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We show that the lines of every arrangement of n lines in the plane can be colored with O(root n/log n) colors such that no face of the arrangement is monochromatic. This improves a bound of Bose et al. by a circle minus(root/log n) factor. Any further imp ...
Many problems in combinatorial geometry can be formulated in terms of curves or surfaces containing many points of a cartesian product. In 2000, Elekes and Rónyai proved that if the graph of a polynomial f(x, y) contains cn2 points of an n × n × n cartesia ...
Perceptual learning is learning to see. For example in a bisection task, three parallel lines are presented with the central line slightly offset towards the right or the left outer line. Participants indicate the offset direction. Training gradually impro ...
In crowding, perception of a target is deteriorated by flanking elements. Crowding is usually explained by pooling models where target and flanker signals are averaged. We show here that crowding is rather determined by grouping and good Gestalt. We determ ...
Poincaré's uniformisation theorem says that any Riemann surface is conformally equivalent to a unique (up to isometry) surface of constant Gauss curvature 0, 1 or –1. The (topologically) richest of these three worlds is for curvature –1 formed of hyperboli ...
It is shown that the Euclidean group of translations, when treated as a Lie group, generates translations not only in Euclidean space but on any space, curved or not. Translations are then not necessarily vectors (straight lines); they can be any curve com ...
This paper presents a new framework for manifold learning based on a sequence of principal polynomials that capture the possibly nonlinear nature of the data. The proposed Principal Polynomial Analysis (PPA) generalizes PCA by modeling the directions of ma ...
Perceptual learning is learning to perceive. For example, in a bisection task three parallel lines are presented. The central line is slightly offset towards the right or the left outer line. Observers indicate the offset direction. Training greatly improv ...
Deltas are complex ecogeomorphic systems where features such as channels and interchannel islands are present over a wide range of spatial scales. A quantitative description of the morphology of deltas is fundamental to address how they react to changes in ...
We study the design of sampling trajectories for stable sampling and reconstruction of bandlimited spatial fields using mobile sensors. As a performance metric we use the path density of a set of sampling trajectories, defined as the total distance travele ...
