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.

A derivation of centroid molecular dynamics and other approximate time evolution methods for path integral centroid variables

Abstract: Several methods to approximately evolve path integral centroid variables in real time are presented in this paper, the first of which, the centroid molecular dynamics (CMD) method, is recast into the new formalism of the preceding paper and thereby derived. The approximations involved in the CMD method are thus fully characterized by mathematical derivations. Additional new approaches are also presented: centroid Hamiltonian dynamics (CHD), linearized quantum dynamics (LQD), and a perturbative correction of the LQD method (PT-LQD). The CHD method is shown to be a variation of the CMD method which conserves the approximate time dependent centroid Hamiltonian. The LQD method amounts to a linear approximation for the quantum Liouville equation, while the PT-LQD method includes a perturbative correction to the LQD method. All of these approaches are then tested for the equilibrium position correlation functions of three different one-dimensional nondissipative model systems, and it is shown that certain quant...

Orlicz centroid bodies

Abstract: The sharp affine isoperimetric inequality that bounds the volume of the centroid body of a star body (from below) by the volume of the star body itself is the Busemann-Petty centroid inequality. A decade ago, the $L_p$ analogue of the classical Busemann- Petty centroid inequality was proved. Here, the definition of the centroid body is extended to an Orlicz centroid body of a star body, and the corresponding analogue of the Busemann-Petty centroid inequality is established for convex bodies.

Comparison of centroid computation algorithms in a Shack–Hartmann sensor

Abstract: Analytical theory is combined with extensive numerical simulations to compare different flavours of centroiding algorithms: thresholding, weighted centroid, correlation, quad cell (QC). For each method, optimal parameters are defined in function of photon flux, readout noise and turbulence level. We find that at very low flux the noise of QC and weighted centroid leads the best result, but the latter method can provide linear and optimal response if the weight follows spot displacements. Both methods can work with average flux as low as 10 photons per subaperture under a readout noise of three electrons. At high-flux levels, the dominant errors come from non-linearity of response, from spot truncations and distortions and from detector pixel sampling. It is shown that at high flux, centre of gravity approaches and correlation methods are equivalent (and provide better results than QC estimator) as soon as their parameters are optimized. Finally, examples of applications are given to illustrate the results obtained in the paper.

A Generalized Sorting Strategy for Computer Classifications

Abstract: AGGLOMERATIVE hierarchical methods of computer classification all begin by calculating distance-measures between elements. The hierarchy is then generated by subjecting these measures to a sorting-strategy, which depends essentially on the definition of a distance-measure between groups of elements. In nearest-neighbour sorting, this is defined as the distance between the closest pair of elements, one in each group. Macnaughton-Smith has pointed out that much more intense clustering can be produced by taking the most remote pair of elements (furthest-neighbour sorting). In group-average sorting1 the distance is defined as the mean of all between-group inter-element distances; in centroid sorting it is the distance between group centroids, defined by a conventional Euclidean model. In median2 sorting the distance of a third group from two which have just fused depends on the previous three inter-group distances in the manner of Apollonius's theorem. Although the earlier of these strategies have received some comparative assessment1,3–5 no attempt seems to have been made to generalize them into a single system. As a result, quite different computer strategies have commonly been used, necessitating a separate computer program for each.

A Framework for Automatic Clustering of Parametric MIMO Channel Data Including Path Powers

Abstract: We present a solution to the problem of identifying clusters from MIMO measurement data in a data window, with a minimum of user interaction. Conventionally, visual inspection has been used for the cluster identification. However this approach is impractical for a large amount of measurement data. Moreover, visual methods lack an accurate definition of a "cluster" itself. We introduce a framework that is able to cluster multi-path components (MPCs), decide on the number of clusters, and discard outliers. For clustering we use the K-means algorithm, which iteratively moves a number of cluster centroids through the data space to minimize the total difference between MPCs and their closest centroid. We significantly improve this algorithm by following changes: (i) as the distance metric we use the multi- path component distance (MCD), (ii) the distances are weighted by the powers of the MPCs. The implications of these changes result in a definition of a "cluster" itself that appeals to intuition. We assess the performance of the new algorithm by clustering real-world measurement data from an indoor big hall environment.