Related papers: Dark soliton detection using persistent homology

To analyze the topological properties of the given discrete data, one needs to consider a continuous transform called filtration. Persistent homology serves as a tool to track changes of homology in the filtration. The outcome of the…

Topological data analysis is a powerful framework for extracting useful topological information from complex datasets. Recent work has shown its application for the dynamical analysis of classical dissipative systems through a…

Transport mode detection is a classification problem aiming to design an algorithm that can infer the transport mode of a user given multimodal signals (GPS and/or inertial sensors). It has many applications, such as carbon footprint…

Persistent homology is an effective method for extracting topological information, represented as persistent diagrams, of spatial structure data. Hence it is well-suited for the study of protein structures. Attempts to incorporate…

Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field.…

Bose-Einstein condensate (BEC) exhibits a variety of fascinating and unexpected macroscopic phenomena, and has attracted sustained attention in recent years--particularly in the field of solitons and associated nonlinear phenomena.…

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…

Deep learning architectures based on convolutional neural networks tend to rely on continuous, smooth features. While this characteristics provides significant robustness and proves useful in many real-world tasks, it is strikingly…

Topological Data Analysis (TDA) offers a suite of computational tools that provide quantified shape features in high dimensional data that can be used by modern statistical and predictive machine learning (ML) models. In particular,…

Persistent Homology is a fairly new branch of Computational Topology which combines geometry and topology for an effective shape description of use in Pattern Recognition. In particular it registers through "Betti Numbers" the presence of…

Adopting a mean-field description for a two-component atomic Bose-Einstein condensate, we study the stat- ics and dynamics of dark-bright solitons in the presence of localized impurities. We use adiabatic perturbation theory to derive an…

Computational color constancy that requires esti- mation of illuminant colors of images is a fundamental yet active problem in computer vision, which can be formulated into a regression problem. To learn a robust regressor for color…

Solitons are nonlinear solitary waves which maintain their shape over time and through collisions, occurring in a variety of nonlinear media from plasmas to optics. We present an experimental and theoretical study of hydrodynamic phenomena…

In this paper, we propose a novel framework for dynamical analysis of human actions from 3D motion capture data using topological data analysis. We model human actions using the topological features of the attractor of the dynamical system.…

We study detection of collapse in high-dimensional point clouds, where mass concentrates near a lower-dimensional set relative to a non-collapsed geometry. We propose persistent homology-based test statistics under two well-studied…

The CYGNO experiment employs an optical-readout Time Projection Chamber (TPC) to search for rare low-energy interactions using finely resolved scintillation images. While the optical readout provides rich topological information, it…

The topology of the large-scale structure of the universe contains valuable information on the underlying cosmological parameters. While persistent homology can extract this topological information, the optimal method for parameter…

Strong gravitational lensing is a promising way of uncovering the nature of dark matter, by finding perturbations to images that cannot be well accounted for by modeling the lens galaxy without additional structure, be it subhalos (smaller…

Persistent homology probes topological properties from point clouds and functions. By looking at multiple scales simultaneously, one can record the births and deaths of topological features as the scale varies. In this paper we use a…

Sparse systems are usually parameterized by a tuning parameter that determines the sparsity of the system. How to choose the right tuning parameter is a fundamental and difficult problem in learning the sparse system. In this paper, by…