Local resilience for squares of almost spanning cycles in sparse random graphs

In 1962, P\'osa conjectured that a graph $G=(V, E)$ contains a square of a Hamiltonian cycle if $\delta(G)\ge 2n/3$. Only more than thirty years later Koml\'os, S\'ark\H{o}zy, and Szemer\'edi proved this conjecture using the so-called Blow-Up Lemma. Here we extend their result to a random graph setting. We show that for every $\epsilon > 0$ and $p=n^{-1/2+\epsilon}$ a.a.s. every subgraph of $G_{n,p}$ with minimum degree at least $(2/3+\epsilon)np$ contains the square of a cycle on $(1-o(1))n$ vertices. This is almost best possible in three ways: (1) for $p\ll n^{-1/2}$ the random graph will not contain any square of a long cycle (2) one cannot hope for a resilience version for the square of a spanning cycle (as deleting all edges in the neighborhood of single vertex destroys this property) and (3) for $c<2/3$ a.a.s. $G_{n,p}$ contains a subgraph with minimum degree at least $cnp$ which does not contain the square of a path on $(1/3+c)n$ vertices

The rotating spectrometer: New biotechnology for cell separations

An instrument for biochemical studies, called the rotating spectrometer, separates previously inseparable cell cultures. The rotating spectrometer is intended for use in pharmacological studies which require fractional splitting of heterogeneous cell cultures based on cell morphology and swimming behavior. As a method to separate and concentrate cells in free solution, the rotating method requires active organism participation and can effectively split the large class of organisms known to form spontaneous patterns. Examples include the biochemical star, an organism called Tetrahymena pyriformis. Following focusing in a rotated frame, the separation is accomplished using different radial dependencies of concentrated algal and protozoan species. The focusing itself appears as concentric rings and arises from the coupling between swimming direction and Coriolis forces. A dense cut is taken at varying radii and extraction is replenished at an inlet. Unlike standard separation and concentrating techniques such as filtration or centrifugation, the instrument is able to separate motile from immotile fractions. For a single pass, typical split efficiencies can reach 200 to 300 percent compared to the inlet concentration

A biosensor for cadmium based on bioconvective patterns

An 'in vitro' method for monitoring cadmium, one of the most lethal bivalent heavy metals, can detect biologically active levels. The effects of cadmium tend to concentrate in protozoa far above natural levels and therein begin transferring through freshwater food chains to animals and humans. In a small sample volume (approximately 5 ml) the method uses the toxic response to the protozoa, Tetrahymena pyriformis, to cadmium. The assay relies on macroscopic bioconvective patterns to measure the toxic response, giving a sensitivity better than 1 micro-g/1 and a toxicity threshold to 7 micro-g/1 for Cd(2+). Cadmium hinders pattern formation in a dose-dependent manner. Arrested organism growth arises from slowed division and mutation to non-dividing classes. Unlike previous efforts, this method can be performed in a shallow flow device and does not require electronic or chemical analyses to monitor toxicity

A proposed non-intrusive method for finding coefficients of slip and molecular reflectivity in microgravity

A proposed experimental program to look at a series of vapor transport properties measured along solid and liquid surfaces is described. The research objectives proposed are: (1) with accuracy otherwise unobtainable on ground, to determine the coefficient of slip measured between gases and the surfaces of liquids and solids; (2) for the first time, to classify and tabulate dominant surface effects found for a variety of solids, particularly those crystalized by vapor transport; and (3) to extend understanding of settling rates predicted for cosmic dust and condensed vapor falling through planetary atmospheres. The method used to obtain these objectives, has aided, to an order of magnitude, understanding of various liquid-gas interfaces such as oil and water. But to date, no similar characterization has proved successful for solids or liquids of uncertain densities. Likewise, no data exist in either ground-based research or as part of a microgravity program that, when collected with the high accuracy expected in low gravity, could definitely settle outstanding questions in kinetic theory, molecular dynamics, and cosmic physics