Related papers: Kolmogorov Space in Time Series Data

A new method of metric space investigation, based on classification of its finite subspaces, is suggested. It admits to derive information on metric space properties which is encoded in metric. The method describes geometry in terms of only…

Most currently used tensor regression models for high-dimensional data are based on Tucker decomposition, which has good properties but loses its efficiency in compressing tensors very quickly as the order of tensors increases, say greater…

Time series data captures properties that change over time. Such data occurs widely, ranging from the scientific and medical domains to the industrial and environmental domains. When the properties in time series exhibit spatial variations,…

This article continues the study of computable elementary topology started by the author and T. Grubba in 2009 and extends the author's 2010 study of axioms of computable separation. Several computable T3- and Tychonoff separation axioms…

We describe the construction of a geometric invariant characterising initial data for the Kerr-Newman spacetime. This geometric invariant vanishes if and only if the initial data set corresponds to exact Kerr-Newman initial data, and so…

We introduce a closed-form method for identification of discrete-time linear time-variant systems from data, formulating the learning problem as a regularized least squares problem where the regularizer favors smooth solutions within a…

This paper presents a technique for reduced-order Markov modeling for compact representation of time-series data. In this work, symbolic dynamics-based tools have been used to infer an approximate generative Markov model. The time-series…

This book introduces the new research area of Geometric Data Science, where data can represent any real objects through geometric measurements. The first part of the book focuses on finite point sets. The most important result is a complete…

Let $(M,g)$ be a spacetime. That is, $M$ is a real manifold of dimension $4$ equipped with a Lorentzian metric $g$. We show that any separation of time and space in $M$ is equivalent to introducing a (non-smooth) Riemann metric $h$. If $h$…

Data-driven model discovery of complex dynamical systems is typically done using sparse optimization, but it has a fundamental limitation: sparsity in that the underlying governing equations of the system contain only a small number of…

With the rapid development of web services, large amounts of time series data are generated and accumulated across various domains such as finance, healthcare, and online platforms. As such data often co-evolves with multiple variables…

Time series, characterized by a sequence of data points organized in a discrete-time order, are ubiquitous in real-world scenarios. Unlike other data modalities, time series present unique challenges in learning and modeling due to their…

In this paper we prove estimates on the behaviour of the Kolmogorov-Sinai entropy relative to a partition for randomly perturbed dynamical systems. Our estimates use the entropy for the unperturbed system and are obtained using the notion…

Most numerical methods for time integration use real time steps. Complex time steps provide an additional degree of freedom, as we can select the magnitude of the step in both the real and imaginary directions. By time stepping along…

We define a pseudometric on the set of all unbounded subsets of a metric space. The Kolmogorov quotient of this pseudometric space is a complete metric space. The definition of the pseudometric is guided by the principle that two unbounded…

Modeling time series data remains a pervasive issue as the temporal dimension is inherent to numerous domains. Despite significant strides in time series forecasting, high noise-to-signal ratio, non-normality, non-stationarity, and lack of…

Cyber-physical system applications such as autonomous vehicles, wearable devices, and avionic systems generate a large volume of time-series data. Designers often look for tools to help classify and categorize the data. Traditional machine…

This paper is concerned with Kolmogorov's two-equation model for the free turbulence in three dimensions. We first discuss scaling laws for slightly more general two-equation models to highlight the special role of the model devised by…

This paper is devoted to the observability of a class of two-dimensional Kolmogorov-type equations presenting a quadratic degeneracy. We give lower and upper bounds for the critical time. These bounds coincide in symmetric settings, giving…

We suggest a novel method of clustering and exploratory analysis of temporal event sequences data (also known as categorical time series) based on three-dimensional data grid models. A data set of temporal event sequences can be represented…