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Frieze patterns, as introduced by Coxeter in the 1970s, are closely related to cluster algebras without coefficients. A suitable generalization of frieze patterns, linked to cluster algebras with coefficients, has only briefly appeared in an unpublished manuscript by Propp. In this paper, we study these frieze patterns with coefficients systematically and prove various fundamental results, generalizing classic results for frieze patterns. As a consequence, we see how frieze patterns with coefficients can be obtained from classic frieze patterns by cutting out subpolygons from the triangulated polygons associated with classic Conway–Coxeter frieze patterns. We address the question of which frieze patterns with coefficients can be obtained in this way and solve this problem completely for triangles. Finally, we prove a finiteness result for frieze patterns with coefficients by showing that for a given boundary sequence there are only finitely many (nonzero) frieze patterns with coefficients with entries in a subset of the complex numbers without an accumulation point.
We examine the impact of the World Trade Organization (WTO) Government Procurement Agreement (GPA) on government procurement practices in the European Union (EU). We analyse empirically whether the WTO GPA is effective in promoting non-discriminatory, open, transparent, competitive, and cost-effective government procurement. To study this question, we use a unique data set recently released by the EU, covering more than three million tenders conducted in the European Economic Area, Switzerland, and Macedonia during the years 2006–2016. We find that the WTO GPA promotes competition by increasing the probability of awarding a contract to a foreign firm. In addition, the WTO GPA significantly lowers corruption risk by decreasing the number of contracts with single bidders, and by decreasing total number of wins by a single firm. Finally, the WTO GPA fosters cost-effective public procurement by lowering the probability that the procurement price is higher than estimated cost.
This paper considers the agenda for UK trade negotiations over the post-Brexit period. There are several groups of countries that will need to be dealt with and we consider the priorities among them. Negotiations with the WTO and the EU are the most important and the most pressing in time, and should be pursued simultaneously. On the former, the UK must try quickly to establish its independent WTO status, which will be greatly facilitated by minimising the changes it proposes to its tariffs schedules. On the EU the UK needs to consider the choices between remaining in the customs union, creating an FTA with the EU and maintaining the ‘regulatory union’ that is the European Economic Area (EEA). Only when relations with the EU and WTO are clear will it be feasible to negotiate trade deals of various sorts with other countries, ranging from those with which we already have deals via the EU to those that currently trade with us on ‘WTO rules’. All of this takes time and we argue that it may be worth pursuing transitional arrangements to extend certain current trading arrangements a few years beyond Brexit in order to make time for serious negotiations.
This paper presents an assessment of the surplus grass production in the Region of Southern Denmark, and the perspectives of utilizing it in local biogas production. Grass production represents a significant role in the Danish agricultural sector. However, statistical data show an excess production of averagely 12% in the period 2006–2012. Based on spatial analyses and statistical data, the geographical distribution of grass production and consumption was estimated and mapped for the Region of Southern Denmark. An excess production of grass was estimated for several of the municipalities in the Region of Southern Denmark, but the excess production was found to be quite sensitive to the management practice of the grass fields and the productivity of the grass. The yields of excess grass estimated in the sensitive and conservative scenario were found to be sufficient to serve a sole co-substrate in 2–8 biogas plants using animal manure as primary feedstock. The yields in the intensive scenario were assessed to be sufficient to serve a sole co-substrate in 8–16 biogas plants. Alternatively, at least 31% of the regionally produced maize which is exported to the biogas sector could annually be substituted by methane produced from the production of excess grass. The intensive scenario was estimated to have significantly higher grass yields than the sensitive and conservative scenario. The environmental impacts of intensified agricultural management should, however, be assessed carefully in order to ensure that the ecosystems are not increasingly being burdened. The potential of utilizing residual grass for energy production in the region or as an alternative to the maize exported to Northern Germany, was concluded to seem as a promising possibility for a sustainable development of the regional biogas sector. Furthermore, it could provide incentives for establishing new biogas plants in the region and thereby increase the share of manure being digested anaerobically, which could help extrapolate the environmental and climate related benefits documented for the use of digested animal manure as fertilizer on agricultural land.
The (usual) Caldero–Chapoton map is a map from the set of objects of a category to a Laurent polynomial ring over the integers. In the case of a cluster category, it maps reachable indecomposable objects to the corresponding cluster variables in a cluster algebra. This formalizes the idea that the cluster category is a categorification of the cluster algebra. The definition of the Caldero–Chapoton map requires the category to be 2-Calabi-Yau, and the map depends on a cluster-tilting object in the category. We study a modified version of the Caldero–Chapoton map which requires only that the category have a Serre functor and depends only on a rigid object in the category. It is well known that the usual Caldero–Chapoton map gives rise to so-called friezes, for instance, Conway–Coxeter friezes. We show that the modified Caldero–Chapoton map gives rise to what we call generalized friezes and that, for cluster categories of Dynkin type A, it recovers the generalized friezes introduced by combinatorial means in recent work by the authors and Bessenrodt.
Cardinal William Allen, Robert Persons, S. J. and the Rev. Gregory Martin supervised the production in about 1581 of a discussion of cases of consciences, which were intended for the use by students trained for the English mission at the Venerable English College, Rome. The principal manuscript copy of these cases previously known is missing a final section. This has now turned up in the Library of the Society of Antiquaries of London. This article consists of an introduction to the manuscript sources, the cases and their doctrine; a transcript of the Latin text; and a translation of it into English.
The effects of varying dietary digestible protein (DP) and digestible energy (DE) content on performance, nutrient retention efficiency and the de novo lipogenesis of DP origin were examined in triplicate groups of gilthead sea bream (Sparus aurata), fed nine extruded experimental diets. In order to trace the metabolic fate of dietary protein, 1·8 % fishmeal was replaced with isotope-labelled whole protein (>98 % 13C). The experiment was divided into a growth period lasting 89 d, growing fish from approximately 140 to 350 g, followed by a 3 d period feeding isotope-enriched diets. Isotope ratio MS was applied to quantify the 13C enrichment of whole-body lipid from dietary DP. Between 18·6 and 22·4 % of the carbon derived from protein was recovered in the lipid fraction of the fish, and between 21·6 and 30·3 % of the total lipid deposited could be attributed to dietary protein. DP retention was significantly improved by reductions in dietary DP:DE ratio, while the opposite was true for apparent digestible lipid retention. Both overall DE retention and whole-body proximate composition of whole fish were largely unaffected by dietary treatments, while feed conversion ratios were significantly improved with increasing dietary energy density. The present study suggests that gilthead sea bream efficiently utilises dietary nutrients over a wide range of DP:DE ratios and energy densities. In addition, they appear to endeavour a certain body energy status rather than maximising growth, which in the present trial was apparent from inherently high de novo lipogenesis originating from DP.
Depression is a common and costly comorbidity in dementia. There are very few data on the cost-effectiveness of antidepressants for depression in dementia and their effects on carer outcomes.
To evaluate the cost-effectiveness of sertraline and mirtazapine compared with placebo for depression in dementia.
A pragmatic, multicentre, randomised placebo-controlled trial with a parallel cost-effectiveness analysis (trial registration: ISRCTN88882979 and EudraCT 2006-000105-38). The primary cost-effectiveness analysis compared differences in treatment costs for patients receiving sertraline, mirtazapine or placebo with differences in effectiveness measured by the primary outcome, total Cornell Scale for Depression in Dementia (CSDD) score, over two time periods: 0–13 weeks and 0–39 weeks. The secondary evaluation was a cost-utility analysis using quality-adjusted life years (QALYs) computed from the Euro-Qual (EQ-5D) and societal weights over those same periods.
There were 339 participants randomised and 326 with costs data (111 placebo, 107 sertraline, 108 mirtazapine). For the primary outcome, decrease in depression, mirtazapine and sertraline were not cost-effective compared with placebo. However, examining secondary outcomes, the time spent by unpaid carers caring for participants in the mirtazapine group was almost half that for patients receiving placebo (6.74 v. 12.27 hours per week) or sertraline (6.74 v. 12.32 hours per week). Informal care costs over 39 weeks were £1510 and £1522 less for the mirtazapine group compared with placebo and sertraline respectively.
In terms of reducing depression, mirtazapine and sertraline were not cost-effective for treating depression in dementia. However, mirtazapine does appear likely to have been cost-effective if costing includes the impact on unpaid carers and with quality of life included in the outcome. Unpaid (family) carer costs were lower with mirtazapine than sertraline or placebo. This may have been mediated via the putative ability of mirtazapine to ameliorate sleep disturbances and anxiety. Given the priority and the potential value of supporting family carers of people with dementia, further research is warranted to investigate the potential of mirtazapine to help with behavioural and psychological symptoms in dementia and in supporting carers.
The effects of replacing a digestible energy source from fat (fish oil) with carbohydrate (wheat starch) on performance, glycogenesis and de novo lipogenesis was examined in triplicate groups of juvenile gilthead sea bream (Sparus aurata), fed four extruded experimental diets. In order to trace the metabolic fate of dietary starch, 0·7 % wheat starch was replaced with isotope-labelled starch (>98 % 13C). Fish were fed the experimental diets for three consecutive 10 d periods, and isotope ratio MS was applied to quantify 13C enrichment of liver and whole-body glycogen and lipid pools over the three feeding periods. Glycogenesis originating from dietary starch accounted for up to 68·8 and 38·8 % of the liver and whole-body glycogen pools, respectively, while up to 16·7 % of the liver lipid could be attributed to dietary starch. Between 5 and 8 % of dietary starch carbon was recovered in whole-body lipid, and estimated deposition rates of de novo synthesised lipid originating from starch ranged from 18·7 to 123·7 mg/kg biomass per d. Dietary treatments did not significantly affect growth, feed performance or body composition of the fish, while the hepatosomatic index and glycogen content of whole fish and livers correlated directly with dietary starch inclusion level. The study suggests that gilthead sea bream efficiently synthesises glycogen from both dietary starch and endogenous sources. In contrast, lipogenesis from carbon derived from starch seems to play a minor role in overall lipid synthesis and deposition under the specified experimental conditions.
Systemic corticosteroids are a mainstay of treatment for many pediatric medical conditions. Although their impact on the central nervous system has been well-studied in animal models and adults, less is known about such effects in pediatric populations. The current study investigated acute effects of corticosteroids on memory, executive functions, emotion, and behavior in children and adolescents with inflammatory bowel disease (IBD). Patients 8–17 years with IBD (Crohn's disease, CD; ulcerative colitis, UC) on high-dose prednisone (n = 33) and IBD patients in remission off steroids (n = 33) completed standardized neuropsychological tests and behavior rating scales. In the IBD sample as a whole, few steroid effects were found for laboratory cognitive measures, but steroid-treated patients were rated as exhibiting more problems with emotional, and to a lesser extent with cognitive function in daily life. Steroid effects, assessed by laboratory measures and questionnaires, were more prevalent in CD than UC patients; UC patients on steroids sometimes performed better than controls. Sleep disruption also predicted some outcomes, diminishing somewhat the magnitude of the steroid effects. Corticosteroid therapy can have acute effects on cognition, emotion, and behavior in chronically ill children; the clinical and long-term significance of these effects require further investigation. (JINS, 2012, 19, 1–14)
Globally, areas categorically known to be free of human visitation are rare, but still exist in Antarctica. Such areas may be among the most pristine locations remaining on Earth and, therefore, be valuable as baselines for future comparisons with localities impacted by human activities, and as sites preserved for scientific research using increasingly sophisticated future technologies. Nevertheless, unvisited areas are becoming increasingly rare as the human footprint expands in Antarctica. Therefore, an understanding of historical and contemporary levels of visitation at locations across Antarctica is essential to a) estimate likely cumulative environmental impact, b) identify regions that may have been impacted by non-native species introductions, and c) inform the future designation of protected areas under the Antarctic Treaty System. Currently, records of Antarctic tourist visits exist, but little detailed information is readily available on the spatial and temporal distribution of national governmental programme activities in Antarctica. Here we describe methods to fulfil this need. Using information within field reports and archive and science databases pertaining to the activities of the United Kingdom as an illustration, we describe the history and trends in its operational footprint in the Antarctic Peninsula since c. 1944. Based on this illustration, we suggest that these methodologies could be applied productively more generally.
The host range of a mixture of Choristoneura fumiferana (Clemens) nucleopolyhedroviruses (CfMNPV and CfDefNPV) was investigated using a per os bioassay of larvae of 29 species of Lepidoptera and adult males of Megachile rotundata (F.) (Hymenoptera: Megachilidae). Using a whole-genomic DNA probe, positive results were obtained in 8 of 10 Tortricidae: Archips cerasivorana (Fitch), Choristoneura fractivittana (Clemens), C. fumiferana, Choristoneura occidentalis Freeman, Choristoneura pinus pinus Freeman, Choristoneura rosaceana (Harris), Clepsis persicana (Fitch), and Cydia pomonella (L.); one Crambidae: Ostrinia nubilalis (Hübner); one arctiine Erebidae: Estigmene acrea (Drury); and two Noctuidae: Oligia illocata (Walker) and Pyrrhia exprimens (Walker). Mortality rates were highest among C. fumiferana, C. occidentalis, C. pinus pinus, A. cerasivorana, and C. pomonella. Sequenced polymerase chain reaction (PCR) amplicons from infected individuals from several species confirmed that the primer sets amplified the target viruses. CfMNPV was consistently found in virus-fed C. fumiferana; whereas, CfDefNPV was present only occasionally. The presence of CfMNPV and CfDefNPV in A. cerasivorana was confirmed by PCR and DNA sequencing. Significant treatment-mortality rates were induced in the noctuids P. exprimens and Acronicta impleta Walker; PCR determined that both viruses were present in treated P. exprimens but only CfMNPV was present in A. impleta. No virus was detected in M. rotundata.