We study the canonical weak distributive law $\delta$ of powerset monad over semimodule for a certain class semirings containing, in particular, positive semifields. For this subclass we characterise as convex closure free set. Using abstract theory laws, compose and monads via $\delta$, obtaining subsets semimodule.

Paredaens and Van Gucht proved that the at relational algebra has the same expressive power as the nested relational algebra as far as queries over at relations and with at results are concerned We provide a new very direct proof of this fact using a simulation technique Our technique is also applied to partially answer a question posed by Suciu and Paredaens regarding the complexity of evaluat...

Mobile robot navigation is one of the basic problems in robotics. In this paper, a new approach is proposed for autonomous mobile robot navigation in an unknown environment. The proposed approach is based on learning virtual parallel paths that propel the mobile robot toward the track using a multi-layer, feed-forward neural network. For training, a human operator navigates the mobile robot in ...

Monads are used for various applications in computer science, and well-known is e.g. the interpretation of morphisms in the Kleisli category of the term monad as variable substitutions assigning variables to terms. An application building upon this observation is the equivalence between most general unifiers and co-equalizers in this category [13]. In this paper we will use monads with addition...

We investigate the off-forward matrix element of the light cone vector operator for a dressed quark state in light-front Hamiltonian perturbation theory. We obtain the corresponding splitting functions in a straightforward way. We show that the end point singularity is canceled by the contribution from the normalization of state. Considering mixing with the gluon operator, we verify the helicit...

Linearized dynamics models for manipulators are useful in robot analysis, motion planning, and control applications. In this paper we use techniques from the spatial operator algebra to obtain closed form operator expressions for two types of linearized dynamics models, the Linearized Inverse and Forward Dynamics Models. We rst develop spatially recursive algorithms of O(n) and O(n) complexity ...

Abstract In this work, we propose and analyse forward-backward-type algorithms for finding a zero of the sum finitely many monotone operators, which are not based on reduction to two operator inclusion in product space. Each iteration studied requires one resolvent evaluation per set-valued operator, forward cocoercive evaluations operator. Unlike existing methods, structure proposed suitable d...

In the context of standard abstract interpretation theory, we deene and study a systematic operator of reduced relative power for composing functionally abstract domains. The reduced relative power of two abstract domains D1 (the exponent) and D2 (the base) consists in a suitably deened lattice of monotone functions from D1 to D2, called dependencies, and it is a generalization of the Cousot an...