Related papers: Approximating the mapping between systems exhibiti…
A new approach is proposed to the integrated analysis of the time structure of synchronization of multidimensional chaotic systems. The method allows one to diagnose and quantitatively evaluate the intermittency characteristics during…
In this paper, we introduce the concept of nearly convex set-valued mappings and investigate fundamental properties of these mappings. Additionally, we establish a geometric approach for generalized differentiation of nearly convex…
General invariants of a geometric mapping of a symmetric affine connection space are obtained in this paper. These invariants are generalizations of the previous obtained basic invariants (see [16]). Moreover, these invariants are related…
This paper describes a system for supporting coarse-grained location-based synchronisation. This type of synchronisation may occur when people need only some awareness about the location of others within the specific context of an on-going…
In this paper, we develop a theory about the relationship between invariant and equivariant maps with regard to a group $G$. We then leverage this theory in the context of deep neural networks with group symmetries in order to obtain novel…
This paper over-approximates the reachable sets of a continuous-time uncertain system using the sensitivity of its trajectories with respect to initial conditions and uncertain parameters. We first prove the equivalence between an existing…
We consider time-dependent dynamical systems arising as sequential compositions of self-maps of a probability space. We establish conditions under which the Birkhoff sums for multivariate observations, given a centering and a general…
Sufficient conditions for global stabilization of nonlinear systems with delayed input by means of approximate predictors are presented. An approximate predictor is a mapping which approximates the exact values of the stabilizing input for…
We study a random dynamical system such that one transformation is randomly selected from a family of transformations and then applied on each iteration. For such random dynamical systems, we consider estimates of absolutely continuous…
Two-dimensional mappings obtained by coupling two piecewise increasing expanding maps are considered. Their dynamics is described when the coupling parameter increases in the expanding domain. By introducing a coding and by analysing an…
This study presents a method for constructing a sequence of approximate solutions of increasing accuracy to general equilibrium models on nonlocal domains. The method is based on a technique originated from dynamical systems theory. The…
We point out the existence of a transition from partial to global generalized synchronization (GS) in symmetrically coupled structurally different time-delay systems of different orders using the auxiliary system approach and the mutual…
Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…
Many current challenges involve understanding the complex dynamical interplay between the constituents of systems. Typically, the number of such constituents is high, but only limited data sources on them are available. Conventional…
Harmonicity of holomorphic maps between various subclasses of almost contact metric manifolds is discussed. Consequently, some new results are obtained. Also some known results are recovered, some of them are generalized and some of them…
In this paper, we consider the class of generalized {\Phi}-strongly monotone mappings and the methods of approximating a solution of equations of Hammerstein type. Auxiliary mapping is defined for nonlinear integral equations of Hammerstein…
In this paper we investigate a problem of approximation of continuous mappings by smooth mappings with nonnegative Jacobian.
We apply the topological quantization method to some gravitational fields which can be represented as generalized harmonic maps. This representation extends the well-known concept of harmonic maps and allows us to describe some solutions to…
In this paper we show how to approximate ("learn") a function f, where X and Y are metric spaces.
Datasets often have their intrinsic symmetries, and particular deep-learning models called equivariant or invariant models have been developed to exploit these symmetries. However, if some or all of these symmetries are only approximate,…