This paper is about two arrangements of hyperplanes. The first — the Shi arrangement — was introduced by Jian-Yi Shi to describe the Kazhdan-Lusztig cells in the affine Weyl group of type A. The second — the Ish arrangement — was recently defined by the first author who used the two arrangements together to give a new interpretation of the q, t-Catalan numbers of Garsia and Haiman. In the prese...

Cyanidium caldarium wild type and III-C mutant lacking phycobilisomes were compared with respect to the ultrastructural organization of particles on the freeze-fractured thylakoid membrane.In the wild type, the particles on the exoplasmic fracture face were arranged in the same manner as that reported for the phycobilisomes on the membrane surface. The phycobilisomes constitute the major part o...

Low-angle X-ray diffraction patterns were obtained from ordered ultracentrifugal pellets of zoet receptor disk membranes which had been either treated with antirhodopsin serum, normal rabbit serum, serum albumin, or untreated prior to sedimentation. A preliminary analysis of these patterns indicated: (a) differences between antirhodopsin serum treated and untreated preparations are due to conju...

In order to study the growth of heterogeneity in granular systems, we investigate the quasi-static deformation of monodisperse particle systems with regular initial arrangements. We construct a linearized model by limiting our consideration to infinitesimal deformations. Assuming Coulomb friction, we introduce new variables to express the slippage distances of particles in contact. The results ...

An optical trapping system with a single-mode lensed fiber probe inserted at an angle is built; this system is simpler and more flexible than conventional optical tweezers. Two lasers, with 632.8- and 1550-nm wavelengths, are employed to trap and manipulate yeast cells and polystyrene microspheres. Nine yeast cells are manipulated to form a letter "T." Finally, the manipulation performed with v...

The ultrastructure of photoreceptor cells of the crayfish (P. clarkii) has been examined by means of thin sections and freeze-fracturing. The study reveals that in the photoreceptor membranes there are particles associated primarily with the A faces of freeze-fracture preparations which have a mean diameter of 80-84 A and a density of 6,600 per per micrometer2. Treatment of the retina with digi...

We study an elementary problem of the topological robotics: collective motion of a set of n distinct particles which one has to move from an initial configuration to a final configuration, with the requirement that no collisions occur in the process of motion. The ultimate goal is to construct an algorithm which will perform this task once the initial and the final configurations are given. Thi...