Related papers: Persistent Homology analysis for solar magnetogram…
It is shown that the description of the solar cycle that takes into account the odd zonal harmonic of the solar magnetic field allows us to deepen our knowledge of two important aspects of the solar activity. First, to clarify and expand…
For nearly three decades, spatial games have produced a wealth of insights to the study of behavior and its relation to population structure. However, as different rules and factors are added or altered, the dynamics of spatial models often…
Regions of quiet Sun generally exhibit a complex distribution of small-scale magnetic field structures, which interact with the near-surface turbulent convective motions. Furthermore, it is probable that some of these magnetic fields are…
Magnetic fields are essential ingredients of many physical processes in the interiors and envelopes of cool stars. Yet their direct detection and characterisation is notoriously difficult, requiring high-quality observations and advanced…
We use topological data analysis to study "functional networks" that we construct from time-series data from both experimental and synthetic sources. We use persistent homology with a weight rank clique filtration to gain insights into…
Context. The Sun's complex corona is the source of the solar wind and interplanetary magnetic field. While the large scale morphology is well understood, the impact of variations in coronal properties on the scale of a few degrees on…
In this paper we present a new approach to computing homology (with field coefficients) and persistent homology. We use concepts from discrete Morse theory, to provide an algorithm which can be expressed solely in terms of simple graph…
This chapter provides an overview of the magnetic activity of the Sun and stars, discussing its underlying physical origin, manifestations, and fundamental role in exoplanet studies. It begins with a summary of the Sun's magnetic activity…
The slow solar wind is generally believed to result from the interaction of open and closed coronal magnetic flux at streamers and pseudostreamers. We use 3-dimensional magnetohydrodynamic simulations to determine the detailed structure and…
In this work, we present SoFT: Solar Feature Tracking, a novel feature-tracking tool developed in Python and designed to detect, identify, and track magnetic elements in the solar atmosphere. It relies on a watershed segmentation algorithm…
Persistent homology is a popular tool in Topological Data Analysis. It provides numerical characteristics of data sets which reflect global geometric properties. In order to be useful in practice, for example for feature generation in…
Topological data analysis provides a set of tools to uncover low-dimensional structure in noisy point clouds. Prominent amongst the tools is persistence homology, which summarizes birth-death times of homological features using data objects…
Persistent homology is an important methodology in topological data analysis which adapts theory from algebraic topology to data settings. Computing persistent homology produces persistence diagrams, which have been successfully used in…
Potential Field Source Surface (PFSS) models are widely used to study the solar corona and form the basis for solar wind forecasting, yet often fail to reproduce observed properties of coronal holes. We analyze 702 observed coronal holes…
Persistent homology provides a robust methodology to infer topological structures from point cloud data. Here we explore the persistent homology of point clouds embedded into a probabilistic setting, exploiting the theory of point…
One of the primary areas of interest in applied algebraic topology is persistent homology, and, more specifically, the persistence diagram. Persistence diagrams have also become objects of interest in topological data analysis. However,…
Helioseismology has revealed the internal density and rotation profiles of the Sun. Yet, knowledge of its magnetic fields and meridional circulation is confined much closer to the surface, and latitudinal entropy gradients are below…
An overview is given about recent developments and results of comprehensive simulations of magneto-convective processes in the near-surface layers and photosphere of the Sun. Simulations now cover a wide range of phenomena, from whole…
A topological shape analysis is proposed and utilized to learn concepts that reflect shape commonalities. Our approach is two-fold: i) a spatial topology analysis of point cloud segment constellations within objects. Therein constellations…
Algorithms for persistent homology and zigzag persistent homology are well-studied for persistence modules where homomorphisms are induced by inclusion maps. In this paper, we propose a practical algorithm for computing persistence under…