Related papers: Mixing coded systems
We introduce and study two properties of dynamical systems: topologically transitive and topologically mixing under the set-valued setting. We prove some implications of these two topological properties for set-valued functions and…
We present a sufficient condition that a pseudointegrable system has weak mixing property. The result is derived from Veech's weak mixing theorem for interval exhange [Veech, W.A. Amer.J.Math. {\bf 106}, 1331 (1984)]. We also present an…
Given a switched system, we introduce weakly mixing sets of type 1, 2 and Xiong chaotic sets of type 1, 2 with respect to a given set and show that they are equivalent respectively.
A class of examples is constructed to show that for strictly stationary Markov chains that are reversible, the simultaneous mixing rates for the $\rho$-mixing and strong mixing ($\alpha$-mixing) conditions can be fairly arbitrary, within…
We consider population dynamics on a network of patches, each of which has a the same local dynamics, with different population scales (carrying capacities). It is reasonable to assume that if the patches are coupled by very fast migration…
In two previous papers we constructed new families of completely regular codes by concatenation methods. Here we determine cases in which the new codes are completely transitive. For these cases we also find the automorphism groups of such…
We show that for every positive integer $k$, there exist $k$ consecutive primes having the property that if any digit of any one of the primes, including any of the infinitely many leading zero digits, is changed, then that prime becomes…
Strong blocking sets and their counterparts, minimal codes, attracted lots of attention in the last years. Combining the concatenating construction of codes with a geometric insight into the minimality condition, we explicitly provide…
In this contribution, the transitivity property of commutative first-order linear time-varying systems is investigated with and without initial conditions. It is proven that transitivity property of first-order systems holds with and…
A subclass of coded systems containing synchronized systems is the family of half-synchronized systems. In this note, we will consider them and show that the property half-synchronized lifts under hyperbolic maps. This enables us to define…
Say that a finite group $G$ is mixable if a product of random elements, each chosen independently from two options, can distribute uniformly on $G$. We present conditions and obstructions to mixability. We show that $2$-groups, the…
For a commutative non-autonomous dynamical system we show that topological transitivity of the non-autonomous system induced on probability measures (hyperspaces) is equivalent to the weak mixing of the induced systems. Several counter…
For nonstationary, strongly mixing sequences of random variables taking their values in a finite-dimensional Euclidean space, with the partial sums being normalized via matrix multiplication, with certain standard conditions being met, the…
We prove a strong law of large numbers for a class of strongly mixing processes. Our result rests on recent advances in understanding of concentration of measure. It is simple to apply and gives finite-sample (as opposed to asymptotic)…
Elements $a,b$ of a semigroup $S$ are said to be \emph{primarily conjugate} or just \emph{p-conjugate}, if there exist $x,y\in S^1$ such that $a=xy$ and $b=yx$. The p-conjugacy relation generalizes conjugacy in groups, but for general…
We discuss the transition paths in a coupled bistable system consisting of interacting multiple identical bistable motifs. We propose a simple model of coupled bistable gene circuits as an example, and show that its transition paths are…
The phase diagrams and transitions of nonequilibrium systems with multiplicative noise are studied theoretically. We show the existence of both strong and weak-coupling critical behavior, of two distinct active phases, and of a nonzero…
We establish an abstract, effective, exponential large deviations type estimate for Markov systems satisfying a weaker form of mixing. We employ this result to derive such estimates, as well as a central limit theorem, for the skew product…
We introduce a stochastic algorithm that acts as a prime number generator. The dynamics of such algorithm gives rise to a continuous phase transition which separates a phase where the algorithm is able to reduce a whole set of integers into…
A propositional proof system $P$ has the strong feasible disjunction property iff there is a constant $c \geq 1$ such that whenever $P$ admits a size $s$ proof of $\bigvee_i \alpha_i$ with no two $\alpha_i$ sharing an atom then one of…