Related papers: Kolmogorov Space in Time Series Data

Techniques from topological data analysis (TDA) have proven effective in studying time-dependent data arising in dynamic systems, such as animal swarming behavior and spatiotemporal patterns in neuroscience. While early algorithms leveraged…

Experiments using 3D Lagrangian tracking are used to investigate Kolmogorov scaling below the bubble size in bubble-induced turbulence (BIT). Second and third order structure functions reveal approximate Kolmogorov scaling for homogeneous…

A topological computation method, called the MGSTD method, is applied to time-series data obtained from meteorological measurement. The method gives decomposition of the dynamics into invariant sets and gradient-like transitions between…

This monograph is centred at the intersection of three mathematical topics, that are theoretical in nature, yet with motivations and relevance deep rooted in applications: the linear inverse problems on abstract, in general…

We show that Poincar\'e invariance directly implies the existence of a complexified Minkowski space whose real and imaginary directions unify spacetime and spin, which we dub spinspacetime. Despite the intrinsic noncommutativity of spin,…

We study the phase space of spatially homogeneous and isotropic cosmology in general scalar-tensor theories. A reduction to a two-dimensional phase space is performed when possible-in these situations the phase space is usually a…

Let $|A|$ denote the cardinality of a finite set $A$. For any real number $x$ define $t(x)=x$ if $x\geq1$ and 1 otherwise. For any finite sets $A,B$ let $\delta(A,B)$ $=$ $\log_{2}(t(|B\cap\bar{A}||A|))$. We define {This appears as…

One approach to understanding complex data is to study its shape through the lens of algebraic topology. While the early development of topological data analysis focused primarily on static data, in recent years, theoretical and applied…

We begin from the generalised eight-dimensional Minkowski spacetime structure, previously developed in Clifford geometric algebra $ C\ell(\Re^3) $. We propose that this is the correct algebraic representation for physical three-dimensional…

We show that the ``time'' t_s defined via spin clusters in the Ising model coupled to 2d gravity leads to a fractal dimension d_h(s) = 6 of space-time at the critical point, as advocated by Ishibashi and Kawai. In the unmagnetized phase,…

We describe spinors in Minkowskian spaces with arbitrary signature and their role in the classification of space-time superalgebras and their R-symmetries in any dimension.

In a previous work, "pure data" is proposed as an axiomatic foundation for mathematics and computing, based on "finite sequence" as the foundational concept rather than based on logic or type. Within this framework, objects with…

We propose a parsimonious spatiotemporal model for time series data on a spatial grid. Our model is capable of dealing with high-dimensional time series data that may be collected at hundreds of locations and capturing the spatial…

Temporal data, notably time series and spatio-temporal data, are prevalent in real-world applications. They capture dynamic system measurements and are produced in vast quantities by both physical and virtual sensors. Analyzing these data…

We study the quantization of geometry in the presence of a cosmological constant, using a discretiza- tion with constant-curvature simplices. Phase space turns out to be compact and the Hilbert space finite dimensional for each link. Not…

This paper develops a new class of Rosenbrock-type integrators based on a Krylov space solution of the linear systems. The new family, called Rosenbrock-Krylov (Rosenbrock-K), is well suited for solving large scale systems of ODEs or…

Reduced order models (ROMs) that capture flow dynamics are of interest for decreasing computational costs for simulation as well as for model-based control approaches. This work presents a data-driven framework for minimal-dimensional…

In the following we are going to describe how macroscopic space-time is supposed to emerge as an orderparameter manifold or superstructure floating in a stochastic discrete network structure. As in preceeding work (mentioned below), our…

Within the scope of a static cylindrically symmetric space-time we study the behavior of a nonlinear spinor field that depends on time and radial coordinates. It is found that the presence of nontrivial non-diagonal components of the…

We consider toy cosmological models in which a classical, homogeneous, spinor field provides a dominant or sub-dominant contribution to the energy-momentum tensor of a flat Friedmann-Robertson-Walker universe. We find that, if such a field…