A Poset Connected to Artin Monoids of Simply Laced Type

Let W be a Weyl group whose type is a simply laced Dynkin diagram. On several W-orbits of sets of mutually commuting reflections, a poset is described which plays a role in linear representatons of the corresponding Artin group A. The poset generalizes many properties of the usual order on positive roots of W given by height. In this paper, a linear representation of the positive monoid of A is defined by use of the poset

BMW algebras of simply laced type

It is known that the recently discovered representations of the Artin groups of type A_n, the braid groups, can be constructed via BMW algebras. We introduce similar algebras of type D_n and E_n which also lead to the newly found faithful representations of the Artin groups of the corresponding types. We establish finite dimensionality of these algebras. Moreover, they have ideals I_1 and I_2 with I_2 contained in I_1 such that the quotient with respect to I_1 is the Hecke algebra and I_1/I_2 is a module for the corresponding Artin group generalizing the Lawrence-Krammer representation. Finally we give conjectures on the structure, the dimension and parabolic subalgebras of the BMW algebra, as well as on a generalization of deformations to Brauer algebras for simply laced spherical type other than A_n.Comment: 39 page

Tangle and Brauer Diagram Algebras of Type Dn

A generalization of the Kauffman tangle algebra is given for Coxeter type Dn. The tangles involve a pole or order 2. The algebra is shown to be isomorphic to the Birman-Murakami-Wenzl algebra of the same type. This result extends the isomorphism between the two algebras in the classical case, which in our set-up, occurs when the Coxeter type is of type A with index n-1. The proof involves a diagrammatic version of the Brauer algebra of type Dn in which the Temperley-Lieb algebra of type Dn is a subalgebra.Comment: 33 page

BMW algebras of simply laced type

It is known that the recently discovered representations of the Artin groups of type A_n, the braid groups, can be constructed via BMW algebras. We introduce similar algebras of type D_n and E_n which also lead to the newly found faithful representations of the Artin groups of the corresponding types. We establish finite dimensionality of these algebras. Moreover, they have ideals I_1 and I_2 with I_2 contained in I_1 such that the quotient with respect to I_1 is the Hecke algebra and I_1/I_2 is a module for the corresponding Artin group generalizing the Lawrence-Krammer representation. Finally we give conjectures on the structure, the dimension and parabolic subalgebras of the BMW algebra, as well as on a generalization of deformations to Brauer algebras for simply laced spherical type other than A_n

OpenMI: the essential concepts and their implications for legacy software

International audienceInformation & Communication Technology (ICT) tools such as computational models are very helpful in designing river basin management plans (rbmp-s). However, in the scientific world there is consensus that a single integrated modelling system to support e.g. the implementation of the Water Framework Directive cannot be developed and that integrated systems need to be very much tailored to the local situation. As a consequence there is an urgent need to increase the flexibility of modelling systems, such that dedicated model systems can be developed from available building blocks. The HarmonIT project aims at precisely that. Its objective is to develop and implement a standard interface for modelling components and other relevant tools: The Open Modelling Interface (OpenMI) standard. The OpenMI standard has been completed and documented. It relies entirely on the "pull" principle, where data are pulled by one model from the previous model in the chain. This paper gives an overview of the OpenMI standard, explains the foremost concepts and the rational behind it

Tangle and Brauer diagram algebras of type D_n

A generalization of the Kauffman tangle algebra is given for Coxeter type D_n. The tangles involve a pole of order 2. The algebra is shown to be isomorphic to the Birman–Murakami–Wenzl algebra of the same type. This result extends the isomorphism between the two algebras in the classical case, which, in our set-up, occurs when the Coxeter type is A_(n - 1). The proof involves a diagrammatic version of the Brauer algebra of type Dn of which the generalized Temperley–Lieb algebra of type D_n is a subalgebra

Dairy consumption and cardiometabolic diseases: systematic review and updated meta-analyses of prospective cohort studies

Purpose of Review Dairy products contain both beneficial and harmful nutrients in relation to cardiometabolic diseases. Here, we provide the latest scientific evidence regarding the relationship between dairy products and cardiometabolic diseases by reviewing the literature and updating meta-analyses of observational studies. Recent Findings We updated our previous meta-analyses of cohort studies on type 2 diabetes, coronary heart disease (CHD), and stroke with nine studies and confirmed previous results. Total dairy and low-fat dairy (per 200 g/d) were inversely associated with a 3–4% lower risk of diabetes. Yogurt was non-linearly inversely associatedwith diabetes (RR = 0.86, 95%CI: 0.83–0.90 at 80 g/ d). Total dairy and milk were not associated with CHD (RR~1.0). An increment of 200 g of daily milk intake was associated with an 8% lower risk of stroke. Summary The latest scientific evidence confirmed neutral or beneficial associations between dairy products and risk of cardiometabolic diseases

Milk and dairy consumption and risk of cardiovascular diseases and all-cause mortality: dose-response meta-analysis of prospective cohort studies

With a growing number of prospective cohort studies, an updated dose-response meta-analysis of milk and dairy products with all-cause mortality, coronary heart disease (CHD) or cardiovascular disease (CVD) have been conducted. PubMed, Embase and Scopus were searched for articles published up to September 2016. Random-effect meta-analyses with summarised dose-response data were performed for total (high-fat/low-fat) dairy, milk, fermented dairy, cheese and yogurt. Non-linear associations were investigated using the spine models and heterogeneity by subgroup analyses. A total of 29 cohort studies were available for meta-analysis, with 938,465 participants and 93,158 mortality, 28,419 CHD and 25,416 CVD cases. No associations were found for total (high-fat/low-fat) dairy, and milk with the health outcomes of mortality, CHD or CVD. Inverse associations were found between total fermented dairy (included sour milk products, cheese or yogurt; per 20 g/day) with mortality (RR 0.98, 95% CI 0.97-0.99; I2 = 94.4%) and CVD risk (RR 0.98, 95% CI 0.97-0.99; I2 = 87.5%). Further analyses of individual fermented dairy of cheese and yogurt showed cheese to have a 2% lower risk of CVD (RR 0.98, 95% CI 0.95-1.00; I2 = 82.6%) per 10 g/day, but not yogurt. All of these marginally inverse associations of totally fermented dairy and cheese were attenuated in sensitivity analyses by removing one large Swedish study. This meta-analysis combining data from 29 prospective cohort studies demonstrated neutral associations between dairy products and cardiovascular and all-cause mortality. For future studies it is important to investigate in more detail how dairy products can be replaced by other foods

Milk and dairy products: good or bad for human health? An assessment of the totality of scientific evidence

Background: There is scepticism about health effects of dairy products in the public, which is reflected in an increasing intake of plant-based drinks, for example, from soy, rice, almond, or oat. Objective: This review aimed to assess the scientific evidence mainly from meta-analyses of observational studies and randomised controlled trials, on dairy intake and risk of obesity, type 2 diabetes, cardiovascular disease, osteoporosis, cancer, and all-cause mortality. Results: The most recent evidence suggested that intake of milk and dairy products was associated with reduced risk of childhood obesity. In adults, intake of dairy products was shown to improve body composition and facilitate weight loss during energy restriction. In addition, intake of milk and dairy products was associated with a neutral or reduced risk of type 2 diabetes and a reduced risk of cardiovascular disease, particularly stroke. Furthermore, the evidence suggested a beneficial effect of milk and dairy intake on bone mineral density but no association with risk of bone fracture. Among cancers, milk and dairy intake was inversely associated with colorectal cancer, bladder cancer, gastric cancer, and breast cancer, and not associated with risk of pancreatic cancer, ovarian cancer, or lung cancer,while the evidence for prostate cancer risk was inconsistent.Finally,consumption of milk and dairy products was not associated with all-cause mortality. Calcium-fortified plant-based drinks have been included as an alternative to dairy products in the nutrition recommendations in several countries. However, nutritionally, cow’s milk and plant-based drinks are completely different foods,and an evidence-based conclusion on the health value of the plant-based drinks requires more studies in humans. Conclusion: The totality of available scientific evidence supports that intake of milk and dairy products contribute to meet nutrient recommendations, and may protect against the most prevalent chronic diseases, whereas very few adverse effects have been reported