Design and development of a low temperature, inductance based high frequency ac susceptometer

We report on the development of an induction based low temperature high frequency ac susceptometer capable of measuring at frequencies up to 3.5 MHz and at temperatures between 2 K and 300 K. Careful balancing of the detection coils and calibration have allowed a sample magnetic moment resolution of $5\times10^{-10} Am^2$ at 1 MHz. We will discuss the design and characterization of the susceptometer, and explain the calibration process. We also include some example measurements on the spin ice material CdEr$_2$S$_4$ and iron oxide based nanoparticles to illustrate functionality

"Random" gentamicin concentrations do not predict trough levels in neonates receiving once daily fixed dose regimens

BACKGROUND: Monitoring plasma gentamicin concentrations in neonates 24 hours after a once daily dose (4 mg/kg) often necessitates additional blood sampling. In adults a nomogram has been developed enabling evaluation of gentamicin doses by sampling concentrations with other blood tests, 4 – 16 hours after administration. We attempted to develop a similar nomogram for neonates. METHODS: In addition to standard 24 hour sampling to monitor trough concentrations, one additional "random" gentamicin concentration was measured in each of 50 neonates <4 days of age (median gestation 33 weeks [28–41]), when other blood samples were clinically necessary, 4 – 20 hours after gentamicin administration. 24 hour concentrations of >1 mg/L were considered high, and an indication to extend the dosing interval. RESULTS: Highest correlation (r(2 )= 0.51) of plasma gentamicin concentration against time (4 to 20 hours) was with logarithmic regression. A line drawn 0.5 mg/L below the true regression line resulted in all babies with 24 hr gentamicin concentrations >1 mg/L having the additional "random" test result above that line, i.e. 100% sensitivity for 24 hour concentrations>1 mg/L, though only 58% specificity. Having created the nomogram, 39 further babies (median gestation 34 weeks [28–41]), were studied and results tested against the nomogram. In this validation group, sensitivity of the nomogram for 24 hr concentrations >1 mg/L was 92%; specificity 14%, positive predictive value 66%, and negative predictive value 50%. Prematurity (≤ 37 weeks) was a more sensitive (94%) and specific (61%) indicator of high 24-hour concentrations. 62 (87%) of 71 preterm babies had high 24-hour concentrations. CONCLUSION: It was not possible to construct a nomogram to predict gentamicin concentrations at 24 hours in neonates with a variety of gestational ages. Dosage tailored to gestation with monitoring of trough concentrations remains management of choice

Rigorous confidence intervals for critical probabilities

We use the method of Balister, Bollobas and Walters to give rigorous 99.9999% confidence intervals for the critical probabilities for site and bond percolation on the 11 Archimedean lattices. In our computer calculations, the emphasis is on simplicity and ease of verification, rather than obtaining the best possible results. Nevertheless, we obtain intervals of width at most 0.0005 in all cases

Powers of Hamilton cycles in pseudorandom graphs

We study the appearance of powers of Hamilton cycles in pseudorandom graphs, using the following comparatively weak pseudorandomness notion. A graph $G$ is $(\varepsilon,p,k,\ell)$-pseudorandom if for all disjoint $X$ and $Y\subset V(G)$ with $|X|\ge\varepsilon p^kn$ and $|Y|\ge\varepsilon p^\ell n$ we have $e(X,Y)=(1\pm\varepsilon)p|X||Y|$. We prove that for all $\beta>0$ there is an $\varepsilon>0$ such that an $(\varepsilon,p,1,2)$-pseudorandom graph on $n$ vertices with minimum degree at least $\beta pn$ contains the square of a Hamilton cycle. In particular, this implies that $(n,d,\lambda)$-graphs with $\lambda\ll d^{5/2 }n^{-3/2}$ contain the square of a Hamilton cycle, and thus a triangle factor if $n$ is a multiple of $3$. This improves on a result of Krivelevich, Sudakov and Szab\'o [Triangle factors in sparse pseudo-random graphs, Combinatorica 24 (2004), no. 3, 403--426]. We also extend our result to higher powers of Hamilton cycles and establish corresponding counting versions.Comment: 30 pages, 1 figur

Continuous Percolation Phase Transitions of Two-dimensional Lattice Networks under a Generalized Achlioptas Process

The percolation phase transitions of two-dimensional lattice networks under a generalized Achlioptas process (GAP) are investigated. During the GAP, two edges are chosen randomly from the lattice and the edge with minimum product of the two connecting cluster sizes is taken as the next occupied bond with a probability $p$. At $p=0.5$, the GAP becomes the random growth model and leads to the minority product rule at $p=1$. Using the finite-size scaling analysis, we find that the percolation phase transitions of these systems with $0.5 \le p \le 1$ are always continuous and their critical exponents depend on $p$. Therefore, the universality class of the critical phenomena in two-dimensional lattice networks under the GAP is related to the probability parameter $p$ in addition.Comment: 7 pages, 14 figures, accepted for publication in Eur. Phys. J.

Exact eigenspectrum of the symmetric simple exclusion process on the complete, complete bipartite, and related graphs

We show that the infinitesimal generator of the symmetric simple exclusion process, recast as a quantum spin-1/2 ferromagnetic Heisenberg model, can be solved by elementary techniques on the complete, complete bipartite, and related multipartite graphs. Some of the resulting infinitesimal generators are formally identical to homogeneous as well as mixed higher spins models. The degeneracies of the eigenspectra are described in detail, and the Clebsch-Gordan machinery needed to deal with arbitrary spin-s representations of the SU(2) is briefly developed. We mention in passing how our results fit within the related questions of a ferromagnetic ordering of energy levels and a conjecture according to which the spectral gaps of the random walk and the interchange process on finite simple graphs must be equal.Comment: Final version as published, 19 pages, 4 figures, 40 references given in full forma

The information sources and journals consulted or read by UK paediatricians to inform their clinical practice and those which they consider important: a questionnaire survey

Background: Implementation of health research findings is important for medicine to be evidence-based. Previous studies have found variation in the information sources thought to be of greatest importance to clinicians but publication in peer-reviewed journals is the traditional route for dissemination of research findings. There is debate about whether the impact made on clinicians should be considered as part of the evaluation of research outputs. We aimed to determine first which information sources are generally most consulted by paediatricians to inform their clinical practice, and which sources they considered most important, and second, how many and which peer-reviewed journals they read. Methods: We enquired, by questionnaire survey, about the information sources and academic journals that UK medical paediatric specialists generally consulted, attended or read and considered important to their clinical practice. Results: The same three information sources – professional meetings & conferences, peerreviewed journals and medical colleagues – were, overall, the most consulted or attended and ranked the most important. No one information source was found to be of greatest importance to all groups of paediatricians. Journals were widely read by all groups, but the proportion ranking them first in importance as an information source ranged from 10% to 46%. The number of journals read varied between the groups, but Archives of Disease in Childhood and BMJ were the most read journals in all groups. Six out of the seven journals previously identified as containing best paediatric evidence are the most widely read overall by UK paediatricians, however, only the two most prominent are widely read by those based in the community. Conclusion: No one information source is dominant, therefore a variety of approaches to Continuing Professional Development and the dissemination of research findings to paediatricians should be used. Journals are an important information source. A small number of key ones can be identified and such analysis could provide valuable additional input into the evaluation of clinical research outputs