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Implications of Non-Differentiable Entropy on a Space-Time Manifold
Entropy, 2015 Assuming that the motions of a complex system structural units take place on continuous, but non-differentiable curves of a space-time manifold, the scale relativity model with arbitrary constant fractal dimension (the hydrodynamic and wave function ...
Alina Gavrilut +2 more
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Geometric Neural Ordinary Differential Equations: From Manifolds to Lie Groups [PDF]
EntropyNeural ordinary differential equations (neural ODEs) are a well-established tool for optimizing the parameters of dynamical systems, with applications in image classification, optimal control, and physics learning.
Yannik P. Wotte +2 more
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Novel theorems for the cotangent bundle endowed with metallic structures on a differentiable manifold [PDF]
HeliyonThe present paper aims to study the complete, horizontal and diagonal lifts of metallic structures in the cotangent bundle. Furthermore, the Nijenhuis tensor of a metallic structure is calculated and its integrability conditions by means of partial ...
Mohammad Nazrul Islam Khan, Nahid Fatima
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Manifold topological deep learning for biomedical data [PDF]
Nature CommunicationsRecently, topological deep learning (TDL), which integrates algebraic topology with deep neural networks, has achieved significant success in processing point-cloud data and has emerged as a promising paradigm in data science.
Xiang Liu +5 more
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Qualia as control-theoretic constructs for autonomous agents: event phase space as an action-oriented semantic safety layer [PDF]
Frontiers in Robotics and AIAutonomous systems face a fundamental complexity barrier in open-world environments: decomposing scenes into discrete entities and searching over combinatorial action spaces leads to prohibitive computational costs, yet biological agents navigate ...
Vladimir Suvorov
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Analysis of High-Dimensional Coordination in Human Movement Using Variance Spectrum Scaling and Intrinsic Dimensionality [PDF]
EntropyFull-body movement involving multi-segmental coordination has been essential to our evolution as a species, but its study has been focused mostly on the analysis of one-dimensional data.
Dobromir Dotov +3 more
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A DIFFERENTIABLE STRUCTURE ON A FINITE DIMENSIONAL REAL VECTOR SPACE AS A MANIFOLD
Barekeng, 2023 There are three conditions for a topological space to be said a topological manifold of dimension : Hausdorff space, second-countable, and the existence of homeomorphism of a neighborhood of each point to an open subset of or -dimensional locally ...
Edi Kurniadi
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On conformal transformations of metrics of Riemannian paracomplex manifolds
Дифференциальная геометрия многообразий фигур, 2021 A 2n-dimensional differentiable manifold M with -structure is a Riemannian almost paracomplex manifold. In the present paper, we consider conformal transformations of metrics of Riemannian paracomplex manifolds.
S.E. Stepanov +2 more
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International Journal of Analysis and Applications, 2022 Manifolds with fλ(6,4) structure was defined and studied in the past. Later the geometry of tangent and cotangent bundles in a differentiable manifold with fλ(6,4) structure was studied.
Manisha M. Kankarej, Jai Pratap Singh
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Machines, 2023 Kinematic control of redundant serial manipulators has been carried out for the past half century based primarily on a generalized inverse velocity formulation that is known to have mathematical deficiencies.
Adrian Peidro, Edward J. Haug
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