Third‐order Cartesian overset mesh adaptation method for solving steady compressible flows

A third‐order mesh generation and adaptation method is presented for solving the steady compressible Euler equations. For interior points, a third‐order scheme is used on Cartesian and curvilinear meshes. Concerning the mesh adaptation, the method of Meakin is also extended to third order. The accuracy of the new overset mesh adaptation method is demonstrated by a grid convergence study for 2‐D inviscid model problems and results are compared with a second‐order method. Finally, the method is applied to the computation of an inviscid 3‐D flow around a hovering blade of the ONERA 7A helicopter rotor exhibiting an improvement in the wake capture. With a 7 million point mesh, the tip vortex can be followed for more than three rotor revolutions with the third‐order method. The CPU time needed for this calculation is only 3% higher than with a conventional second‐order method. Copyright © 2007 John Wiley & Sons, Ltd.     

An Integrated Circuit for Two-Dimensional Edge-Detection with Local Adaptation Based on Retinal Networks

We designed an integrated circuit for edge detection of a two-dimensional image based on the vertebrate outer retina, which has wide dynamic range in image processing. The unit circuit is simple, and operates as a current-mode analog metal-oxide-semiconductor (MOS) circuit. In order to extract edges from an image composed of bright and dark domains, the circuit realizes a function called local adaptation in which the sensitivity adapts to local brightness of the image. Simulation results, using the simulation program with integrated circuit emphasis (SPICE), of two-dimensional Gaussian-distributed images in which the intensity ranged over four orders of magnitude, showed the local adaptation. As a result, the intensity of output images was in the range of one order of magnitude. Furthermore, as the simulation result of real images, it was shown that edges in the dark domain, which was five times darker than the bright domain, were successfully detected as the bright domain in which input photocurrents ranged over two orders of magnitude.     

Color Appearance Explained,Predicted and Confirmed by the Concept of Recognized Visual Space of Illumination

Ten years have passed since we proposed a new concept called recognized visual space of illumination (RVSI). The central idea of the concept assumes that our brain first recognizes how a space is illuminated and then judges colors of anything seen in the space in relation to the RVSI constructed for the space. In another expression we say that the space is recognized first and the color perception next. In this paper some of our experiments that proved the appropriateness of the concept will be introduced. When a white paper was seen through a colored filter we could perceive the paper as white at the same instant we recognized a space through and beyond the filter. When an achromatic patch independent from the room illumination was observed under colored illumination its appearance immediately changed to that roughly opponent to the illumination color. When two gray patches of the same lightness were drawn in a picture of a white grating on a black background on a way that one appeared to locate on this side of the grating and the other in the other side, the former appeared brighter. These all confirmed the predictions based on the RVSI concept.     

A Network of Analog Metal Oxide Semiconductor Circuits for Motion Detection with Local Adaptation to a Background Image

Inspired by a mechanism of biological vision systems, a model and a network of analog metal oxide semiconductor (MOS) circuits are proposed which display an optical flow with local adaptation to the relative velocity of a background image. A function of displaying an optical flow successfully worked as a result of simulations using the simulation program with integrated circuit emphasis (SPICE). A function of varying an optical flow at a certain instant by local adaptation was also demonstrated. The proposed network is suitable for the realization of a large-scale integrated circuit (LSI), which displays an optical flow with local adaptation to the local velocity of a background.     

Color Discrimination Characteristics Depending on the Background Color in the (<Emphasis Type="Italic">L</Emphasis>, <Emphasis Type="Italic">M</Emphasis>) Plane of a Cone Space

We investigated color discriminability on the background color. The measurement was carried out at over 21 background colors in (L, M) plane of a cone space by four observers. We used low temporal stimulus frequency (1 Hz) so that threshold was determined by the red-green opponent mechanism. Results showed that color discriminability depends on the background colors. Threshold was higher with a more saturated background color. This suggests that the sensitivity of the red-green opponent mechanism is high when the mechanism’s output is small and increases with the output levels of the mechanism. To confirm this relationship between the red-green mechanism and color discriminability, color appearance depending the background color was also evaluated. There was a strong correlation between the sensitivity and the perceived whiteness. Both sensitivity and whiteness value were highest at around the equal energy white point and decreased with increase in the difference between background color and equal energy white. This suggests that the adaptation state of the red-green opponent color controls color discrimination.     

A posteriori error control for finite element approximations of elliptic eigenvalue problems

We develop a new approach to a posteriori error estimation for Galerkin finite element approximations of symmetric and nonsymmetric elliptic eigenvalue problems. The idea is to embed the eigenvalue approximation into the general framework of Galerkin methods for nonlinear variational equations. In this context residual-based a posteriori error representations are available with explicitly given remainder terms. The careful evaluation of these error representations for the concrete situation of an eigenvalue problem results in a posteriori error estimates for the approximations of eigenvalues as well as eigenfunctions. These suggest local error indicators that are used in the mesh refinement process.     

Adaptive, Restart, Randomized Greedy Heuristics for Maximum Clique

This paper presents some adaptive restart randomized greedy heuristics for MAXIMUM CLIQUE. The algorithms are based on improvements and variations of previously-studied algorithms by the authors. Three kinds of adaptation are studied: adaptation of the initial state (AI) given to the greedy heuristic, adaptation of vertex weights (AW) on the graph, and no adaptation (NA). Two kinds of initialization of the vertex-weights are investigated: unweighted initialization (w _i := 1) and degree-based initialization (w _i := d _i where d _i is the degree of vertex i in the graph). Experiments are conducted on several kinds of graphs (random, structured) with six combinations: {NA, AI, and AW} × {unweighted initialization, degree-based initialization. A seventh state of the art semi-greedy algorithm, DMclique, is evaluated as a benchmark algorithm. We concentrate on the problem of finding large cliques in large, dense graphs in a relatively short amount of time. We find that the different strategies produce different effects, and that different algorithms work best on different kinds of graphs.     

Minimization of the Truncation Error by Grid Adaptation

A new grid adaptation strategy, which minimizes the truncation error of a pth-order finite difference approximation, is proposed. The main idea of the method is based on the observation that the global truncation error associated with discretization on nonuniform meshes can be minimized if the interior grid points are redistributed in an optimal sequence. The method does not explicitly require the truncation error estimate, and at the same time, it allows one to increase the design order of approximation globally by one, so that the same finite difference operator reveals superconvergence properties on the optimal grid. Another very important characteristic of the method is that if the differential operator and the metric coefficients are evaluated identically by some hybrid approximation, then the single optimal grid generator can be employed in the entire computational domain independently of points where the hybrid discretization switches from one approximation to another. Generalization of the present method to multiple dimensions is presented. Numerical calculations of several one-dimensional and one two-dimensional test examples demonstrate the performance of the method and corroborate the theoretical results.     

Adaptive Free-Knot Splines

This article proposes a function estimation procedure using free-knot splines as well as an associated algorithm for implementation in nonparametric regression. In contrast to conventional splines with knots confined to distinct design points, the splines allow selection of knot numbers and replacement of knots at any location and repeated knots at the same location. This exibility leads to an adaptive spline estimator that adapts any function with inhomogeneous smoothness, including discontinuity, which substantially improves the representation power of splines. Due to uses of a large class of spline functions, knot selection becomes extremely important. The existing knot selection schemes—such as stepwise selection—suffer the difficulty of knot confounding and are unsuitable for our purpose. A new knot selection scheme is proposed using an evolutionary Monte Carlo algorithm and an adaptive model selection criterion. The evolutionary algorithm locates the optimal knots accurately, whereas the adaptive model selection strategy guards against the selection error in searching through a large candidate knot space. The performance of the procedure is examined and illustrated via simulations. The procedure provides a significant improvement in performance over the other competing adaptive methods proposed in the literature. Finally, usefulness of the procedure is illustrated by an application to actual dataset.     

A local pseudo arc-length method for hyperbolic conservation laws

A local pseudo arc-length method（LPALM）for solving hyperbolic conservation laws is presented in this paper.The key idea of this method comes from the original arc-length method,through which the critical points are bypassed by transforming the computational space.The method is based on local changes of physical variables to choose the discontinuous stencil and introduce the pseudo arc-length parameter,and then transform the governing equations from physical space to arc-length space.In order to solve these equations in arc-length coordinate,it is necessary to combine the velocity of mesh points in the moving mesh method,and then convert the physical variable in arclength space back to physical space.Numerical examples have proved the effectiveness and generality of the new approach for linear equation,nonlinear equation and system of equations with discontinuous initial values.Non-oscillation solution can be obtained by adjusting the parameter and the mesh refinement number for problems containing both shock and rarefaction waves.