We consider the problem of traveling among random points in Euclidean space, when only a random fraction of the pairs are joined by traversable connections. In particular, we show a threshold for a pair of points to be connected by a geodesic of length arbitrarily close to their Euclidean distance, and analyze the minimum length Traveling Salesperson Tour, extending the BeardwoodHalton-Hammersl...

Graphs are attached to the n-dimensional space Z 2r where Z2r is the ring with 2 r elements using an analogue of Euclidean distance. The graphs are shown to be non-Ramanujan for r=4. Comparisons are made with Euclidean graphs attached to Z pr for p an odd prime. The percentage of non-zero eigenvalues of the adjacency operator attached to these 1nite Euclidean graphs is shown to tend to zero as ...

Let f be a function that is analytic in the unit disc. We give new estimates, and new proofs of existing estimates, of the Euclidean length of the image under f of a radial segment in the unit disc. Our methods are based on the hyperbolic geometry of plane domains, and we address some new questions that follow naturally from this approach.

While the size of multimedia database increases, the demand for efficient search for multimedia data becomes more and more urgent. Most recent works on audio classification and retrieval adopt Euclidean distance as their distance measures. However, Euclidean distance is not a perceptual distance measure for some audio features. The purpose of this work is to derive two new distance measures for...

Graphs are attached to 2r where 2r is the ring with 2 r elements using an analogue of Euclidean distance. M.R. DeDeo (2003) showed that these graphs are non-Ramanujan for r 4. In this paper, we will show that finite Euclidean graphs attached to 2r are non Ramanujan for r 2 except for r = 2 and d = 2, 3. Together with the results in Medrano et al. (1998), this implies that finite Euclidean graph...

We show that the Euclidean distance degree of a real orthogonally invariant matrix variety equals the Euclidean distance degree of its restriction to diagonal matrices. We illustrate how this result can greatly simplify calculations in concrete circumstances.

This pilot study investigates the phonetic realisation of Estonian Swedish long close vowels comparing them with Central Swedish and Finland Swedish counterparts. It appears that in the Rickul variety of Estonian Swedish there is a distinction between only three long close vowels. The analysed vowels of Estonian Swedish are more similar to those of Central Swedish than Finland Swedish, as measu...

ABSTRACT Broadcasting is the process of disseminating a message from a node of a communication network to all other nodes as quickly as possible. In this paper we consider Manhattan Street Networks (MSNs) which are mesh-structured, toroidal, directed, regular networks such that locally they resemble the geographical topology of the avenues and streets of Manhattan. Previous work on these networ...

The feature of our method different from other fuzzy grey relation method for supermixed multiple attribute group decision-making is that all of the subjective and objective weights are obtained by interval grey number and that the group decisionmaking is performed based on the relative approach degree of grey TOPSIS, the relative approach degree of grey incidence and the relative membership de...