Abstract We continue our study of the mixed Einstein–Hilbert action as a functional pseudo-Riemannian metric and linear connection. Its geometrical part is total scalar curvature on smooth manifold endowed with distribution or foliation. develop variational formulas for quantities extrinsic geometry metric-affine space use them to derive Euler–Lagrange equations (which in case space-time are an...

The long standing problem of the ordering ambiguity in the definition of the Hamilton operator for a point particle in curved space is naturally resolved by using the powerful geometric calculus based on Clifford Algebra. The momentum operator is defined to be the vector derivative (the gradient) multiplied by −i; it can be expanded in terms of basis vectors γμ as p = −iγ∂μ. The product of two ...

Choice tests, which are often used to examine animal preferences, can be difficult to interpret when no clear choice has been made or when using very young animals which exclude test repetition. We present a new method to evaluate the behavior in a choice test based on the orientation of the animal and illustrate its use when facing those conditions. Using rat pups in an open field maze with a ...

We propose a method for accelerating computation of an object detector based on a linear classifier when objects are expressed by binary feature vectors. Our key idea is to decompose a real-valued weight vector of the linear classifier into a weighted sum of a few ternary basis vectors so as to preserve the original classification scores. Our datadependent decomposition algorithm can approximat...