Analysing the Mutational Pathways of a von Neumann Self- reproducer within the Avida World

Exploring the Point-mutation Space of a von Neumann Self-reproducer within the Avida World

The architecture of machine self-reproduction originally formulated by John von Neumann is studied within the artificial life system Avida. We describe a hand-designed von Neumann style self-reproducer, and report initial results from an exhaustive search of its single-point-mutation space. Unsurprisingly, the majority of mutants are simply sterile, and have no long-term evolutionary potential;...

Calculating Different Topological Indices of Von Neumann Regular Graph of Z_(p^α )

By the Von Neumann regular graph of R, we mean the graph that its vertices are all elements of R such that there is an edge between vertices x,y if and only if x+y is a von Neumann regular element of R, denoted by G_Vnr (R). For a commutative ring R with unity, x in R is called Von Neumann regular if there exists x in R such that a=a2 x. We denote the set of Von Neumann regular elements by V nr...

Various topological forms of Von Neumann regularity in Banach algebras

We study topological von Neumann regularity and principal von Neumann regularity of Banach algebras. Our main objective is comparing these two types of Banach algebras and some other known Banach algebras with one another. In particular, we show that the class of topologically von Neumann regular Banach algebras contains all $C^*$-algebras, group algebras of compact abelian groups and ...

The James and von Neumann-Jordan type constants and uniform normal structure in Banach spaces

Recently, Takahashi has introduced the James and von Neumann-Jordan type constants. In this paper, we present some sufficient conditions for uniform normal structure and therefore the fixed point property of a Banach space in terms of the James and von Neumann-Jordan type constants and the Ptolemy constant. Our main results of the paper significantly generalize and improve many known results in...

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras