Counting Hamilton cycles in sparse random directed graphs

Let D(n,p) be the random directed graph on n vertices where each of the n(n-1) possible arcs is present independently with probability p. A celebrated result of Frieze shows that if $p\ge(\log n+\omega(1))/n$ then D(n,p) typically has a directed Hamilton cycle, and this is best possible. In this paper, we obtain a strengthening of this result, showing that under the same condition, the number of directed Hamilton cycles in D(n,p) is typically $n!(p(1+o(1)))^{n}$. We also prove a hitting-time version of this statement, showing that in the random directed graph process, as soon as every vertex has in-/out-degrees at least 1, there are typically $n!(\log n/n(1+o(1)))^{n}$ directed Hamilton cycles

Assigning channels via the meet-in-the-middle approach

We study the complexity of the Channel Assignment problem. By applying the meet-in-the-middle approach we get an algorithm for the $\ell$-bounded Channel Assignment (when the edge weights are bounded by $\ell$) running in time $O^*((2\sqrt{\ell+1})^n)$. This is the first algorithm which breaks the $(O(\ell))^n$ barrier. We extend this algorithm to the counting variant, at the cost of slightly higher polynomial factor. A major open problem asks whether Channel Assignment admits a $O(c^n)$-time algorithm, for a constant $c$ independent of $\ell$. We consider a similar question for Generalized T-Coloring, a CSP problem that generalizes \CA. We show that Generalized T-Coloring does not admit a $2^{2^{o\left(\sqrt{n}\right)}} {\rm poly}(r)$-time algorithm, where $r$ is the size of the instance.Comment: SWAT 2014: 282-29

Spacelab energetic ion mass spectrometer

Basic design criteria are given for an ion mass spectrometer for use in studying magnetospheric ion populations. The proposed instrument is composed of an electrostatic analyzer followed by a magnetic spectrometer and simultaneously measures the energy per unit and mass per unit charge of the ion species. An electromagnet is used for momentum analysis to extend the operational energy range over a much wider domain than is possible with the permanent magnets used in previous flights. The energetic ion source regions, ion energization mechanisms, field line tracing, coordinated investigations, and orbit considerations are discussed and operations of the momentum analyzer and of the electrostatic energy analyzer are examined

A study of omega bands and Ps6 pulsations on the ground, at low altitude and at geostationary orbit

We investigate the electrodynamic coupling between auroral omega bands and the inner magnetosphere. The goal of this study is to determine the features to which omega bands map in the magnetosphere. To establish the auroral-magnetosphere connection, we appeal to the case study analysis of the data rich event of September 26, 1989. At 6 magnetic local time (MLT), two trains of Ps6 pulsations (ground magnetic signatures of omega bands) were observed to drift over the Canadian Auroral Network For the OPEN Program Unified Study (CANOPUS) chain. At the same time periodic ionospheric flow patterns moved through the collocated Bistatic Auroral Radar System (BARS) field of view. Similar coincident magnetic variations were observed by GOES 6, GOES 7 and SCATHA, all of which had magnetic foot points near the CANOPUS/BARS stations. SCATHA, which was located at 6 MLT, 0.5 RE earthward of GOES 7 observed the 10 min period pulsations, whereas GOES 7 did not. In addition, DMSP F6 and F8 were over-flying the region and observed characteristic precipitation and flow signatures. From this fortunate constellation of ground and space observations, we conclude that auroral omega bands are the electrodynamic signature of a corrugated current sheet (or some similar spatially localized magnetic structure) in the near-Earth geostationary magnetosphere

Virus-mediated transient expression techniques enable gene function studies in black-grass

Even though considerable progress has been made in weed ecology, weed molecular biology has been hindered by an inability to genetically manipulate weeds. Genetic manipulation is essential to demonstrate a causative relationship between genotype and phenotype. Herein we demonstrate that virus-mediated transient expression techniques developed for other monocots can be used in black-grass (Alopecurus myosuroides) for loss- and gain-of-function studies. We not only use virus induced gene silencing (VIGS) to create the black-grass exhibiting reduced PHYTOENE DESATURASE expression and virus-mediated overexpression (VOX) to drive GREEN FLUORESCENT PROTEIN, we demonstrate these techniques are applicable to testing hypotheses related to herbicide resistance in black-grass. We use VIGS to demonstrate that AmGSTF1 is necessary for the resistant biotype Peldon to survive fenoxaprop application and show the heterologous expression of the bialaphos resistance gene with VOX is sufficient to confer resistance to an otherwise lethal dose of glufosinate. Black-grass is the most problematic weed for winter-cereal farmers in the UK and Western Europe as it has rapidly evolved adaptions that allow it to effectively avoid current integrated weed management practices. Black-grass also reduces yields and therefore directly threatens food security and productivity. Novel disruptive technologies which mitigate resistance evolution and enable better control over this pernicious weed are therefore required. These virus-mediated protocols offer a step change in our ability to alter genes of interest under controlled laboratory conditions and therefore to gain a molecular-level understanding of how black-grass can survive in the agri-environment

Executive functioning in preschool children: Performance on A-Not-B and other delayed response format tasks

The A-not-B (AB) task has been hypothesized to measure executive/frontal lobe function; however, the developmental and measurement characteristics of this task have not been investigated. The present study examined performance on AB and comparison tasks adapted from developmental and neuroscience literature in 117 1.9-5.5 yr old preschool children. Age significantly predicted performance on AB, Delayed Alternation, Spatial Reversal, Color Reversal, and Self-Control tasks. A 4-factor analytic model best fit task performance data. AB task indices loaded on 2 factors with measures from the Self-Control and Delayed Alternation tasks, respectively. AB indices did not load with those from the reversal tasks despite similarities in task administration and presumed cognitive demand (working memory). These results indicate that AB is sensitive to individual differences in age-related performance in preschool children and suggest that AB performance is related to both working memory and inhibition processes in this age range

Newly qualified physical education teachers’ experiences of developing subject knowledge prior to, during and after a Postgraduate Certificate in Education course

Office for Standards in Education (OFSTED) inspections of secondary Postgraduate Certificate in Education (PGCE) physical education courses in England between 1996 and 1998 (OFSTED, 1999) were critical of student teachers' subject knowledge. The purpose of this study was to investigate the development of subject knowledge and influences on the development of that subject knowledge in a sample of three newly qualified teachers (NQTs) who had completed a PGCE physical education course in England. The research comprised semi-structured interviews and analysis of documentation. Among these three NQTs there were some similarities, but more differences in terms of the development of subject knowledge as well as different influences on the development of subject knowledge. These results suggest that teacher educators may need to be flexible in how they approach and support the development of student teachers' subject knowledge. Results also suggest that teacher educators should work more closely with colleagues teaching sports-related undergraduate degree courses to support the development of subject knowledge for those students who wish to progress to a PGCE physical education course

Six Peaks Visible in the Redshift Distribution of 46,400 SDSS Quasars Agree with the Preferred Redshifts Predicted by the Decreasing Intrinsic Redshift Model

The redshift distribution of all 46,400 quasars in the Sloan Digital Sky Survey (SDSS) Quasar Catalog III, Third Data Release, is examined. Six Peaks that fall within the redshift window below z = 4, are visible. Their positions agree with the preferred redshift values predicted by the decreasing intrinsic redshift (DIR) model, even though this model was derived using completely independent evidence. A power spectrum analysis of the full dataset confirms the presence of a single, significant power peak at the expected redshift period. Power peaks with the predicted period are also obtained when the upper and lower halves of the redshift distribution are examined separately. The periodicity detected is in linear z, as opposed to log(1+z). Because the peaks in the SDSS quasar redshift distribution agree well with the preferred redshifts predicted by the intrinsic redshift relation, we conclude that this relation, and the peaks in the redshift distribution, likely both have the same origin, and this may be intrinsic redshifts, or a common selection effect. However, because of the way the intrinsic redshift relation was determined it seems unlikely that one selection effect could have been responsible for both.Comment: 12 pages, 12 figure, accepted for publication in the Astrophysical Journa

A measure of majorisation emerging from single-shot statistical mechanics

The use of the von Neumann entropy in formulating the laws of thermodynamics has recently been challenged. It is associated with the average work whereas the work guaranteed to be extracted in any single run of an experiment is the more interesting quantity in general. We show that an expression that quantifies majorisation determines the optimal guaranteed work. We argue it should therefore be the central quantity of statistical mechanics, rather than the von Neumann entropy. In the limit of many identical and independent subsystems (asymptotic i.i.d) the von Neumann entropy expressions are recovered but in the non-equilbrium regime the optimal guaranteed work can be radically different to the optimal average. Moreover our measure of majorisation governs which evolutions can be realized via thermal interactions, whereas the nondecrease of the von Neumann entropy is not sufficiently restrictive. Our results are inspired by single-shot information theory.Comment: 54 pages (15+39), 9 figures. Changed title / changed presentation, same main results / added minor result on pure bipartite state entanglement (appendix G) / near to published versio