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sc is a cross-platform, free, TUI, spreadsheet and calculator application that runs on Unix and Unix-like operating systems. It has also been ported to Windows. It can be accessed through a terminal emulator, and has a simple interface and keyboard shortcuts resembling the key bindings of the Vim text editor. It can be used in a similar manner ...
A vector field V defined on an open set S is called a gradient field or a conservative field if there exists a real-valued function (a scalar field) f on S such that = = (,,, …,). The associated flow is called the gradient flow , and is used in the method of gradient descent .
An example of a solenoidal vector field, (,) = (,) In vector calculus a solenoidal vector field (also known as an incompressible vector field , a divergence-free vector field , or a transverse vector field ) is a vector field v with divergence zero at all points in the field: ∇ ⋅ v = 0. {\displaystyle \nabla \cdot \mathbf {v} =0.}
Many boosting algorithms rely on the notion of a margin to assign weight to samples. If a convex loss is utilized (as in AdaBoost or LogitBoost, for instance) then a sample with a higher margin will receive less (or equal) weight than a sample with a lower margin. This leads the boosting algorithm to focus weight on low-margin samples.
In the study of mathematics, and especially of differential geometry, fundamental vector fields are instruments that describe the infinitesimal behaviour of a smooth Lie group action on a smooth manifold. Such vector fields find important applications in the study of Lie theory, symplectic geometry, and the study of Hamiltonian group actions.
If the interior product of a vector field with the symplectic form is an exact form (and in particular, a closed form), then it is called a Hamiltonian vector field. If the first De Rham cohomology group H 1 ( M ) {\displaystyle H^{1}(M)} of the manifold is trivial, all closed forms are exact, so all symplectic vector fields are Hamiltonian.
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