Related papers: Persistent Homology and String Vacua
Modern business and economic datasets often exhibit nonlinear, multi-scale structures that traditional linear tools under-represent. Topological Data Analysis (TDA) offers a geometric lens for uncovering robust patterns, such as connected…
We apply topological data analysis to the behavior of C. elegans, a widely-studied model organism in biology. In particular, we use topology to produce a quantitative summary of complex behavior which may be applied to high-throughput data.…
Persistent topological properties of an image serve as an additional descriptor providing an insight that might not be discovered by traditional neural networks. The existing research in this area focuses primarily on efficiently…
Topological Data Analysis (TDA) combines computational topology and data science to extract and analyze intrinsic topological and geometric structures in data set in a metric space. While the persistent homology (PH), a widely used tool in…
Assume that a finite set of points is randomly sampled from a subspace of a metric space. Recent advances in computational topology have provided several approaches to recovering the geometric and topological properties of the underlying…
Topological data analysis and its main method, persistent homology, provide a toolkit for computing topological information of high-dimensional and noisy data sets. Kernels for one-parameter persistent homology have been established to…
Understanding the response of an output variable to multi-dimensional inputs lies at the heart of many data exploration endeavours. Topology-based methods, in particular Morse theory and persistent homology, provide a useful framework for…
Topological data analysis (TDA) aims to extract noise-robust features from a data set by examining the number and persistence of holes in its topology. We show that a computational problem closely related to a core task in TDA --…
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.…
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…
Computational topology provides a tool, persistent homology, to extract quantitative descriptors from structured objects (images, graphs, point clouds, etc). These descriptors can then be involved in optimization problems, typically as a…
We introduce topological methods for quantifying spatially heterogeneous dynamics, and use these tools to analyze particle-tracking data for a quasi-two-dimensional granular system of air-fluidized beads on approach to jamming. In…
Topological Data Analysis (TDA) allows us to extract powerful topological and higher-order information on the global shape of a data set or point cloud. Tools like Persistent Homology or the Euler Transform give a single complex description…
Information networks are becoming increasingly popular to capture complex relationships across various disciplines, such as social networks, citation networks, and biological networks. The primary challenge in this domain is measuring…
Persistent topological Laplacians constitute a new class of tools in topological data analysis (TDA). They are motivated by the necessity to address challenges encountered in persistent homology when handling complex data. These Laplacians…
Persistent homology is a powerful mathematical tool that summarizes useful information about the shape of data allowing one to detect persistent topological features while one adjusts the resolution. However, the computation of such…
Features such as photon rings, jets, or hot. spots can leave particular topological signatures in a black hole image. As such, topological data analysis can be used to characterize images resulting from high resolution observations…
We study properties of flux vacua in type IIB string theory in several simple but illustrative models. We initiate the study of the relative frequencies of vacua with vanishing superpotential W=0 and with certain discrete symmetries. For…
Finding an optimal parameter of a black-box function is important for searching stable material structures and finding optimal neural network structures, and Bayesian optimization algorithms are widely used for the purpose. However, most of…
Topological data analysis (TDA) is a rising branch in modern applied mathematics. It extracts topological structures as features of a given space and uses these features to analyze digital data. Persistent homology, one of the central tools…