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Continuous Symmetry Measures
"... We advance the notion that for many realistic issues involving symmetry in chemistry, it is more natural to analyse symmetry properties in terms of a continuous scale rather than in terms of "yes or no". Justification of that approach is dealt with at some detail using examples such as: sy ..."
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Cited by 27 (5 self)
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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
Extensions and Foundations of the Continuous Symmetry Measure
, 2008
"... 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 of fi ..."
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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
Closedform solution of absolute orientation using unit quaternions
 J. Opt. Soc. Am. A
, 1987
"... 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 closedform solution to the leastsquares pr ..."
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Cited by 989 (4 self)
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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 closedform solution to the least
EndtoEnd Routing Behavior in the Internet
, 1996
"... The largescale 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 endtoend route measurements conducted using repeated “traceroutes” ..."
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Cited by 655 (13 self)
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The largescale 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 endtoend route measurements conducted using repeated “traceroutes
Features of similarity.
 Psychological Review
, 1977
"... Similarity plays a fundamental role in theories of knowledge and behavior. It serves as an organizing principle by which individuals classify objects, form concepts, and make generalizations. Indeed, the concept of similarity is ubiquitous in psychological theory. It underlies the accounts of stimu ..."
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Cited by 1455 (2 self)
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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
Continuous Symmetry Measures, IV: Chirality
"... 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) mole ..."
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Cited by 4 (2 self)
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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
Continuous Symmetry Measures, II: Symmetry Groups and the Tetrahedron
, 1993
"... 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, 78447851 (1992)) to any symmetry group in two and three dimensions. Using the Continuous Symmetry Measure (CSM ..."
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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, 78447851 (1992)) to any symmetry group in two and three dimensions. Using the Continuous Symmetry Measure
Sharpening Geometric Inequalities using Computable Symmetry Measures
, 2014
"... 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 by the dimen ..."
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Cited by 1 (1 self)
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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
Similarity and Symmetry Measures for Convex Shapes Using Minkowski Addition
, 1997
"... This paper is devoted to similarity and symmetry measures for convex shapes whose definition is based on Minkowski addition and the BrunnMinkowski inequality. This means in particular that these measures are regionbased, in contrast to most of the literature, where one considers contourbased meas ..."
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Cited by 16 (0 self)
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This paper is devoted to similarity and symmetry measures for convex shapes whose definition is based on Minkowski addition and the BrunnMinkowski inequality. This means in particular that these measures are regionbased, in contrast to most of the literature, where one considers contour
FRACTAL DIMENSION AS A SYMMETRY MEASURE IN 3D BRAIN MRI ANALYSIS
"... 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 threedimensional (3D) brain magnetic resonance (MR) images. The m ..."
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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 threedimensional (3D) brain magnetic resonance (MR) images
Results 1  10
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