相关论文: Textile systems on lambda-graph systems

We show that the image of a subshift $X$ under various injective morphisms of symbolic algebraic varieties over monoid universes with algebraic variety alphabets is a subshift of finite type, resp. a sofic subshift, if and only if so is…

The dynamics of symbolic systems, such as multidimensional subshifts of finite type or cellular automata, are known to be closely related to computability theory. In particular, the appropriate tools to describe and classify topological…

Let $G$ be a countable monoid and let $A$ be an Artinian group (resp. an Artinian module). Let $\Sigma \subset A^G$ be a closed subshift which is also a subgroup (resp. a submodule) of $A^G$. Suppose that $\Gamma$ is a finitely generated…

An important question in dynamical systems is the classification problem, i.e., the ability to distinguish between two isomorphic systems. In this work, we study the topological factors between a family of multidimensional substitutive…

Many graph algorithms can be viewed as sets of rules that are iteratively applied, with the number of iterations dependent on the size and complexity of the input graph. Existing machine learning architectures often struggle to represent…

Separated graphs provide a powerful combinatorial tool for approximating dynamical systems. This paper details the explicit construction of Bratteli-like separated graphs -- a generalization of classical Bratteli diagrams -- that encode the…

For a ${\mathbb Z}^{d}$-topological dynamical system $(X, T, {\mathbb Z}^{d})$, an isomomorphism is a self-homeomorphism $\phi : X\to X$ such that for some matrix $M\in {\rm GL}(d,{\mathbb Z})$ and any ${n}\in {\mathbb Z}^{d}$, $\phi\circ…

The dynamics of a linear dynamical system over a finite field can be described by using the elementary divisors of the corresponding matrix. It is natural to extend the investigation to a general finite commutative ring. In a previous…

The collective dynamics of interacting dynamical units on a network crucially depends on the properties of the network structure. Rather than considering large but finite graphs to capture the network, one often resorts to graph limits and…

In 1988 Boyle and Krieger defined sub-matrices for representation matrices of sofic shift. This paper presents some details of relations between integral sub-matrices and representation matrices. Besides, we express a new version of the…

Sabidussi's theorem [Duke Math. J. 28, 1961] gives necessary and sufficient conditions under which the automorphism group of a lexicographic product of two graphs is a wreath product of the respective automorphism groups. We prove a quantum…

We study two-dimensional subshifts whose horizontal trace (a.k.a. projective subdynamics) contains only points of finite support. Our main result is a classification result for such subshifts satisfying a minimality property. As…

\begin{abstract} In this paper, we investigate a shift arising from graph $G$. We prove that any $k$-dimensional shift of finite type can be generated through a $k$-dimensional graph. We investigate the structure of the shift space using…

Given a free group $F_k$ of rank $k\ge 2$ with a fixed set of free generators we associate to any homomorphism $\phi$ from $F_k$ to a group $G$ with a left-invariant semi-norm a generic stretching factor, $\lambda(\phi)$, which is a…

The human ability to synchronize the feedback from all their senses inspired recent works in multi-task and multi-modal learning. While these works rely on expensive supervision, our multi-task graph requires only pseudo-labels from expert…

In this article we study how a subshift can simulate another one, where the notion of simulation is given by operations on subshifts inspired by the dynamical systems theory (factor, projective subaction...). There exists a correspondence…

We propose a method that leverages graph neural networks, multi-level message passing, and unsupervised training to enable real-time prediction of realistic clothing dynamics. Whereas existing methods based on linear blend skinning must be…

Automorphism groups are intrincate conjugacy invariants for subshifts, which can reveal important features of the dynamical structure of a shift action. One important case is the study of automorphism groups when the underlying subshift has…

We give sufficient conditions for stability of a continuous-time linear switched system consisting of finitely many subsystems. The switching between subsystems is governed by an underlying graph. The results are applicable to switched…

Gauge theories are important descriptions for many physical phenomena and systems in quantum computation. Automorphism of gauge group naturally gives global symmetries of gauge theories. In this work we study such symmetries in gauge…