The number of meets between two subsets of a lattice

AbstractLet L be a lattice of divisors of an integer (isomorphically, a direct product of chains). We prove |A| |B| ⩽ |L| |A ∧ B| for any A, B ⊃ L, where |·| denotes cardinality and A ∧ B = {a ∧ b: a ϵ A, b ϵ B}. |A ∧ B| attains its minimum for fixed |A|, |B| when A and B are ideals. |·| can be replaced by certain other weight functions. When the n chains are of equal size k, the elements may be viewed as n-digit k-ary numbers. Then for fixed |A|, |B|, |A ∧ B| is minimized when A and B are the |A| and |B| smallest n-digit k-ary numbers written backwards and forwards, respectively. |A ∧ B| for these sets is determined and bounded. Related results are given, and conjectures are made

A generalized model for fuel channel bore estimation in AGR cores

One of the major life-limiting factors of an Advanced Gas-cooled Reactor (AGR) nuclear power station is the graphite core as it cannot be repaired or replaced and therefore detailed information about the health of the core is vital for continued safe operation. The graphite bricks that comprise the core experience gradual degradation during operation as a result of irradiation. Routine physical inspection of the graphite core fuel channels is performed by specialist inspection equipment during outages every 12 months to 3 years. It has also been shown to be advantageous to supplement this periodic inspection information with analysis of operational data which can provide additional insights into the core health. One such approach is through the use of online monitoring data called the Fuel Grab Load Trace (FGLT). An FGLT is a measure of the perceived load of the fuel assembly with contributions from aerodynamic forces and frictional forces, which is related to bore diameter. This paper describes enhancements to existing analysis of FGLT data which, to date, has focussed solely on using data from a single reactor at a time to build bore estimation models, by considering data from multiple reactors to produce a generalised model of bore estimation. This paper initially describes the process of producing a bore estimation from an FGLT by isolating the contribution that relates to the fuel channel bore and then discusses the limitations with the existing bore estimation model. Improvements are then proposed for the bore estimation model and a detailed assessment is undertaken to understand the effect of each of these proposed improvements. In addition, the effect of introducing non-linear regression models to further enhance the bore estimation is explored. The existing model is trained on data from one reactor in the UK and therefore the results produced from it are only applicable to this reactor. However, out of the remaining 13 nuclear reactors currently in operation, 3 also have a similar construction to the reactor the model is trained on, and these should all produce similar FGLT data. Therefore, a generalised model is proposed that produces bore estimations for four AGRs station’s reactors, compared with one previously. It is shown that this approach offers an improved overall bore estimation model

Periodic variability of spotted M dwarfs in WTS

This is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.We present an analysis of the photometric variability of M dwarfs in the WFCAM Transit Survey, selected from spectral types inferred by their WTS and SDSS colours, with periods detected using a Lomb-Scargle Periodogram Analisys. We estimate population membership of these objects from their tangential velocities and photometric parralaxes. Examples of M dwarfs with variable light curve morphologuies are found. We discuss possible causes for this and make use of models of spotted stars in our interpretation of the results

Chemotherapy versus supportive care in advanced non-small cell lung cancer: improved survival without detriment to quality of life

BACKGROUND: In 1995 a meta-analysis of randomised trials investigating the value of adding chemotherapy to primary treatment for non-small cell lung cancer (NSCLC) suggested a small survival benefit for cisplatin-based chemotherapy in each of the primary treatment settings. However, the metaanalysis included many small trials and trials with differing eligibility criteria and chemotherapy regimens. METHODS: The aim of the Big Lung Trial was to confirm the survival benefits seen in the meta-analysis and to assess quality of life and cost in the supportive care setting. A total of 725 patients were randomised to receive supportive care alone (n = 361) or supportive care plus cisplatin-based chemotherapy (n = 364). RESULTS: 65% of patients allocated chemotherapy (C) received all three cycles of treatment and a further 27% received one or two cycles. 74% of patients allocated no chemotherapy (NoC) received thoracic radiotherapy compared with 47% of the C group. Patients allocated C had a significantly better survival than those allocated NoC: HR 0.77 (95% CI 0.66 to 0.89, p = 0.0006), median survival 8.0 months for the C group v 5.7 months for the NoC group, a difference of 9 weeks. There were 19 (5%) treatment related deaths in the C group. There was no evidence that any subgroup benefited more or less fromchemotherapy. No significant differences were observed between the two groups in terms of the pre-defined primary and secondary quality of life end points, although large negative effects of chemotherapy were ruled out. The regimens used proved to be cost effective, the extra cost of chemotherapy being offset by longer survival. CONCLUSIONS: The survival benefit seen in this trial was entirely consistent with the NSCLC meta-analysis and subsequent similarly designed large trials. The information on quality of life and cost should enablepatients and their clinicians to make more informed treatment choices

Curvature corrections and Kac-Moody compatibility conditions

We study possible restrictions on the structure of curvature corrections to gravitational theories in the context of their corresponding Kac--Moody algebras, following the initial work on E10 in Class. Quant. Grav. 22 (2005) 2849. We first emphasize that the leading quantum corrections of M-theory can be naturally interpreted in terms of (non-gravity) fundamental weights of E10. We then heuristically explore the extent to which this remark can be generalized to all over-extended algebras by determining which curvature corrections are compatible with their weight structure, and by comparing these curvature terms with known results on the quantum corrections for the corresponding gravitational theories.Comment: 27 page

Random Sierpinski network with scale-free small-world and modular structure

In this paper, we define a stochastic Sierpinski gasket, on the basis of which we construct a network called random Sierpinski network (RSN). We investigate analytically or numerically the statistical characteristics of RSN. The obtained results reveal that the properties of RSN is particularly rich, it is simultaneously scale-free, small-world, uncorrelated, modular, and maximal planar. All obtained analytical predictions are successfully contrasted with extensive numerical simulations. Our network representation method could be applied to study the complexity of some real systems in biological and information fields.Comment: 7 pages, 9 figures; final version accepted for publication in EPJ

Duration and Magnitude of Postoperative Risk of Venous Thromboembolism after Cholecystectomy: A Population-Based Cohort Study

Background: This study aimed to identify burden and risk of VTE associated with cholecystectomy in England. Methods: An historical cohort study of cholecystectomy patients from 2001-2011 was undertaken using linked primary (Clinical Practice Research Datalink) and secondary (Hospital Episode Statistics) care data. Crude rates and adjusted hazard ratios (HRs) were calculated for risk of VTE following cholecystectomy using Cox regression.Results: 24 677 patients were identified with a rate of VTE in the first year following cholecystectomy of 2.80 per 1000 person years (95% CI 2.18-3.59). Patients aged >/=70 vs aged 30 vs BMI less than 0 had 2.4-fold increase in risk (HR 2.42, 95% CI 1.40–4.18); open vs. laparoscopic operation had 3-fold increase in risk (HR 2.94, 95% CI 1.55–5.55). Compared to general population, VTE risk was the highest in the first 30 days post-operatively with 9.9-fold risk following emergency cholecystectomy and 4.5-fold risk after inpatient cholecystectomy (HR 9.90, 95% CI 4.42–22.21; HR 4.54, 95% CI 2.85–7.21). Conclusions: Cholecystectomy is associated with a low absolute risk of VTE and we have identified high risk groups including the elderly, obese and those having open surgery

Généralisation du diagramme de Voronoï et placement de formes géométriques complexes dans un nuage de points.

La géométrie algorithmique est une discipline en pleine expansion dont l'objet est la conception d'algorithmes résolvant des problèmes géométriques. De tels algorithmes sont très utiles notamment dans l'ingénierie, l'industrie et le multimédia. Pour être performant, il est fréquent qu'un algorithme géométrique utilise des structures de données spécialisées.Nous nous sommes intéressés à une telle structure : le diagramme de Voronoï et avons proposé une généralisation de celui-ci. Ladite généralisation résulte d'une extension du prédicat du disque vide (prédicat propre à toute région de Voronoï) à une union de disques. Nous avons analysé les régions basées sur le prédicat étendu et avons proposé des méthodes pour les calculer par ordinateur.Par ailleurs, nous nous sommes intéressés aux problèmes de placement de formes , thème récurrent en géométrie algorithmique. Nous avons introduit un formalisme universel pour de tels problèmes et avons, pour la première fois, proposé une méthode de résolution générique, en ce sens qu'elle est apte à résoudre divers problèmes de placement suivant un même algorithme.Nos travaux présentent, d'une part, l'avantage d'élargir le champ d'application de structures de données basées sur Voronoï. D'autre part, ils facilitent de manière générale l'utilisation de la géométrie algorithmique, en unifiant définitions et algorithmes associés aux problèmes de placement de formes.Computational geometry is an active branch of computer science whose goal is the design of efficient algorithms solving geometric problems. Such algorithms are useful in domains like engineering, industry and multimedia. In order to be efficient, algorithms often use special data structures.In this thesis we focused on such a structure: the Voronoi diagram. We proposed a new generalized diagram. We have proceeded by extending the empty disk predicate (satisfied by every Voronoi region) to an arbitrary union of disks. We have analyzed the new plane regions based on the extended predicate, and we designed algorithms for computing them.Then, we have considered another topic, which is related to the first one: shape placement problems. Such problems have been studied repeatedly by researchers in computational geometry. We introduced new notations along with a global framework for such problems. We proposed, for the first time a generic method, which is able to solve various placement problems using a single algorithm.Thus, our work extend the scope of Voronoi based data structures. It also simplifies the practical usage of placement techniques by unifying the associated definitions and algorithms.MULHOUSE-SCD Sciences (682242102) / SudocSudocFranceF

Improved explicability for pump diagnostics in nuclear power plants

To ensure the continued safe operation of many of the UK's fleet of advanced gas-cooled reactors (AGRs) effective and reliable monitoring of several of the key plant items is essential. Out of these key items, a significant portion of these are rotating plant assets, one asset in particular that is crucial to the operation of the station are the boiler feed pumps (BFPs). The BFPs in an AGR station move water from a condenser into a boiler, the water is then heated which produces steam and this steam turns the electricity-generating turbines. Currently, the operator of the AGR stations employs a time-based maintenance strategy for BFP assets: after a defined amount of time each asset is removed, replaced with a rotated spare, and a complete overhaul is then performed on the removed asset. This procedure can result in the removal of an asset before any significant wear has occurred, therefore increasing maintenance and generation costs. Conversely, this could result in an unplanned outage due to a component failure which leads to both a decrease in power output of the station and hence a decrease in revenue for the operator. Because these pumps are essential for the generation of electricity there are several pressure, temperature, vibration and speed parameters constantly monitored during the operation of this asset. Currently, data analysts have to manually analyse all this data by following a set diagnosis process, the consequential time burden on the analyst is therefore extremely high. Data-driven approaches to solve this problem, and other similar problems, have the capability to produce accurate results similar to what the analysts can achieve in a fraction of the time. However, the majority of these techniques are black box techniques and lack explicability which is often a requirement for problems involving critical assets in the nuclear industry. The main outcomes of this work are to address the time burden placed on the analysts by automating elements of the existing diagnosis process, through the implementation of an intelligent rule-based expert system, that provides adequate explicability to the user to satisfy requirements. Additionally, a recurring problem in the design of expert systems for industry is the cost involved with the knowledge elicitation process. Here we propose a questionnaire style approach, similar to what the domain experts currently use, to extract this knowledge without the need for a structured interview. By using this information a signal-to-symbol transformation algorithm is designed to assign time periods symbols that relate to the various rules defined by the domain experts. The final system combines the data-driven signal-to-symbol transformation algorithm and the rule-based expert system to produce a hybrid system that can be used to classify defects based on a set of rules and also explain to the user the reasoning behind this solution

The structural basis for high‐affinity uptake of lignin‐derived aromatic compounds by proteobacterial TRAP transporters

The organic polymer lignin is a component of plant cell walls, which like (hemi)-cellulose is highly abundant in nature and relatively resistant to degradation. However, extracellular enzymes released by natural microbial consortia can cleave the β-aryl ether linkages in lignin, releasing monoaromatic phenylpropanoids that can be further catabolised by diverse species of bacteria. Biodegradation of lignin is therefore important in global carbon cycling, and its natural abundance also makes it an attractive biotechnological feedstock for the industrial production of commodity chemicals. Whilst the pathways for degradation of lignin-derived aromatics have been extensively characterised, much less is understood about how they are recognised and taken up from the environment. The purple phototrophic bacterium Rhodopseudomonas palustris can grow on a range of phenylpropanoid monomers and is a model organism for studying their uptake and breakdown. R. palustris encodes a tripartite ATP-independent periplasmic (TRAP) transporter (TarPQM) linked to genes encoding phenylpropanoid-degrading enzymes. The periplasmic solute-binding protein component of this transporter, TarP, has previously been shown to bind aromatic substrates. Here, we determine the high-resolution crystal structure of TarP from R. palustris as well as the structures of homologous proteins from the salt marsh bacterium Sagittula stellata and the halophile Chromohalobacter salexigens, which also grow on lignin-derived aromatics. In combination with tryptophan fluorescence ligand-binding assays, our ligand-bound co-crystal structures reveal the molecular basis for high-affinity recognition of phenylpropanoids by these TRAP transporters, which have potential for improving uptake of these compounds for biotechnological transformations of lignin