Related papers: Tree shift topological entropy
The aim of this note is to introduce a notion of dynamical entropy, which we call infinite-product entropy, for probability measures on (countable) infinite cartesian product of any measurable space with itself. The idea behind the…
Comparison-based algorithms are algorithms for which the execution of each operation is solely based on the outcome of a series of comparisons between elements. Comparison-based computations can be naturally represented via the following…
We study a quantum phase transition between a phase which is topologically ordered and one which is not. We focus on a spin model, an extension of the toric code, for which we obtain the exact ground state for all values of the coupling…
We consider so-called simple families of labelled trees, which contain, e.g., ordered, unordered, binary and cyclic labelled trees as special instances, and study the global and local behaviour of the number of inversions. In particular we…
Over some types of trees with a given number of vertices, which trees minimize or maximize the total number of subtrees or leaf containing subtrees are studied. Here are some of the main results:\ (1)\, Sharp upper bound on the total number…
Systems whose organization displays causal asymmetry constraints, from evolutionary trees to river basins or transport networks, can be often described in terms of directed paths (causal flows) on a discrete state space. Such a set of paths…
The term "overlapping" refers to a certain fairly simple type of piecewise continuous function from the unit interval to itself and also to a fairly simple type of iterated function system (IFS) on the unit interval. A correspondence…
We introduce a new family of shift spaces --- the subordinate shifts. Using subordinate shifts we prove in an elementary way that for every nonnegative real number $t$ there is a shift space with entropy $t$.
We establish necessary and sufficient conditions for suspension flows over certain families of shift spaces to be topologically mixing. We also show the similarities and differences between this case and the smooth measure theoretic setting…
The entropy of network ensembles characterizes the amount of information encoded in the network structure, and can be used to quantify network complexity, and the relevance of given structural properties observed in real network datasets…
The aim of this article is to find appropriate definitions for shifts of finite type and sofic shifts in a general context of symbolic dynamics. We start showing that the classical definitions of shifts of finite type and sofic shifts, as…
Various standard texts on differential topology maintain that the level-preserving map defined by the track of an isotopy of embeddings is itself an embedding. This note describes a simple counterexample to this assertion.
Higher-dimensional binary shifts of number-theoretic origin with positive topological entropy are considered. We are particularly interested in analysing their symmetries and extended symmetries. They form groups, known as the topological…
In this note a notion of generalized topological entropy for arbitrary subsets of the space of all sequences in a compact topological space is introduced. It is shown that for a continuous map on a compact space the generalized topological…
We study topological factors of rank-one subshifts and prove that those factors that are themselves subshifts are either finite or isomorphic to the original rank-one subshifts. Thus, we completely characterize the subshift factors of…
We give entropy estimates for two canonical non commutative shifts on $C^*$-algebras associated to some topological graphs $E=(E^0,E^1,s,r)$, defined using a basis of the corresponding Hilbert bimodule $H(E)$. We compare their entropies…
In gauge theories the presence of constraints can obstruct expressing the global Hilbert space as a tensor product of the Hilbert spaces corresponding to degrees of freedom localized in complementary regions. In algebraic terms, this is due…
We show that if the complexity difference function p(n+1)-p(n) of a infinite minimal shift is bounded, then the the automorphism group of the one-sided shift is finite, and the automorphism group of the corresponding two-sided shift "modulo…
We present a graph theoretical approach to the configurational statistics of random tree-like objects, such as randomly branching polymers. In particular, for ideal trees we show that Pr\"ufer labelling provides: (i) direct access to the…
Tree transductions are binary relations of finite trees. For tree transductions defined by non-deterministic top-down tree transducers, inclusion, equivalence and synthesis problems are known to be undecidable. Adding origin semantics to…