Related papers: A panorama of specification-like properties and th…
We propose a new definition of preimage entropy dimension for continuous maps on compact metric spaces, investigate fundamental properties of the preimage entropy dimension, and compare the preimage entropy dimension with the topological…
The paper deals with continuous and compact mappings generated by the Fourier transform between distinguished function spaces on $\mathbb{R}^n$. The degree of compactness will be measured in terms of related entropy numbers. We are more…
The notion of stochastic shadowing property is introduced. Relations to stochastic stability and standard shadowing are studied. Using tent map as an example it is proved that, in contrast to what happens for standard shadowing, there are…
This article is a discussion of some characteristic properties in connection with global models, particularly for the application of prediction, such as the approximation property, the interpolation property and the transmission property.
We present a conceptual framework that unifies a variety of evaluation metrics for different structured prediction tasks (e.g. event and relation extraction, syntactic and semantic parsing). Our framework requires representing the outputs…
We explore the ability of word embeddings to capture both semantic and morphological similarity, as affected by the different types of linguistic properties (surface form, lemma, morphological tag) used to compose the representation of each…
This paper is concerned with the study of various notions of shadowing of dynamical systems induced by a sequence of maps, so-called time varying maps, on a metric space. We define and study the shadowing, h-shadowing, limit shadowing,…
We study shadowing-type properties for set-valued dynamical systems. In particular, we investigate the periodic shadowing property and its relationship with expansivity and chain transitivity. We establish that for positively expansive…
For a real or complex one-dimensional map satisfying a weak hyperbolicity assumption, we study the existence and statistical properties of physical measures, with respect to geometric reference measures. We also study geometric properties…
The Chapter starts with introductory information about quantitative linguistics notions, like rank--frequency dependence, Zipf's law, frequency spectra, etc. Similarities in distributions of words in texts with level occupation in quantum…
High-order phenomena play crucial roles in many systems of interest, but their analysis is often highly nontrivial. There is a rich literature providing a number of alternative information-theoretic quantities capturing high-order…
We define a general notion of entropy in elementary, algebraic terms. Based on that, weak forms of a scalar product and a distance measure are derived. We give basic properties of these quantities, generalize the Cauchy-Schwarz inequality,…
Different aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize…
There are two basic ways of weakening the definition of the well-known metric regularity property by fixing one of the points involved in the definition. The first resulting property is called metric subregularity and has attracted a lot of…
The literature on concurrency theory offers a wealth of examples of characteristic-formula constructions for various behavioural relations over finite labelled transition systems and Kripke structures that are defined in terms of fixed…
We define some pointwise properties of topological dynamical systems and give pointwise conditions for such a system possesses positive topological entropy. We give sufficient conditions to obtain positive topological entropy for maps which…
The theory of descriptive nearness is usually adopted when dealing with sets that share some common properties even when the sets are not spatially close, i.e., the sets have no members in common. Set description results from the use of…
In this paper we present the quantity, which is an entanglement parameter. Its origin is very intriguing, because its construction is motivated by separability criteria based on uncertainty relation. We show that this quantity is…
A discussion is presented, within a simple unifying scheme, about different types of symmetry of PDE's, with the introduction and a precise characterization of the notions of "standard" and "weak" conditional symmetries, together with their…
This lecture is devoted to review some of the main properties of multisymplectic geometry. In particular, after reminding the standard definition of multisymplectic manifold, we introduce its characteristic submanifolds, the canonical…