Beta-splines are a class of splines with applications in the construction of curves and surfaces for computer-aided geometric design. One of the salient features of the Beta-spline is that the curves and surfaces thus constructed are geometrically continuous, a more general notion of continuity than the one used in ordinary B-splines. The basic building block for Beta-splines of order k is a se...

From January 20 to 25 2008, the Dagstuhl Seminar 08041 Recurrent Neural NetworksModels, Capacities, and Applications was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as ...

Danvy’s functional unparsing problem (Danvy 1998) is to implement a typesafe ‘printf’ function, which converts a sequence of heterogeneous arguments to a string according to a given format. The dual problem is to implement a type-safe ‘scanf’ function, which extracts a sequence of heterogeneous arguments from a string by interpreting (Friedman and Wand 1984, 2008) the same format as an equally ...

We propose and implement an algorithm for solving an overdetermined system of partial differential equations in one unknown. Our approach relies on Bour-Mayer method to determine compatibility conditions via Jacobi-Mayer brackets. We solve compatible systems recursively by imitating what one would do with pen and paper: Solve one equation, substitute the solution into the remaining equations an...

Here we present/implement an algorithm to find Liouvillian first integrals of dynamical systems in the plane. In [1], we have introduced the basis for the present implementation. The particular form of such systems allows reducing it to a single rational first order ordinary differential equation (rational first order ODE). We present a set of software routines in Maple 10 for solving rational ...

This paper presents a framework for a theory of granularity, which is seen as a means of constructing simple theories out of more complex ones. A transitive indistinguishability relation can be defined by means of a set of relevant predicates, allowing simplification of a theory of complex phenomena into computationally tractable local theories, or granularities. Nontransitive indistinguishabil...

Rewriting induction (Reddy, 1990) is an automated proof method for inductive theorems of term rewriting systems. Reasoning by the rewriting induction is based on the noetherian induction on some reduction order and the original rewriting induction is not capable of proving theorems which are not orientable by that reduction order. To deal with such theorems, Bouhoula (1995) as well as Dershowit...

We consider the problem of symbolic reachability analysis of higher-order context-free processes. These models are generalizations of the context-free processes (also called BPA processes) where each process manipulates a data structure which can be seen as a nested stack of stacks. Our main result is that, for any higher-order context-free process, the set of all predecessors of a given regula...