Search results for "vector [correlation function]"

Validity of automated refraction after segmented refractive multifocal intraocular lens implantation

2017

Aim To evaluate the clinical utility of automated refraction (AR) and keratometry (KR) compared with subjective or manifest refraction (MR) after cataract or refractive lens exchange surgery with implantation of Lentis Mplus X (Oculentis GmbH) refractive multifocal intraocular lens (IOL). Methods Eighty-six eyes implanted with the Lentis Mplus X multifocal IOL were included. MR was performed in all patients followed by three consecutive AR measurements using the Topcon KR-8000 autorefractor. Assessment of repeatability of consecutive AR before and after dilation with phenylephrine 10%, and comparison of the AR and KR with MR using vector analysis were performed at 3mo follow-up. Results Ana…

Artificial Mosaics by Gradient Vector Flow

2008

Partial Data Problems and Unique Continuation in Scalar and Vector Field Tomography

2022

AbstractWe prove that if P(D) is some constant coefficient partial differential operator and f is a scalar field such that P(D)f vanishes in a given open set, then the integrals of f over all lines intersecting that open set determine the scalar field uniquely everywhere. This is done by proving a unique continuation property of fractional Laplacians which implies uniqueness for the partial data problem. We also apply our results to partial data problems of vector fields.

An explicit unconditionally stable numerical solution of the advection problem in irrotational flow fields

2004

[1] A new methodology for the Eulerian numerical solution of the advection problem is proposed. The methodology is based on the conservation of both the zero- and the first-order spatial moments inside each element of the computational domain and leads to the solution of several small systems of ordinary differential equations. Since the systems are solved sequentially (one element after the other), the method can be classified as explicit. The proposed methodology has the following properties: (1) it guarantees local and global mass conservation, (2) it is unconditionally stable, and (3) it applies second-order approximation of the concentration and its fluxes inside each element. Limitati…

Champs de vecteurs analytiques commutants, en dimension 3 ou 4: existence de zeros communs

1992

One proves the existence of a common zero for any two ℝ-analytic commuting vector fields on a 4-dimensional manifold with not zero Euler characteristic. A local version of this result remains true on 3-manifolds.

Two-phase routing in three-dimensional blocked optical tori

2014

The contribution of this paper is an all-optical 3D network architecture. We describe scheduled, two-phase routing for it. The three-dimensional blocked optical torus BOT of block size b consists of b2 × b2 × b2 nodes for the first phase routing. Processors are evenly deployed at the underlying torus so that every bth node consists of a processor. Additionally, a BOT consists of b3 blocks of b × b × b subnetworks for the second phase routing. Routing of each packet is done in two phases. Firstly, packets are routed from source processor to an intermediate target node at the target block. Secondly, packets are routed from the intermediate targets at the target block to the target processor (…

Visual understanding of divergence and curl: Visual cues promote better learning

2019

Prior research has shown that students struggle to indicate whether vector field plots have zero or non-zero curl or divergence. In an instruction-based eye-tracking study, we investigated whether visual cues (VC) provided in the vector field plot can foster students’ understanding of these concepts. The VC were only present during instruction and highlighted conceptual information about vector decomposition and partial derivatives. Thirty-two physics majors were assigned to two groups, one was instructed with VC about the problemsolving strategy, and one without. The results show that students in VC-condition performed better, responded with higher confidence, experienced less mental effor…

Assessing Transfer Entropy in cardiovascular and respiratory time series: A VARFI approach

2021

In the study of complex biomedical systems represented by multivariate stochastic processes, such as the cardiovascular and respiratory systems, an issue of great relevance is the description of the system dynamics spanning multiple temporal scales. Recently, the quantification of multiscale complexity based on linear parametric models, incorporating autoregressive coefficients and fractional integration, encompassing short term dynamics and long-range correlations, was extended to multivariate time series. Within this Vector AutoRegressive Fractionally Integrated (VARFI) framework formalized for Gaussian processes, in this work we propose to estimate the Transfer Entropy, or equivalently G…

Relationship between volume and energy of vector fields

2001

Abstract A unified study of energy and volume functionals is presented here by determining the critical points of a functional that extends simultaneously energy and volume and that is defined on the product of the manifold of smooth maps C∞(M,N) times the manifold M of riemannian metrics on M. The restriction of this functional to different submanifolds of the space of vector fields X (M)× M is also considered, and used to study several functionals generalizing volume and energy or total bending of vector fields