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 set of weights from duality and gravity is presented, choosing the centroid weights to approximate normal vectors and estimate the principle curvatures, which will lead to a better estimation than the area-weights.
51 citations
TL;DR: In this article, the authors present an analysis of the Feynman path centroid density that provides new insight into the correspondence between the path integral and the Schrodinger formulations of statistical mechanics.
Abstract: We present an analysis of the Feynman path centroid density that provides new insight into the correspondence between the path integral and the Schr\"odinger formulations of statistical mechanics. The path centroid density is a central concept for several approximations (centroid molecular dynamics, quantum transition state theory, and pure quantum self-consistent harmonic approximation) that are used in path integral studies of thermodynamic and dynamical properties of quantum particles. The centroid density is related to the quasi-static response of the equilibrium system to an external force. The path centroid dispersion is the canonical correlation of the position operator, that measures the linear change in the mean position of a quantum particle upon the application of a constant external force. At low temperatures, this quantity provides an approximation to the excitation energy of the quantum system. In the zero temperature limit, the particle's probability density obtained by fixed centroid path integrals corresponds to the probability density of minimum energy wave packets, whose average energy define the Feynman effective classical potential.
51 citations
TL;DR: A fast centroid molecular dynamics methodology is proposed in which the effective centroid forces are predetermined through a force-matching algorithm applied to a standard path integral molecular dynamics simulation, which greatly reduces the computational cost of generating centroid trajectories, thus extending the applicability of CMD.
Abstract: A fast centroid molecular dynamics (CMD) methodology is proposed in which the effective centroid forces are predetermined through a force-matching algorithm applied to a standard path integral molecular dynamics simulation. The resulting method greatly reduces the computational cost of generating centroid trajectories, thus extending the applicability of CMD. The method is applied to the study of liquid para-hydrogen at two state points and liquid ortho-deuterium at one state point. The static and dynamical results are compared to those obtained from full adiabatic CMD simulations and found to be in excellent agreement for all three systems; the transport properties are also compared to experiment and found to have a similar level of agreement.
51 citations
TL;DR: Experiments demonstrate that the promise of DCore lies in its power to recognize extremely complex patterns and its high performance in real applications, for example, image segmentation and face clustering, regardless of the dimensionality of the space in which the data are embedded.
51 citations
05 Nov 2007
TL;DR: To address the same problem with an additional constraint that devices are required to be placed uniformly to average out the parasitic errors, a grid-based approach is proposed which is fast and promising, and has high scalability that even large data sets can be handled effectively.
Abstract: In order to reduce parasitic mismatch in analog circuits, some groups of devices are required to share a common centroid while being placed. Devices are split into smaller ones and placed with a common center point. We will address this problem of handling common centroid constraint in placement. A new representation called center-based corner block list (C-CBL) is proposed which is a natural extension of corner block list (CBL) [1] to represent a common centroid placement of a set of device pairs. C-CBL is complete and non-redundant in representing any common centroid mosaic packings with pairs of blocks to be matched. To address the same problem with an additional constraint that devices are required to be placed uniformly to average out the parasitic errors, a grid-based approach is proposed. Experimental results show that both approaches are fast and promising, and have high scalability that even large data sets can be handled effectively.
51 citations