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Rule Systems for Run-time Monitoring: from EAGLE to RULER
Get PDFIn Barringer et al. (2004,Vol. 2937, LNCS), EAGLE was introduced as a general purpose rule-based temporal logic for specifying run-time monitors. A novel interpretative trace-checking scheme via stepwise transformation of an EAGLE monitoring formula was defined and implemented. However, even though EAGLE presents an elegant formalism for the expression of complex trace properties, EAGLE's interpretation scheme is complex and appears difficult to implement efficiently. In this article, we introduce RULER, a primitive conditional rule-based system, which has a simple and easily implemented algorithm for effective run-time checking, and into which one can compile a wide range of temporal logics and other specification formalisms used for run-time verification. As a formal demonstration, we provide a translation scheme for linear-time propositional temporal logic with a proof of translation correctness. We then introduce a parameterized version of RULER, in which rule names may have rule-expression or data parameters, which then coincides with the same expressivity as EAGLE with data arguments. RULER with just rule-expression parameters extend the expressiveness of RULER strictly beyond the class of context-free languages. For the language classes expressible in propositional RULER, the addition of rule-expression and data parameters enables more compact translations. Finally, we outline a few simple syntactic extensions of ‘core’ RULER that can lead to further conciseness of specification but still enabling easy and efficient implementation
A simple yet effective a posteriori estimator for classical mixed approximation of Stokes equations
Get PDFThe implementation of quadratic velocity, linear pressure finite element approximation methods for the steady-state incompressible (Navier-)
Stokes equations is addressed in this work. Three types of a posteriori error indicator are introduced and are shown to give global error estimates that are equivalent to the true discretisation error. Computational results suggest that the solution of local Poisson problems provides a cost-effective error estimation strategy, both from the perspective of accurate estimation of the global error and for the purpose of selecting elements for refinement within a contemporary self-adaptive refinement algorithm
Geometric structure in the tempered dual of the p-adic group SL(4)
Get PDFWe confirm the Aubert-Baum-Plymen conjecture for part of the tempered dual of the p-adic group SL(4). This requires some very detailed representation theory. Of special interest is the case of SL(4,Q_2). Here, there is a tetrahedron of reducibility, and the extended quotient performs a deconstruction: it creates the ordinary quotient and six unit intervals. The six intervals are then assembled into the six edges of a tetrahedron, and create a perfect model of reducibility. The L-packets in this article all conform to the L-packet conjecture in http://eprints.ma.man.ac.uk/1504
Mine Valuation in the Presence of a Stochastic Ore-Grade Uncertainty
Get PDFMining companies world-wide are faced
with the problem of how to accurately value and plan
extraction projects subject to uncertainty in both future
price and ore grade. Whilst the methodology
of modelling price uncertainty is reasonably well understood, modelling ore-grade uncertainty is a much
harder problem to formulate, and when attempts have
been made the solutions take unfeasibly long times
to compute. By treating the grade uncertainty as a
stochastic variable in the amount extracted from the
resource, this paper provides a new approach to the
problem. We show that this method is well-posed,
since it can realistically re
flect the geology of the situation,
and in addition it enables solutions to be derived
in the order of a few seconds. A comparison is
made between a real mine valuation where the prior
estimate of ore grade variation is taken as fact, and
our approach, where we treat it as an uncertain estimate
Coverage processes on spheres and condition numbers for linear programming
Get PDFThis paper has two agendas. Firstly, we exhibit new results for coverage processes. Let be the probability that spherical caps of angular radius in do not cover the whole sphere . We give an exact formula for in the case and an upper bound for in the case which tends to when . In the case this yields upper bounds for the expected number of spherical caps of radius that are needed to cover . Secondly, we study the condition number of the linear programming feasibility problem where is randomly chosen according to the standard normal distribution. We exactly determine the distribution of conditioned to being feasible and provide an upper bound on the distribution function in the infeasible case. Using these results, we show that for all , the sharpest bound for this expectancy as of today. Both agendas are related through a result which translates between coverage and condition
The Discontinuous Galerkin Method for Conservation Laws
Get PDFThe aim of this project is to study discontinuous Galerkin methods applied to coupled systems of partial differential equations in conservative form in 1D and 2D.
In 1D, a formulation was successfully implemented to solve continuous problems for the advection and shallow water equations. Discontinuous problems for the inviscid Burgers� equation and a breaking dam problem were also investigated and the effectiveness of h- and p-refinement discussed. An alternate set of shallow water equations were derived yielding equivalent results for a continuous problem but different numerical solutions for the breaking dam problem. These anomalous results highlight the importance of enforcing conservation of the correct conserved physical variables in cases when solutions exhibit shocks.
A 2D slope limiter, applicable to quadrilateral elements, is implemented and numerical results obtained for a smoothed breaking dam problem in 2D. A comparison is made between these results and those from a finite volume method (results by Chris Johnson) and indicate that, for this particular problem, both methods resolve the shock over the same length scale
A 195,747,435 vertex graph related to the Fischer group Fi23 ,part II
Get PDFIn this, the second of a three part series, we continue studying G, the point-line collinearity graph of the maximal 2-local geometry for Fischer's second largest simple group Fi23. Most of our attention is focussed upon consolidating our
earlier knowledge of the third disc of an arbitrary vertex of G
Green Correspondence for virtually pro-p groups
Get PDFLet p be prime, k a finite field of characteristic p, and G a virtually pro-p group. We prove an analogue of the Green Correspondence for finitely generated modules over the completed group algebra k[[G]]