of polymers and large random objects. A versatile, simple tool is developed as a continuous symmetry measure. Its main property is the ability to quantify the distance of a given (distorted molecular) shape from any chosen element of symmetry. The generality of this symmetry measure allows one to compare

A quantum mechanical extension of the continuous symmetry measures (CMS) proposed by Avnir et al. is described. The theoretical framework is essentially based in a simple extension of the HMO approach, leading to compute molecular CSM energy spectra, constituting a useful step for construction

Finding the relationship between two coordinate systems using pairs of measurements of the coordinates of a number of points in both systems is a classic photogrammetric task. It finds applications in stereophotogrammetry and in robotics. I present here a closed-form solution to the least

The large-scale behavior of routing in the Internet has gone virtually without any formal study, the exception being Chinoy's analysis of the dynamics of Internet routing information [Ch93]. We report on an analysis of 40,000 end-to-end route measurements conducted using repeated “traceroutes

nonnegative number, called their distance, in accord with the following three axioms: Minimality: dða; bÞ b dða; aÞ ¼ 0: Symmetry: dða; bÞ ¼ dðb; aÞ: The triangle inequality: dða; bÞ þ dðb; cÞ b dða; cÞ: To evaluate the adequacy of the geometric approach, let us examine the validity of the metric axioms when

We extend the treatment of symmetry as a continuous molecular structural property (J. Am. Chem. Soc. 1993, 115, 8278) to chirality. Rather than labeling objects as being either chiral or achiral, we provide an exact quantitative measure of this property, which allows one to distinguish (chiral

We treat symmetry as a continuous property rather than a discrete "yes or no" one. Here we generalize the approach developed for symmetry elements (Part I, J. Am. Chem. Soc. 114, 7844-7851 (1992)) to any symmetry group in two and three dimensions. Using the Continuous Symmetry Measure

Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the convex body. Since these coefficients are bounded

This paper is devoted to similarity and symmetry measures for convex shapes whose definition is based on Minkowski addition and the Brunn-Minkowski inequality. This means in particular that these measures are region-based, in contrast to most of the literature, where one considers contour

In brain image analysis, the automatic identification of symmetry plane has various applications. This paper presents a new method that uses the concept of fractal dimension as a quantitative measure for identifying symmetry plane in three-dimensional (3D) brain magnetic resonance (MR) images