Related papers: Topological Analysis of High-Resolution CMB Maps
The measurements of the temperature and polarisation anisotropies of the Cosmic Microwave Background (CMB) by the ESA Planck mission have strongly supported the current concordance model of cosmology. However, the latest cosmological data…
Tumor segmentation in whole-slide images of histology slides is an important step towards computer-assisted diagnosis. In this work, we propose a tumor segmentation framework based on the novel concept of persistent homology profiles…
We address the question of to what accuracy remote sensing images of the surface of planets can be matched, so that the possible displacement of features on the surface can be accurately measured. This is relevant in the context of the…
High-dimensional data, characterized by many features, can be difficult to visualize effectively. Dimensionality reduction techniques, such as PCA, UMAP, and t-SNE, address this challenge by projecting the data into a lower-dimensional…
Multiplexed imaging allows multiple cell types to be simultaneously visualised in a single tissue sample, generating unprecedented amounts of spatially-resolved, biological data. In topological data analysis, persistent homology provides…
Mapper is an algorithm that summarizes the topological information contained in a dataset and provides an insightful visualization. It takes as input a point cloud which is possibly high-dimensional, a filter function on it and an open…
Writing an uncomplicated, robust, and scalable three-dimensional convex hull algorithm is challenging and problematic. This includes, coplanar and collinear issues, numerical accuracy, performance, and complexity trade-offs. While there are…
We introduce a novel gradient descent algorithm extending the well-known Gradient Sampling methodology to the class of stratifiably smooth objective functions, which are defined as locally Lipschitz functions that are smooth on some regular…
Currently, state-of-the-art exploration methods maintain high-resolution map representations in order to optimize exploration goals in each step that maximizes information gain. However, during exploring, those "optimal" selections could…
In this survey, we explore recent literature on finding the cores of higher graphs using geometric and topological means. We study graphs, hypergraphs, and simplicial complexes, all of which are models of higher graphs. We study the notion…
The central goal of this thesis is to develop methods to experimentally study topological phases. We do so by applying the powerful toolbox of quantum simulation techniques with cold atoms in optical lattices. To this day, a complete…
High-resolution Doppler spectroscopy is a powerful tool for identifying molecular species in the atmospheres of both transiting and non-transiting exoplanets. Currently, such data is analysed using cross-correlation techniques to detect the…
We present a simple and efficient method for refining maps or correspondences by iterative upsampling in the spectral domain that can be implemented in a few lines of code. Our main observation is that high quality maps can be obtained even…
Persistent homology has been devised as a promising tool for the topological simplification of complex data. However, it is computationally intractable for large data sets. In this work, we introduce multiresolution persistent homology for…
Spatial scientometrics has attracted a lot of attention in the very recent past. The visualization methods (density maps) presented in this paper allow for an analysis revealing regions of excellence around the world using computer programs…
We explore the low-l likelihood of the angular spectrum C(l) of masked CMB temperature maps using an adaptive importance sampler. We find that, in spite of a partial sky coverage, the likelihood distribution of each C(l) closely follows an…
We propose a novel meshless method to compute harmonic maps and conformal maps for surfaces embedded in the Euclidean 3-space, using point cloud data only. Given a surface, or a point cloud approximation, we simply use the standard cubic…
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…
Cosmic microwave background (CMB) temperature and polarization observations indicate that in the best-fit $\Lambda$ Cold Dark Matter model of the Universe, the local geometry is consistent with at most a small amount of positive or negative…
Topological data analysis is a relatively new branch of machine learning that excels in studying high dimensional data, and is theoretically known to be robust against noise. Meanwhile, data objects with mixed numeric and categorical…