Solutions to gravity with quadratic Lagrangians are found for the simple case where the only nonconstant metric component is the lapse N and the Riemann tensor takes the form R .itj = −kikj , i, j = 1, 2, 3; thus these solutions depend on cross terms in the Riemann tensor and therefore complement the linearized theory where it is the derivatives of the Riemann tensor that matter. The relationsh...

Discriminative clustering (DC) finds a Voronoi partitioning of a primary data space that, while consisting of local partitions, simultaneously maximizes information about auxiliary data categories. DC is useful in exploration and in finding more coarse or refined versions of already existing categories. Theoretical results suggest that Voronoi partitions in the socalled Fisher metric would outp...

We consider transformations of the (metric) Quadratic Assignment Problem (QAP), that exploit the metric structure of a given instance. We show in particular, how the structural properties of rectangular grids can be used to improve a given lower bound. Our work is motivated by previous research of G.S. Palubetskes, and it extends a bounding approach proposed by J. Chakrapani and J. Skorin-Kapov...

The paper is devoted to metrization of probability spaces through the introduction of a quadratic differential metric in the parameter space of the probability distributions. For this purpose, a d-entropy functional is defined on the probability space and its Hessian along a direction of the tangent space of the parameter space is taken as the metric. The distance between two probability distri...

A non-autonomous sub-Riemannian problem is considered: Since periodicity with respect to the independent variable is assumed, one can define the averaged problem. In the case of the minimization of the energy, the averaged Hamiltonian remains quadratic in the adjoint variable. When it is non-degenerate, a Riemannian problem and the corresponding metric can be uniquely associated to the averaged...