Lines Missing Every Random Point

We prove that there is, in every direction in Euclidean space, a line that misses every computably random point. We also prove that there exist, in every direction in Euclidean space, arbitrarily long line segments missing every double exponential time random point.Comment: Added a section: "Betting in Doubly Exponential Time.

Persistence of a particle in the Matheron-de Marsily velocity field

We show that the longitudinal position $x(t)$ of a particle in a $(d+1)$-dimensional layered random velocity field (the Matheron-de Marsily model) can be identified as a fractional Brownian motion (fBm) characterized by a variable Hurst exponent $H(d)=1-d/4$ for $d2$. The fBm becomes marginal at $d=2$. Moreover, using the known first-passage properties of fBm we prove analytically that the disorder averaged persistence (the probability of no zero crossing of the process $x(t)$ upto time $t$) has a power law decay for large $t$ with an exponent $\theta=d/4$ for $d<2$ and $\theta=1/2$ for $d\geq 2$ (with logarithmic correction at $d=2$), results that were earlier derived by Redner based on heuristic arguments and supported by numerical simulations (S. Redner, Phys. Rev. E {\bf 56}, 4967 (1997)).Comment: 4 pages Revtex, 1 .eps figure included, to appear in PRE Rapid Communicatio

The <i>Castalia</i> mission to Main Belt Comet 133P/Elst-Pizarro

We describe Castalia, a proposed mission to rendezvous with a Main Belt Comet (MBC), 133P/Elst-Pizarro. MBCs are a recently discovered population of apparently icy bodies within the main asteroid belt between Mars and Jupiter, which may represent the remnants of the population which supplied the early Earth with water. Castalia will perform the first exploration of this population by characterising 133P in detail, solving the puzzle of the MBC’s activity, and making the first in situ measurements of water in the asteroid belt. In many ways a successor to ESA’s highly successful Rosetta mission, Castalia will allow direct comparison between very different classes of comet, including measuring critical isotope ratios, plasma and dust properties. It will also feature the first radar system to visit a minor body, mapping the ice in the interior. Castalia was proposed, in slightly different versions, to the ESA M4 and M5 calls within the Cosmic Vision programme. We describe the science motivation for the mission, the measurements required to achieve the scientific goals, and the proposed instrument payload and spacecraft to achieve these

Recent studies on radiation induced F-center and colloid particle formation in synthetic NaCl and natural rock salt

Radiation induced F-center and Na metal colloid formation have been studied, at temperatures between 100 and 350/sup 0/C, in melt growth synthetic NaCl crystals and natural rock salt samples, using equipment for making optical measurements during 1 to 3 MeV electron irradiation. In both types of NaCl the damage formation kinetics are qualitatively similar. However, there are large quantitative differences which depend on irradiation temperature, dose rate, total dose, inherent strain, strain applied prior to irradiation and other factors. Natural rock salt samples from different localities exhibit markedly different radiation induced colloid formation rates. An extrapolation of the current data to the doses expected in radioactive waste depositories indicate that natural salt immediately adjacent to the planned waste canisters could develop between 0.1 and 50% colloidal sodium in 40 to 1000 years. 3 figures

The financial imperative of physicians to control demand of laboratory testing

It is an integral component of doctor s duty of care to understand the significant impact laboratory testing has on the expense and ultimate quality of healthcare patients receive, yet the costs of these tests are poorly perceived. Utilising semi-structured interviews and questionnaires, we assessed surgeons perceived costs of two commonly encountered clinical scenarios requiring out of hours laboratory testing. Of the 35 participants only 23.3% (n=7) accurately estimated the overall cost. The most expensive test was Type and Screen at 83, with 77.3% (n=17) underestimating the cost. Non-consultant hospital doctors qualified for 3 years were more likely to underestimate on-call costs (p=0.042). It is of utmost importance to improve the knowledge of all surgeons of the financial implications of investigations. Through education we can potentially reduce un-warranted costs and fulfil our duty of care in the most cost efficient manner

Exploring High-Order Functional Interactions via Structurally-Weighted LASSO Models

Abstract. A major objective of brain science research is to model and quantify functional interaction patterns among neural networks, in the sense that meaningful interaction patterns reflect the working mechanisms of neural systems and represent their relationships with the external world. Most current research approaches in the neuroimaging field, however, focus on pair-wise functional/effective connectivity and are thus unable to handle high-order, network-scale functional interactions. In this paper, we propose a novel structurally-weighted LASSO (SW-LASSO) regression model to represent the functional interaction among multiple regions of interests (ROIs) based on resting state fMRI (rsfMRI) data. In particular, the structural connectivity constraints derived from diffusion tenor imaging (DTI) data are used to guide the selection of the weights, thus adaptively adjusting the penalty levels of different coefficients which correspond to different ROIs. The robustness and accuracy of our models are evaluated and demonstrated via a series of carefully designed experiments. In an application example, the generated regression graphs show different assortative mixing patterns between Mild Cognitive Impairment (MCI) patients and normal controls (NC). Our results indicate that the proposed model has promising potential to enable the construction of highorder functional networks and their applications in clinical datasets