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· Zenodo (CERN European Organi...· 0 citations
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.· Zenodo (CERN European Organi...· 0 citations
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.· Zenodo (CERN European Organi...· 0 citations
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.· Zenodo (CERN European Organi...· 0 citations
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.· Zenodo (CERN European Organi...· 0 citations
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