Pruning Algorithms for Pretropisms of Newton Polytopes

Pretropisms are candidates for the leading exponents of Puiseux series that represent solutions of polynomial systems. To find pretropisms, we propose an exact gift wrapping algorithm to prune the tree of edges of a tuple of Newton polytopes. We prefer exact arithmetic not only because of the exact input and the degrees of the output, but because of the often unpredictable growth of the coordinates in the face normals, even for polytopes in generic position. We provide experimental results with our preliminary implementation in Sage that compare favorably with the pruning method that relies only on cone intersections.Comment: exact, gift wrapping, Newton polytope, pretropism, tree pruning, accepted for presentation at Computer Algebra in Scientific Computing, CASC 201

Multigraded Castelnuovo-Mumford Regularity

We develop a multigraded variant of Castelnuovo-Mumford regularity. Motivated by toric geometry, we work with modules over a polynomial ring graded by a finitely generated abelian group. As in the standard graded case, our definition of multigraded regularity involves the vanishing of graded components of local cohomology. We establish the key properties of regularity: its connection with the minimal generators of a module and its behavior in exact sequences. For an ideal sheaf on a simplicial toric variety X, we prove that its multigraded regularity bounds the equations that cut out the associated subvariety. We also provide a criterion for testing if an ample line bundle on X gives a projectively normal embedding.Comment: 30 pages, 5 figure

Captain Jinks

80.7568.184 – “Captain Jinks”: T. Maclagan: Oliver Ditson & Co.: n.d.: Voice

Captain Jinks

1. I am Captain Jinks of the Horse Marines, I often live beyond my means, I sport young ladies in their teens, To cut a swell in the army. I teach the ladies how to dance, how to dance, how to dance, I teach the ladies how to dance, For I\u27m their pet in the army. I\u27m Captain Jinks of the Horse Marines, I give my horse good corn and beans; Of course its quite beyond my means, Tho a Captain in the army. 2. I join\u27d my corps when twenty-one, Of course I thought it capital fun; When the enemy came, then off I run, I wasn\u27t cut out for the army. When I left home mama she cried, mama she cried, mama she cried, When I left home mama she cried He aint cut out for the army. 3, The first day I went out to drill The bugle sound made me quite ill. At the Balance step my hat it fell, And that wouldn\u27t do for the army. The officers they all did shout, they all cried out, they all did shout, The officers they all did shout Oh that\u27s the Cure of the army ! 4. My Tailor\u27s bills came in so fast Forc\u27d me one day to leave at last, And ladies too no more did cast Sheep\u27s eyes at me in the army. My Creditors at me did shout, at me did shout, at me did shout, My Creditors at me did shout, Why kick him out of the army

Determinants of impact : towards a better understanding of encounters with the arts

The article argues that current methods for assessing the impact of the arts are largely based on a fragmented and incomplete understanding of the cognitive, psychological and socio-cultural dynamics that govern the aesthetic experience. It postulates that a better grasp of the interaction between the individual and the work of art is the necessary foundation for a genuine understanding of how the arts can affect people. Through a critique of philosophical and empirical attempts to capture the main features of the aesthetic encounter, the article draws attention to the gaps in our current understanding of the responses to art. It proposes a classification and exploration of the factors—social, cultural and psychological—that contribute to shaping the aesthetic experience, thus determining the possibility of impact. The ‘determinants of impact’ identified are distinguished into three groups: those that are inherent to the individual who interacts with the artwork; those that are inherent to the artwork; and ‘environmental factors’, which are extrinsic to both the individual and the artwork. The article concludes that any meaningful attempt to assess the impact of the arts would need to take these ‘determinants of impact’ into account, in order to capture the multidimensional and subjective nature of the aesthetic experience

On the Ethics of Trade Credit: Understanding Good Payment Practice in the Supply Chain

In spite of its commercial importance and signs of clear concern in public policy arenas, trade credit has not been subjected to systematic, extended analysis in the business ethics literature, even where suppliers as a stakeholder group have been considered. This paper makes the case for serious consideration of the ethics of trade credit and explores the issues surrounding slow payment of debts. It discusses trade debt as a kind of promise, but— noting that not all promises are good ones—goes on to develop an analysis of the ethics of trade credit grounded in an understanding of its fundamental purpose. Making a distinction between ‘‘operating’’ trade credit and ‘‘financial’’ trade credit, the paper provides an account of the maximum period for which it is appropriate for one company to delay payment to another from which it has purchased goods or services. The concern of commentators and policy makers that companies should not take too long to pay their debts is affirmed, but the understanding of what timely payment means is significantly finessed, with one conclusion being that, if debts have not already been settled according to acceptable standard terms of trade, cash should pass quickly back along the supply chain once the customer in the final product market has paid. The analysis has implications not only for companies that take credit but also for external parties that seek to rate companies or set regulations according to speed of payment—an approach that is shown to be misleadingly simplistic, albeit well intentioned. A corresponding important responsibility for suppliers, not to extend excessive credit (and thus act as a quasi-bank), also follows from the analysis developed. Having provided a novel analysis of an important business problem, the paper then discusses some of the related practical issues and makes suggestions for further research

Business ethics as practice

In this article we develop a conceptualization of business ethics as practice. Starting from the view that the ethics that organizations display in practice will have been forged through an ongoing process of debate and contestation over moral choices, we examine ethics in relation to the ambiguous, unpredictable, and subjective contexts of managerial action. Furthermore, we examine how discursively constituted practice relates to managerial subjectivity and the possibilities of managers being moral agents. The article concludes by discussing how the 'ethics as practice' approach that we expound provides theoretical resources for studying the different ways that ethics manifest themselves in organizations as well as providing a practical application of ethics in organizations that goes beyond moralistic and legalistic approaches. © 2006 British Academy of Management

Exenatide once weekly versus placebo in Parkinson's disease: a randomised, double-blind, placebo-controlled trial

BACKGROUND: Exenatide, a glucagon-like peptide-1 (GLP-1) receptor agonist, has neuroprotective effects in preclinical models of Parkinson's disease. We investigated whether these effects would be apparent in a clinical trial. METHODS: In this single-centre, randomised, double-blind, placebo-controlled trial, patients with moderate Parkinson's disease were randomly assigned (1:1) to receive subcutaneous injections of exenatide 2 mg or placebo once weekly for 48 weeks in addition to their regular medication, followed by a 12-week washout period. Eligible patients were aged 25-75 years, had idiopathic Parkinson's disease as measured by Queen Square Brain Bank criteria, were on dopaminergic treatment with wearing-off effects, and were at Hoehn and Yahr stage 2·5 or less when on treatment. Randomisation was by web-based randomisation with a two strata block design according to disease severity. Patients and investigators were masked to treatment allocation. The primary outcome was the adjusted difference in the Movement Disorders Society Unified Parkinson's Disease Rating Scale (MDS-UPDRS) motor subscale (part 3) in the practically defined off-medication state at 60 weeks. All efficacy analyses were based on a modified intention-to-treat principle, which included all patients who completed any post-randomisation follow-up assessments. The study is registered at ClinicalTrials.gov (NCT01971242) and is completed. FINDINGS: Between June 18, 2014, and March 13, 2015, 62 patients were enrolled and randomly assigned, 32 to exenatide and 30 to placebo. Our primary analysis included 31 patients in the exenatide group and 29 patients in the placebo group. At 60 weeks, off-medication scores on part 3 of the MDS-UPDRS had improved by 1·0 points (95% CI -2·6 to 0·7) in the exenatide group and worsened by 2·1 points (-0·6 to 4·8) in the placebo group, an adjusted mean difference of -3·5 points (-6·7 to -0·3; p=0·0318). Injection site reactions and gastrointestinal symptoms were common adverse events in both groups. Six serious adverse events occurred in the exenatide group and two in the placebo group, although none in either group were judged to be related to the study interventions. INTERPRETATION: Exenatide had positive effects on practically defined off-medication motor scores in Parkinson's disease, which were sustained beyond the period of exposure. Whether exenatide affects the underlying disease pathophysiology or simply induces long-lasting symptomatic effects is uncertain. Exenatide represents a major new avenue for investigation in Parkinson's disease, and effects on everyday symptoms should be examined in longer-term trials. FUNDING: Michael J Fox Foundation for Parkinson's Research