Machine Learning the Tangent Space of Dynamical Instabilities from Data
Sign Up to like & getrecommendations! Published in 2019 at "Chaos"
DOI: 10.1063/1.5120830
Abstract: For a large class of dynamical systems, the optimally time-dependent (OTD) modes, a set of deformable orthonormal tangent vectors that track directions of instabilities along any trajectory, are known to depend "pointwise" on the state… read more here.
Keywords: machine learning; space; learning tangent; dynamical instabilities ... See more keywords
Tangent space to the manifold of critical classical Hamiltonians representable by tensor networks.
Sign Up to like & getrecommendations! Published in 2019 at "Physical review. E"
DOI: 10.1103/physreve.100.023306
Abstract: We introduce a scheme to perform Monte Carlo renormalization group with the coupling constants of the system Hamiltonian encoded in a tensor network. With this scheme we compute the tangent space to the manifold of… read more here.
Keywords: space manifold; tensor; tangent space; manifold critical ... See more keywords
Manifold Learning via Linear Tangent Space Alignment (LTSA) for Accelerated Dynamic MRI With Sparse Sampling
Sign Up to like & getrecommendations! Published in 2022 at "IEEE Transactions on Medical Imaging"
DOI: 10.1109/tmi.2022.3207774
Abstract: The spatial resolution and temporal frame-rate of dynamic magnetic resonance imaging (MRI) can be improved by reconstructing images from sparsely sampled ${k}$ -space data with mathematical modeling of the underlying spatiotemporal signals. These models include… read more here.
Keywords: dynamic mri; linear tangent; space; space alignment ... See more keywords
Tangent space symmetries in general relativity and teleparallelism
Sign Up to like & getrecommendations! Published in 2021 at "International Journal of Geometric Methods in Modern Physics"
DOI: 10.1142/s0219887821400089
Abstract: This paper looks at how changes of coordinates on a pseudo-Riemannian manifold induce homogeneous linear transformations on its tangent spaces. We see that a pseudo-orthonormal frame in a given tangent space is the basis for… read more here.
Keywords: linear transformations; space symmetries; tangent space; basis ... See more keywords
Tangent space alignment: Transfer learning for Brain-Computer Interface
Sign Up to like & getrecommendations! Published in 2022 at "Frontiers in Human Neuroscience"
DOI: 10.3389/fnhum.2022.1049985
Abstract: Statistical variability of electroencephalography (EEG) between subjects and between sessions is a common problem faced in the field of Brain-Computer Interface (BCI). Such variability prevents the usage of pre-trained machine learning models and requires the… read more here.
Keywords: computer interface; transfer; brain computer; transfer learning ... See more keywords