Related papers: Towards Scalable Persistence-Based Topological Opt…

This article studies the robust version of persistent homology based on trimming methodology to capture the geometric feature through support of the data in presence of outliers. Precisely speaking, the proposed methodology works when the…

Topological data analysis is becoming increasingly relevant to support the analysis of unstructured data sets. A common assumption in data analysis is that the data set is a sample---not necessarily a uniform one---of some high-dimensional…

In the current industry, the development of optimized mechanical components able to satisfy the customer requirements evolves quickly. Therefore, companies are asked for efficient solutions to improve their products in terms of stiffness…

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…

Functionally Graded Materials (FGMs) made of soft constituents have emerged as promising material-structure systems in potential applications across many engineering disciplines, such as soft robots, actuators, energy harvesting, and tissue…

Datasets with sheer volume have been generated from fields including computer vision, medical imageology, and astronomy whose large-scale and high-dimensional properties hamper the implementation of classical statistical models. To tackle…

Stable Diffusion (SD) has evolved DDPM (Denoising Diffusion Probabilistic Model) based image generation significantly by denoising in latent space instead of feature space. This popularized DDPM-based image generation as the cost and…

This study introduces a novel computational framework for Robust Topology Optimization (RTO) considering imprecise random field parameters. Unlike the worst-case approach, the present method provides upper and lower bounds for the mean and…

Persistent homology is a popular and powerful tool for capturing topological features of data. Advances in algorithms for computing persistent homology have reduced the computation time drastically -- as long as the algorithm does not…

Spiking neural networks have gained significant attention due to their brain-like information processing capabilities. The use of surrogate gradients has made it possible to train spiking neural networks with backpropagation, leading to…

Reconstructing models from unorganized point clouds presents a significant challenge, especially when the models consist of multiple components represented by their surface point clouds. Such models often involve point clouds with noise…

Understanding the decision-making processes of large language models is critical given their widespread applications. To achieve this, we aim to connect a formal mathematical framework - zigzag persistence from topological data analysis -…

Topology optimization (TO) is a popular and powerful computational approach for designing novel structures, materials, and devices. Two computational challenges have limited the applicability of TO to a variety of industrial applications.…

Topological loss based on persistent homology has shown promise in various applications. A topological loss enforces the model to achieve certain desired topological property. Despite its empirical success, less is known about the…

This paper presents a practical approach for the optimization of topological simplification, a central pre-processing step for the analysis and visualization of scalar data. Given an input scalar field f and a set of "signal" persistence…

This paper addresses the problem of generating dense point clouds from given sparse point clouds to model the underlying geometric structures of objects/scenes. To tackle this challenging issue, we propose a novel end-to-end learning-based…

We analyze the convergence of gradient-based optimization algorithms that base their updates on delayed stochastic gradient information. The main application of our results is to the development of gradient-based distributed optimization…

Poisson likelihood models have been prevalently used in imaging, social networks, and time series analysis. We propose fast, simple, theoretically-grounded, and versatile, optimization algorithms for Poisson likelihood modeling. The Poisson…

Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks training. We show that this problem can be solved by discretizing the…

Topology optimization techniques have been applied in integrated optics and nanophotonics for the inverse design of devices with shapes that cannot be conceived by human intuition. At optical frequencies, these techniques have only been…