Improved bounds for Hadwiger's covering problem via thin-shell estimates

A central problem in discrete geometry, known as Hadwiger's covering problem, asks what the smallest natural number $N\left(n\right)$ is such that every convex body in ${\mathbb R}^{n}$ can be covered by a union of the interiors of at most $N\left(n\right)$ of its translates. Despite continuous efforts, the best general upper bound known for this number remains as it was more than sixty years ago, of the order of ${2n \choose n}n\ln n$. In this note, we improve this bound by a sub-exponential factor. That is, we prove a bound of the order of ${2n \choose n}e^{-c\sqrt{n}}$ for some universal constant $c>0$. Our approach combines ideas from previous work by Artstein-Avidan and the second named author with tools from Asymptotic Geometric Analysis. One of the key steps is proving a new lower bound for the maximum volume of the intersection of a convex body $K$ with a translate of $-K$; in fact, we get the same lower bound for the volume of the intersection of $K$ and $-K$ when they both have barycenter at the origin. To do so, we make use of measure concentration, and in particular of thin-shell estimates for isotropic log-concave measures. Using the same ideas, we establish an exponentially better bound for $N\left(n\right)$ when restricting our attention to convex bodies that are $\psi_{2}$. By a slightly different approach, an exponential improvement is established also for classes of convex bodies with positive modulus of convexity

Replication, Pathogenesis and Transmission of Pandemic (H1N1) 2009 Virus in Non-Immune Pigs

The declaration of the human influenza A pandemic (H1N1) 2009 (H1N1/09) raised important questions, including origin and host range [1,2]. Two of the three pandemics in the last century resulted in the spread of virus to pigs (H1N1, 1918; H3N2, 1968) with subsequent independent establishment and evolution within swine worldwide [3]. A key public and veterinary health consideration in the context of the evolving pandemic is whether the H1N1/09 virus could become established in pig populations [4]. We performed an infection and transmission study in pigs with A/California/07/09. In combination, clinical, pathological, modified influenza A matrix gene real time RT-PCR and viral genomic analyses have shown that infection results in the induction of clinical signs, viral pathogenesis restricted to the respiratory tract, infection dynamics consistent with endemic strains of influenza A in pigs, virus transmissibility between pigs and virus-host adaptation events. Our results demonstrate that extant H1N1/09 is fully capable of becoming established in global pig populations. We also show the roles of viral receptor specificity in both transmission and tissue tropism. Remarkably, following direct inoculation of pigs with virus quasispecies differing by amino acid substitutions in the haemagglutinin receptor-binding site, only virus with aspartic acid at position 225 (225D) was detected in nasal secretions of contact infected pigs. In contrast, in lower respiratory tract samples from directly inoculated pigs, with clearly demonstrable pulmonary pathology, there was apparent selection of a virus variant with glycine (225G). These findings provide potential clues to the existence and biological significance of viral receptor-binding variants with 225D and 225G during the 1918 pandemic [5]

“It’s hard to tell”. The challenges of scoring patients on standardised outcome measures by multidisciplinary teams: a case study of Neurorehabilitation

Background Interest is increasing in the application of standardised outcome measures in clinical practice. Measures designed for use in research may not be sufficiently precise to be used in monitoring individual patients. However, little is known about how clinicians and in particular, multidisciplinary teams, score patients using these measures. This paper explores the challenges faced by multidisciplinary teams in allocating scores on standardised outcome measures in clinical practice. Methods Qualitative case study of an inpatient neurorehabilitation team who routinely collected standardised outcome measures on their patients. Data were collected using non participant observation, fieldnotes and tape recordings of 16 multidisciplinary team meetings during which the measures were recited and scored. Eleven clinicians from a range of different professions were also interviewed. Data were analysed used grounded theory techniques. Results We identified a number of instances where scoring the patient was 'problematic'. In 'problematic' scoring, the scores were uncertain and subject to revision and adjustment. They sometimes required negotiation to agree on a shared understanding of concepts to be measured and the guidelines for scoring. Several factors gave rise to this problematic scoring. Team members' knowledge about patients' problems changed over time so that initial scores had to be revised or dismissed, creating an impression of deterioration when none had occurred. Patients had complex problems which could not easily be distinguished from each other and patients themselves varied in their ability to perform tasks over time and across different settings. Team members from different professions worked with patients in different ways and had different perspectives on patients' problems. This was particularly an issue in the scoring of concepts such as anxiety, depression, orientation, social integration and cognitive problems. Conclusion From a psychometric perspective these problems would raise questions about the validity, reliability and responsiveness of the scores. However, from a clinical perspective, such characteristics are an inherent part of clinical judgement and reasoning. It is important to highlight the challenges faced by multidisciplinary teams in scoring patients on standardised outcome measures but it would be unwarranted to conclude that such challenges imply that these measures should not be used in clinical practice for decision making about individual patients. However, our findings do raise some concerns about the use of such measures for performance management

18S rRNA is a reliable normalisation gene for real time PCR based on influenza virus infected cells

Background: One requisite of quantitative reverse transcription PCR (qRT-PCR) is to normalise the data with an internal reference gene that is invariant regardless of treatment, such as virus infection. Several studies have found variability in the expression of commonly used housekeeping genes, such as beta-actin (ACTB) and glyceraldehyde-3-phosphate dehydrogenase (GAPDH), under different experimental settings. However, ACTB and GAPDH remain widely used in the studies of host gene response to virus infections, including influenza viruses. To date no detailed study has been described that compares the suitability of commonly used housekeeping genes in influenza virus infections. The present study evaluated several commonly used housekeeping genes [ACTB, GAPDH, 18S ribosomal RNA (18S rRNA), ATP synthase, H+ transporting, mitochondrial F1 complex, beta polypeptide (ATP5B) and ATP synthase, H+ transporting, mitochondrial Fo complex, subunit C1 (subunit 9) (ATP5G1)] to identify the most stably expressed gene in human, pig, chicken and duck cells infected with a range of influenza A virus subtypes. Results: The relative expression stability of commonly used housekeeping genes were determined in primary human bronchial epithelial cells (HBECs), pig tracheal epithelial cells (PTECs), and chicken and duck primary lung-derived cells infected with five influenza A virus subtypes. Analysis of qRT-PCR data from virus and mock infected cells using NormFinder and BestKeeper software programmes found that 18S rRNA was the most stable gene in HBECs, PTECs and avian lung cells. Conclusions: Based on the presented data from cell culture models (HBECs, PTECs, chicken and duck lung cells) infected with a range of influenza viruses, we found that 18S rRNA is the most stable reference gene for normalising qRT-PCR data. Expression levels of the other housekeeping genes evaluated in this study (including ACTB and GPADH) were highly affected by influenza virus infection and hence are not reliable as reference genes for RNA normalisation

A note on Santal\'{o} inequality for the polarity transform and its reverse

We prove a Santal\'{o} and a reverse Santal\'{o} inequality for the polarity transform, which was recently re-discovered by Artstein-Avidan and Milman, in the class consisting of (even) log-concave functions attaining their maximal value 1 at the origin, also called geometric log-cancave functions. The bounds are sharp up to the optimal universal constants.Comment: 10 pages, 1 figure. Section 5 from the previous version was deleted. A characterization of an equality case in Proposition 2 was adde

Evaluation of ELISA and haemagglutination inhibition as screening tests in serosurveillance for H5/H7 avian influenza in commercial chicken flocks

Avian influenza virus (AIV) subtypes H5 and H7 can infect poultry causing low pathogenicity (LP) AI, but these LPAIVs may mutate to highly pathogenic AIV in chickens or turkeys causing high mortality, hence H5/H7 subtypes demand statutory intervention. Serological surveillance in the European Union provides evidence of H5/H7 AIV exposure in apparently healthy poultry. To identify the most sensitive screening method as the first step in an algorithm to provide evidence of H5/H7 AIV infection, the standard approach of H5/H7 antibody testing by haemagglutination inhibition (HI) was compared with an ELISA, which detects antibodies to all subtypes. Sera (n = 1055) from 74 commercial chicken flocks were tested by both methods. A Bayesian approach served to estimate diagnostic test sensitivities and specificities, without assuming any 'gold standard'. Sensitivity and specificity of the ELISA was 97% and 99.8%, and for H5/H7 HI 43% and 99.8%, respectively, although H5/H7 HI sensitivity varied considerably between infected flocks. ELISA therefore provides superior sensitivity for the screening of chicken flocks as part of an algorithm, which subsequently utilises H5/H7 HI to identify infection by these two subtypes. With the calculated sensitivity and specificity, testing nine sera per flock is sufficient to detect a flock seroprevalence of 30% with 95% probability