Related papers: Amorphic complexity
A given dynamics for a composite quantum system can exhibit several distinct properties for the asymptotic entanglement behavior, like entanglement sudden death, asymptotic death of entanglement, sudden birth of entanglement, etc. A…
We extend Matveev's complexity of 3-manifolds to PL compact manifolds of arbitrary dimension, and we study its properties. The complexity of a manifold is the minimum number of vertices in a simple spine. We study how this quantity changes…
The exact order of mixing for zero-dimensional algebraic dynamical systems is not entirely understood. Here non-Archimedean norms in function fields of positive characteristic are used to exhibit an asymptotic shape in non-mixing sequences…
We compute the asymptotic temporal behavior of the dynamical complexity associated with the maximum probability trajectories on Gaussian statistical manifolds in presence of correlations between the variables labeling the macrostates of the…
We study the dynamics of the attractor of the doubling map with an asymmetrical hole by associating to each hole an element of the lexicographic world. A description of the topological entropy function is given. We show that the set of…
The importance of structured, complex connectivity patterns found in several real-world systems is to a great extent related to their respective effects in constraining and even defining the respective dynamics. Yet, while complex networks…
We introduce the topological complexity of the work map associated to a robot system. In broad terms, this measures the complexity of any algorithm controlling, not just the motion of the configuration space of the given system, but the…
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…
Random neural networks are dynamical descriptions of randomly interconnected neural units. These show a phase transition to chaos as a disorder parameter is increased. The microscopic mechanisms underlying this phase transition are unknown,…
We obtain general results on the dynamics of exactly conical geometries, where we use the notion of boundaries at infinity to characterize asymptotic behavior. As we demonstrate in examples, these notions also apply to smooth geometries…
We consider a complex-valued linear mixture model, under discrete weakly stationary processes. We recover latent components of interest, which have undergone a linear mixing. We study asymptotic properties of a classical unmixing estimator,…
We introduce invariants, called shifting numbers, that measure the asymptotic amount by which an autoequivalence of a triangulated category translates inside the category. The invariants are analogous to Poincare translation numbers that…
We develop a general compactification framework to facilitate analysis of nonlinear nonautonomous ODEs where nonautonomous terms decay asymptotically. The strategy is to compactify the problem: the phase space is augmented with a bounded…
We use the complexity function of an invariant, not necessary closed, subset of a two-sided shift space to compute the polynomial entropy of the induced dynamics on the hyperspace of continua for certain one-dimensional dynamical systems.…
In this paper, we study the complicated dynamics of infinite dimensional random dynamical systems which include deterministic dynamical systems as their special cases in a Polish space. Without assuming any hyperbolicity, we proved if a…
Let $(X,G)$ be a minimal equicontinuous dynamical system, where $X$ is a compact metric space and $G$ some topological group acting on $X$. Under very mild assumptions, we show that the class of regular almost automorphic extensions of…
Many measurements on soft condensed matter (e.g., biological and materials) systems track low-dimensional observables projected from the full system phase space as a function of time. Examples are dynamic structure factors, spectroscopic…
Complexity is an important metric for appropriate characterization of different classes of irregular signals, observed in the laboratory or in nature. The literature is already rich in the description of such measures using a variety of…
Asymptotic formulae for the mechanical and electric fields in a piezoelectric body with a small void are derived and justified. Such results are new and useful for applications in the field of design of smart materials. In this way the…
In this paper, we investigate the asymptotic properties of a particular class of state-dependent sweeping processes. While extensive research has been conducted on the existence and uniqueness of solutions for sweeping processes, there is a…