General Position Subsets and Independent Hyperplanes in d-Space

Erd\H{o}s asked what is the maximum number $\alpha(n)$ such that every set of $n$ points in the plane with no four on a line contains $\alpha(n)$ points in general position. We consider variants of this question for $d$-dimensional point sets and generalize previously known bounds. In particular, we prove the following two results for fixed $d$: - Every set $H$ of $n$ hyperplanes in $\mathbb{R}^d$ contains a subset $S\subseteq H$ of size at least $c \left(n \log n\right)^{1/d}$, for some constant $c=c(d)>0$, such that no cell of the arrangement of $H$ is bounded by hyperplanes of $S$ only. - Every set of $cq^d\log q$ points in $\mathbb{R}^d$, for some constant $c=c(d)>0$, contains a subset of $q$ cohyperplanar points or $q$ points in general position. Two-dimensional versions of the above results were respectively proved by Ackerman et al. [Electronic J. Combinatorics, 2014] and by Payne and Wood [SIAM J. Discrete Math., 2013].Comment: 8 page

Improving Rasterization Using Distributed Archetypes

Recent advances in cacheable models and psychoacoustic algorithms have paved the way for redundancy. After years of technical research into agents, we disconfirm the construction of consistent hashing. Our focus in this paper is not on whether the little-known introspec- tive algorithm for the visualization of redun- dancy by Martinez is recursively enumerable, but rather on proposing an analysis of Internet QoS (Tivoli)

Postirradiation behavior of p-channel charge-coupled devices irradiated at 153 K

The displacement damage hardness that can be achieved using p-channel charge-coupled devices (CCD) was originally demonstrated in 1997, and since then a number of other studies have demonstrated an improved tolerance to radiation-induced CTI when compared to n-channel CCDs. A number of recent studies have also shown that the temperature history of the device after the irradiation impacts the performance of the detector, linked to the mobility of defects at different temperatures. This study describes the initial results from an e2v technologies p-channel CCD204 irradiated at 153 K with a 10 MeV equivalent proton fluences of 1.24×109 and 1.24×1011 protons cm-2. The dark current, cosmetic quality and the number of defects identified using trap pumping immediately were monitored after the irradiation for a period of 150 hours with the device held at 153 K and then after different periods of time at room temperature. The device also exhibited a flatband voltage shift of around 30 mV / krad, determined by the reduction in full well capacity

Temporal changes in gamma dose rates in the Esk Estuary, UK

Over the last 30 years there has been a reduction in the radioactive discharges from the UK's Sellafield site. Radionuclide activity concentrations in the environment around Sellafield have declined as a result. However, routine monitoring results from the nearby Esk Estuary show a less clear trend, with fluctuations in gamma dose rate measurements being reported from year to year. A comprehensive survey (n = 576) of gamma dose rates in the Esk Estuary was undertaken in 2007 and the data compared to a similar survey carried out in 1989. There was a highly statistically significant decrease in the external gamma dose rates within the Esk Estuary between 1989 and 2007. The measured total gamma dose rate range in 2007 was 0.064 - 0.235 μGy h-1with a mean of 0.123 μGy h-1. This equates to a maximum exposure of 0.200 μSv h-1. There was no evidence of large-scale sediment redistribution under current conditions. However, there was limited evidence to suggest that part of the reason for the reduction in measured dose rates was the burial of contaminated sediment deposits by uncontaminated sediments transported by tidal processes

Proximity Drawings of High-Degree Trees

A drawing of a given (abstract) tree that is a minimum spanning tree of the vertex set is considered aesthetically pleasing. However, such a drawing can only exist if the tree has maximum degree at most 6. What can be said for trees of higher degree? We approach this question by supposing that a partition or covering of the tree by subtrees of bounded degree is given. Then we show that if the partition or covering satisfies some natural properties, then there is a drawing of the entire tree such that each of the given subtrees is drawn as a minimum spanning tree of its vertex set

A heuristic for the distribution of point counts for random curves over a finite field

How many rational points are there on a random algebraic curve of large genus $g$ over a given finite field $\mathbb{F}_q$? We propose a heuristic for this question motivated by a (now proven) conjecture of Mumford on the cohomology of moduli spaces of curves; this heuristic suggests a Poisson distribution with mean $q+1+1/(q-1)$. We prove a weaker version of this statement in which $g$ and $q$ tend to infinity, with $q$ much larger than $g$.Comment: 16 pages; v2: refereed version, Philosophical Transactions of the Royal Society A 201

Measuring Value in Mediation: A Case Study of Workplace Mediation in City Government

Published in cooperation with the American Bar Association Section of Dispute Resolutio