Related papers: Kolmogorov Space in Time Series Data
With the increasing availability of high-dimensional data, analysts often rely on exploratory data analysis to understand complex data sets. A key approach to exploring such data is dimensionality reduction, which embeds high-dimensional…
Time reversal symmetry is studied in a space with noncommutativity of coordinates and noncommutativity of momenta of canonical type. The circular motion is examined as an apparent example of time reversal symmetry breaking in the space. On…
The concept of conformal field theory provides a general classification of statistical systems on two-dimensional geometries at the point of a continuous phase transition. Considering the finite-size scaling of certain special observables,…
Understanding large amounts of spatiotemporal data from particle-based simulations, such as molecular dynamics, often relies on the computation and analysis of aggregate measures. These, however, by virtue of aggregation, hide structural…
This article contains a detailed and rigorous proof of the construction of a geometric invariant for initial data sets for the Einstein vacuum field equations. This geometric invariant vanishes if and only if the initial data set…
This paper proposes a Matrix Error Correction Model to identify cointegration relations in matrix-valued time series. We hereby allow separate cointegrating relations along the rows and columns of the matrix-valued time series and use…
We briefly show how the use of topological spaces and $\sigma$-algebras in physics can be rederived and understood as the fundamental requirement of experimental verifiability. We will see that a set of experimentally distinguishable…
We consider the nonlinear Kolmogorov equation posed in a Hilbert space $H$, not necessarily of finite dimension. This model was recently studied by Cox et al. [24] in the framework of weak convergence rates of stochastic wave models. Here,…
While general relativity provides a complete geometric theory of gravity, it fails to explain the other three forces of nature, i.e., electromagnetism and weak and strong interactions. We require the quantum field theory (QFT) to explain…
By Kolmogorov Complexity,two number-theoretic problems are solved in different way than before,one problem is Maxim Kontsevich and Don Bernard Zagier's Problem 3 \emph{Exhibit at least one number which does not belong to} $ \mathcal{P}$…
A "tensor space" is a vector space equipped with a finite collection of multi-linear forms. In previous work, we showed that (for each signature) there exists a universal homogeneous tensor space, which is unique up to isomorphism. Here we…
Complex networks represent system dynamics through the interactions of a set of anomalous time series. Consider the problem of computing correlations for highly correlated pairs of time series across sliding windows. Efficiently computing…
Vasiliev equations facilitate globally defined formulations of higher-spin gravity in various correspondence spaces associated with different phases of the theory. In the four-dimensional case this induces a map from a generally covariant…
We begin showing that for even dimensional vector spaces $V$ all automorphisms of their Clifford algebras are inner. So all orthogonal transformations of $V$ are restrictions to $V$ of inner automorphisms of the algebra. Thus under…
It seems to be a common belief that the space in which we live is a space-time manifold of dimension at least four. In the present article we wish to draw attention to a slightly different possibility - a space-time pseudomanifold (or even…
The general world model for homogeneous and isotropic universe has been roposed. For this purpose, we introduce a global and fiducial system of reference (world reference frame) constructed on a 5-dimensional space-time that is embedding…
Twisted period integrals are ubiquitous in theoretical physics and mathematics, where they inhabit a finite-dimensional vector space governed by an inner product known as the intersection number. In this work, we uncover the associated…
A new class of distances appropriate for measuring similarity relations between sequences, say one type of similarity per distance, is studied. We propose a new ``normalized information distance'', based on the noncomputable notion of…
We consider a natural class of time-periodic infinite-dimensional nonlinear Hamiltonian systems modelling the interaction of a classical mechanical system of particles with a scalar wave field. When the field is defined on a space torus…
Time series are ubiquitous in our data rich world. In what follows I will describe how ideas from dynamical systems and topological data analysis can be combined to gain insights from time-varying data. We will see several applications to…