Related papers: A Distributed Approach for Persistent Homology Com…
Persistent homology (PH) is a rigorous mathematical theory that provides a robust descriptor of data in the form of persistence diagrams (PDs) which are 2D multisets of points. Their variable size makes them, however, difficult to combine…
Persistent homology (PH) has recently emerged as a powerful tool for extracting topological features. Integrating PH into machine learning and deep learning models enhances topology awareness and interpretability. However, most PH methods…
In this paper, three Computational Topology methods (namely effective homology, persistent homology and discrete vector fields) are mixed together to produce algorithms for homological digital image processing. The algorithms have been…
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…
Persistent homology is a popular computational tool for analyzing the topology of point clouds, such as the presence of loops or voids. However, many real-world datasets with low intrinsic dimensionality reside in an ambient space of much…
Analysing data from Smoothed Particle Hydrodynamics (SPH) simulations is about understanding global fluid properties rather than individual fluid elements. Therefore, in order to properly understand the outcome of such simulations it is…
We present a parallelizable algorithm for computing the persistent homology of a filtered chain complex. Our approach differs from the commonly used reduction algorithm by first computing persistence pairs within local chunks, then…
Persistent homology (PH) is a relatively new field in applied mathematics that studies the components and shapes of discrete data. In this work, we demonstrate that PH can be used as a universal framework to identify phases in spin models,…
Smoothing filter is the method of choice for image preprocessing and pattern recognition. We present a new concurrent method for smoothing 2D object in binary case. Proposed method provides a parallel computation while preserving the…
Biological and physical systems often exhibit distinct structures at different spatial/temporal scales. Persistent homology is an algebraic tool that provides a mathematical framework for analyzing the multi-scale structures frequently…
We present the results from a two-day study in which we discussed various implementations of Smooth Particle Hydrodynamics (SPH), one of the leading methods used across a variety of areas of large-scale astrophysical simulations. In…
Persistent homology (PH) is one of the main methods used in Topological Data Analysis. An active area of research in the field is the study of appropriate notions of PH representatives, which allow to interpret the meaning of the…
Persistent homology (PH) is a rigorous mathematical theory that provides a robust descriptor of data in the form of persistence diagrams (PDs). PDs exhibit, however, complex structure and are difficult to integrate in today's machine…
Persistent Homology (PH) offers stable, multi-scale descriptors of intrinsic shape structure by capturing connected components, loops, and voids that persist across scales, providing invariants that complement purely geometric…
3-D shape is important to chemistry, but how important? Machine learning works best when the inputs are simple and match the problem well. Chemistry datasets tend to be very small compared to those generally used in machine learning so we…
Persistent Homology (PH) is a useful tool to study the underlying structure of a data set. Persistence Diagrams (PDs), which are 2D multisets of points, are a concise summary of the information found by studying the PH of a data set.…
The extension of persistent homology to multi-parameter setups is an algorithmic challenge. Since most computation tasks scale badly with the size of the input complex, an important pre-processing step consists of simplifying the input…
Persistent homology is an important methodology in topological data analysis which adapts theory from algebraic topology to data settings. Computing persistent homology produces persistence diagrams, which have been successfully used in…
Persistent homology is a tool that can be employed to summarize the shape of data by quantifying homological features. When the data is an object in $\mathbb{R}^d$, the (augmented) persistent homology transform ((A)PHT) is a family of…
Persistent Homology is a widely used topological data analysis tool that creates a concise description of the topological properties of a point cloud based on a specified filtration. Most filtrations used for persistent homology depend…