Topic
Centroid
About: Centroid is a research topic. Over the lifetime, 4110 publications have been published within this topic receiving 53637 citations. The topic is also known as: barycenter (geometry) & geometric center of a plane figure.
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TL;DR: A new shape descriptor is presented, which is based on the centroid–radii model and the Haar wavelet transform, which can achieve more accurate shape feature and implement more efficient retrieval under multi-resolution.
22 citations
22 citations
TL;DR: It is proved that all the considered problems are strongly NP-hard and that, in general, there is no fully polynomial-time approximation scheme for them (unless P = NP).
Abstract: Some problems of partitioning a finite set of points of Euclidean space into two clusters are considered. In these problems, the following criteria are minimized: (1) the sum over both clusters of the sums of squared pairwise distances between the elements of the cluster and (2) the sum of the (multiplied by the cardinalities of the clusters) sums of squared distances from the elements of the cluster to its geometric center, where the geometric center (or centroid) of a cluster is defined as the mean value of the elements in that cluster. Additionally, another problem close to (2) is considered, where the desired center of one of the clusters is given as input, while the center of the other cluster is unknown (is the variable to be optimized) as in problem (2). Two variants of the problems are analyzed, in which the cardinalities of the clusters are (1) parts of the input or (2) optimization variables. It is proved that all the considered problems are strongly NP-hard and that, in general, there is no fully polynomial-time approximation scheme for them (unless P = NP).
22 citations
TL;DR: Nonlinear quantum correlation functions in the high and low temperature regimes computed for model potentials are in remarkably good agreement with the corresponding exact results, suggesting that the method represents an effective and accurate approach for the investigation of general quantum time correlated functions in systems with many degrees of freedom.
Abstract: A new approach for the calculation of nonlinear quantum time correlation functions within the path-integral centroid dynamics formalism is presented. This approach combines information on the real-time dynamics obtained from centroid molecular dynamics with classical operators with information on the corresponding imaginary-time dynamics obtained from path-integral molecular dynamics. Nonlinear quantum correlation functions in the high and low temperature regimes computed for model potentials are in remarkably good agreement with the corresponding exact results, suggesting that the method represents an effective and accurate approach for the investigation of general quantum time correlation functions in systems with many degrees of freedom.
22 citations
TL;DR: A ranking method for ordering fuzzy numbers based on area, mode, spreads and weights of generalized fuzzy numbers is described, which can rank various types of fuzzy numbers and also crisp numbers which are considered to be a special case of fuzzyNumbers.
Abstract: This paper describes a ranking method for ordering fuzzy numbers based on area, mode, spreads and weights of generalized fuzzy numbers. The area used in this method is obtained from the generalized trapezoidal fuzzy number, first by splitting the generalized trapezoidal fuzzy numbers into three plane figures and then calculating the centroids of each plane figure followed by the centroid of these centroids and then finding the area of this centroid from origin which is a process of defuzzification proposed in this paper. This method is simple in evaluation and can rank various types of fuzzy numbers and also crisp numbers which are considered to be a special case of fuzzy numbers.
22 citations