something of a standard test for the performance of a spike train metric. In this comment, the recently proposed Lp VictorPurpura metric is used to cluster spiking responses to zebra finch songs, recorded from field L of anesthetized zebra finch. It is found that for these data the Lp metrics with p > 1 modestly outperf...