Fast Color Space Transformations Using Minimax Approximations

Color space transformations are frequently used in image processing, graphics, and visualization applications. In many cases, these transformations are complex nonlinear functions, which prohibits their use in time-critical applications. In this paper, we present a new approach called Minimax Approximations for Color-space Transformations (MACT).We demonstrate MACT on three commonly used color space transformations. Extensive experiments on a large and diverse image set and comparisons with well-known multidimensional lookup table interpolation methods show that MACT achieves an excellent balance among four criteria: ease of implementation, memory usage, accuracy, and computational speed

On Euclidean Norm Approximations

Euclidean norm calculations arise frequently in scientific and engineering applications. Several approximations for this norm with differing complexity and accuracy have been proposed in the literature. Earlier approaches were based on minimizing the maximum error. Recently, Seol and Cheun proposed an approximation based on minimizing the average error. In this paper, we first examine these approximations in detail, show that they fit into a single mathematical formulation, and compare their average and maximum errors. We then show that the maximum errors given by Seol and Cheun are significantly optimistic.Comment: 9 pages, 1 figure, Pattern Recognitio

Competition between species can drive public-goods cooperation within a species

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 40-43).Costly cooperative strategies are vulnerable to exploitation by cheats. Microbial studies have suggested that cooperation can be maintained in nature by mechanisms such as reciprocity, spatial structure and multi-level selection. So far, however, almost all laboratory experiments aimed at understanding cooperation have relied on studying a single species in isolation. In contrast, species in the wild live within complex communities where they interact with other species. Little effort has focused on understanding the effect of interspecies competition on the evolution of cooperation within a species. We test this relationship by using sucrose metabolism of budding yeast as a model cooperative system. We find that when co-cultured with a bacterial competitor, yeast populations become more cooperative compared to isolated populations. We show that this increase in cooperation within yeast is mainly driven by resource competition imposed by the bacterial competitor. A similar increase in cooperation is observed iby Hasan Celiker.S.M

Comments on "On Approximating Euclidean Metrics by Weighted t-Cost Distances in Arbitrary Dimension"

Mukherjee (Pattern Recognition Letters, vol. 32, pp. 824-831, 2011) recently introduced a class of distance functions called weighted t-cost distances that generalize m-neighbor, octagonal, and t-cost distances. He proved that weighted t-cost distances form a family of metrics and derived an approximation for the Euclidean norm in $\mathbb{Z}^n$. In this note we compare this approximation to two previously proposed Euclidean norm approximations and demonstrate that the empirical average errors given by Mukherjee are significantly optimistic in $\mathbb{R}^n$. We also propose a simple normalization scheme that improves the accuracy of his approximation substantially with respect to both average and maximum relative errors.Comment: 7 pages, 1 figure, 3 tables. arXiv admin note: substantial text overlap with arXiv:1008.487

Competition between species can stabilize public-goods cooperation within a species

Competition between species is a major ecological force that can drive evolution. Here, we test the effect of this force on the evolution of cooperation within a species. We use sucrose metabolism of budding yeast, Saccharomyces cerevisiae, as a model cooperative system that is subject to social parasitism by cheater strategies. We find that when cocultured with a bacterial competitor, Escherichia coli, the frequency of cooperator phenotypes in yeast populations increases dramatically as compared with isolated yeast populations. Bacterial competition stabilizes cooperation within yeast by limiting the yeast population density and also by depleting the public goods produced by cooperating yeast cells. Both of these changes induced by bacterial competition increase the cooperator frequency because cooperator yeast cells have a small preferential access to the public goods they produce; this preferential access becomes more important when the public good is scarce. Our results indicate that a thorough understanding of species interactions is crucial for explaining the maintenance and evolution of cooperation in nature.United States. National Institutes of Health (GM085279‐02)National Science Foundation (U.S.) (PHY‐1055154)Alfred P. Sloan Foundation (BR2011‐066

An Efficient Finite Element Method with Exponential Mesh Refinement for the Solution of the Allen-Cahn Equation in Non-Convex Polygons

In this paper we consider the numerical solution of the Allen-Cahn type diffuse interface model in a polygonal domain. The intersection of the interface with the re-entrant corners of the polygon causes strong corner singularities in the solution. To overcome the effect of these singularities on the accuracy of the approximate solution, for the spatial discretization we develop an efficient finite element method with exponential mesh refinement in the vicinity of the singular corners, that is based on (k−1)-th order Lagrange elements, k≥2 an integer. The problem is fully discretized by employing a first-order, semi-implicit time stepping scheme with the Invariant Energy Quadratization approach in time, which is an unconditionally energy stable method. It is shown that for the error between the exact and the approximate solution, an accuracy of O(hk+τ) is attained in the L2-norm for the number of O(h−2lnh−1) spatial elements, where h and τ are the mesh and time steps, respectively. The numerical results obtained support the analysis made.</p

A Highly-Accurate Finite Element Method with Exponentially Compressed Meshes for the Solution of the Dirichlet Problem of the generalized Helmholtz Equation with Corner Singularities

In this study, a highly-accurate, conforming finite element method is developed and justified for the solution of the Dirichlet problem of the generalized Helmholtz equation on domains with re-entrant corners. The k−th order Lagrange elements are used for the discretization of the variational form of the problem on exponentially compressed polar meshes employed in the neighbourhood of the corners whose interior angle is απ, α≠1∕2, and on the triangular and curved mesh formed in the remainder of the polygon. The exponentially compressed polar meshes are constructed such that they are transformed to square meshes using the Log-Polar transformation, simplifying the realization of the method significantly. For the error bound between the exact and the approximate solution obtained by the proposed method, an accuracy of O(h k),h mesh size and k≥1 an integer, is obtained in the H 1-norm. Numerical experiments are conducted to support the theoretical analysis made. The proposed method can be applied for dealing with the corner singularities of general nonlinear parabolic partial differential equations with semi-implicit time discretization. </p