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that is a non-parametrizable manifold embedded in a high- dimensional ambient space. In these cases, the use of sampling- based path planners is cumbersome since samples in the ambient space have low probability ...
the revolution of parameterized shape curves. We formalize the basement membrane as a two- dimensional composite differentiable manifold . In order to reproduce realistic tissue anatomy, we inferred statistical ...
switching, adjusting the maximum curvature of the path through parameter design. Yu et al. [17] proposed a method based on polynomial curves to plan trajectories and speeds for intelligent vehicle lane ...
constitute the solution manifold (illustrated by the black mesh). (B) Illustration of the Hessian- based decomposition of the mean score in the case of two- dimensional actions. The action-to-score mapping ...
and methods). Fig 3D shows how both between- and within-subject grasp similarity are significantly higher than the similarity between random grasps only constrained by accessible object geometry (t(7)=9.96, p ...
. Random walk- based method The algorithm based on the random walk process generally considers the global topology, extracts the features of each node through the random walk, obtains the low- dimensional ...
complexity of differentiation manifolds with several subpopulations in high- dimensional gene space. Projection of the velocities onto non-parametric nonlinear embeddings (which do not have gene-defined axes ...
, making it robust against local perturbations due to noise. Note that such trajectories will inevitably be one- dimensional , and cannot be combined to form higher dimensional structures (such as sheets ...
of the two (Fig 1B, example 2). Lower dimensionality has nearly always been neglected in the biological literature because it would never be found by random sampling. However, we are not aware of theorems ...
. On the one hand, deterministic optimal control (DOC) theory focused on the planning stage and sought to explain average motor behaviors in humans or animals. The minimum jerk and minimum torque change models ...
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