A combinatorial framework for discrete vector bundles with connection is introduced on simplicial complexes, with discrete curvature, gauge transformations, and flat connections computing twisted de Rham cohomology.
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Introduces tangential Bayes denoiser for Riemannian Gaussian mixtures on manifolds via spectral Laplace-Beltrami approximation, with nearly Bayes risk in low noise and minimax optimality on the circle.
Generalizes Landau-Ginzburg models of Dubrovin-Zhang form to Dynkin type A, develops a pole-collision comparison on Hurwitz space strata, and proves a prepotential structural result plus the Ma-Zuo conjecture for arbitrary rank and dimension.
An open-sourced Unified Autonomy Stack fuses LiDAR, radar, vision and inertial data with sampling-based planning and control barrier functions to deliver resilient autonomy on aerial and ground robots in challenging real-world settings.
The thesis constructs the étale fundamental group via the étale topology and recovers it alongside topological and motivic versions through Tannakian duality.
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The Unified Autonomy Stack: Toward a Blueprint for Generalizable Robot Autonomy
An open-sourced Unified Autonomy Stack fuses LiDAR, radar, vision and inertial data with sampling-based planning and control barrier functions to deliver resilient autonomy on aerial and ground robots in challenging real-world settings.