The expander constructions based on algebraic methods can give expanders that are both explicit (i.e. we can quickly construct the graph, or even obtain neighborhood information without constructing the entire graph, and Ramanujan, meaning that the spectral gap is essentially as large as possible. It also follows from this spectral bound that the edge expansion of Ramanujan graphs is essentiall...

A hemagglutination-inhibitory mucoprotein from human urine has been studied with the electron microscope. It consists of filaments, with diameters of 40 to > 240 A, composed of smaller fibrils. In the two-dimensional projection of the electron micrographs, the single fibrils often show a zig-zag course with a periodicity of 100 to 140 A; the single branch of a zig-zag measures about 60 A in len...

Markov chain Monte Carlo methods provide an essential tool in statistics for sampling from complex probability distributions. While the standard approach to MCMC involves constructing discrete-time reversible Markov chains whose transition kernel is obtained via the Metropolis-Hastings algorithm, there has been recent interest in alternative schemes based on piecewise deterministic Markov proce...

Optical excitation of surface plasmons polaritons (SPPs) on a 'zig-zag diffraction grating' is explored. The fabricated silver grating consists of sub-wavelength grooves 'zig-zagged' along their length, providing a diffractive periodicity to visible radiation. SPPs propagating in the diffraction plane and scattered by an odd number of grating vectors are only excited by TE polarized radiation, ...

In this work, we present a comparison between two techniques of image compression. In the first case, the image is divided in blocks which are collected according to zig-zag scan. In the second one, we apply the Fast Cosine Transform to the image, and then the transformed image is divided in blocks which are collected according to zig-zag scan too. Later, in both cases, the Karhunen-Loève trans...

Abstract Simplicial presheaves on cartesian spaces provide a general notion of smooth spaces. There is corresponding version the singular complex functor, which maps to simplicial sets. We consider localisation (projective or injective) model category at morphisms become weak equivalences under functor. prove that this agrees with motivic-style $$\mathbb {R}$$ <mml:math xmlns:mml="http://www.w3...