In the sequel, we outline necessary and sufficient condition to existence of extremas a function on self-similar set, describe discrete gradient algorithm find extrema.

We measure the statistical distribution of the local density of optical states (LDOS) on disordered semicontinuous metal films. We show that LDOS fluctuations exhibit a maximum in a regime where fractal clusters dominate the film surface. These large fluctuations are a signature of surface-plasmon localization on the nanometer scale.

Many children fail to master fraction arithmetic even after years of instruction, a failure that hinders their learning of more advanced mathematics as well as their occupational success. To test hypotheses about why children have so many difficulties in this area, we created a computational model of fraction arithmetic learning and presented it with the problems from a widely used textbook ser...

Because the time to respond to a stimulus depend markedly on expectation, measurements of reaction time can, conversely, provide information about the brain's estimate of the probability of a stimulus. Previous studies have shown that the quantitative relationship between reaction time and static, long-term expectation or prior probability can be explained economically by the LATER model of dec...

The 3D structure of randomly polarized light fields is exemplified by its polarization singularities: lines along which the polarization is purely circular (C lines) and surfaces on which the polarization is linear (L surfaces). We visualize these polarization singularities experimentally in vector laser speckle fields, and in numerical simulations of random wave superpositions. Our results con...

Zipf's law is the most common statistical distribution displaying scaling behavior. Cities, populations or firms are just examples of this seemingly universal law. Although many different models have been proposed, no general theoretical explanation has been shown to exist for its universality. Here, we show that Zipf's law is, in fact, an inevitable outcome of a very general class of stochasti...

, i.e. just above the dissociation threshold, was carefully examined. Rotational distribution observed was compared with statistical one calculated by phase space theory. Two distinct types of rotational distributions were found; one of them exhibits non-statistical distribution while the other is statistical one expected by phase space theory. In the case that a vibronic energy of the initial ...

In this paper, we propose a technique for segmenting visual textures using features extracted from the reponses of Ga,bor filters, appropria.tely selec tecl to be tuned to texture components of the input image. In the proposed method segmentation is achieved by detecting boundaries between adjacent textured regions, and this segmentation algorithm works as follows. The input image is first filt...

The paper describes a fast system for appearance based image recognition . It uses local invariant descriptors and efficient nearest neighbor search. First, local affine invariant regions are found nested at multiscale intensity extremas. These regions are characterized by nine generalized color moment invariants. An efficient novel method called HPAT (hyper-polyhedron with adaptive threshold) ...