相关论文: Topological Mixing of Random Substitutions

We provide the set of filters (saturated submonoids) in a commutative monoid with a topology (like the spectrum of a ring) and study the resulting spaces.

This paper provides a systematic study of fundamental combinatorial properties of one-dimensional, two-sided infinite simple Toeplitz subshifts. Explicit formulas for the complexity function, the palindrome complexity function and the…

Nonparametric estimation of a mixing density based on observations from the corresponding mixture is a challenging statistical problem. This paper surveys the literature on a fast, recursive estimator based on the predictive recursion…

Popular network models such as the mixed membership and standard stochastic block model are known to exhibit distinct geometric structure when embedded into $\mathbb{R}^{d}$ using spectral methods. The resulting point cloud concentrates…

Studying distributed computing through the lens of algebraic topology has been the source of many significant breakthroughs during the last two decades, especially in the design of lower bounds or impossibility results for deterministic…

We study proximal random reshuffling for minimizing the sum of locally Lipschitz functions and a proper lower semicontinuous convex function without assuming coercivity or the existence of limit points. The algorithmic guarantees pertaining…

This study presents special cases of inconsistent pairwise comparisons PC matrices and analysis of their eigenvalue-based inconsistency index using mathematical methods. All studied special cases of PC matrices are Toeplitz matrices with…

In recent years, topological data analysis has been utilized for a wide range of problems to deal with high dimensional noisy data. While text representations are often high dimensional and noisy, there are only a few work on the…

A permutation statistic is substring-compatible if its value on a permutation determines its value on every substring of that permutation. We construct the substring coalgebra of such a statistic, an analog of the shuffle algebra of a…

In [2], while studying a relevant class of polyominoes that tile the plane by translation, i.e., double square polyominoes, the authors found that their boundary words, encoded by the Freeman chain coding on a four letters alphabet, have…

We define a generic algorithmic framework to prove pure discrete spectrum for the substitutive symbolic dynamical systems associated with some infinite families of Pisot substitutions. We focus on the families obtained as finite products of…

We prove decidability results on the existence of constant subsequences of uniformly recurrent morphic sequences along arithmetic progressions. We use spectral properties of the subshifts they generate to give a first algorithm deciding…

Matrix models are a promising candidate for a nonperturbative formulation of the superstring theory. It is possible to study how the standard model and other phenomenological models appear from the matrix model, and estimate the probability…

We show that topological mixing, weak mixing and total transitivity are equivalent for coded systems. We provide an example of a mixing coded system which cannot be approximated by any increasing sequence of mixing shifts of finite type,…

In this paper, we find an elementary approach for double sums where the inner sum is binomial but incomplete. We apply our core identity and its relatives to double sums involving famous numbers such as harmonic numbers, Fibonacci numbers,…

Intersection homology is a topological invariant which detects finer information in a space than ordinary homology. Using ideas from classical simple homotopy theory, we construct local combinatorial transformations on simplicial complexes…

The restricted polynomially-tilted pairwise interaction (RPPI) distribution gives a flexible model for compositional data. It is particularly well-suited to situations where some of the marginal distributions of the components of a…

The random Fibonacci chain is a generalisation of the classical Fibonacci substitution and is defined as the rule mapping $0\mapsto 1$ and $1 \mapsto 01$ with probability $p$ and $1 \mapsto 10$ with probability $1-p$ for $0<p<1$ and where…

A deck of $n$ cards are shuffled by repeatedly taking off the top card, flipping it with probability $1/2$, and inserting it back into the deck at a random position. This process can be considered as a Markov chain on the group $B_n$ of…

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…