Related papers: Multicore Homology via Mayer Vietoris
We compute the homology of random \v{C}ech complexes over a homogeneous Poisson process on the d-dimensional torus, and show that there are, coarsely, two phase transitions. The first transition is analogous to the Erd\H{o}s-R\'enyi phase…
We optimize the jet mixing using large eddy simulations (LES) at a Reynolds number of $3000$. Key methodological enablers consist of Bayesian optimization, a surrogate model enhanced by deep learning, and persistent data topology for…
Using persistent homology to guide optimization has emerged as a novel application of topological data analysis. Existing methods treat persistence calculation as a black box and backpropagate gradients only onto the simplices involved in…
Reconstructing 3D objects from images is inherently an ill-posed problem due to ambiguities in geometry, appearance, and topology. This paper introduces collaborative inverse rendering with persistent homology priors, a novel strategy that…
We study Vietoris-Rips complexes of metric wedge sums and metric gluings. We show that the Vietoris-Rips complex of a wedge sum, equipped with a natural metric, is homotopy equivalent to the wedge sum of the Vietoris-Rips complexes. We also…
To fully exploit the performance potential of modern multi-core processors, machine learning and data mining algorithms for big data must be parallelized in multiple ways. Today's CPUs consist of multiple cores, each following an…
Data-parallel problems demand ever growing floating-point (FP) operations per second under tight area- and energy-efficiency constraints. In this work, we present Manticore, a general-purpose, ultra-efficient chiplet-based architecture for…
Micro-macro models provide a powerful tool to study the relationship between microscale mechanisms and emergent macroscopic behavior. However, the detailed microscopic modeling may require tracking and evolving a high-dimensional…
Matrix reduction is the standard procedure for computing the persistent homology of a filtered simplicial complex with $m$ simplices. Its output is a particular decomposition of the total boundary matrix, from which the persistence diagrams…
Persistent homology, a powerful mathematical tool for data analysis, summarizes the shape of data through tracking topological features across changes in different scales. Classical algorithms for persistent homology are often constrained…
Liposomes that achieve a heterogeneous and spatially organized surface through phase separation have been recognized to be a promising platform for delivery purposes. However, their design and optimization through experimentation can be…
Computing on encrypted data is a promising approach to reduce data security and privacy risks, with homomorphic encryption serving as a facilitator in achieving this goal. In this work, we accelerate homomorphic operations using the…
We describe a parallel solver for the discretized weakly singular space-time boundary integral equation of the spatially two-dimensional heat equation. The global space-time nature of the system matrices leads to improved parallel…
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…
Matrix multiplication is a foundational operation in scientific computing and machine learning, yet its computational complexity makes it a significant bottleneck for large-scale applications. The shift to parallel architectures, primarily…
Particle tracking in large-scale numerical simulations of turbulent flows presents one of the major bottlenecks in parallel performance and scaling efficiency. Here, we describe a particle tracking algorithm for large-scale parallel…
A modern graphics processing unit (GPU) is able to perform massively parallel scientific computations at low cost. We extend our implementation of the checkerboard algorithm for the two dimensional Ising model [T. Preis et al., J. Comp.…
Persistent homology (PH) is a recently developed theory in the field of algebraic topology to study shapes of datasets. It is an effective data analysis tool that is robust to noise and has been widely applied. We demonstrate a general…
Hypergraph partitioning is an important preprocessing step for optimizing data placement and minimizing communication volumes in high-performance computing applications. To cope with ever growing problem sizes, it has become increasingly…
Massively-parallel graph algorithms have received extensive attention over the past decade, with research focusing on three memory regimes: the superlinear regime, the near-linear regime, and the sublinear regime. The sublinear regime is…