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Taiwanese Journal of Mathematics, ISSN 1027-5487, 6/2015, Volume 19, Issue 3, pp. 691 - 702
In this paper we prove two sharp inequalities involving the normalized scalar curvature and the generalized normalized -Casorati curvatures for slant submanifolds in quaternionic space forms... 
Mathematical manifolds | Tangents | Tensors | Real numbers | Hyperplanes | Scalars | Mathematical inequalities | Curvature | Quaternionic space form | Scalar curvature | Shape operator | Slant submanifold | Optimal inequality | Mean curvature | δ-Casorati curvature | MATHEMATICS | LAGRANGIAN SUBMANIFOLDS | delta-Casorati curvature | CHEN INEQUALITIES | Mathematics - Differential Geometry
Journal Article
Neurocomputing, ISSN 0925-2312, 2007, Volume 70, Issue 7, pp. 1547 - 1553
Journal Article
Physical Review B - Condensed Matter and Materials Physics, ISSN 1098-0121, 11/2015, Volume 92, Issue 20
We develop tangent space methods for projected entangled-pair states (PEPS) that provide direct access to the low-energy sector of strongly-correlated two-dimensional quantum systems... 
RENORMALIZATION-GROUP | PHASES | PHYSICS, CONDENSED MATTER | LIQUID-HELIUM | ANYONS | SYSTEMS | BOND GROUND-STATES | SPECTRUM | QUANTUM SPIN CHAINS | MATRIX PRODUCT STATES | ANTIFERROMAGNETS | Low energy | Tangents | Condensed matter | Ground state | Spectra | Dispersions | Excitation spectra | Magnons
Journal Article
The International Journal of Robotics Research, ISSN 0278-3649, 1/2016, Volume 35, Issue 1-3, pp. 5 - 29
...) rotational joints make the state space highly non-linear. The proposed method represents three principal contributions to address these challenges... 
noise projection | optimal importance function | Articulated | particle filter | tangent space | tracking | kinematic chain | ROBOTICS | Tangents (Geometry) | Usage | Algorithms | Atoms & subatomic particles | Handles | Rotational states | Stability | Singularities | Parameterization | Parametrization | Nonlinearity | Mathematical models | Proposals | Estimates
Journal Article
International Journal of Neural Systems, ISSN 0129-0657, 12/2019, Volume 29, Issue 10, p. 1950025
The performance of a brain–computer interface (BCI) will generally improve by increasing the volume of training data on which it is trained. However, a... 
multivariate empirical-mode decomposition (MEMD) | subject-specific multivariate empirical-mode decomposition-based filtering (SS-MEMDBF) | brain-computer interface (BCI) | DECOMPOSITION | COVARIATE SHIFT | Motor imagery | NOISE | tangent space | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | covariance matrix
Journal Article
Advances in Applied Clifford Algebras, ISSN 0188-7009, 2/2019, Volume 29, Issue 1, pp. 1 - 16
In this paper we present various results about the six dimensional vectors obtained from the tangent operators of spatial motion, called as screws, in Lorentzian space... 
Tangent operator | Theoretical, Mathematical and Computational Physics | 51B20 | L -matrix multiplication | Physics | Lorentzian space | Mathematical Methods in Physics | Secondary 53A17 | Screw | Primary 70B10 | Kinematic | Applications of Mathematics | Physics, general | L-matrix multiplication | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | MOTION | ROTATIONS | QUATERNIONS | Algebra
Journal Article
IEEE Transactions on Neural Networks and Learning Systems, ISSN 2162-237X, 09/2016, Volume 27, Issue 9, pp. 1827 - 1839
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 05/2017, Volume 145, Issue 5, pp. 2255 - 2270
weakly filtered and diffeological spaces, whose tangent spaces are easier to understand... 
Tangent space | Tangent bundle | Diffeological bundle | MATHEMATICS | MATHEMATICS, APPLIED | diffeological bundle | tangent bundle | Mathematics - Differential Geometry
Journal Article
Mechanical Systems and Signal Processing, ISSN 0888-3270, 11/2018, Volume 112, pp. 44 - 60
Journal Article
Neural Processing Letters, ISSN 1370-4621, 6/2016, Volume 43, Issue 3, pp. 727 - 744
We propose a novel supervised dimensionality reduction method named local tangent space discriminant analysis (TSD... 
Dimensionality reduction | Computational Intelligence | Supervised learning | Computer Science | Artificial Intelligence (incl. Robotics) | Manifold learning | Statistical Physics, Dynamical Systems and Complexity | Tangent space
Journal Article
Journal Article
Neurocomputing, ISSN 0925-2312, 01/2016, Volume 174, pp. 18 - 30
...) in the high-dimensional space. The local tangent space alignment (LTSA) method has been used to perform the manifold production and the single hidden layer feedforward network (SLFN... 
High-dimensional space | Manifold learning | Extreme learning machine | Local tangent space alignment | REGRESSION | HIDDEN NODES | RECOGNITION | ALGORITHM | CLASSIFICATION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | NEURAL-NETWORKS | ALIGNMENT | NONLINEAR DIMENSIONALITY REDUCTION | FRAMEWORK | FEEDFORWARD NETWORKS | Information science | Analysis
Journal Article
Computer Aided Geometric Design, ISSN 0167-8396, 01/2015, Volume 32, pp. 50 - 68
Journal Article
Annals of Mathematics, ISSN 0003-486X, 5/2007, Volume 165, Issue 3, pp. 843 - 941
D. Mumford conjectured in [33] that the rational cohomology of the stable moduli space of Riemann surfaces is a polynomial algebra generated by certain classes $\kappa _{i}$ of dimension 2i... 
Morphisms | Equivalence relation | Vertical tangents | Maps | Mathematical theorems | Functors | Mathematical vectors | Vertices | Endless loops | MATHEMATICS | BUNDLES | THEOREM | SETS | CLASSIFICATION | MAPPING CLASS GROUP | HOMOTOPY | HOMOLOGY
Journal Article
Classical and Quantum Gravity, ISSN 0264-9381, 12/2015, Volume 33, Issue 1, pp. 15006 - 15014
... a Wick rotation directly in the tangent space using considerably less structure: a timelike, future pointing vector field, which need not be killing or hypersurface orthogonal... 
Euclidean methods | black holes | wick rotation | PHYSICS, MULTIDISCIPLINARY | ASTRONOMY & ASTROPHYSICS | PHYSICS, PARTICLES & FIELDS | Tangents | Wicks | Euclidean geometry | Black holes (astronomy) | Generators | Mathematical models | Formalism | Quantum gravity | Physics - General Relativity and Quantum Cosmology
Journal Article
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), ISSN 0302-9743, 2016, Volume 10040, pp. 541 - 552
Journal Article
Annals of Mathematics, ISSN 0003-486X, 5/2017, Volume 185, Issue 3, pp. 957 - 990
.... We also obtain a new series of Teichmüller curves in ℳ₄, and new SL₂(ℝ)-invariant varieties in the moduli spaces of quadratic differentials and holomorphic 1-forms. 
Conic sections | Tangents | Mathematical theorems | Algebra | Coordinate systems | Mathematical surfaces | Curves | Cylinders | Polygons | MATHEMATICS | TEICHMULLER CURVES | VEECH SURFACES | BILLIARDS | INVARIANT
Journal Article
PLoS ONE, ISSN 1932-6203, 09/2017, Volume 12, Issue 9, p. e0184972
Journal Article
Journal of Neural Engineering, ISSN 1741-2560, 06/2018, Volume 15, Issue 4, p. 046021
Journal Article
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