Motivated by the study of cellular automata algorithmic and dynamics, we investigate an extension of ultimately periodic words to twodimensional infinite words: collisions. A natural composition operation on tilings leads to a catenation operation on collisions. By existence of aperiodic tile sets, ultimately periodic tilings of the plane cannot generate all possible tilings but exhibit some us...

An emerging consensus claims that ‘subjective’ (mis)perceptions of income inequality better explain redistributive preferences than actual ‘objective’ conditions. In this article, we critically re-assess view. We compare perceived and positions as predictors for redistribution. argue is partly endogenous to its effect on conditional ideology. Using an original survey experiment from Switzerland...

In this paper, the ultimately exponentially bounded estimate problem of nonlinear stochastic discrete−time systems under generalized Lipschitz conditions is considered. A new sufficient condition making estimation error system uniformly in mean square sense given. The gain matrix can be obtained by solving inequality. last section, numerical examples are provided verify effectiveness conclusions.