In [Rao, SoCG 1999], it is shown that every n-point Euclidean metric with polynomial spread admits a Euclidean embedding with k-dimensional distortion bounded by O( √ log n log k), a result which is tight for constant values of k. We show that this holds without any assumption on the spread, and give an improved bound of O( √ log n(log k)). Our main result is an upper bound of O( √ log n log lo...

The use of development threat as a tool in conservation prioritization is becoming increasingly common. When used as a component of a larger planning methodology that may include factors such as biological integrity, area, and connectivity, degree of threat may help an organization to protect a larger amount of land that it would otherwise have been able to. I develop two models of development:...

For a domain Ω ⊂ C, the Kerzman-Stein operator is the skewhermitian part of the Cauchy operator acting on L(bΩ), which is defined with respect to Euclidean measure. In this paper we compute the spectrum of the Kerzman-Stein operator for three domains whose boundaries consist of two circular arcs: a strip, a wedge, and an annulus. We also treat the case of a domain bounded by two logarithmic spi...

In this paper, we present two feature extraction methods for two-dimensional face recognition. Our approaches are based on facial feature points detection then compute the Euclidean Distance between all pairs of this points for a first method (ED-FFP) and Geodesic Distance in the second approach (GD-FFP). These measures are employed as inputs to a commonly used classification techniques such as...

In this paper, block distance matrices are introduced. Suppose F is a square block matrix in which each block is a symmetric matrix of some given order. If F is positive semidefinite, the block distance matrix D is defined as a matrix whose (i, j)-block is given by Dij = Fii+Fjj−2Fij . When each block in F is 1 × 1 (i.e., a real number), D is a usual Euclidean distance matrix. Many interesting ...

Because classical fast vector quantization(VQ) algorithms can't be used in the LSF vector quantizers that use varying weighted Euclidean distance, a novel fast VQ search algorithm —CRVQCS (Constrained Range Vector Quantization based on Component Searching) is presented in this paper. The CRVQ-CS algorithm works well with the varying weighted Euclidean distance and yields the same result as full...

This paper focuses on two main issues; first one is the impact of combination of multi-sensor images on the supervised learning classification accuracy using segment Fusion (SF). The second issue attempts to undertake the study of supervised machine learning classification technique of remote sensing images by using four classifiers like Parallelepiped (Pp), Mahalanobis Distance (MD), MaximumLi...

Recently, many scholars investigated interval, triangular, and trapezoidal approximations of fuzzy numbers. These researches can be grouped into two classes: the Euclidean distance class and the non-Euclidean distance class. Most approximations in the Euclidean distance class can be calculated by formulas, but calculating approximations in the other class is more complicated. In this paper, we ...

The ability to estimate distance and time to spatial goals is fundamental for survival. In cases where a region of space must be navigated around to reach a location (circumnavigation), the distance along the path is greater than the straight-line Euclidean distance. To explore how such circumnavigation impacts on estimates of distance and time, we tested participants on their ability to estima...