Finsler geometrical path integral

The Geometrical Representation of Path

The path planning problem for arbitrary devices is rst and foremost a geometrical problem. For the eld of control theory, advanced mathematical techniques have been developed to describe and use geometry. In this paper, we use the notions of the ow of vector elds and geodesics in metric spaces to formalize and unify path planning problems. A path planning algorithm based on ow propagation is br...

The universal path integral

Path integrals calculate probabilities by summing over classical configurations of variables such as fields, assigning each configuration a phase equal to the action of that configuration. This paper defines a universal path integral, which sums over all computable structures. This path integral contains as sub-integrals all possible computable path integrals, including those of field theory, t...

Path - integral Evidence

Here we present a Bayesian formalism for the goodness-of-fit that is the evidence for a fixed functional form over the evidence for all functions that are a general perturbation about this form. This is done under the assumption that the statistical properties of the data can be modelled by a multivariate Gaussian distribution. We use this to show how one can optimise an experiment to find evid...

Q-deformed Path Integral

Using differential and integral calculi on the quantum plane which are invariant with respect to quantum inhomogeneous Euclidean group E(2) q , we construct path integral representation for the quantum mechanical evolution operator kernel of q-oscillator.

Path Integral Control