Upward Three-Dimensional Grid Drawings of Graphs

A \emph{three-dimensional grid drawing} of a graph is a placement of the vertices at distinct points with integer coordinates, such that the straight line segments representing the edges do not cross. Our aim is to produce three-dimensional grid drawings with small bounding box volume. We prove that every $n$-vertex graph with bounded degeneracy has a three-dimensional grid drawing with $O(n^{3/2})$ volume. This is the broadest class of graphs admiting such drawings. A three-dimensional grid drawing of a directed graph is \emph{upward} if every arc points up in the z-direction. We prove that every directed acyclic graph has an upward three-dimensional grid drawing with $(n^3)$ volume, which is tight for the complete dag. The previous best upper bound was $O(n^4)$. Our main result is that every $c$-colourable directed acyclic graph ($c$ constant) has an upward three-dimensional grid drawing with $O(n^2)$ volume. This result matches the bound in the undirected case, and improves the best known bound from $O(n^3)$ for many classes of directed acyclic graphs, including planar, series parallel, and outerplanar

Increasing follow-up questionnaire response rates in a randomized controlled trial of telehealth for depression: three embedded controlled studies

Background: Attrition is problematic in trials, and may be exacerbated in longer studies, telehealth trials and participants with depression – three features of The Healthlines Study. Advance notification, including a photograph and using action-oriented email subject lines might increase response rates, but require further investigation. We examined the effectiveness of these interventions in three embedded Healthlines studies. Methods: Based in different trial sites, participants with depression were alternately allocated to be pre-called or not ahead of the 8-month follow-up questionnaire (Study 1), randomized to receive a research team photograph or not with their 12-month questionnaire (Study 2), and randomized to receive an action-oriented (‘ACTION REQUIRED’) or standard (‘Questionnaire reminder’) 12-month email reminder (Study 3). Participants could complete online or postal questionnaires, and received up to five questionnaire reminders. The primary outcome was completion of the Patient Health Questionnaire (PHQ-9). Secondary outcome measures were the number of reminders and time to questionnaire completion. Results: Of a total of 609 Healthlines depression participants, 190, 251 and 231 participants were included in Studies 1–3 (intervention: 95, 126 and 115), respectively. Outcome completion was ≥90 % across studies, with no differences between trial arms (Study 1: OR 0.38, 95 % CI 0.07–2.10; Study 2: OR 0.84, 95 % CI 0.26–2.66; Study 3: OR 0.53 95 % CI 0.19–1.49). Pre-called participants were less likely to require a reminder (48.4 % vs 62.1 %, OR 0.41, 95 % CI 0.21–0.78), required fewer reminders (adjusted difference in means −0.67, 95 % CI −1.13 to −0.20), and completed follow-up quicker (median 8 vs 15 days, HR 1.35, 95 % CI 1.00–1.82) than control subjects. There were no significant between-group differences in Studies 2 or 3. Conclusions: Eventual response rates in this trial were high, with no further improvement from these interventions. While the photograph and email interventions were ineffective, pre-calling participants reduced time to completion. This strategy might be helpful when the timing of study completion is important. Researchers perceived a substantial benefit from the reduction in reminders with pre-calling, despite no overall decrease in net effort after accounting for pre-notification

The effect of ring size on the selective carboxylation of cycloalkene oxides

Carbon dioxide utilisation technology can contribute to the reduction of atmospheric CO2 levels both through its sequestration from flue gases and indirectly by relieving pressure on conventional feedstocks in chemical manufacturing. A promising approach is to employ CO2 to produce valuable cyclic carbonates (CCs) in reaction with suitable epoxides. This also has the advantage that carbon dioxide replaces toxic and hazardous reactants such as phosgene. In earlier work we have investigated the synthesis of epoxides from cycloalkenes using supported gold and gold–palladium nanoparticles as catalysts and oxygen from air as the oxidant under solvent free conditions. A strong dependence of epoxide selectivity on ring size was observed with C5 < C6 < C7 ≪ C8. In this study we extend this work to the investigation of cycloaddition of CO2 to different cycloalkene oxides with the ultimate aim of designing a process in which both epoxidation of an alkene and incorporation of CO2 could be achieved in a single process. However, we have found the opposite trend for the selectivity to carbonates: smaller ring cycloalkene oxides giving the highest carbonate selectivities while large rings do not yield CCs at all. The product distributions suggest that an alternative ring opening of the epoxides to yield alcohols and ketones is preferred under all the experimental conditions explored for larger ring systems. Additionally, the mechanism of the CC synthesis using a quaternary ammonium salt and ZnBr2 as the catalyst system was investigated using DFT methods. The results of the calculations support the experimental findings

Why Effective Medium Theory Fails in Granular Materials

Experimentally it is known that the bulk modulus, K, and shear modulus, \mu, of a granular assembly of elastic spheres increase with pressure, p, faster than the p^1/3 law predicted by effective medium theory (EMT) based on Hertz-Mindlin contact forces. To understand the origin of these discrepancies, we perform numerical simulations of granular aggregates under compression. We show that EMT can describe the moduli pressure dependence if one includes the increasing number of grain-grain contacts with p. Most important, the affine assumption (which underlies EMT), is found to be valid for K(p) but breakdown seriously for \mu(p). This explains why the experimental and numerical values of \mu(p) are much smaller than the EMT predictions.Comment: 4 pages, 5 figures, http://polymer.bu.edu/~hmaks

Statistical Mechanics Analysis of LDPC Coding in MIMO Gaussian Channels

Using analytical methods of statistical mechanics, we analyse the typical behaviour of a multiple-input multiple-output (MIMO) Gaussian channel with binary inputs under LDPC network coding and joint decoding. The saddle point equations for the replica symmetric solution are found in particular realizations of this channel, including a small and large number of transmitters and receivers. In particular, we examine the cases of a single transmitter, a single receiver and the symmetric and asymmetric interference channels. Both dynamical and thermodynamical transitions from the ferromagnetic solution of perfect decoding to a non-ferromagnetic solution are identified for the cases considered, marking the practical and theoretical limits of the system under the current coding scheme. Numerical results are provided, showing the typical level of improvement/deterioration achieved with respect to the single transmitter/receiver result, for the various cases.Comment: 25 pages, 7 figure

Renormalization Group Analysis of a Quivering String Model of Posture Control

Scaling concepts and renormalization group (RG) methods are applied to a simple linear model of human posture control consisting of a trembling or quivering string subject to damping and restoring forces. The string is driven by uncorrelated white Gaussian noise intended to model the corrections of the physiological control system. We find that adding a weak quadratic nonlinearity to the posture control model opens up a rich and complicated phase space (representing the dynamics) with various non-trivial fixed points and basins of attraction. The transition from diffusive to saturated regimes of the linear model is understood as a crossover phenomenon, and the robustness of the linear model with respect to weak non-linearities is confirmed. Correlations in posture fluctuations are obtained in both the time and space domain. There is an attractive fixed point identified with falling. The scaling of the correlations in the front-back displacement, which can be measured in the laboratory, is predicted for both the large-separation (along the string) and long-time regimes of posture control.Comment: 20 pages, 13 figures, RevTeX, accepted for publication in PR

The International Bathymetric Chart of the Arctic Ocean (IBCAO) Version 3.0

[1] The International Bathymetric Chart of the Arctic Ocean (IBCAO) released its first gridded bathymetric compilation in 1999. The IBCAO bathymetric portrayals have since supported a wide range of Arctic science activities, for example, by providing constraint for ocean circulation models and the means to define and formulate hypotheses about the geologic origin of Arctic undersea features. IBCAO Version 3.0 represents the largest improvement since 1999 taking advantage of new data sets collected by the circum-Arctic nations, opportunistic data collected from fishing vessels, data acquired from US Navy submarines and from research ships of various nations. Built using an improved gridding algorithm, this new grid is on a 500 meter spacing, revealing much greater details of the Arctic seafloor than IBCAO Version 1.0 (2.5 km) and Version 2.0 (2.0 km). The area covered by multibeam surveys has increased from ∼6% in Version 2.0 to ∼11% in Version 3.0

A cytogenetic follow-up of some highly irradiated victims of the Chernobyl accident

Altres ajuts: The authors wish to thank INTAS (research grant no. 97-1152) for financial support for this workA follo w-up of 10 highly irradiated men, mostly reactor crew, from the Chernobyl accident is described. Their pre-accident medical conditions and relevant medical status approximately 10-13 y later are listed. A comparison is made between estimates of their average whole-body penetrating radiation doses derived from several biological parameters. First estimates were based on their presenting severity of prodromal sickness, early changes in blood cell counts and dicentric chromosome aberrations in lymphocytes. In three cases ESR measurements on tooth enamel were also made. Retrospective dosimetry using FISH translocations was attempted 10-13 y later. This showed good agreement for those patients with the lower earlier dose estimates, up to about 3 Gy. For the others, extending up to about 12 Gy, the translocations indicated lower values, suggesting that in these cases translocations had somewhat declined. Repeated chromosomal examinations during the follow-up period showed an expected decline in dicentric frequencies. The pattern of decline was bi-phasic with a more rapid first phase, with a half-life of ∼4 months followed by a slower decline with half-lives around 2-4 y. The rapid phase persisted for a longer time in those patients who had received the highest doses. 10-13 y later dicentric levels were still above normal background, but well below the translocation frequencies

A nipple shield delivery system for oral drug delivery to breastfeeding infants : Microbicide delivery to inactivate HIV

A new drug delivery method for infants is presented which incorporates an active pharmaceutical ingredient (API)-loaded insert into a nipple shield delivery system (NSDS). The API is released directly into milk during breastfeeding. This study investigates the feasibility of using the NSDS to deliver the microbicide sodium dodecyl sulfate (SDS), with the goal of preventing mother-to-child transmission (MTCT) of HIV during breastfeeding in low-resource settings, when there is no safer alternative for the infant but to breastfeed. SDS has been previously shown to effectively inactivate HIV in human milk. An apparatus was developed to simulate milk flow through and drug release from a NSDS. Using this apparatus milk was pulsed through a prototype device containing a non-woven fiber insert impregnated with SDS and the microbicide was rapidly released. The total SDS release from inserts ranged from 70 to 100% of the average 0.07 g load within 50 ml (the volume of a typical breastfeed). Human milk spiked with H9/HIVIIIB cells was also passed through the same set-up. Greater than 99% reduction of cell-associated HIV infectivity was achieved in the first 10 ml of milk. This proof of concept study demonstrates efficient drug delivery to breastfeeding infants is achievable using the NSDS