We discuss bipermutive cellular automata from a combinatorial and topological perspective. We prove a type of topological randomizing property for bipermutive CA, show that the commutator of a bipermutive CA is always small and that bipermutive affine CA have only affine CA in their commutator. We show the last result also in the multidimensional case, proving a conjecture of [Moore-Boykett, 97].

By adopting theories as primitive components of a logic and recognizing that formulae are just presentation details we arrive at the concept of topological institution. In a topological institution, we have, for each signature , a frame of theories, a set of interpretation structures and a satisfaction relation. More precisely, we have, for each signature, a topological system. We show how to e...

In this paper, a new definition of locally convex L-topological vector spaces is given. The relationship between this new definition and the previous definition of locally convex L-topological vector spaces given by Yan and Fang in 1999 is investigated. Moreover, the concept of generalized L-fuzzy semi-norm is introduced. By using a family of generalized L-fuzzy semi-norms, a characterization o...

Contrary to the property of achromaticity (independence of wavelength) usually associated with topological phases, we describe conditions under which topological phases encountered in optics can show sharp changes and reversals for small changes in wavelength, a phenomenon originating in the occurrence of phase singularities, earlier observed in interference experiments. OCIS Codes:(230.5440) P...

This paper shows the interest of basing a mechanical mesh upon an efficient topological model in order to give any simulation the ability to refine this mesh locally and apply topological modifications such as cutting, tear and matter destruction. Refinement and modifications can indeed be combined in order to get a more precise result. The powerful combinatorial map model provides the mathemat...

Evidence from adult psychophysics, brain imaging, and honeybee's behaviour has been reported to support the notion that topological properties are the primitives of visual representation (Chen, 1982 Science 218 699-700). Here, we ask how the sensitivity to topological property might originate during development. Specifically, we tested 1.5- to 6-month-old infants' visual sensitivity for topolog...

Dynamic Topological Logic (DT L) is a modal logic which combines spatial and temporal modalities for reasoning about dynamic topological systems, which are pairs consisting of a topological space X and a continuous function f : X → X. The function f is seen as a change in one unit of time; within DT L one can model the long-term behavior of such systems as f is iterated. One class of dynamic to...

A topological graph is a graph drawn in the plane so that its vertices are represented by points, and its edges are represented by Jordan curves connecting the corresponding points, with the property that any two curves have at most one point in common. We define two canonical classes of topological complete graphs, and prove that every topological complete graph with n vertices has a canonical...

A scheme for an algebraic quantization of the causal sets of Sorkin et al. is presented. The suggested scenario is along the lines of a similar algebraization and quantum interpretation of finitary topological spaces due to Zapatrin and this author. To be able to apply the latter procedure to causal sets Sorkin’s ‘semantic switch’ from ‘partially ordered sets as finitary topological spaces’ to ...

Digital memcomputing machines (DMMs) are non-linear dynamical systems designed so that their equilibrium points are solutions of the Boolean problem they solve. In a previous work [Chaos 27, 023107 (2017)] it was argued that when DMMs support solutions of the associated Boolean problem then strange attractors cannot coexist with such equilibria. In this work, we demonstrate such conjecture. In ...