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Under mild assumptions, we remove all traces of the axiom of choice from the construction of the maximal globally hyperbolic Cauchy development in general relativity. The construction relies on the notion of direct union manifolds, which we review. The con ...
American Institute of Physics2013
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Extracting low dimensional structure from high dimensional data arises in many applications such as machine learning, statistical pattern recognition, wireless sensor networks, and data compression. If the data is restricted to a lower dimensional subspace ...
Institute of Electrical and Electronics Engineers2012
Currently, the best theoretical description of fundamental matter and its gravitational interaction is given by the Standard Model (SM) of particle physics and Einstein's theory of General Relativity (GR). These theories contain a number of seemingly unrel ...
We extend the notion of general coordinate invariance to many-body, not necessarily relativistic, systems. As an application, we investigate nonrelativistic general covariance in Galilei-invariant systems. The peculiar transformation rules for the backgrou ...
Many applications in computational science require computing the elements of a function of a large matrix. A commonly used approach is based on the the evaluation of the eigenvalue decomposition, a task that, in general, involves a computing time that scal ...
Amer Physical Soc2014
An analytical formula for the shape derivative of the magnetic field integral equation (MFIE) method of moments (MoM) system matrix (or impedance matrix) is derived and validated against finite difference formulas. The motivation for computing the shape de ...
Institute of Electrical and Electronics Engineers2013
We study the radiation of gravitational waves by self-gravitating binary systems in the low-energy limit of Horava gravity. We find that the predictions for the energy-loss formula of general relativity are modified already for Newtonian sources: the quadr ...
We study the general class of gravitational field theories constructed on the basis of scale invariance (and therefore absence of any mass parameters) and invariance under transverse diffeomorphisms, which are the 4-volume conserving coordinate transformat ...
We propose a natural extension of Horava's model for quantum gravity, which is free from the notorious pathologies of the original proposal. The new model endows the scalar graviton mode with a regular quadratic action and remains power-counting renormaliz ...
This paper deals with the finite horizon stochastic optimal control problem with the expectation of the 1-norm as the objective function and jointly Gaussian, although not necessarily independent, disturbances. We develop an approximation strategy that sol ...