Averages of Fourier coefficients of Siegel modular forms and representation of binary quadratic forms by quadratic forms in four variables

Let $-d$ be a a negative discriminant and let $T$ vary over a set of representatives of the integral equivalence classes of integral binary quadratic forms of discriminant $-d$. We prove an asymptotic formula for $d \to \infty$ for the average over $T$ of the number of representations of $T$ by an integral positive definite quaternary quadratic form and obtain results on averages of Fourier coefficients of linear combinations of Siegel theta series. We also find an asymptotic bound from below on the number of binary forms of fixed discriminant $-d$ which are represented by a given quaternary form. In particular, we can show that for growing $d$ a positive proportion of the binary quadratic forms of discriminant $-d$ is represented by the given quaternary quadratic form.Comment: v5: Some typos correcte

Pain patterns and descriptions in patients with radicular pain: Does the pain necessarily follow a specific dermatome?

<p>Abstract</p> <p>Background</p> <p>It is commonly stated that nerve root pain should be expected to follow a specific dermatome and that this information is useful to make the diagnosis of radiculopathy. There is little evidence in the literature that confirms or denies this statement. The purpose of this study is to describe and discuss the diagnostic utility of the distribution of pain in patients with cervical and lumbar radicular pain.</p> <p>Methods</p> <p>Pain drawings and descriptions were assessed in consecutive patients diagnosed with cervical or lumbar nerve root pain. These findings were compared with accepted dermatome maps to determine whether they tended to follow along the involved nerve root's dermatome.</p> <p>Results</p> <p>Two hundred twenty-six nerve roots in 169 patients were assessed. Overall, pain related to cervical nerve roots was non-dermatomal in over two-thirds (69.7%) of cases. In the lumbar spine, the pain was non-dermatomal in just under two-thirds (64.1%) of cases. The majority of nerve root levels involved non-dermatomal pain patterns except C4 (60.0% dermatomal) and S1 (64.9% dermatomal). The sensitivity (SE) and specificity (SP) for dermatomal pattern of pain are low for all nerve root levels with the exception of the C4 level (Se 0.60, Sp 0.72) and S1 level (Se 0.65, Sp 0.80), although in the case of the C4 level, the number of subjects was small (n = 5).</p> <p>Conclusion</p> <p>In most cases nerve root pain should not be expected to follow along a specific dermatome, and a dermatomal distribution of pain is not a useful historical factor in the diagnosis of radicular pain. The possible exception to this is the S1 nerve root, in which the pain does commonly follow the S1 dermatome.</p

Leaf litter decomposition in temperate deciduous forest stands with a decreasing fraction of beech (Fagus sylvatica)

We hypothesised that the decomposition rates of leaf litter will increase along a gradient of decreasing fraction of the European beech (Fagus sylvatica) and increasing tree species diversity in the generally beech-dominated Central European temperate deciduous forests due to an increase in litter quality. We studied the decomposition of leaf litter including its lignin fraction in monospecific (pure beech) stands and in stands with up to five tree genera (Acer spp., Carpinus betulus, Fagus sylvatica, Fraxinus excelsior, Tilia spp.) using a litterbag approach. Litter and lignin decomposition was more rapid in stand-representative litter from multispecific stands than in litter from pure beech stands. Except for beech litter, the decomposition rates of species-specific tree litter did not differ significantly among the stand types, but were most rapid in Fraxinus excelsior and slowest in beech in an interspecific comparison. Pairwise comparisons of the decomposition of beech litter with litter of the other tree species (except for Acerplatanoides) revealed a “home field advantage” of up to 20% (more rapid litter decomposition in stands with a high fraction of its own species than in stands with a different tree species composition). Decomposition of stand-representative litter mixtures displayed additive characteristics, not significantly more rapid than predicted by the decomposition of litter from the individual tree species. Leaf litter decomposition rates were positively correlated with the initial N and Ca concentrations of the litter, and negatively with the initial C:N, C:P and lignin:N ratios. The results support our hypothesis that the overall decomposition rates are mainly influenced by the chemical composition of the individual litter species. Thus, the fraction of individual tree species in the species composition seems to be more important for the litter decomposition rates than tree species diversity itself

Clinical research without consent in adults in the emergency setting: a review of patient and public views

<p>Abstract</p> <p>Background</p> <p>In emergency research, obtaining informed consent can be problematic. Research to develop and improve treatments for patients admitted to hospital with life-threatening and debilitating conditions is much needed yet the issue of research without consent (RWC) raises concerns about unethical practices and the loss of individual autonomy. Consistent with the policy and practice turn towards greater patient and public involvement in health care decisions, in the US, Canada and EU, guidelines and legislation implemented to protect patients and facilitate acute research with adults who are unable to give consent have been developed with little involvement of the lay public. This paper reviews research examining public opinion regarding RWC for research in emergency situations, and whether the rules and regulations permitting research of this kind are in accordance with the views of those who ultimately may be the most affected.</p> <p>Methods</p> <p>Seven electronic databases were searched: Medline, Embase, CINAHL, Cochrane Database of Systematic Reviews, Philosopher's Index, Age Info, PsychInfo, Sociological Abstracts and Web of Science. Only those articles pertaining to the views of the public in the US, Canada and EU member states were included. Opinion pieces and those not published in English were excluded.</p> <p>Results</p> <p>Considering the wealth of literature on the perspectives of professionals, there was relatively little information about public attitudes. Twelve studies employing a range of research methods were identified. In five of the six questionnaire surveys around half the sample did <it>not </it>agree generally with RWC, though paradoxically, a higher percentage would <it>personally </it>take part in such a study. Unfortunately most of the studies were not designed to investigate individuals' views in any depth. There also appears to be a level of mistrust of medical research and some patients were more likely to accept an experimental treatment 'outside' of a research protocol.</p> <p>Conclusion</p> <p>There are too few data to evaluate whether the rules and regulations permitting RWC protects – or is acceptable to – the public. However, any attempts to engage the public should take place in the context of findings from further basic research to attend to the apparently paradoxical findings of some of the current surveys.</p

Development and evaluation of an instrument for the critical appraisal of randomized controlled trials of natural products

<p>Abstract</p> <p>Background</p> <p>The efficacy of natural products (NPs) is being evaluated using randomized controlled trials (RCTs) with increasing frequency, yet a search of the literature did not identify a widely accepted critical appraisal instrument developed specifically for use with NPs. The purpose of this project was to develop and evaluate a critical appraisal instrument that is sufficiently rigorous to be used in evaluating RCTs of conventional medicines, and also has a section specific for use with single entity NPs, including herbs and natural sourced chemicals.</p> <p>Methods</p> <p>Three phases of the project included: 1) using experts and a Delphi process to reach consensus on a list of items essential in describing the identity of an NP; 2) compiling a list of non-NP items important for evaluating the quality of an RCT using systematic review methodology to identify published instruments and then compiling item categories that were part of a validated instrument and/or had empirical evidence to support their inclusion and 3) conducting a field test to compare the new instrument to a published instrument for usefulness in evaluating the quality of 3 RCTs of a NP and in applying results to practice.</p> <p>Results</p> <p>Two Delphi rounds resulted in a list of 15 items essential in describing NPs. Seventeen item categories fitting inclusion criteria were identified from published instruments for conventional medicines. The new assessment instrument was assembled based on content of the two lists and the addition of a Reviewer's Conclusion section. The field test of the new instrument showed good criterion validity. Participants found it useful in translating evidence from RCTs to practice.</p> <p>Conclusion</p> <p>A new instrument for the critical appraisal of RCTs of NPs was developed and tested. The instrument is distinct from other available assessment instruments for RCTs of NPs in its systematic development and validation. The instrument is ready to be used by pharmacy students, health care practitioners and academics and will continue to be refined as required.</p

How robust are community-based plant bioindicators? Empirical testing of the relationship between Ellenberg values and direct environmental measures in woodland communities

There are several community-based bioindicator systems that use species presence or abundance data as proxies for environmental variables. One example is the Ellenberg system, whereby vegetation data are used to estimate environmental soil conditions. Despite widespread use of Ellenberg values in ecological research, the correlation between bioindicated values and actual values is often an implicit assumption rather than based on empirical evidence. Here, we correlate unadjusted and UK-adjusted Ellenberg values for soil moisture, pH, and nitrate in relation to direct environmental measures for 50 woodland sites in the UK, which were subject to repeat sampling. Our results show the accuracy of Ellenberg values is parameter specific; pH values were a good proxy for direct environmental measures but this was not true for soil moisture, when relationships were weak and non-significant. For nitrates, there were important seasonal differences, with a strong positive logarithmic relationship in the spring but a non-significant (and negative) correlation in summer. The UK-adjusted values were better than, or equivalent to, Ellenberg’s original ones, which had been quantified originally for Central Europe, in all cases. Somewhat surprisingly, unweighted values correlated with direct environmental measures better than did abundance-weighted ones. This suggests that the presence of rare plants can be highly important in accurate quantification of soil parameters and we recommend using an unweighted approach. However, site profiles created only using rare plants were inferior to profiles based on the whole plant community and thus cannot be used in isolation. We conclude that, for pH and nitrates, the Ellenberg system provides a useful estimate of actual conditions, but recalibration of moisture values should be considered along with the effect of seasonality on the efficacy of the system

A systematic review of the reporting of Data Monitoring Committees' roles, interim analysis and early termination in pediatric clinical trials

<p>Abstract</p> <p>Background</p> <p>Decisions about interim analysis and early stopping of clinical trials, as based on recommendations of Data Monitoring Committees (DMCs), have far reaching consequences for the scientific validity and clinical impact of a trial. Our aim was to evaluate the frequency and quality of the reporting on DMC composition and roles, interim analysis and early termination in pediatric trials.</p> <p>Methods</p> <p>We conducted a systematic review of randomized controlled clinical trials published from 2005 to 2007 in a sample of four general and four pediatric journals. We used full-text databases to identify trials which reported on DMCs, interim analysis or early termination, and included children or adolescents. Information was extracted on general trial characteristics, risk of bias, and a set of parameters regarding DMC composition and roles, interim analysis and early termination.</p> <p>Results</p> <p>110 of the 648 pediatric trials in this sample (17%) reported on DMC or interim analysis or early stopping, and were included; 68 from general and 42 from pediatric journals. The presence of DMCs was reported in 89 of the 110 included trials (81%); 62 papers, including 46 of the 89 that reported on DMCs (52%), also presented information about interim analysis. No paper adequately reported all DMC parameters, and nine (15%) reported all interim analysis details. Of 32 trials which terminated early, 22 (69%) did not report predefined stopping guidelines and 15 (47%) did not provide information on statistical monitoring methods.</p> <p>Conclusions</p> <p>Reporting on DMC composition and roles, on interim analysis results and on early termination of pediatric trials is incomplete and heterogeneous. We propose a minimal set of reporting parameters that will allow the reader to assess the validity of trial results.</p

Long-term changes in lowland calcareous grassland plots using Tephroseris integrifolia subsp. integrifolia as an indicator species

We investigated the changes to calcareous grassland plots within protected sites, and whether Tephroseris integrifolia subsp. integrifolia can act as a useful indicator species for re-visitation studies within vegetation predicted to remain relatively stable. Twenty-two plots located across lowland England and all formerly containing T. integrifolia were re-surveyed following the methodology used in the original survey undertaken in the 1960s. Pseudo-turnover and between-observer bias were minimised by sampling replicate quadrats at each fixed plot using a single surveyor and at a similar time of year as the original survey. Qualitative details concerning grazing management were obtained for all sites. In contrast to other long-term re-visitation studies, all our study plots were intact and retained diverse, herb-rich vegetation, demonstrating the value of site protection. However, there were clear shifts in vegetation composition, most notably where T. integrifolia was absent, as shown by an increase in Ellenberg fertility and moisture signifying nutrient enrichment, and a decrease in the cover of low-growing, light-demanding specialists, with a change likely to be associated predominantly with grazing management. Whereas in the mid-20th century the greatest threat to calcareous grassland was habitat loss, undergrazing or temporary neglect now appears to pose the principal threat. Distinctive species such as T. integrifolia with marked sensitivity to habitat change provide a potentially useful tool for rapid assessment and monitoring of site quality. Focusing monitoring on such species allows non-expert observers to recognise the early stages of habitat degradation, providing, in effect, a “health check” on individual sites and groups of sites