A Bichromatic Incidence Bound and an Application

We prove a new, tight upper bound on the number of incidences between points and hyperplanes in Euclidean d-space. Given n points, of which k are colored red, there are O_d(m^{2/3}k^{2/3}n^{(d-2)/3} + kn^{d-2} + m) incidences between the k red points and m hyperplanes spanned by all n points provided that m = \Omega(n^{d-2}). For the monochromatic case k = n, this was proved by Agarwal and Aronov. We use this incidence bound to prove that a set of n points, no more than n-k of which lie on any plane or two lines, spans \Omega(nk^2) planes. We also provide an infinite family of counterexamples to a conjecture of Purdy's on the number of hyperplanes spanned by a set of points in dimensions higher than 3, and present new conjectures not subject to the counterexample.Comment: 12 page

Obtaining wildlife values information for management: the wildlife attitudes and values scale (WAVS).

22 page

A guide to managing human activity on national wildlife refuges.

78 page

A performance evaluation of commercial fibrinogen reference preparations and assays for Clauss and PT-derived fibrinogen

The wide availability of fibrinogen estimations based on the prothrombin time (PT-Fg) has caused concern about the variability and clinical utility of fibrinogen assays. In a multi-centre study, we investigated fibrinogen assays using various reagents and analysers, Clauss assays generally gave good agreement, although one reagent gave 15-30% higher values in DIC and thrombolysis. Two commercial reference preparations had much lower potencies than the manufacturers declared, and plasma turbidity influenced parallelism in some Clauss assays, PT-Fg assays gave higher values than Clauss and showed calibrant dependent effects, the degree of disparity correlating with calibrant and test sample turbidity. Analyser and thromboplastin dependent differences were noted. The relationship between Clauss and PT-Fg assays was sigmoid, and the plateau of maximal PT-Fg differed by about 2 g/l between reagents. ELISA and immunonephelometric assays correlated well, but with a high degree of scatter. Antigen levels were higher than Clauss, but slightly lower than PT-Fg assays, which appeared to be influenced by degraded fibrinogen. Clauss assays are generally reproducible between centres, analysers and reagents, but PT-Fg assays are not reliable in clinical settings

Tensile strained InxGa1−xPIn_{x}Ga_{1-x}P membranes for cavity optomechanics

We investigate the optomechanical properties of tensile-strained ternary InGaP nanomembranes grown on GaAs. This material system combines the benefits of highly strained membranes based on stoichiometric silicon nitride, with the unique properties of thin-film semiconductor single crystals, as previously demonstrated with suspended GaAs. Here we employ lattice mismatch in epitaxial growth to impart an intrinsic tensile strain to a monocrystalline thin film (approximately 30 nm thick). These structures exhibit mechanical quality factors of 2*10^6 or beyond at room temperature and 17 K for eigenfrequencies up to 1 MHz, yielding Q*f products of 2*10^12 Hz for a tensile stress of ~170 MPa. Incorporating such membranes in a high finesse Fabry-Perot cavity, we extract an upper limit to the total optical loss (including both absorption and scatter) of 40 ppm at 1064 nm and room temperature. Further reductions of the In content of this alloy will enable tensile stress levels of 1 GPa, with the potential for a significant increase in the Q*f product, assuming no deterioration in the mechanical loss at this composition and strain level. This materials system is a promising candidate for the integration of strained semiconductor membrane structures with low-loss semiconductor mirrors and for realizing stacks of membranes for enhanced optomechanical coupling.Comment: 10 pages, 3 figure

Lines, Circles, Planes and Spheres

Let $S$ be a set of $n$ points in $\mathbb{R}^3$, no three collinear and not all coplanar. If at most $n-k$ are coplanar and $n$ is sufficiently large, the total number of planes determined is at least $1 + k \binom{n-k}{2}-\binom{k}{2}(\frac{n-k}{2})$. For similar conditions and sufficiently large $n$, (inspired by the work of P. D. T. A. Elliott in \cite{Ell67}) we also show that the number of spheres determined by $n$ points is at least $1+\binom{n-1}{3}-t_3^{orchard}(n-1)$, and this bound is best possible under its hypothesis. (By $t_3^{orchard}(n)$, we are denoting the maximum number of three-point lines attainable by a configuration of $n$ points, no four collinear, in the plane, i.e., the classic Orchard Problem.) New lower bounds are also given for both lines and circles.Comment: 37 page

A system of relational syllogistic incorporating full Boolean reasoning

We present a system of relational syllogistic, based on classical propositional logic, having primitives of the following form: Some A are R-related to some B; Some A are R-related to all B; All A are R-related to some B; All A are R-related to all B. Such primitives formalize sentences from natural language like `All students read some textbooks'. Here A and B denote arbitrary sets (of objects), and R denotes an arbitrary binary relation between objects. The language of the logic contains only variables denoting sets, determining the class of set terms, and variables denoting binary relations between objects, determining the class of relational terms. Both classes of terms are closed under the standard Boolean operations. The set of relational terms is also closed under taking the converse of a relation. The results of the paper are the completeness theorem with respect to the intended semantics and the computational complexity of the satisfiability problem.Comment: Available at http://link.springer.com/article/10.1007/s10849-012-9165-

Isotropic-nematic phase transition in suspensions of filamentous virus and the neutral polymer Dextran

We present an experimental study of the isotropic-nematic phase transition in an aqueous mixture of charged semi-flexible rods (fd virus) and neutral polymer (Dextran). A complete phase diagram is measured as a function of ionic strength and polymer molecular weight. At high ionic strength we find that adding polymer widens the isotropic-nematic coexistence region with polymers preferentially partitioning into the isotropic phase, while at low ionic strength the added polymer has no effect on the phase transition. The nematic order parameter is determined from birefringence measurements and is found to be independent of polymer concentration (or equivalently the strength of attraction). The experimental results are compared with the existing theoretical predictions for the isotropic-nematic transition in rods with attractive interactions.Comment: 8 Figures. To be published in Phys. Rev. E. For more information see http://www.elsie.brandeis.ed

Advanced composite rudders for DC-10 aircraft: Design, manufacturing, and ground tests

Design synthesis, tooling and process development, manufacturing, and ground testing of a graphite epoxy rudder for the DC-10 commercial transport are discussed. The composite structure was fabricated using a unique processing method in which the thermal expansion characteristics of rubber tooling mandrels were used to generate curing pressures during an oven cure cycle. The ground test program resulted in certification of the rudder for passenger-carrying flights. Results of the structural and environmental tests are interpreted and detailed development of the rubber tooling and manufacturing process is described. Processing, tooling, and manufacturing problems encountered during fabrication of four development rudders and ten flight-service rudders are discussed and the results of corrective actions are described. Non-recurring and recurring manufacturing labor man-hours are tabulated at the detailed operation level. A weight reduction of 13.58 kg (33 percent) was attained in the composite rudder

Nematic phase transitions in mixtures of thin and thick colloidal rods

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