The Average Distance between Two Zones

On Approximating the Average Distance Between

A Distance Between Channels: the average error of mismatched channels

Two channels are equivalent if their maximum likelihood (ML) decoders coincide for every code. We show that this equivalence relation partitions the space of channels into a generalized hyperplane arrangement. With this, we define a coding distance between channels in terms of their ML-decoders which is meaningful from the decoding point of view, in the sense that the closer two channels are, t...

a cross-comparative dtudy between two textbook series in terms of the presentation of politeness

چکیده ندارد.

The Continuous Procrustes Distance between Two Surfaces

The Procrustes distance is used to quantify the similarity or dissimilarity of (3-dimensional) shapes, and extensively used in biological morphometrics. Typically each (normalized) shape is represented by N landmark points, chosen to be homologous (i.e. corresponding to each other), as much as possible, and the Procrustes distance is then computed as infR ∑N j=1 ‖Rxj − xj‖, where the minimizati...

Relation between Randić Index and Average Distance of Trees

The Randić index R(G) of a graph G is the sum of weights (deg(u) deg(v))−0.5 over all edges uv of G, where deg(v) denotes the degree of a vertex v. We prove that for any tree T with n1 leaves R(T ) ≥ ad(T ) + max(0,n1 − 2), where ad(T ) is the average distance between vertices of T . As a consequence we resolve the conjecture R(G) ≥ ad(G) given by Fajtlowicz in 1988 for the case when G is a tree.