Evaluating the rank generating function of a graphic 2-polymatroid

We consider the complexity of the two-variable rank generating function, $S$, of a graphic 2-polymatroid. For a graph $G$, $S$ is the generating function for the number of subsets of edges of $G$ having a particular size and incident with a particular number of vertices of $G$. We show that for any $x,y \in \mathbb{Q}$ with $xy \not = 1$, it is $\#$P-hard to evaluate $S$ at $(x,y)$. We also consider the $k$-thickening of a graph and computing $S$ for the $k$-thickening of a graph

The complexity of two graph orientation problems

This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2012 ElsevierWe consider two orientation problems in a graph, namely the minimization of the sum of all the shortest path lengths and the minimization of the diameter. Our main result is that for each positive integer k, there is a linear-time algorithm that decides for a planar graph Gwhether there is an orientation for which the diameter is at most k. We also extend this result from planar graphs to any minor-closed family F not containing all apex graphs. In contrast, it is known to be NP-complete to decide whether a graph has an orientation such that the sum of all the shortest path lengths is at most an integer specified in the input. We give a simpler proof of this result.This work is partially supported by EC Marie Curie programme NET-ACE (MEST-CT-2004-6724), and Heilbronn Institute for Mathematical Research, Bristol

The equivalence of two graph polynomials and a symmetric function

The U-polynomial, the polychromate and the symmetric function generalization of the Tutte polynomial due to Stanley are known to be equivalent in the sense that the coefficients of any one of them can be obtained as a function of the coefficients of any other. The definition of each of these functions suggests a natural way in which to strengthen them which also captures Tutte's universal V-function as a specialization. We show that the equivalence remains true for the strong functions thus answering a question raised by Dominic Welsh

Minimizing the oriented diameter of a planar graph

We consider the problem of minimizing the diameter of an orientation of a planar graph. A result of Chvátal and Thomassen shows that for general graphs, it is NP-complete to decide whether a graph can be oriented so that its diameter is at most two. In contrast to this, for each constant l, we describe an algorithm that decides if a planar graph G has an orientation with diameter at most l and runs in time O(c|V|), where c depends on l

A systematic review of studies reporting on neuropsychological and functional domains used for assessment of recovery from delirium in acute hospital patients

Objectives: Assessing for recovery in delirium is essential in guiding ongoing investigation and treatment. Yet, there is little scrutiny and no research or clinical consensus on how recovery should be measured. We reviewed studies which used tests of neuropsychological domains and functional ability to track recovery of delirium longitudinally in acute hospital settings. / Methods/Design: We systematically searched databases (MEDLINE, PsycInfo, CINAHL, Embase, ClinicalTrials.gov, Cochrane Central Register of Controlled Trials), from inception to October 14th, 2022. Inclusion criteria were: adult acute hospital patients (≥18 years) diagnosed with delirium by a validated tool; 1+ repeat assessment using an assessment tool measuring domains of delirium/functional recovery ≤7 days from baseline. Two reviewers independently screened articles, performed data extraction, and assessed risk of bias. A narrative data synthesis was completed. / Results: From 6533 screened citations, we included 39 papers (reporting 32 studies), with 2370 participants with delirium. Studies reported 21 tools with an average of four repeat assessments including baseline (range 2–10 assessments within ≤7 days), measuring 15 specific domains. General cognition, functional ability, arousal, attention and psychotic features were most commonly assessed for longitudinal change. Risk of bias was moderate to high for most studies. / Conclusions: There was no standard approach for tracking change in specific domains of delirium. The methodological heterogeneity of studies was too high to draw firm conclusions on the effectiveness of assessment tools to measure delirium recovery. This highlights the need for standardised methods for assessing recovery from delirium

Regional differences in APD restitution can initiate wavebreak and re-entry in cardiac tissue: A computational study

Background Regional differences in action potential duration (APD) restitution in the heart favour arrhythmias, but the mechanism is not well understood. Methods We simulated a 150 × 150 mm 2D sheet of cardiac ventricular tissue using a simplified computational model. We investigated wavebreak and re-entry initiated by an S1S2S3 stimulus protocol in tissue sheets with two regions, each with different APD restitution. The two regions had a different APD at short diastolic interval (DI), but similar APD at long DI. Simulations were performed twice; once with both regions having steep (slope > 1), and once with both regions having flat (slope < 1) APD restitution. Results Wavebreak and re-entry were readily initiated using the S1S2S3 protocol in tissue sheets with two regions having different APD restitution properties. Initiation occurred irrespective of whether the APD restitution slopes were steep or flat. With steep APD restitution, the range of S2S3 intervals resulting in wavebreak increased from 1 ms with S1S2 of 250 ms, to 75 ms (S1S2 180 ms). With flat APD restitution, the range of S2S3 intervals resulting in wavebreak increased from 1 ms (S1S2 250 ms), to 21 ms (S1S2 340 ms) and then 11 ms (S1S2 400 ms). Conclusion Regional differences in APD restitution are an arrhythmogenic substrate that can be concealed at normal heart rates. A premature stimulus produces regional differences in repolarisation, and a further premature stimulus can then result in wavebreak and initiate re-entry. This mechanism for initiating re-entry is independent of the steepness of the APD restitution curve

Hsp90 governs dispersion and drug resistance of fungal biofilms

Fungal biofilms are a major cause of human mortality and are recalcitrant to most treatments due to intrinsic drug resistance. These complex communities of multiple cell types form on indwelling medical devices and their eradication often requires surgical removal of infected devices. Here we implicate the molecular chaperone Hsp90 as a key regulator of biofilm dispersion and drug resistance. We previously established that in the leading human fungal pathogen, Candida albicans, Hsp90 enables the emergence and maintenance of drug resistance in planktonic conditions by stabilizing the protein phosphatase calcineurin and MAPK Mkc1. Hsp90 also regulates temperature-dependent C. albicans morphogenesis through repression of cAMP-PKA signalling. Here we demonstrate that genetic depletion of Hsp90 reduced C. albicans biofilm growth and maturation in vitro and impaired dispersal of biofilm cells. Further, compromising Hsp90 function in vitro abrogated resistance of C. albicans biofilms to the most widely deployed class of antifungal drugs, the azoles. Depletion of Hsp90 led to reduction of calcineurin and Mkc1 in planktonic but not biofilm conditions, suggesting that Hsp90 regulates drug resistance through different mechanisms in these distinct cellular states. Reduction of Hsp90 levels led to a marked decrease in matrix glucan levels, providing a compelling mechanism through which Hsp90 might regulate biofilm azole resistance. Impairment of Hsp90 function genetically or pharmacologically transformed fluconazole from ineffectual to highly effective in eradicating biofilms in a rat venous catheter infection model. Finally, inhibition of Hsp90 reduced resistance of biofilms of the most lethal mould, Aspergillus fumigatus, to the newest class of antifungals to reach the clinic, the echinocandins. Thus, we establish a novel mechanism regulating biofilm drug resistance and dispersion and that targeting Hsp90 provides a much-needed strategy for improving clinical outcome in the treatment of biofilm infections

A pilot Internet "Value of Health" Panel: recruitment, participation and compliance

Objectives To pilot using a panel of members of the public to provide preference data via the Internet Methods A stratified random sample of members of the general public was recruited and familiarised with the standard gamble procedure using an Internet based tool. Health states were perdiodically presented in "sets" corresponding to different conditions, during the study. The following were described: Recruitment (proportion of people approached who were trained); Participation (a) the proportion of people trained who provided any preferences and (b) the proportion of panel members who contributed to each "set" of values; and Compliance (the proportion, per participant, of preference tasks which were completed). The influence of covariates on these outcomes was investigated using univariate and multivariate analyses. Results A panel of 112 people was recruited. 23% of those approached (n = 5,320) responded to the invitation, and 24% of respondents (n = 1,215) were willing to participate (net = 5.5%). However, eventual recruitment rates, following training, were low (2.1% of those approached). Recruitment from areas of high socioeconomic deprivation and among ethnic minority communities was low. Eighteen sets of health state descriptions were considered over 14 months. 74% of panel members carried out at least one valuation task. People from areas of higher socioeconomic deprivation and unmarried people were less likely to participate. An average of 41% of panel members expressed preferences on each set of descriptions. Compliance ranged from 3% to 100%. Conclusion It is feasible to establish a panel of members of the general public to express preferences on a wide range of health state descriptions using the Internet, although differential recruitment and attrition are important challenges. Particular attention to recruitment and retention in areas of high socioeconomic deprivation and among ethnic minority communities is necessary. Nevertheless, the panel approach to preference measurement using the Internet offers the potential to provide specific utility data in a responsive manner for use in economic evaluations and to address some of the outstanding methodological uncertainties in this field

Cosmogenic neutron production at the Sudbury Neutrino Observatory

Neutrons produced in nuclear interactions initiated by cosmic-ray muons present an irreducible background to many rare-event searches, even in detectors located deep underground. Models for the production of these neutrons have been tested against previous experimental data, but the extrapolation to deeper sites is not well understood. Here we report results from an analysis of cosmogenically produced neutrons at the Sudbury Neutrino Observatory. A specific set of observables are presented, which can be used to benchmark the validity of geant4 physics models. In addition, the cosmogenic neutron yield, in units of 10-4 cm2/(g·μ), is measured to be 7.28±0.09(stat)-1.12+1.59(syst) in pure heavy water and 7.30±0.07(stat)-1.02+1.40(syst) in NaCl-loaded heavy water. These results provide unique insights into this potential background source for experiments at SNOLAB