Related papers: A spectral sequence for parallelized persistence
The ability to timely process significant amounts of continuously updated spatial data is mandatory for an increasing number of applications. Parallelism enables such applications to face this data-intensive challenge and allows the devised…
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…
These notes offer a unified introduction to spectral methods for the study of complex systems. They are intended as an operative manual rather than a theorem-proof textbook: the emphasis is on tools, identities, and perspectives that can be…
Persistent homology is a mathematical tool used for studying the shape of data by extracting its topological features. It has gained popularity in network science due to its applicability in various network mining problems, including…
We apply persistent homology, the dominant tool from the field of topological data analysis, to study electoral redistricting. Our method combines the geographic information from a political districting plan with election data to produce a…
One of the primary areas of interest in applied algebraic topology is persistent homology, and, more specifically, the persistence diagram. Persistence diagrams have also become objects of interest in topological data analysis. However,…
Persistent homology is a powerful tool for characterizing the topology of a data set at various geometric scales. When applied to the description of molecular structures, persistent homology can capture the multiscale geometric features and…
In this paper, a novel parallel hybrid iterative method is proposed for finding a common element of the set of solutions of a system of equilibrium problems, the set of solutions of variational inequalities for inverse strongly monotone…
We introduce a data distribution scheme for $\mathcal{H}$-matrices and a distributed-memory algorithm for $\mathcal{H}$-matrix-vector multiplication. Our data distribution scheme avoids an expensive $\Omega(P^2)$ scheduling procedure used…
Polyspectral estimation is a problem of great importance in the analysis of nonlinear time series that has applications in biomedical signal processing, communications, geophysics, image, radar, sonar and speech processing, etc. Higher…
Multicore parallel programming has some very difficult problems such as deadlocks during synchronizations and race conditions brought by concurrency. Added to the difficulty is the lack of a simple, well-accepted computing model for…
Computing fixed-radius near-neighbor graphs is an important first step for many data analysis algorithms. Near-neighbor graphs connect points that are close under some metric, endowing point clouds with a combinatorial structure. As…
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…
An Important tool in the field topological data analysis is known as persistent Homology (PH) which is used to encode abstract representation of the homology of data at different resolutions in the form of persistence diagram (PD). In this…
We study the grokking phenomenon through the lens of topology. Using persistent homology on point clouds derived from the embedding matrices of a range of models trained on modular arithmetic with varying primes, we identify a clear and…
The theory of multidimensional persistence captures the topology of a multifiltration -- a multiparameter family of increasing spaces. Multifiltrations arise naturally in the topological analysis of scientific data. In this paper, we give a…
Recent years have witnessed an increased interest in the application of persistent homology, a topological tool for data analysis, to machine learning problems. Persistent homology is known for its ability to numerically characterize the…
Leveraging Trace Theory, we investigate the efficient parallelization of direct solvers for large linear equation systems. Our focus lies on a multi-frontal algorithm, and we present a methodology for achieving near-optimal scheduling on…
Tree kernels are fundamental tools that have been leveraged in many applications, particularly those based on machine learning for Natural Language Processing tasks. In this paper, we devise a parallel implementation of the sequential…
Motivated by persistent homology and topological data analysis, we consider formal sums on a metric space with a distinguished subset. These formal sums, which we call persistence diagrams, have a canonical 1-parameter family of metrics…