On Semigroup Presentations and Efficiency

The purpose of this paper is twofold. First we determine some forms of the relations in a finite semigroup presentation with zero deficiency which does or does not define a group. Moreover, we conclude that a finite Rees matrix semigroup M [G; I, Λ; P] is efficient when G is efficient and the index sets I, Λ are finite.     

A note on W-I-continuous functions

In [1], Aç?kgöz et al. introduced and investigated the notions of w-I-continuous and w*-I-continuous functions in ideal topological spaces. In this paper, we investigate their relationships with continuous and θ-continuous functions.     

Compactifications whose remainders are zero dimensional and retract

LetX be a locally compact non compact space. Necessary and sufficient conditions forfX/X to be a retract offX are given wherefX is the Freudenthal compactification ofX. LetX be a locally compact and zero dimensional space,m be any cardinal number andJ be a set with cardinalitym. It is proved thatX has a dyadic family of powerm if and only if there exist and compactificationY ofX such thatY/X=2 ^J andY/X is a retract ofY.     

On semigroup presentations and efficiency

The purpose of this paper is twofold. First we determine some forms of the relations in a finite semigroup presentation with zero deficiency which does or does not define a group. Moreover, we conclude that a finite Rees matrix semigroup M [G; I, Λ; P] is efficient when G is efficient and the index sets I, Λ are finite.     

Incremental evolution of fast moving and sensing simulated snake-like robot with multiobjective GP and strongly-typed crossover

In genetic programming (GP), most often the search space grows in a greater than linear fashion as the number of tasks required to be accomplished increases. This is a cause for one of the greatest problems in evolutionary computation; scalability. The aim of the work presented here is to facilitate the evolution of complex designs that have multiple features. We use a combination of mechanisms specifically designed to facilitate the fast evolution of systems with multiple objectives. These mechanisms are; a genetic transposition inspired seeding, a strongly-typed crossover, and a multiobjective optimization. We demonstrate that, when used together, these mechanisms not only improve the performance of GP but also the reliability of the final designs. We investigate the effect of the aforementioned mechanisms, the main focus being on genetic transposition inspired seeding and strongly typed crossover, on the efficiency of GP employed for the coevolution of locomotion gaits and sensing of a simulated snake-like robot (Snakebot). Experimental results show that the mechanism set forth contribute to significant increase in the efficiency of the evolution of fast moving and sensing Snakebots as well as the robustness of the final designs.