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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 evidence for a fixed function over perturbations about this function. We apply this formalism to an illustrative problem of measuring perturbations in the dark energy equation of state about a cosmological constant.
In Path Integral control problems a representation of an optimally controlled dynamical system can be formally computed and serve as a guidepost to learn a parametrized policy. The Path Integral Cross-Entropy (PICE) method tries to exploit this, but
Through a very careful analysis of Diracs 1932 paper on the Lagrangian in Quantum Mechanics as well as the second and third editions of his classic book {it The Principles of Quantum Mechanics}, I show that Diracs contributions to the birth of the pa
Fractional derivatives are nonlocal differential operators of real order that often appear in models of anomalous diffusion and a variety of nonlocal phenomena. Recently, a version of the Schrodinger Equation containing a fractional Laplacian has bee
We present a policy search method for learning complex feedback control policies that map from high-dimensional sensory inputs to motor torques, for manipulation tasks with discontinuous contact dynamics. We build on a prior technique called guided p
We propose an idea of the constrained Feynman amplitude for the scattering of the charged lepton and the virtual W-boson, $l_{beta} + W_{rho} rightarrow l_{alpha} + W_{lambda}$, from which the conventional Pontecorvo oscillation formula of relativist