In this paper, we study the matrix period and competition of Toeplitz matrices over a binary Boolean ring B={0,1}. Given subsets S T {1,…,n−1}, an n×n A=Tn〈S;T〉 is defined to have 1 as (i,j)-entry if only j−i∈S or i−j∈T. We show that max⁡S+min⁡T≤n min⁡S+max⁡T≤n, then A has d/d′ where d=gcd⁡(s+t|s∈S,t∈T) d′=gcd⁡(d,min⁡S). Moreover, it shown limit sequence {Am(AT)m}m=1∞ directed sum all ones exce...

In the last couple of years many works have been devoted to Abelian complexity of words. Recently, Constantinescu and Ilie (Bulletin EATCS 89, 167–170, 2006) introduced the notion of Abelian period. We show that a word w of length n over an alphabet of size σ can have Θ(n2) distinct Abelian periods. However, to the best of our knowledge, no efficient algorithm is known for computing these perio...

In this paper we study age-varying plasticities across different components in an artificial neural network performing a reinforcement learning task. An evolutionary algorithm is given the task of mapping the age of agents to the plasticity levels of different network components. The results show that patterns of plasticity resembling biological sensitive periods appear, and that these periods ...