Related papers: On linearly ordered sets of chain components

Let $E(X,f)$ be the Ellis semigroup of a dynamical system $(X,f)$ where $X$ is a compact metric space. We analyze the cardinality of $E(X,f)$ for a compact countable metric space $X$. A characterization when $E(X,f)$ and $E(X,f)^* = E(X,f)…

Many algorithms for processing probabilistic networks are dependent on the topological properties of the problem's structure. Such algorithms (e.g., clustering, conditioning) are effective only if the problem has a sparse graph captured by…

We reinvestigate the dynamical behavior of a first order scalar nonlinear delay differential equation with piecewise linearity and identify several interesting features in the nature of bifurcations and chaos associated with it as a…

We deal here with the issue of determinism versus randomness in time series. One wishes to identify their relative weights in a given time series. Two different tools have been advanced in the literature to such effect, namely, i) the…

Perfect adaptation in a dynamical system is the phenomenon that one or more variables have an initial transient response to a persistent change in an external stimulus but revert to their original value as the system converges to…

The beautiful structures of single and multi-domain proteins are clearly ordered in some fashion but cannot be readily classified using group theory methods that are successfully used to describe periodic crystals. For this reason, protein…

Partial orders may be used for modeling and summarising ranking data when the underlying order relations are less strict than a total order. They are a natural choice when the data are lists recording individuals' positions in queues in…

Many set theorists point to the linearity phenomenon in the hierarchy of consistency strength, by which natural theories tend to be linearly ordered and indeed well ordered by consistency strength. Why should it be linear? In this paper I…

A continuous map $f$ from a compact interval $I$ into itself is densely (resp. generically) chaotic if the set of points $(x,y)$ such that $\limsup_{n\to+\infty}|f^n(x)-f^n(y)|>0$ and $\liminf_{n\to+\infty} |f^n(x)-f^n(y)|=0$ is dense…

Let $(E,\xi)={\rm ind}(E_n, \xi_n)$ be an inductive limit of a sequence $(E_n, \xi_n)_{n\in N}$ of locally convex spaces and let every step $(E_n, \xi_n)$ be endowed with a partial order by a pointed convex (solid) cone $S_n$. In the…

Many systems across the sciences evolve through a combination of multiplicative growth and diffusive transport. In the presence of disorder, these systems tend to form localized structures which alternate between long periods of relative…

We prove structural stability under perturbations for a class of discrete-time dynamical systems near a non-hyperbolic fixed point. We reformulate the stability problem in terms of the well-posedness of an infinite-dimensional nonlinear…

Structural causal models describe how the components of a robotic system interact. They provide both structural and functional information about the relationships that are present in the system. The structural information outlines the…

The study of deterministic chaos continues to be one of the important problems in the field of nonlinear dynamics. Interest in the study of chaos exists both in low-dimensional dynamical systems and in large ensembles of coupled…

Requiring that the causal structure between different parties is well-defined imposes constraints on the correlations they can establish, which define so-called causal correlations. Some of these are known to have a "dynamical" causal order…

Let $(X,d)$ be a compact metric space and $f:X \to X$ be a self-map. The compact dynamical system $(X,f)$ is called sensitive or sensitivity depends on initial conditions, if there is a positive constant $\delta$ such that in each non-empty…

This is a survey article on trees, with a modest number of proofs to give a flavor of the way these topologies can be efficiently handled. Trees are defined in set-theorist fashion as partially ordered sets in which the elements below each…

The stable functionality of networked systems is a hallmark of their natural ability to coordinate between their multiple interacting components. Yet, strikingly, real-world networks seem random and highly irregular, apparently lacking any…

A frame in an $n$-dimensional Hilbert space $H_n$ is a possibly redundant collection of vectors $\{f_i\}_{i\in I}$ that span the space. A tight frame is a generalization of an orthonormal basis. A frame $\{f_i\}_{i\in I}$ is said to be…

A criterion on the asymptotic stability of fractional-order systems with incomensurate orders is proposed in this paper. Existing methods always assume order parameters be rational numbers or the ratios of any two orders be rational…