Related papers: Core Bifiltration
The Rips filtration over a finite metric space and its corresponding persistent homology are prominent methods in TDA to summarise the shape of data. Crucial to their use is the bottleneck stability result. A generalisation of the Rips…
In topological data analysis, persistent homology is used to study the "shape of data". Persistent homology computations are completely characterized by a set of intervals called a bar code. It is often said that the long intervals…
Appropriately representing elements in a database so that queries may be accurately matched is a central task in information retrieval; recently, this has been achieved by embedding the graphical structure of the database into a manifold in…
We extend the method of antisymmetrized molecular dynamics to investigate dineutron correlation. We apply this method to $^{10}$Be as an example and investigate the motion of two neutrons around a largely deformed $^8$Be core by analyzing…
We present DisPerSE, a novel approach to the coherent multi-scale identification of all types of astrophysical structures, and in particular the filaments, in the large scale distribution of matter in the Universe. This method and…
We consider circle packings and, more generally, Delaunay circle patterns - arrangements of circles arising from a Delaunay decomposition of a finite set of points - on surfaces equipped with a complex projective structure. Motivated by a…
We present a simple experimental realization of a two-dimensional floating body that can remain in equilibrium in any orientation. This system is based on a class of shapes known as Zindler curves, which possess the remarkable geometric…
Persistent homology of the Rips filtration allows to track topological features of a point cloud over scales, and is a foundational tool of topological data analysis. Unfortunately, the Rips-filtration is exponentially sized, when…
Cardiac structure segmentation plays an important role in medical analysis procedures. Images' blurred boundaries issue always limits the segmentation performance. To address this difficult problem, we presented a novel network structure…
We study the connection between discrete Morse theory and persistent homology in the context of shape reconstruction methods. Specifically, we consider the construction of Wrap complexes, introduced by Edelsbrunner as a subcomplex of the…
We trace movements of certain points in space-time along their corresponding continuous path. We partition the space at every moment of time using alpha-Complexes, Voronoi medusa is then the collection or union of restricted Voronoi cells…
The corner-based detection paradigm enjoys the potential to produce high-quality boxes. But the development is constrained by three factors: 1) Hard to match corners. Heuristic corner matching algorithms can lead to incorrect boxes,…
In this paper, we propose an effective point cloud generation method, which can generate multi-resolution point clouds of the same shape from a latent vector. Specifically, we develop a novel progressive deconvolution network with the…
Fundamental theories and models of many-body physics can be probed in experiments on ultracold atoms held in place by electromagnetic fields. In particular, of considerable interest are systems under curved confinement, since they can yield…
The goal of coreset selection methods is to identify representative subsets of datasets for efficient model training. Yet, existing methods often ignore the possibility of annotation errors and require fixed pruning ratios, making them…
CNNs and computational models of biological vision share some fundamental principles, which opened new avenues of research. However, fruitful cross-field research is hampered by conventional CNN architectures being based on spatially and…
We extend a modal theory of diffraction by a set of parallel fibers to deal with the case of a hard boundary: that is a structure made for instance of air-holes inside a dielectric matrix. Numerical examples are given concerning some…
Reconstructing models from unorganized point clouds presents a significant challenge, especially when the models consist of multiple components represented by their surface point clouds. Such models often involve point clouds with noise…
In this paper, we introduce new density-sensitive bifiltrations for data using the framework of Dowker complexes. Previously, Dowker complexes were studied to address directional or bivariate data whereas density-sensitive bifiltrations on…
We propose a functorial framework for persistent homology based on finite topological spaces and their associated posets. Starting from a finite metric space, we associate a filtration of finite topologies whose structure maps are…