Related papers: Persistent Homology and String Vacua
Topological data analysis is an approach to study shape of a data set by means of topology. Its main object of study is the persistence diagram, which represents the topological features of the data set at different spatial resolutions.…
In recent years, graph theory has been widely employed to probe several language properties. More specifically, the so-called word adjacency model has been proven useful for tackling several practical problems, especially those relying on…
Determination of the nature of the dynamical state of a system as a function of its parameters is an important problem in the study of dynamical systems. This problem becomes harder in experimental systems where the obtained data is…
Topological data analysis (TDA) provides insight into data shape. The summaries obtained by these methods are principled global descriptions of multi-dimensional data whilst exhibiting stable properties such as robustness to deformation and…
While topological data analysis has emerged as a powerful paradigm for structural inference, its foundational tools, notably persistent homology and the persistent Laplacian, are frequently insensitive to localized structural fluctuations…
Persistent homology is an area within topological data analysis (TDA) that can uncover different dimensional holes (connected components, loops, voids, etc.) in data. The holes are characterized, in part, by how long they persist across…
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…
We present a way to apply topological data analysis for classifying encrypted bits into distinct classes. Persistent homology is applied to generate topological features of a point cloud obtained from sets of encryptions. We see that this…
This article studies the robust version of persistent homology based on trimming methodology to capture the geometric feature through support of the data in presence of outliers. Precisely speaking, the proposed methodology works when the…
Machine learning models for repeated measurements are limited. Using topological data analysis (TDA), we present a classifier for repeated measurements which samples from the data space and builds a network graph based on the data topology.…
In recent years there has been noticeable interest in the study of the "shape of data". Among the many ways a "shape" could be defined, topology is the most general one, as it describes an object in terms of its connectivity structure:…
This thesis is concerned with a realisation of topological theories in terms of statistical models known as Calabi-Yau crystals. The thesis starts with an introduction and review of topological field and string theories. Subsequently…
Link prediction is an important learning task for graph-structured data. In this paper, we propose a novel topological approach to characterize interactions between two nodes. Our topological feature, based on the extended persistent…
Persistent Homology is a widely used topological data analysis tool that creates a concise description of the topological properties of a point cloud based on a specified filtration. Most filtrations used for persistent homology depend…
Topological data analysis (TDA) studies the shape patterns of data. Persistent homology is a widely used method in TDA that summarizes homological features of data at multiple scales and stores them in persistence diagrams (PDs). In this…
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…
Topological data analysis (TDA) is an emerging mathematical concept for characterizing shapes in complex data. In TDA, persistence diagrams are widely recognized as a useful descriptor of data, and can distinguish robust and noisy…
In this paper, we propose a method that extends the persistence-based topological data analysis (TDA) that is typically used for characterizing shapes to general networks. We introduce the concept of the community tree, a tree structure…
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…
In real-world systems, the relationships and connections between components are highly complex. Real systems are often described as networks, where nodes represent objects in the system and edges represent relationships or connections…