Titlebook: Explorations in the Mathematics of Data Science; The Inaugural Volume Simon Foucart,Stephan Wojtowytsch Book 2024 The Editor(s) (if applica

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Learning Collective Behaviors from Observation, designed to elucidate emergent phenomena within intricate systems of interacting agents. Our approach not only ensures theoretical convergence guarantees but also exhibits computational efficiency when handling high-dimensional observational data. The methods adeptly reconstruct both first- and sec

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Provably Accelerating Ill-Conditioned Low-Rank Estimation via Scaled Gradient Descent, Even with Ov corrupted, linear measurements. Through the lens of matrix and tensor factorization, one of the most popular approaches is to employ simple iterative algorithms such as gradient descent (GD) to recover the low-rank factors directly, which allow for small memory and computation footprints. However,

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CLAIRE: Scalable GPU-Accelerated Algorithms for Diffeomorphic Image Registration in 3D,age registration is a nonlinear inverse problem. It is about computing a spatial mapping from one image of the same object or scene to another. In diffeomorphic image registration, the set of admissible spatial transformations is restricted to maps that are smooth, are one-to-one, and have a smooth

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Book 2024ty. Chapters are based on talks from CAMDA’s inaugural conference – held in May 2023 – and its seminar series, as well as work performed by members of the Center. They showcase the interdisciplinary nature of data science, emphasizing its mathematical and theoretical foundations, especially those ro

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Linearly Embedding Sparse Vectors from , to , via Deterministic Dimension-Reducing Maps, strategy, is quasideterministic and applies in the real setting. The second one, exploiting Golomb rulers, is explicit and applies to the complex setting. As a stepping stone, an explicit isometric embedding from . to . is presented. Finally, the extension of the problem from sparse vectors to low-rank matrices is raised as an open question.