Related papers: Kolmogorov Space in Time Series Data

In this work we propose a methodology for assessment of pedestrian models continuous in space. With respect to the Kolmogorov-Smirnov distance between two data clouds, representing for instance simulated and the corresponding empirical…

Broadly speaking, twistor theory is a framework for encoding physical information on space-time as geometric data on a complex projective space, known as a twistor space. The relationship between space-time and twistor space is non-local…

We revisit extending the Kolmogorov-Smirnov distance between probability distributions to the multidimensional setting and make new arguments about the proper way to approach this generalization. Our proposed formulation maximizes the…

In this article, we describe a simple covariant characterisation of initial data sets which give rise to Petrov type D vacuum spacetime developments. As an application, we derive an integral invariant which, when restricted to the…

The rise in data has led to the need for dimension reduction techniques, especially in the area of non-scalar variables, including time series, natural language processing, and computer vision. In this paper, we specifically investigate…

The necessity of rejecting the numerical model of geometrical extension is postulated on the basis of the idea of identity of space-time and physical vacuum. An attempt is made to define space-time not via the concept of manifold, but via…

In the geometric data model for spatio-temporal data, introduced by Chomicki and Revesz, spatio-temporal data are modelled as a finite collection of triangles that are transformed by time-dependent affinities of the plane. To facilitate…

We investigate the time behavior of the fragmentation model with Kolmogorov time scales and space contraction resembling the random $\beta$-model of turbulence. The space averages computed at any instant using the entire spatial realization…

We consider dynamical systems for which the spatial extension plays an important role. For these systems, the notions of attractor, epsilon-entropy and topological entropy per unit time and volume have been introduced previously. In this…

A new computational paradigm for the analysis of substructure of the Cosmic Web in cosmological cold dark matter simulations is proposed. We introduce a new data-field --- the flip-flop field ---which carries wealth of information about the…

This paper shows how a time series of measurements of an evolving system can be processed to create an inner time series that is unaffected by any instantaneous invertible, possibly nonlinear transformation of the measurements. An inner…

We introduce the notion of scale to generalize and compare different invariants of metric spaces and their measures. Several versions of scales are introduced such as Hausdorff, packing, box, local and quantization. They moreover are…

The goal of data-driven learning of dynamical systems is to interpret time series as a continuous observation of an underlying dynamical system. This task is not well-posed for a variety of reasons - such as multiple co-existing…

This paper is the second part of a series that develops the mathematical framework necessary for studying field theories on ``T-Minkowski'' noncommutative spacetimes. These spacetimes constitute a class of noncommutative geometries,…

We apply the structure theory of finite dimensional algebras in order to deduce dimension formulas for spaces of period numbers, i.e., complex numbers defined by integrals of algebraic nature. We get a complete and conceptually clear answer…

'Internal spacetime' is a modification of general relativity that was recently introduced as an approximate spacetime geometric model of quantum nonlocality. In an internal spacetime, time is stationary along the worldlines of fundamental…

A problem of current interest is the estimation of spatially distributed processes at locations where measurements are missing. Linear interpolation methods rely on the Gaussian assumption, which is often unrealistic in practice, or…

We suggest necessary conditions of soficness of multidimensional shifts formulated in termsof resource-bounded Kolmogorov complexity. Using this technique we provide examples ofeffective and non-sofic shifts on $\mathbb{Z}^2$ with very low…

Here we have studied the ideas of g*-closed sets, g^tou -sets and Lamda*-closed sets and investigate some of their properties in the spaces of A. D. Alexandroff [1]. We have also studied few separation axioms like T-omega/4,T-3omega/8,…

Complex, oscillatory data arises from a large variety of biological, physical, and social systems. However, the inherent oscillation and ubiquitous noise pose great challenges to current methodology such as linear and nonlinear time series…