Analogies between the crossing number and the tangle crossing number

Tanglegrams are special graphs that consist of a pair of rooted binary trees with the same number of leaves, and a perfect matching between the two leaf-sets. These objects are of use in phylogenetics and are represented with straightline drawings where the leaves of the two plane binary trees are on two parallel lines and only the matching edges can cross. The tangle crossing number of a tanglegram is the minimum crossing number over all such drawings and is related to biologically relevant quantities, such as the number of times a parasite switched hosts. Our main results for tanglegrams which parallel known theorems for crossing numbers are as follows. The removal of a single matching edge in a tanglegram with $n$ leaves decreases the tangle crossing number by at most $n-3$, and this is sharp. Additionally, if $\gamma(n)$ is the maximum tangle crossing number of a tanglegram with $n$ leaves, we prove $\frac{1}{2}\binom{n}{2}(1-o(1))\le\gamma(n)<\frac{1}{2}\binom{n}{2}$. Further, we provide an algorithm for computing non-trivial lower bounds on the tangle crossing number in $O(n^4)$ time. This lower bound may be tight, even for tanglegrams with tangle crossing number $\Theta(n^2)$.Comment: 13 pages, 6 figure

A Longitudinal Study of Bacteriophages as Indicators of Norovirus Contamination of Mussels (Mytilus edulis) and Their Overlying Waters

Sewage pollution leads to the contamination of bivalve shellfish by pathogenic microorganisms. Bacterial indicators support the management of risks associated with the consumption of shellfish; however, they often fail to indicate adequately the potential hazard to human health posed by certain human enteric viruses. Bacteriophages have been proposed as alternative indicators that may more effectively predict the presence of enteric viral pathogens. This study explored the relationships between bacterial indicators (Escherichia coli (E. coli), faecal coliforms (FC) and intestinal enterococci (IE)), phages (somatic (SOMPH), F-specific RNA (F + PH) and human-specific Bacteroides GB-124 phages (GB124PH)) and Norovirus (NoV) (GI/GII) in mussels (Mytilus edulis) and their overlying waters. The bioaccumulation of these indicators and Norovirus in shellfish matrices (e.g., flesh, digestive gland) was investigated bimonthly over a 12-month period in an English estuary. The findings revealed a marked seasonality in the distribution of all organisms, with the highest levels occurring during the autumn/winter months. The levels of all phages in shellfish and their overlying waters correlated better with the levels of Norovirus than with those of bacterial indicators. Somatic coliphages were the indicator that exhibited the strongest correlations with NoV (rho = 0.929). This study suggests that relatively low-cost culture-based phage enumeration appears to offer a more accurate indication of the likely presence of Norovirus in mussels than traditional bacterial indicators

3,3′-Dimethyl-1,1′-(methyl­enedi-p-phenyl­ene)diimidazolium bis­(hexa­fluoro­phosphate)

The title N-heterocyclic carbene compound, C21H22N4 2+·2PF6 −, crystallizes as an inversion twin. There are two independent N-heterocyclic carbene dications (A and B) and four independent hexa­fluoro­phosphate anions in the asymmetric unit. The cations are L-shaped with the benzene rings being inclined to one another by 88.82 (16)° in cation A and 87.03 (16)° in cation B. The imidazole rings make dihedral angles of 35.7 (2) and 32.83 (18)° with the attached benzene rings in cation A, and 30.14 (19) and 31.96 (18)° in cation B. In the crystal, the cations are linked via C—H⋯F hydrogen bonds, forming a three-dimensional network. π–π inter­actions involving the benzene and imidazole rings [centroid–centroid distances = 3.602 (2) and 3.723 (2) Å] and C—H⋯π inter­actions are also present

Dripping Faucet Dynamics Clarified by an Improved Mass-Spring Model

An improved mass-spring model for a dripping faucet is presented. The model is constructed based on the numerical results which we recently obtained from fluid dynamical calculations. Both the fluid dynamical calculations and the present mass-spring model exhibit a variety of complex behavior including transition to chaos in good agreement with experiments. Further, the mass-spring model reveals fundamental dynamics inherent in the dripping faucet system.Comment: 17 pages, 17 figure

A review of the methodological features of systematic reviews in maternal medicine

Background In maternal medicine, research evidence is scattered making it difficult to access information for clinical decision making. Systematic reviews of good methodological quality are essential to provide valid inferences and to produce usable evidence summaries to guide management. This review assesses the methodological features of existing systematic reviews in maternal medicine, comparing Cochrane and non-Cochrane reviews in maternal medicine. Methods Medline, Embase, Database of Reviews of Effectiveness (DARE) and Cochrane Database of Systematic Reviews (CDSR) were searched for relevant reviews published between 2001 and 2006. We selected those reviews in which a minimum of two databases were searched and the primary outcome was related to the maternal condition. The selected reviews were assessed for information on framing of question, literature search and methods of review. Results Out of 2846 citations, 68 reviews were selected. Among these, 39 (57%) were Cochrane reviews. Most of the reviews (50/68, 74%) evaluated therapeutic interventions. Overall, 54/68 (79%) addressed a focussed question. Although 64/68 (94%) reviews had a detailed search description, only 17/68 (25%) searched without language restriction. 32/68 (47%) attempted to include unpublished data and 11/68 (16%) assessed for the risk of missing studies quantitatively. The reviews had deficiencies in the assessment of validity of studies and exploration for heterogeneity. When compared to Cochrane reviews, other reviews were significantly inferior in specifying questions (OR 20.3, 95% CI 1.1–381.3, p = 0.04), framing focussed questions (OR 30.9, 95% CI 3.7- 256.2, p = 0.001), use of unpublished data (OR 5.6, 95% CI 1.9–16.4, p = 0.002), assessment for heterogeneity (OR 38.1, 95%CI 2.1, 688.2, p = 0.01) and use of meta-analyses (OR 3.7, 95% CI 1.3–10.8, p = 0.02). Conclusion This study identifies areas which have a strong influence on maternal morbidity and mortality but lack good quality systematic reviews. Overall quality of the existing systematic reviews was variable. Cochrane reviews were of better quality as compared to other reviews. There is a need for good quality systematic reviews to inform practice in maternal medicine

Measurement of sulfur L2,3 and carbon K edge XANES in a polythiophene film using a high harmonic supercontinuum

We use a high harmonic generated supercontinuum in the soft X-ray region to measure X-ray absorption near edge structure (XANES) spectra in polythiophene (poly(3-hexylthiophene)) films at multiple absorption edges. A few-cycle carrier-envelope phase-stable laser pulse centered at 1800 nm was used to generate a stable soft X-ray supercontinuum, with amplitude gating limiting the generated pulse duration to a single optical half-cycle. We report a quantitative transmission measurement of the sulfur L2,3 edge over the range 160-200 eV and the carbon K edge from 280 to 330 eV. These spectra show all the features previously reported in the XANES spectra of polythiophene, but for the first time they are measured with a source that has an approximately 1 fs pulse duration. This study opens the door to measurements that can fully time-resolve the photoexcited electronic dynamics in these systems

Terahertz underdamped vibrational motion governs protein-ligand binding in solution

Low-frequency collective vibrational modes in proteins have been proposed as being responsible for efficiently directing biochemical reactions and biological energy transport. However, evidence of the existence of delocalized vibrational modes is scarce and proof of their involvement in biological function absent. Here we apply extremely sensitive femtosecond optical Kerr-effect spectroscopy to study the depolarized Raman spectra of lysozyme and its complex with the inhibitor triacetylchitotriose in solution. Underdamped delocalized vibrational modes in the terahertz frequency domain are identified and shown to blue-shift and strengthen upon inhibitor binding. This demonstrates that the ligand-binding coordinate in proteins is underdamped and not simply solvent-controlled as previously assumed. The presence of such underdamped delocalized modes in proteins may have significant implications for the understanding of the efficiency of ligand binding and protein–molecule interactions, and has wider implications for biochemical reactivity and biological function

Quick and accurate Cellular Automata sewer simulator

This is the accepted manuscript. The final version is available from IWA Publishing via the DOI in this recordAs urbanisation and climate change progress, the frequency of flooding will increase. Each flood event causes damage to infrastructure and the environment. It is thus important to minimise the damage caused, which can be done through planning for events, real-time control of networks and risk management. To perform these actions, many different simulations of network behaviour are required involving complex and computationally expensive model runs. This makes fast (i.e. real-time or repetitive) simulations very difficult to carry out using traditional methods, thus there is a requirement to develop computationally efficient and accurate conceptual sewer simulators. A new Cellular Automata (CA) based sewer model is presented which is both fast and accurate. The CA model is Lagrangian in nature in that it represents the flow as blocks, and movement of the blocks through the system is simulated. To determine the number of blocks which should be moved it uses either the Manning's or Hazen-Williams equation depending on the flow conditions to calculate the permitted discharge. A case study of the sewer network in Keighley, Yorkshire, is carried out showing its performance in comparison to traditional sewer simulators. The benchmarks used to verify the results are SIPSON and SWMM5.Engineering and Physical Sciences Research Council (EPSRC

How and When Socially Entrepreneurial Nonprofit Organizations Benefit From Adopting Social Alliance Management Routines to Manage Social Alliances?

Social alliance is defined as the collaboration between for-profit and nonprofit organizations. Building on the insights derived from the resource-based theory, we develop a conceptual framework to explain how socially entrepreneurial nonprofit organizations (SENPOs) can improve their social alliance performance by adopting strategic alliance management routines. We test our framework using the data collected from 203 UK-based SENPOs in the context of cause-related marketing campaign-derived social alliances. Our results confirm a positive relationship between social alliance management routines and social alliance performance. We also find that relational mechanisms, such as mutual trust, relational embeddedness, and relational commitment, mediate the relationship between social alliance management routines and social alliance performance. Moreover, our findings suggest that different types of social alliance motivation can influence the impact of social alliance management routines on different types of the relational mechanisms. In general, we demonstrate that SENPOs can benefit from adopting social alliance management routines and, in addition, highlight how and when the social alliance management routines–social alliance performance relationship might be shaped. Our study offers important academic and managerial implications, and points out future research directions