Statistical learning algorithms often rely on the Euclidean distance. In practice, non-Euclidean or non-metric dissimilarity measures may arise when contours, spectra or shapes are compared by edit distances or as a consequence of robust object matching [1,2]. It is an open issue whether such measures are advantageous for statistical learning or whether they should be constrained to obey the me...

Firefly algorithm is a meta-heuristic stochastic search with strong robustness and easy implementation. However, it also has some shortcomings, such as the "oscillation" phenomenon caused by too many attractions, which makes convergence speed slow or premature. In original FA, full attraction model consume lot of evaluation times, time complexity high. Therefore, this paper, novel firefly (EMDm...

Multilayer Perceptrons (MLPs) use scalar products to compute weighted activation of neurons providing decision borders using combinations of soft hyperplanes. The weighted fun-in activation function corresponds to Euclidean distance functions used to compute similarities between input and weight vector. Replacing the fan-in activation function by non-Euclidean distance function offers a natural...

Let f : D → C be an analytic function on the unit disc which is in the Dirichlet class, so the Euclidean area of the image, counting multiplicity, is finite. The Euclidean length of a radial arc of hyperbolic length ρ is then o(ρ). In this note we consider the corresponding results when f maps into the unit disc with the hyperbolic metric or the Riemann sphere with the spherical metric. Similar...

We show (a) that any entire graphic self-shrinking solution to the Lagrangian mean curvature flow in C with the Euclidean metric is flat; (b) that any space-like entire graphic self-shrinking solution to the Lagrangian mean curvature flow in C with the pseudo-Euclidean metric is flat if the Hessian of the potential is bounded below quadratically; and (c) the Hermitian counterpart of (b) for the...

Given a scattering metric on the Euclidean space. We consider the Schrödinger equation corresponding to the metric, and study the propagation of singularities for the solution in terms of the homogeneous wavefront set. We also prove that the notion of the homogeneous wavefront set is essentially equivalent to that of the quadratic scattering wavefront set introduced by J. Wunsch [21]. One of th...