Related papers: Topological Persistence Machine of Phase Transitio…
Topological metamaterials exhibit unusual behaviors at their boundaries, such as unidirectional chiral waves, that are protected by a topological feature of their band structure. The ability to tune such a material through a topological…
High-dimensional data must be highly structured to be learnable. Although the compositional and hierarchical nature of data is often put forward to explain learnability, quantitative measurements establishing these properties are scarce.…
In this paper, we propose Quasi Zigzag Persistent Homology (QZPH) as a framework for analyzing time-varying data by integrating multiparameter persistence and zigzag persistence. To this end, we introduce a stable topological invariant that…
Topological data analysis (TDA) is a tool from data science and mathematics that is beginning to make waves in environmental science. In this work, we seek to provide an intuitive and understandable introduction to a tool from TDA that is…
The laminar-to-turbulent transition remains a fundamental and enduring challenge in fluid mechanics. Its complexity arises from the intrinsic nonlinearity and extreme sensitivity to external disturbances. This transition is critical in a…
Data quality is crucial for the successful training, generalization and performance of machine learning models. We propose to measure the quality of a subset concerning the dataset it represents, using topological data analysis techniques.…
We show that topological phases include disordered materials if the underlying invariant is interpreted as originating from coarse geometry. This coarse geometric framework, grounded in physical principles, offers a natural setting for the…
This article proposes a topological method that extracts hierarchical structures of various amorphous solids. The method is based on the persistence diagram (PD), a mathematical tool for capturing shapes of multiscale data. The input to the…
Topological phase transitions track changes in topological properties of a system and occur in real materials as well as quantum engineered systems, all of which differ greatly in terms of dimensionality, symmetries, interactions, and…
Topological Data Analysis (TDA) can be used to detect and characterize holes in an image, such as zero-dimensional holes (connected components) or one-dimensional holes (loops). However, there is currently no widely accepted statistical…
Persistent homology is a cornerstone of topological data analysis, offering a multiscale summary of topology with robustness to nuisance transformations, such as rotations and small deformations. Persistent homology has seen broad use…
In the area of topological and geometric treatment of phase transitions and symmetry breaking in Hamiltonian systems, in a recent paper some general sufficient conditions for these phenomena in $\mathbb{Z}_2$-symmetric systems (i.e.…
Although classifying topological quantum phases have attracted great interests, the absence of local order parameter generically makes it challenging to detect a topological phase transition from experimental data. Recent advances in…
We implement a computational pipeline based on a recent machine learning technique, namely the Topological Data Analysis (TDA), that has the capability of extracting powerful information-carrying topological features. We apply such a method…
Can the topology of a network that consists of many particles interacting with each other change in complexity when a phase transition occurs? The answer to this question is particularly interesting to understand the nature of phase…
Phase coarsening is a fundamental process of microstructure evolution in multiphase materials. A thorough understanding of its kinetics is of great significance for material processing and performance. Generally, coarsening can be divided…
The predictions of mean-field electrodynamics can now be probed using direct numerical simulations of random flows and magnetic fields. When modelling astrophysical MHD, it is important to verify that such simulations are in agreement with…
Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems. Methods from topological data analysis, e.g., persistent homology, enable us to obtain such information,…
Classifying phases of matter is a central problem in physics. For quantum mechanical systems, this task can be daunting owing to the exponentially large Hilbert space. Thanks to the available computing power and access to ever larger data…
Topological phase transitions, which do not adhere to Landau's phenomenological model (i.e. a spontaneous symmetry breaking process and vanishing local order parameters) have been actively researched in condensed matter physics. Machine…