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This article describes a purely analytic approach to urn models of the generalized or extended P\'olya-Eggenberger type, in the case of two types of balls and constant ``balance,'' that is, constant row sum. The treatment starts from a quasilinear first-order partial differential equation associated with a combinatorial renormalization of the model and bases itself on elementary conformal mapping arguments coupled with singularity analysis techniques. Probabilistic consequences in the case of ``subtractive'' urns are new representations for the probability distribution of the urn's composition at any time n, structural information on the shape of moments of all orders, estimates of the speed of convergence to the Gaussian limit and an explicit determination of the associated large deviation function. In the general case, analytic solutions involve Abelian integrals over the Fermat curve x^h+y^h=1. Several urn models, including a classical one associated with balanced trees (2-3 trees and fringe-balanced search trees) and related to a previous study of Panholzer and Prodinger, as well as all urns of balance 1 or 2 and a sporadic urn of balance 3, are shown to admit of explicit representations in terms of Weierstra\ss elliptic functions: these elliptic models appear precisely to correspond to regular tessellations of the Euclidean plane.Comment: Published at http://dx.doi.org/10.1214/009117905000000026 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Abstract. The mallba project tackles the resolution of combinatorial optimization problems using algorithmic skeletons implemented in C ++ . mallba offers three families of generic resolution methods: exact, heuristic and hybrid. Moreover, for each resolution method, mallba provides three different implementations: sequential, parallel for local area networks, and parallel for wide area networks (currently under development). This paper shows the architecture of the mallba library, presents some of its skeletons and offers several computational results to show the viability of the approach.

In finite labelled transition systems the problems of deciding strong bisimilarity, observation equivalence and observation congruence are P-complete under many-one NC -reducibility. As a consequence, algorithms for automated analysis of finite state systems based on bisimulation seem to be inherently sequential in the following sense: the design of an NC algorithm to solve any of these problems will require an algorithmic breakthrough, which is exceedingly hard to achieve.

An orchestration is a multi-threaded computation which invokes a number of remote services. In practice the responsiveness of a web-service fluctuates with demand; during surges in activity service responsiveness may be degraded, perhaps even to the point of failure. An uncertainty profile formalises a user's perception of the effects of stress on an orchestration of web-services; it describes a strategic situation, modelled by a zero-sum angel-daemon game. Stressed webservice scenarios are analysed, using game theory, in a realistic way, lying between over-optimism (services are entirely reliable) and over-pessimism (all services are broken). The "resilience" of an uncertainty profile can be assessed using the valuation of its associated zero-sum game. In order to demonstrate the validity of the approach we consider two measures of resilience and a number of different stress models. It is shown how (i) uncertainty profiles can be ordered by risk (as measured by game valuations) and (ii) the structural properties of risk partial orders can be analysed.

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