Universal finite-to-one map and universal countable dimensional spaces

Universal Countable Borel quasi-Orders

In recent years, much work in descriptive set theory has been focused on the Borel complexity of naturally occurring classification problems, in particular, the study of countable Borel equivalence relations and their structure under the quasi-order of Borel reducibility. Following the approach of Louveau and Rosendal in [8] for the study of analytic equivalence relations, we study countable Bo...

Mani and shapur a universal faith for e universal kingdom

Intrinsically universal one-dimensional quantum cellular automata

We give a one-dimensional quantum cellular automata (QCA) capable of simulating all others. By this we mean that the initial configuration and the local transition rule of any one-dimensional QCA can be encoded within the initial configuration of the universal QCA. Several steps of the universal QCA will then correspond to one step of the simulated QCA. The simulation preserves the topology in ...

A One-Dimensional Physically Universal Cellular Automaton

Physical universality of a cellular automaton was defined by Janzing in 2010 as the ability to implement an arbitrary transformation of spatial patterns. In 2014, Schaeffer gave a construction of a two-dimensional physically universal cellular automaton. We construct a one-dimensional version of the automaton.

Criticality in non-linear one-dimensional maps: RG universal map and non-extensive entropy

We consider the period-doubling and intermittency transitions in iterated nonlinear one-dimensional maps to corroborate unambiguously the validity of Tsallis’ non-extensive statistics at these critical points. We study the map xn+1 = xn + u |xn| , z > 1, as it describes generically the neighborhood of all of these transitions. The exact renormalization group (RG) fixed-point map and perturbatio...