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Sponsored AI Networking Cookbook: Practical recipes for AI-assisted network automation and development AI Networking Cookbook: Practical recipes for AI-assisted network automation and development

Author

Tsutomu T. Takeuchi

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#diffusion models Open access Sep 2026

On identifiability limits of phase-space information in Schr\"odinger Bridges for post shell-crossing gravitational structure formation

Many nonlinear dynamical systems remain deterministic and invertible in their full state space while becoming non-identifiable after projection onto reduced observables. Gravitational shell crossing provides a canonical example: the collisionless phase-space flow remains Hamiltonian, whereas the configuration-space map...

Shun Arai, Tsutomu T. Takeuchi · 0 citations
#diffusion models Open access Sep 2026

Diffusion Geometry for Galaxy Bulk-Flow Reconstruction I: Foundations and Full-Vector Validation

We formulate a diffusion-spectral field-reconstruction framework based on diffusion geometry for reconstructing cosmological vector fields from finite and nonuniformly distributed galaxy point clouds. Low-frequency eigenfunctions of a Markov operator defined on the point cloud are used as a global basis shared by the C...

Tsutomu T. Takeuchi, Gayathri Asok, Hai-Xia Ma et al. · 0 citations
#diffusion models Open access Sep 2026

Diffusion Geometry for Galaxy Bulk-Flow Reconstruction II: Three-Dimensional Potential-Flow Reconstruction from Radial Velocities

Reconstructing a three-dimensional velocity field from radial peculiar velocities is non-identifiable because the radial observation operator has a large null space, even when a finite design matrix is formally full rank. Building on Paper I, we construct a potential-flow-constrained estimator from diffusion eigenfunct...

Tsutomu T. Takeuchi, Gayathri Asok, Hai-Xia Ma et al. · 0 citations
#diffusion models Open access Sep 2026

Diffusion Geometry for Galaxy Bulk-Flow Reconstruction I: Foundations and Full-Vector Validation

We formulate a diffusion-spectral field-reconstruction framework based on diffusion geometry for reconstructing cosmological vector fields from finite and nonuniformly distributed galaxy point clouds. Low-frequency eigenfunctions of a Markov operator defined on the point cloud are used as a global basis shared by the C...

Tsutomu T. Takeuchi, Gayathri Asok, Hai-Xia Ma et al. · 0 citations
#diffusion models Open access Sep 2026

Diffusion Geometry for Galaxy Bulk-Flow Reconstruction II: Three-Dimensional Potential-Flow Reconstruction from Radial Velocities

Reconstructing a three-dimensional velocity field from radial peculiar velocities is non-identifiable because the radial observation operator has a large null space, even when a finite design matrix is formally full rank. Building on Paper I, we construct a potential-flow-constrained estimator from diffusion eigenfunct...

Tsutomu T. Takeuchi, Gayathri Asok, Hai-Xia Ma et al. · 0 citations

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