The generalized 3-edge-connectivity of lexicographic product graphs

The generalized $k$-edge-connectivity $\lambda_k(G)$ of a graph $G$ is a generalization of the concept of edge-connectivity. The lexicographic product of two graphs $G$ and $H$, denoted by $G\circ H$, is an important graph product. In this paper, we mainly study the generalized 3-edge-connectivity of $G \circ H$, and get upper and lower bounds of $\lambda_3(G \circ H)$. Moreover, all bounds are sharp.Comment: 14 page

Brownian bridges to submanifolds

We introduce and study Brownian bridges to submanifolds. Our method involves proving a general formula for the integral over a submanifold of the minimal heat kernel on a complete Riemannian manifold. We use the formula to derive lower bounds, an asymptotic relation and derivative estimates. We also see a connection to hypersurface local time. This work is motivated by the desire to extend the analysis of path and loop spaces to measures on paths which terminate on a submanifold

A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry

We present here a review of the fundamental topics of Hartree-Fock theory in Quantum Chemistry. From the molecular Hamiltonian, using and discussing the Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock equations for the electronic problem. Special emphasis is placed in the most relevant mathematical aspects of the theoretical derivation of the final equations, as well as in the results regarding the existence and uniqueness of their solutions. All Hartree-Fock versions with different spin restrictions are systematically extracted from the general case, thus providing a unifying framework. Then, the discretization of the one-electron orbitals space is reviewed and the Roothaan-Hall formalism introduced. This leads to a exposition of the basic underlying concepts related to the construction and selection of Gaussian basis sets, focusing in algorithmic efficiency issues. Finally, we close the review with a section in which the most relevant modern developments (specially those related to the design of linear-scaling methods) are commented and linked to the issues discussed. The whole work is intentionally introductory and rather self-contained, so that it may be useful for non experts that aim to use quantum chemical methods in interdisciplinary applications. Moreover, much material that is found scattered in the literature has been put together here to facilitate comprehension and to serve as a handy reference.Comment: 64 pages, 3 figures, tMPH2e.cls style file, doublesp, mathbbol and subeqn package

The Postcranial Skeleton of an Exceptionally Complete Individual of the Plated Dinosaur Stegosaurus stenops (Dinosauria: Thyreophora) from the Upper Jurassic Morrison Formation of Wyoming, U.S.A.

Copyright: © 2015 Maidment et al. This is an open access article distributed under the terms of the Creative Commons Attribution License [4.0], which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. The attached file is the published version of the article

A systematic review of Vancouver B2 and B3 periprosthetic femoral fractures

Aims The aim of this study was to investigate the outcomes of Vancouver type B2 and B3 fractures by performing a systematic review of the methods of surgical treatment which have been reported. Materials and Methods A systematic search was performed in Ovid MEDLINE, Embase and the Cochrane Central Register of Controlled Trials. For inclusion, studies required a minimum of ten patients with a Vancouver type B2 and/or ten patients with a Vancouver type B3 fracture, a minimum mean follow-up of two years and outcomes which were matched to the type of fracture. Studies were also required to report the rate of re-operation as an outcome measure. The protocol was registered in the PROSPERO database. Results A total of 22 studies were included based on the eligibility criteria, including 343 B2 fractures and 167 B3 fractures. The mean follow-up ranged from 32 months to 74 months. Of 343 Vancouver B2 fractures, the treatment in 298 (86.8%) involved revision arthroplasty and 45 (12.6%) were treated with internal fixation alone. A total of 37 patients (12.4%) treated with revision arthroplasty and six (13.3%) treated by internal fixation only underwent further re-operation. Of 167 Vancouver B3 fractures, the treatment in 160 (95.8%) involved revision arthroplasty and eight (4.8%) were treated with internal fixation without revision. A total of 23 patients (14.4%) treated with revision arthroplasty and two (28.6%) treated only with internal fixation required re-operation. Conclusion A significant proportion, particularly of B2 fractures, were treated without revision of the stem. These were associated with a higher rate of re-operation. The treatment of B3 fractures without revision of the stem resulted in a high rate of re-operation. This demonstrates the importance of careful evaluation and accurate characterisation of the fracture at the time of presentation to ensure the correct management. There is a need for improvement in the reporting of data in case series recording the outcome of the surgical treatment of periprosthetic fractures. We have suggested a minimum dataset to improve the quality of data in studies dealing with these fractures

Morphological and Geochemical Evidence of Eumelanin Preservation in the Feathers of the Early Cretaceous Bird, Gansus yumenensis

Recent studies have shown evidence for the preservation of colour in fossilized soft tissues by imaging melanosomes, melanin pigment containing organelles. This study combines geochemical analyses with morphological observations to investigate the preservation of melanosomes and melanin within feathers of the Early Cretaceous bird, Gansus yumenensis. Scanning electron microscopy reveals structures concordant with those previously identified as eumelanosomes within visually dark areas of the feathers but not in lighter areas or sedimentary matrices. Fourier transform infrared analyses show different spectra for the feathers and their matrices; melanic functional groups appear in the feather including carboxylic acid and ketone groups that are not seen in the matrix. When mapped, the carboxylic acid group absorption faithfully replicates the visually dark areas of the feathers. Electron Paramagnetic Resonance spectroscopy of one specimen demonstrates the presence of organic signals but proved too insensitive to resolve melanin. Pyrolysis gas chromatography mass spectrometry shows a similar distribution of aliphatic material within both feathers that are different from those of their respective matrices. In combination, these techniques strongly suggest that not only do the feathers contain endogenous organic material, but that both geochemical and morphological evidence supports the preservation of original eumelanic pigment residue

Pediatric DXA: technique and interpretation

This article reviews dual X-ray absorptiometry (DXA) technique and interpretation with emphasis on the considerations unique to pediatrics. Specifically, the use of DXA in children requires the radiologist to be a “clinical pathologist” monitoring the technical aspects of the DXA acquisition, a “statistician” knowledgeable in the concepts of Z-scores and least significant changes, and a “bone specialist” providing the referring clinician a meaningful context for the numeric result generated by DXA. The patient factors that most significantly influence bone mineral density are discussed and are reviewed with respect to available normative databases. The effects the growing skeleton has on the DXA result are also presented. Most important, the need for the radiologist to be actively involved in the technical and interpretive aspects of DXA is stressed. Finally, the diagnosis of osteoporosis should not be made on DXA results alone but should take into account other patient factors

Indirect comparison of interventions using published randomised trials: systematic review of PDE-5 inhibitors for erectile dysfunction

BACKGROUND: There are no randomised and properly blinded trials directly comparing one PDE-5 inhibitor with another in a normal home setting. Valid indirect comparisons with a common comparator must examine equivalent doses, similar duration, similar populations, with the same outcomes reported in the same way. METHODS: Published randomised, double-blind trials of oral PDE-5 inhibitors for erectile dysfunction were sought from reference lists in previous reviews and electronic searching. Analyses of efficacy and harm were carried out for each treatment, and results compared where there was a common comparator and consistency of outcome reporting, using equivalent doses. RESULTS: Analysis was limited by differential reporting of outcomes. Sildenafil trials were clinically and geographically more diverse. Tadalafil and vardenafil trials tended to use enriched enrolment. Using all trials, the three interventions were similar for consistently reported efficacy outcomes. Rates of successful intercourse for sildenafil, tadalafil and vardenafil were 65%, 62%, and 59%, with placebo rates of 23–28%. The rates of improved erections were 76%, 75% and 71%, respectively, with placebo rates of 22–24%, and NNTs of 1.9 or 2.0. Reporting of withdrawals was less consistent, but all-cause withdrawals for sildenafil, tadalafil and vardenafil were 8% 13% and 20%. All three drugs were well tolerated, with headache being the most commonly reported event at 13–17%. There were few serious adverse events. CONCLUSION: There were differences between trials in outcomes reported, limiting comparisons, and the most useful outcomes were not reported. For common outcomes there was similar efficacy between PDE-5 inhibitors

Human resources for health care delivery in Tanzania: a multifaceted problem

BACKGROUND: Recent years have seen an unprecedented increase in funds for procurement of health commodities in developing countries. A major challenge now is the efficient delivery of commodities and services to improve population health. With this in mind, we documented staffing levels and productivity in peripheral health facilities in southern Tanzania. METHOD: A health facility survey was conducted to collect data on staff employed, their main tasks, availability on the day of the survey, reasons for absenteeism, and experience of supervisory visits from District Health Teams. In-depth interview with health workers was done to explore their perception of work load. A time and motion study of nurses in the Reproductive and Child Health (RCH) clinics documented their time use by task. RESULTS: We found that only 14% (122/854) of the recommended number of nurses and 20% (90/441) of the clinical staff had been employed at the facilities. Furthermore, 44% of clinical staff was not available on the day of the survey. Various reasons were given for this. Amongst the clinical staff, 38% were absent because of attendance to seminar sessions, 8% because of long-training, 25% were on official travel and 20% were on leave. RCH clinic nurses were present for 7 hours a day, but only worked productively for 57% of time present at facility. Almost two-third of facilities had received less than 3 visits from district health teams during the 6 months preceding the survey. CONCLUSION: This study documented inadequate staffing of health facilities, a high degree of absenteeism, low productivity of the staff who were present and inadequate supervision in peripheral Tanzanian health facilities. The implications of these findings are discussed in the context of decentralized health care in Tanzania