Related papers: Core Bifiltration
Context. Low-mass star-forming cores differ from their surrounding molecular cloud in turbulence, shape, and density structure. Aims. We aim to understand how dense cores form out of the less dense cloud material by studying the connection…
Multiparameter persistent homology has emerged as a powerful generalization of topological data analysis, capable of encoding multivariate filtrations. However, the algebraic complexity of multiparameter persistence modules, marked by wild…
Object recognition in the presence of background clutter and distractors is a central problem both in neuroscience and in machine learning. However, the performance level of the models that are inspired by cortical mechanisms, including…
Persistent homology is a natural tool for probing the topological characteristics of weighted graphs, essentially focusing on their $0$-dimensional homology. While this area has been substantially studied, we present a new approach to…
Point cloud learning often rests on the premise that observed samples are noisy traces of an underlying geometric object, such as a manifold embedded in a high-dimensional feature space. Yet much of this geometry is not captured directly by…
Community and core-periphery are two widely studied graph structures, with their coexistence observed in real-world graphs (Rombach, Porter, Fowler \& Mucha [SIAM J. App. Math. 2014, SIAM Review 2017]). However, the nature of this…
Geometry and topology constitute complementary descriptors of three-dimensional shape, yet existing benchmark datasets primarily capture geometric information while neglecting topological structure. This work addresses this limitation by…
Diffusion condensation is a dynamic process that yields a sequence of multiscale data representations that aim to encode meaningful abstractions. It has proven effective for manifold learning, denoising, clustering, and visualization of…
Observations of dark cloud cores have been carried out in the mid-infrared using ISOCAM and in the far-infrared using ISOPHOT, both aboard the Infrared Space Observatory. The cores are in most cases detected in emission at 200 and 170…
Persistent homology has become an important tool for extracting geometric and topological features from data, whose multi-scale features are summarized in a persistence diagram. From a statistical perspective, however, persistence diagrams…
The Discrete Morse Theory of Forman appeared to be useful for providing filtration-preserving reductions of complexes in the study of persistent homology. So far, the algorithms computing discrete Morse matchings have only been used for…
Profiling core-periphery structures in networks has attracted significant attention, leading to the development of various methods. Among these, the rich-core method is distinguished for being entirely parameter-free and scalable to large…
The ability to consistently distinguish real protein structures from computationally generated model decoys is not yet a solved problem. One route to distinguish real protein structures from decoys is to delineate the important physical…
Modern deep learning architectures increasingly contend with sophisticated signals that are natively infinite-dimensional, such as time series, probability distributions, or operators, and are defined over irregular domains. Yet, a unified…
Multilayer networks provide a powerful framework for modeling complex systems that capture different types of interactions between the same set of entities across multiple layers. Core-periphery detection involves partitioning the nodes of…
We challenge the common assumption that deeper decoder architectures always yield better performance in point cloud reconstruction. Our analysis reveals that, beyond a certain depth, increasing decoder complexity leads to overfitting and…
Searches for continuous gravitational waves target nearly monochromatic gravitational wave emission from e.g. non-axysmmetric fast-spinning neutron stars. Broad surveys often require to explicitly search for a very large number of different…
Real data is often given as a point cloud, i.e. a finite set of points with pairwise distances between them. An important problem is to detect the topological shape of data --- for example, to approximate a point cloud by a low-dimensional…
We present the results of C18O observations by the Nobeyama Millimeter Array toward dense clumps with radii of ~ 0.3 pc in six cluster-forming regions including massive (proto)stars. We identified 171 cores, whose radius, line width, and…
Advanced representation learning techniques require reliable and general evaluation methods. Recently, several algorithms based on the common idea of geometric and topological analysis of a manifold approximated from the learned data…