A variational approach to second-order multisymplectic field theory

Testing gravity to second post-Newtonian order: A field-theory approach.

A new, field-theory-based framework for discussing and interpreting experimental tests of relativistic gravity, notably at the second post-Newtonian (2PN) level, is introduced. Contrary to previous frameworks which attempted at parametrizing any conceivable phenomenological deviation from general relativity, we focus on the most general class of gravity models of the type suggested by unified t...

Second-order stochastic variational inference

Stochastic gradient descent (SGD), the workhorse of stochastic optimization, is slow in theory (sub-linear convergence) and in practice (thousands of iterations), intuitively for two reasons: 1) Its learning rate schedule is fixed a priori and decays rapidly enough to 0 that is square-summable. This learning rate schedule limits the step size and hence the rate of convergence for a Lipschitz ob...

A nonlinear second order field equation – similarity solutions and relation to a Bellmann-type equation - Applications to Maxwellian Molecules

In this paper Lie’s formalism is applied to deduce classes of solutions of a nonlinear partial differential equation (nPDE) of second order with quadratic nonlinearity. The equation has the meaning of a field equation appearing in the formulation of kinetic models. Similarity solutions and transformations are given in a most general form derived to the first time in terms of reciprocal Jacobian...

Variational Approach to Retinex Theory

Systematic Approach to Design a Finite Time Convergent Differentiator in Second Order Sliding Mode Controller

This paper presents a systematic approach to design a Lyapunov based super twisting differentiator. The differentiator will be shown convergent in a finite time whilst the relevant time is accurately estimated.  This differentiator is the main part to establish the sliding surface in higher order sliding mode. The differentiator  is used in the prescribed control structure  to regulate pressure...