Related papers: Persistent Homology analysis for solar magnetogram…
Persistent homology analysis, a recently developed computational method in algebraic topology, is applied to the study of the phase transitions undergone by the so-called XY-mean field model and by the phi^4 lattice model, respectively. For…
Persistent homology theory is a relatively new but powerful method in data analysis. Using simplicial complexes, classical persistent homology is able to reveal high dimensional geometric structures of datasets, and represent them as…
High-resolution helioseismology observations with the Helioseismic and Magnetic Imager (HMI) onboard Solar Dynamics Observatory (SDO) provide a unique three-dimensional view of the solar interior structure and dynamics, revealing a…
Persistent homology is a branch of computational algebraic topology that studies shapes and extracts features over multiple scales. In this paper, we present an unsupervised approach that uses persistent homology to study divergent behavior…
Solar inertial modes are quasi-toroidal modes of the Sun that are of practical interest as they allow probing the deep convection zone. Since 2010, solar images of the photospheric magnetic field are made available by HMI onboard the Solar…
We discuss recent advances made in modelling the complex magnetohydrodynamics of the Sun using our anelastic spherical harmonics (ASH) code. We have conducted extensive 3--D simulations of compressible convection in rotating spherical…
We propose a functorial framework for persistent homology based on finite topological spaces and their associated posets. Starting from a finite metric space, we associate a filtration of finite topologies whose structure maps are…
The presence of intense magnetic fields in and around sunspots is expected to modify the solar structure and oscillation frequencies. Applying the ring diagram technique to data from the Michelson Doppler Imager (MDI) on board the Solar and…
Solar pores are active regions with large magnetic field strengths and apparent simple magnetic configurations. Their properties resemble the ones found for the sunspot umbra although pores do not show penumbra. Therefore, solar pores…
Persistent homology is a technique recently developed in algebraic and computational topology well-suited to analysing structure in complex, high-dimensional data. In this paper, we exposit the theory of persistent homology from first…
Topological invariants have played a fundamental role in the advancement of theoretical high energy physics. Physicists have used several kinematic techniques to distinguish new physics predictions from the Standard Model (SM) of particle…
In this paper we develop a novel Topological Data Analysis (TDA) approach for studying graph representations of time series of dynamical systems. Specifically, we show how persistent homology, a tool from TDA, can be used to yield a…
Macroscopic wave and oscillatory phenomena ubiquitously detected in the plasma of the corona of the Sun are interpreted in terms of magnetohydrodynamic theory. Fast and slow magnetoacoustic waves are clearly distinguished in observations.…
The convectively driven, weakly magnetized regions of the solar photosphere dominate the Sun's surface at any given time, but the temporal variations of these quiet regions of the photosphere throughout the solar cycle are still not well…
Context: Studying the motions on the solar surface is fundamental for understanding how turbulent convection transports energy and how magnetic fields are distributed across the solar surface. Aims: From horizontal velocity measurements all…
Solar oscillations consist of a rich spectrum of internal acoustic waves and surface gravity waves, stochastically excited by turbulent convection. They have been monitored almost continuously over the last ten years with high-precision…
Persistent homology is a natural tool for probing the topological characteristics of weighted graphs, essentially focusing on their $0$-dimensional homology. While this area has been substantially studied, we present a new approach to…
We define persistent homology groups over any set of spaces which have inclusions defined so that the corresponding directed graph between the spaces is acyclic, as well as along any subgraph of this directed graph. This method…
Using turbulent MHD simulations (magnetic Reynolds numbers up to 8000) and Hinode observations, we study effects of turbulence on measuring the solar magnetic field outside active regions. Firstly, from synthetic Stokes V profiles for the…
Solar and stellar magnetic patches (i.e., magnetic fluxes that reach the surface from the interior) are believed to be the primary sources of a star's atmospheric conditions. Hence, detecting and identifying these features (also known as…