Maximal quadratic modules on *-rings

We generalize the notion of and results on maximal proper quadratic modules from commutative unital rings to $\ast$-rings and discuss the relation of this generalization to recent developments in noncommutative real algebraic geometry. The simplest example of a maximal proper quadratic module is the cone of all positive semidefinite complex matrices of a fixed dimension. We show that the support of a maximal proper quadratic module is the symmetric part of a prime $\ast$-ideal, that every maximal proper quadratic module in a Noetherian $\ast$-ring comes from a maximal proper quadratic module in a simple artinian ring with involution and that maximal proper quadratic modules satisfy an intersection theorem. As an application we obtain the following extension of Schm\" udgen's Strict Positivstellensatz for the Weyl algebra: Let $c$ be an element of the Weyl algebra $\mathcal{W}(d)$ which is not negative semidefinite in the Schr\" odinger representation. It is shown that under some conditions there exists an integer $k$ and elements $r_1,...,r_k \in \mathcal{W}(d)$ such that $\sum_{j=1}^k r_j c r_j^\ast$ is a finite sum of hermitian squares. This result is not a proper generalization however because we don't have the bound $k \le d$.Comment: 11 page

'The show must go on': Event dramaturgy as consolidation of community

Event dramaturgy and cultural performance have not been examined in the literature from a strategic standpoint of fostering the social value of events. Thus, the purpose of this study was to explore the case of the Water Carnival, a celebratory event in a rural community of Southwest Texas, demonstrating the essence of this event as a symbolic social space, wherein event participants instantiate a shared and valued sense of community. A hermeneutical approach was employed, interpreting the event and its symbolisms as a text, combined with findings from ethnographic fieldwork, including participant observation, in-depth interviews and analysis of archival documents. The study examines the ways that dramaturgy in the Water Carnival helps frame the ongoing public discourse for community improvement and enhances social capital. The implications of the study for social leverage of events are discussed. It is suggested that a foundation for strategic social planning is the understanding of events as symbolic social spaces and their embeddedness in community development, which can be accomplished when events are pertinent to public discourse, address community issues, represent an inclusive range of stakeholders, and promote cooperation

Non-polynomial Worst-Case Analysis of Recursive Programs

We study the problem of developing efficient approaches for proving worst-case bounds of non-deterministic recursive programs. Ranking functions are sound and complete for proving termination and worst-case bounds of nonrecursive programs. First, we apply ranking functions to recursion, resulting in measure functions. We show that measure functions provide a sound and complete approach to prove worst-case bounds of non-deterministic recursive programs. Our second contribution is the synthesis of measure functions in nonpolynomial forms. We show that non-polynomial measure functions with logarithm and exponentiation can be synthesized through abstraction of logarithmic or exponentiation terms, Farkas' Lemma, and Handelman's Theorem using linear programming. While previous methods obtain worst-case polynomial bounds, our approach can synthesize bounds of the form $\mathcal{O}(n\log n)$ as well as $\mathcal{O}(n^r)$ where $r$ is not an integer. We present experimental results to demonstrate that our approach can obtain efficiently worst-case bounds of classical recursive algorithms such as (i) Merge-Sort, the divide-and-conquer algorithm for the Closest-Pair problem, where we obtain $\mathcal{O}(n \log n)$ worst-case bound, and (ii) Karatsuba's algorithm for polynomial multiplication and Strassen's algorithm for matrix multiplication, where we obtain $\mathcal{O}(n^r)$ bound such that $r$ is not an integer and close to the best-known bounds for the respective algorithms.Comment: 54 Pages, Full Version to CAV 201

Planning and Leveraging Event Portfolios: Towards a Holistic Theory

This conceptual paper seeks to advance the discourse on the leveraging and legacies of events by examining the planning, management, and leveraging of event portfolios. This examination shifts the common focus from analyzing single events towards multiple events and purposes that can enable cross-leveraging among different events in pursuit of attainment and magnification of specific ends. The following frameworks are proposed: (1) event portfolio planning and leveraging, and (2) analyzing events networks and inter-organizational linkages. These frameworks are intended to provide, at this infancy stage of event portfolios research, a solid ground for building theory on the management of different types and scales of events within the context of a portfolio aimed to obtain, optimize and sustain tourism, as well as broader community benefits

A Survey of Satisfiability Modulo Theory

Satisfiability modulo theory (SMT) consists in testing the satisfiability of first-order formulas over linear integer or real arithmetic, or other theories. In this survey, we explain the combination of propositional satisfiability and decision procedures for conjunctions known as DPLL(T), and the alternative "natural domain" approaches. We also cover quantifiers, Craig interpolants, polynomial arithmetic, and how SMT solvers are used in automated software analysis.Comment: Computer Algebra in Scientific Computing, Sep 2016, Bucharest, Romania. 201

Multicentre observational study of adherence to Sepsis Six guidelines in emergency general surgery

Background Evidence-based interventions may reduce mortality in surgical patients. This study documented the prevalence of sepsis, adherence to guidelines in its management, and timing of source control in general surgical patients presenting as an emergency. Methods Patients aged 16 years or more presenting with emergency general surgery problems were identified over a 7-day period and then screened for sepsis compliance (using the Sepsis Six standards, devised for severe sepsis) and the timing of source control (whether radiological or surgical). Exploratory analyses examined associations between the mode (emergency department or general practitioner) and time of admission, adherence to the sepsis guidelines, and outcomes (complications or death within 30 days). Results Of a total of 5067 patients from 97 hospitals across the UK, 911 (18·0 per cent) fulfilled the criteria for sepsis, 165 (3·3 per cent) for severe sepsis and 24 (0·5 per cent) for septic shock. Timely delivery of all Sepsis Six guidelines for patients with severe sepsis was achieved in four patients. For patients with severe sepsis, 17·6–94·5 per cent of individual guidelines within the Sepsis Six were delivered. Oxygen was the criterion most likely to be missed, followed by blood cultures in all sepsis severity categories. Surgery for source control occurred a median of 19·8 (i.q.r. 10·0–35·4) h after diagnosis. Omission of Sepsis Six parameters did not appear to be associated with an increase in morbidity or mortality. Conclusion Although sepsis was common in general surgical patients presenting as an emergency, adherence to severe sepsis guidelines was incomplete in the majority. Despite this, no evidence of harm was apparent

Gains in Statistical Power From Using a Dietary Biomarker in Combination With Self-reported Intake to Strengthen the Analysis of a Diet-Disease Association: An Example From CAREDS

A major problem in detecting diet-disease associations in nutritional cohort studies is measurement error in self-reported intakes, which causes loss of statistical power. The authors propose using biomarkers correlated with dietary intake to strengthen analyses of diet-disease hypotheses and to increase statistical power. They consider combining self-reported intakes and biomarker levels using principal components or a sum of ranks and relating the combined measure to disease in conventional regression analyses. They illustrate their method in a study of the inverse association of dietary lutein plus zeaxanthin with nuclear cataracts, using serum lutein plus zeaxanthin as the biomarker, with data from the Carotenoids in Age-Related Eye Disease Study (United States, 2001–2004). This example demonstrates that the combined measure provides higher statistical significance than the dietary measure or the serum measure alone, and it potentially provides sample savings of 8%–53% over analysis with dietary intake alone and of 6%–48% over analysis with serum level alone, depending on the definition of the outcome variable and the choice of confounders entered into the regression model. The authors conclude that combining appropriate biomarkers with dietary data in a cohort can strengthen the investigation of diet-disease associations by increasing the statistical power to detect them

Keeping it liminal. The Mondiali Antirazzisti (Anti-racist World Cup) as a multifocal interaction ritual

© 2013 Taylor & Francis. This paper examines how social mixing and celebration of diversity can be enabled through sports festivals marked by their carnivalesque atmosphere. Our analysis draws on a longitudinal ethnographic study of the Mondiali Antirazzisti (Anti-racist World Cup), a non-competitive football tournament and intercultural festival featuring the yearly participation of hardcore football fans (ultras), migrant groups, third-sector associations and other informal groups. We consider how the multifocal ritual form of the event helps to create a liminal space in which discrimination and stereotypes can be temporarily challenged. The sources of collective effervescence are multiplied by placing sport games within a wider range of other leisure and cultural activities, thus promoting internal diversity and the inclusion of outsiders. Additionally, social boundaries are also blurred by not emphasising the competitive dimension of the sporting activities, making sporting categorisations more fluid, and breaking down the separation between protagonists and spectators. Nonetheless, considering the transient character of liminality, we also investigate problems and limitations implied by the pursuit of these objectives. It is concluded that, despite a certain degree of self-referentiality, the festival fosters the spreading of anti-discriminatory cultures by enhancing the participants’ reflexivity and feeding their commitment in generating spin-off activities in different local contexts