Matrix-valued random walks and variations on property AT

We reformulate matrix-valued random walks and their associated group actions in terms of dimension groups, suitably modified to deal with measure-theoretic classification. This leads naturally to a notion of rank denoted AT(n), for integers n (approximately transitive, that is, AT, actions constitute the rank one situation). This yields wide classes of examples, and easily verified criteria for basic properties (such as ergodicity) are established. We present an (ergodic) AT(2) action of the integers (from an involution) that is not AT, effectively answering an old question of Thouvenot, but on the other hand, give criteria for matrix-valued random walks to be AT. One of the criteria resembles a result of Mineka on mass cancellation. What are known as bounded AT actions in the literature are shown to be exactly the AT actions for which the corresponding random walk comes from a sequence of Poisson distributions, and we show that the natural involutions on bounded AT actions have orbit space that is AT (unlike more general AT actions), and generically are bounded. We also present a rather unusual ergodic action of the free group on two generators which is AT(2) (and not AT), but is given by a constant sequence (for an amenable group, a constant sequence would yield an uninteresting action)

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

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

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

LNCS

We address the problem of analyzing the reachable set of a polynomial nonlinear continuous system by over-approximating the flowpipe of its dynamics. The common approach to tackle this problem is to perform a numerical integration over a given time horizon based on Taylor expansion and interval arithmetic. However, this method results to be very conservative when there is a large difference in speed between trajectories as time progresses. In this paper, we propose to use combinations of barrier functions, which we call piecewise barrier tube (PBT), to over-approximate flowpipe. The basic idea of PBT is that for each segment of a flowpipe, a coarse box which is big enough to contain the segment is constructed using sampled simulation and then in the box we compute by linear programming a set of barrier functions (called barrier tube or BT for short) which work together to form a tube surrounding the flowpipe. The benefit of using PBT is that (1) BT is independent of time and hence can avoid being stretched and deformed by time; and (2) a small number of BTs can form a tight over-approximation for the flowpipe, which means that the computation required to decide whether the BTs intersect the unsafe set can be reduced significantly. We implemented a prototype called PBTS in C++. Experiments on some benchmark systems show that our approach is effective