This paper presents a Banach space based approach towards a denotational semantics of a probabilistic constraint programming language. This language is based on the concurrent constraint programming paradigm, where randomness is introduced by means of a probabilis-tic choice construct. As a result, we obtain a declarative framework, in which randomised algorithms can be expressed and formalised...

For applications in spatial statistics, an important property of a random set X in R k is its rst contact distribution. This is the distribution of the distance from a xed point 0 to the nearest point of X, where distance is measured using scalar dilations of a xed test set B. We show that, if B is convex and contains a neighbourhood of 0, the rst contact distribution function F B is absolutely...

Let Y be a convex set in IR k deened by polynomial inequalities and equations of degree at most d 2 with integer coeecients of binary length l. We show that if Y \ ZZ k 6 = ;, then Y contains an integral point of binary length ld O(k 4). For xed k, our bound implies a polynomial-time algorithm for computing an integral point y 2 Y. In particular, we extend Lenstra's theorem on the polynomial-ti...

We study a renormalization operator for families of one dimensional maps close to x 7! p + r(1 x ) 2 , 2 ( 1 2 ; 1). Such functions occur in the study of cascades of homoclinic doubling bifurcations in three dimensional di erential equations. For values of close to 1 2 , we prove the existence of a xed point of the renormalization operator, whose linearization at the xed point has two unstable ...

with a xed point of multiplier = e 2 i at the origin. Take to be real and irrational. For generic choice of (in the sense of Baire category), Cremer showed that there is no local linearizing coordinate near the origin. We will say brie y that the origin is a Cremer point, or that P is a Cremer polynomial . According to Sullivan and Douady, the existence of such a Cremer point implies that the J...

A new method for kinematic calibration of a robot is presented, based on triaxial measurement of acceleration by a sensor xed to the robot end-point. The kinematic parameters are evaluated by means of a series of simple tests (two for each joint). In these tests each joint, except the one under consideration, is kept xed. Acceleration and encoder output are then acquired. Simulations and experi...

We consider the modal-calculus due to Kozen, which is a nitary modal logic with least and greatest xed points of monotone operators. We extend the existing duality between the category of modal algebras with homomorphisms and the category of descriptive modal frames with contractions to the case of having xed point operators. As a corollary, we obtain a completeness result for Kozen's original ...

In fractal image compression, the code is given by a contractive aane mapping whose xed point is an approximation to the original image. Usually, the mapping is found by the collage coding method. We propose an algorithm that starts from an initial mapping obtained by collage coding and iteratively provides a sequence of contractive mappings whose xed points are monotonically approaching the or...

The deenition of concepts is a central problem in commonsense reasoning. Many themes in nonmonotonic reasoning concern implicit and explicit deenability. Implicit deenability in nonmonotonic logic is always relative to the context-the current theory of the world. We show that xed point equations provide a generalization of explicit deenability, which correctly captures the relativized context. ...

The existence of stationary solutions to the Povzner equation is established for a class of problems in bounded domains with smooth boundaries. The result holds for general type collision kernels under assumptions of angular cutoo. The boundary conditions with xed in-data and with a linear operator of diiuse reeection type are considered. The method is based on constructing approximate solution...