Related papers: Predicting Euler Characteristics and Constructing …

The Euler Characteristic Transform (ECT) has proven to be a powerful representation, combining geometrical and topological characteristics of shapes and graphs. However, the ECT was hitherto unable to learn task-specific representations. We…

Causal fermion systems and Riemannian fermion systems are proposed as a framework for describing non-smooth geometries. In particular, this framework provides a setting for spinors on singular spaces. The underlying topological structures…

Chirality and topology are intimately related fundamental concepts, which are heavily explored to establish spin-textures as potential magnetic bits in information technology. However, this ambition is inhibited since electrical reading of…

Electrons which are slowly moving through chiral magnetic textures can effectively be described as if they where influenced by electromagnetic fields emerging from the real-space topology. This adiabatic viewpoint has been very successful…

In this work, we investigate the emergence of topological spin textures in a ferromagnetically coupled bilayer chiral magnet by means of Monte Carlo simulations of a classical spin model including exchange interaction, Dzyaloshinskii-Moriya…

Spinless systems exhibit unique topological characteristics compared to spinful ones, stemming from their distinct algebra. Without chiral interactions typically linked to spin, an intriguing yet unexplored interplay between topological and…

Principles of machine learning are applied to models that support skyrmion phases in two dimensions. Successful feature predictions on various phases of the skyrmion model were possible with several layers of convolutional neural network…

The Euler characteristic (EC) is a powerful topological descriptor that can be used to quantify the shape of data objects that are represented as fields/manifolds. Fast methods for computing the EC are required to enable processing of…

Magnetic skyrmions are nanoscale spin textures that their thermal stability originates from the nontrivial topology in nature. Recently, a plethora of topological spin textures have been theoretically predicted or experimentally observed,…

We present a novel approach to understanding the extraordinary diversity of magnetic skyrmion solutions. Our approach combines a new classification scheme with efficient analytical and numerical methods. We introduce the concept of chiral…

Symmetry governs many electronic and photonic phenomena in optics and condensed matter physics. Skyrmions and merons are prominent topological structures in magnetic materials, with the topological features determined by the interplay…

Magnetic skyrmions are topologically wound nanoscale textures of spins whose ambient stability and electrical manipulation in multilayer films have led to an explosion of research activities. While past efforts focused predominantly on…

Photoinduced nonequilibrium spin structure is examined in the double-exchange model, in which itinerant electrons couple with localized spins through the ferromagnetic Hund coupling. In particular, we focus on the transient spin structure…

Topological descriptors, such as the Euler characteristic function and the persistence diagram, have grown increasingly popular for representing complex data. Recent work showed that a carefully chosen set of these descriptors encodes all…

The Euler number is a new topological number recently debuted in the topological physics. Unlike the Chern number defined for a band, it is defined for interbands. We propose a simple model realizing the topological Euler insulator for the…

Topological spin configurations, such as soliton-like spin texture and Dirac electron assemblies, have emerged in recent years in both fundamental science and technological applications. Achieving stable topological spin textures at…

In machine learning, there is a long history of trying to build neural networks that can learn from fewer example data by baking in strong geometric priors. However, it is not always clear a priori what geometric constraints are appropriate…

The model presented in this research predicts ideal chiral crystal and propose a new direction of designing chiral crystals. Skyrmions are topologically protected and structurally assymetric materials with an exotic spin composition. This…

Magnetic moments near zigzag edges in graphene allow complex nanostructures with customised spin properties to be realised. However, computational costs restrict theoretical investigations to small or perfectly periodic structures. Here we…

Euler's elastica constitute an appealing variational image inpainting model. It minimises an energy that involves the total variation as well as the level line curvature. These components are transparent and make it attractive for shape…