White-headed Vultures Trigonoceps occipitalis show visual field characteristics of hunting raptors

The visual fields of Aegypiinae vultures have been shown to be adapted primarily to meet two key perceptual challenges of their obligate carrion-feeding behaviour: scanning the ground and preventing the sun’s image falling upon the retina. However, field observations have shown that foraging White-headed Vultures (Trigonoceps occipitalis) are not exclusively carrion-feeders; they are also facultative predators of live prey. Such feeding is likely to present perceptual challenges that are additional to those posed by carrion-feeding. Binocularity is the key component of all visual fields and in birds it is thought to function primarily in the accurate placement and time of contact of the talons and bill, especially in the location and seizure of food items. We determined visual fields in White-headed Vultures and two species of carrion-eating Gyps vultures, and show that the visual field of White-headed Vultures have more similarities with those of predatory raptors (e.g. Accipitrid hawks), compared with the taxonomically more closely related Gyps vultures. We found that maximum binocular field width in White-headed vultures (30°) is significantly wider than Gyps vultures (20°). The broader binocular fields in White-headed Vultures probably facilitate accurate placement and timing of the talons when capturing evasive live prey

Model-based learning of local image features for unsupervised texture segmentation

Features that capture well the textural patterns of a certain class of images are crucial for the performance of texture segmentation methods. The manual selection of features or designing new ones can be a tedious task. Therefore, it is desirable to automatically adapt the features to a certain image or class of images. Typically, this requires a large set of training images with similar textures and ground truth segmentation. In this work, we propose a framework to learn features for texture segmentation when no such training data is available. The cost function for our learning process is constructed to match a commonly used segmentation model, the piecewise constant Mumford-Shah model. This means that the features are learned such that they provide an approximately piecewise constant feature image with a small jump set. Based on this idea, we develop a two-stage algorithm which first learns suitable convolutional features and then performs a segmentation. We note that the features can be learned from a small set of images, from a single image, or even from image patches. The proposed method achieves a competitive rank in the Prague texture segmentation benchmark, and it is effective for segmenting histological images

On the representation of polyhedra by polynomial inequalities

A beautiful result of Br\"ocker and Scheiderer on the stability index of basic closed semi-algebraic sets implies, as a very special case, that every $d$-dimensional polyhedron admits a representation as the set of solutions of at most $d(d+1)/2$ polynomial inequalities. Even in this polyhedral case, however, no constructive proof is known, even if the quadratic upper bound is replaced by any bound depending only on the dimension. Here we give, for simple polytopes, an explicit construction of polynomials describing such a polytope. The number of used polynomials is exponential in the dimension, but in the 2- and 3-dimensional case we get the expected number $d(d+1)/2$.Comment: 19 pages, 4 figures; revised version with minor changes proposed by the referee

A theorem on the real part of the high-energy scattering amplitude near the forward direction

We show that if for fixed negative (physical) square of the momentum transfer t, the differential cross-section ${d\sigma\over dt}$ tends to zero and if the total cross-section tends to infinity, when the energy goes to infinity, the real part of the even signature amplitude cannot have a constant sign near t = 0.Comment: 7 pages, late