Related papers: Persistent homology-based explicit topological con…
Geometric data pruning methods, while practical for leveraging pretrained models, are fundamentally unstable. Their reliance on extrinsic geometry renders them highly sensitive to latent space perturbations, causing performance to degrade…
This paper brings together three distinct theories with the goal of quantifying shape textures with complex morphologies. Distance fields are central objects in shape representation, while topological data analysis uses algebraic topology…
We study the persistent homology of both functional data on compact topological spaces and structural data presented as compact metric measure spaces. One of our goals is to define persistent homology so as to capture primarily properties…
High-quality training data is the foundation of machine learning and artificial intelligence, shaping how models learn and perform. Although much is known about what types of data are effective for training, the impact of the data's…
This paper presents a density-based topology optimization approach considering additive manufacturing limitations. The presented method considers the minimum size of parts, the minimum size of cavities, the inability of printing overhanging…
Porous structures are widely used in various industries because of their excellent properties. Porous surfaces have no thickness and should be thickened to sheet structures for further fabrication. However, conventional methods for…
Triply periodic minimal surfaces (TPMSs) play a vital role in the design of porous structures, with applications in bone tissue engineering, chemical engineering, and the creation of lightweight models. However, fabrication of TPMSs via…
Modularity is appealing for solving many problems in optimization. It brings the benefits of manufacturability and reconfigurability to structural optimization, and enables a trade-off between the computational performance of a Periodic…
A density-based topology optimization framework is developed to manipulate characteristic modes of conducting surfaces. The adjoint sensitivity analysis provides an efficient computation of the material gradient utilized by the local…
Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field.…
High-order implicit shock tracking is a new class of numerical methods to approximate solutions of conservation laws with non-smooth features. These methods align elements of the computational mesh with non-smooth features to represent them…
This paper introduces persistent homology, which is a powerful tool to characterize the shape of data using the mathematical concept of topology. We explain the fundamental idea of persistent homology from scratch using some examples. We…
We consider a simply supported plate with constant thickness, defined on an unknown multiply connected domain. We optimize its shape according to some given performance functional. Our method is of fixed domain type, easy to be implemented,…
Magnitude homology is an emerging framework that captures the intrinsic topological and geometric features of metric spaces, demonstrating significant potential for topoplogical data analysis and geometric data analysis. This work…
Moving Morphable Component (MMC) based topology optimization approach is an explicit algorithm since the boundary of the entity explicitly described by its functions. Compared with other pixel or node point-based algorithms, it is optimized…
Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we…
Complex non-local behavior makes designing high efficiency and multifunctional metasurfaces a significant challenge. While using libraries of meta-atoms provide a simple and fast implementation methodology, pillar to pillar interaction…
Metal additive manufacturing (AM) processes often fabricate a near-net shape that includes the as-designed part as well as the sacrificial support structures that need to be machined away by subtractive manufacturing (SM), for instance…
This article introduces an algorithm to compute the persistent homology of a filtered complex with various coefficient fields in a single matrix reduction. The algorithm is output-sensitive in the total number of distinct persistent…
In this work, we introduce persistent homology for the analysis of cryo-electron microscopy (cryo-EM) density maps. We identify the topological fingerprint or topological signature of noise, which is widespread in cryo-EM data. For low…