We study probabilistic variants of the description logic EL. For the case where probabilities apply only to concepts, we provide a careful analysis of the borderline between tractability and EXPTIME-completeness. One outcome is that any probability value except zero and one leads to intractability in the presence of general TBoxes, while this is not the case for classical TBoxes. For the case w...

Structured population models in biology lead to integro-differential equations that describe the evolution in time of the population density taking into account a given feature such as the age, the size, or the volume. These models possess interesting analytic properties and have been used extensively in a number of areas. In this article, we consider a size-structured model for cell division a...

We give the exposition of a generalized symmetry approach to reduction of initial value problems for nonlinear evolution equations in one spatial variable. Using this approach we classify the initial value problems for third-order evolution equations that admit reduction to Cauchy problems for systems of two ordinary differential equations. These reductions are shown to correspond to higher con...

One of the goals of the UK research project SafeCap (Overcoming the railway capacity challenges without undermining railway network safety) is to provide railway engineers with a formal modelling framework for analysing safety and capacity of railway systems. To this end, we have proposed a “natural modelling” approach for specifying railway networks in CSP||B [4], and we are developing the cap...

The original de nition of re nement proof obligations in VDM is reviewed and examples are discussed which while being in tuitively sensible pose problems for this de nition of re nement An extended VDM re nement relation is introduced to cope with the prob lems Some non standard applications of the extended re nement proof obligations are discussed

Parameterized complexity has so far been largely con ned to consideration of computational problems as decision or search prob lems However it is becoming evident that the parameterized point of view can lead to new insight into counting problems The goal of this article is to introduce a formal framework in which one may consider parameterized counting problems

The asymptotic properties of the least squares estimator of the cusp in some nonlinear nonregular regression models is investigated via the study of the weak convergence of the least squares process generalizing earlier results in Prakasa Rao ( Statist. Prob. Lett. 3 (1985), 15-18).

Even though the Genetic Programming (GP) mechanism is capable of evolving any computable function, the means through which it does so is inherently flawed: the user must provide the GP engine with an evolutionary pathway toward a solution. Hence Genetic Programming is problematic as a mechanism for generating creative solutions to specific prob-

We study scheduling of unit-time parallel jobs on hypercubes. A parallel job has to be scheduled between its release time and deadline on a subcube of processors. The objective is to maximize the number of early jobs. We provide an efficient 1.5-approximation algorithm for the prob-