Counting faces of randomly-projected polytopes when the projection radically lowers dimension

This paper develops asymptotic methods to count faces of random high-dimensional polytopes. Beyond its intrinsic interest, our conclusions have surprising implications - in statistics, probability, information theory, and signal processing - with potential impacts in practical subjects like medical imaging and digital communications. Three such implications concern: convex hulls of Gaussian point clouds, signal recovery from random projections, and how many gross errors can be efficiently corrected from Gaussian error correcting codes.Comment: 56 page

Quantum search algorithms on a regular lattice

Quantum algorithms for searching one or more marked items on a d-dimensional lattice provide an extension of Grover's search algorithm including a spatial component. We demonstrate that these lattice search algorithms can be viewed in terms of the level dynamics near an avoided crossing of a one-parameter family of quantum random walks. We give approximations for both the level-splitting at the avoided crossing and the effectively two-dimensional subspace of the full Hilbert space spanning the level crossing. This makes it possible to give the leading order behaviour for the search time and the localisation probability in the limit of large lattice size including the leading order coefficients. For d=2 and d=3, these coefficients are calculated explicitly. Closed form expressions are given for higher dimensions

A circumferentially flanged tibial tray minimizes bone-tray shear micromotion

Aseptic loosening of the tibial component is the major complication of total knee arthroplasty. There is an association between early excessive shear micromotion between the bone and the tray of the tibial component and late aseptic loosening. Using non-linear finite element analysis, whether a tibial tray with a circumferentially flanged rim and a mating cut in the proximal tibia could minimize bone-tray shear micromotion was considered. fifteen competing tray designs with various degrees of flange curvature were assessed with the aim of minimizing bone-tray shear micromotion. A trade-off was found between reducing micromotion and increasing peripheral cancellous bone stresses. It was found that, within the limitations of the study, there was a theoretical design that could virtually eliminate micromotion due to axial loads, with minimal bone removal and without the use of screws or pegs

Temperature distribution in an aircraft tire at low ground speeds

An experimental study was conducted to define temperature profiles of 22 x 5.5, type 7, bias ply aircraft tires subjected to freely rolling, yawed rolling, and light braking conditions. Temperatures along the inner wall of freely rolling tires were greater than those near the outer surface. The effect of increasing tire deflection was to increase the temperature within the shoulder and sidewall areas of the tire carcass. The effect of cornering and braking was to increase the treat temperature. For taxi operations at fixed yaw angles, temperature profiles were not symmetric. Increasing the ground speed produced only moderate increases in tread temperature, whereas temperatures in the carcass shoulder and sidewall were essentially unaffected

Maintenance and degradation of proteins in intact and severed axons: Implications for the mechanism of long-term survival of anucleate crayfish axons

Protein maintenance and degradation are examined in the severed distal (anucleate) portions of crayfish medial giant axons (MGAs), which remain viable for over 7 months following axotomy. On polyacrylamide gels, the silver-stained protein banding pattern of anucleate MGAs severed from their cell bodies for up to 4 months remains remarkably similar to that of intact MGAs. At 7 months postseverance, some (but not all) proteins are decreased in anucleate MGAs compared to intact MGAs. To determine the half-life of axonally transported proteins, we radiolabeled MGA cell bodies and monitored the degradation of newly synthesized transported proteins. Assuming exponential decay, proteins in the fast component of axonal transport have an average half-life of 14 d in anucleate MGAs and proteins in the slow component have an average half-life of 17 d. Such half-lives are very unlikely to account for the ability of anucleate MGAs to survive for over 7 months after axotomy.This work was supported by an ATP grant to G.D.B.Neuroscienc

Investigation of a Method for Extraction of Indium from Zinc Flue Dust.

In metallurgical practice today some of the relatively rare metal Indium is recovered as a by-product from the ores of other metals. Indium is a soft, silvery—white metal belonging to the third group of the periodic classification. It is situated just above tin in the electrochemical series