Related papers: Higher order extensions of the Gaussian effective …
Some classic second-order sufficient optimality conditions in the calculus of variations are shown to be equivalent, while also introducing a new equivalent second-order condition which is extremely easy to apply: simply integrate a linear…
Variational approaches to approximate Bayesian inference provide very efficient means of performing parameter estimation and model selection. Among these, so-called variational-Laplace or VL schemes rely on Gaussian approximations to…
A new probabilistic post-processing method for wind vectors is presented in a distributional regression framework employing the bivariate Gaussian distribution. In contrast to previous studies all parameters of the distribution are…
We study a distributed estimation problem in which two remotely located parties, Alice and Bob, observe an unlimited number of i.i.d. samples corresponding to two different parts of a random vector. Alice can send $k$ bits on average to…
This paper first strictly proved that the growth of the second moment of a large class of Gaussian processes is not greater than power function and the covariance matrix is strictly positive definite. Under these two conditions, the maximum…
The previously developed renormalizable perturbative 1/N-expansion in higher dimensional scalar field theories is extended to gauge theories with fermions. It is based on the $1/N_f$-expansion and results in a logarithmically divergent…
We introduce a continuous one-dimensional non-Hermitian matrix gauge potential and study its effect on dynamics of a two-component field. The model is emulated by a system of evanescently coupled nonlinear waveguides with distributed gain…
The Gaussian Effective Potential in a fixed transverse unitarity gauge is studied for the static three-dimensional U(1) scalar electrodynamics (Ginzburg-Landau phenomenological theory of superconductivity). In the broken-symmetry phase the…
We extend the gauge invariant variational approach of Phys. Rev. D52 (1995) 3719, hep-th/9408081, to theories with fermions. As the simplest example we consider the massless Schwinger model in 1+1 dimensions. We show that in this solvable…
In a recent work we have introduced a novel approach to study the effect of weak non-linearities in the transfer function on the information transmitted by an analogue channel, by means of a perturbative diagrammatic expansion. We extend…
The paper is devoted to a comprehensive study of composite models in variational analysis and optimization the importance of which for numerous theoretical, algorithmic, and applied issues of operations research is difficult to overstate.…
We use a Gaussian wave functional for the ground state to reorder the Hamiltonian into a free part with a variationally determined mass and the rest. Once spontaneous symmetry breaking is taken into account, the residual Hamiltonian can, in…
We explore field theories of a single p-form with equations of motions of order strictly equal to two and gauge invariance. We give a general method for the classification of such theories which are extensions to the p-forms of the Galileon…
Sparse variational Gaussian processes (GPs) construct tractable posterior approximations to GP models. At the core of these methods is the assumption that the true posterior distribution over training function values ${\bf f}$ and inducing…
We present a new method to introduce scalar potentials to gauge-invariant chiral models coupled to supergravity. The theories under consideration contain consistent higher-derivative terms which do not give rise to instabilities and ghost…
We propose a variational approach to solve Cauchy problems for parabolic equations and systems independently of regularity theory for solutions. This produces a universal and conceptually simple construction of fundamental solution…
A classical method for risk-sensitive nonlinear control is the iterative linear exponential quadratic Gaussian algorithm. We present its convergence analysis from a first-order optimization viewpoint. We identify the objective that the…
The procedure to find gauge invariant variables for two-parameter nonlinear perturbations in general relativity is considered. For each order metric perturbation, we define the variable which is defined by the appropriate combination with…
In previous work Majda and McLaughlin computed explicit expressions for the $2N$th moments of a passive scalar advected by a linear shear flow in the form of an integral over ${\bf R}^N$. In this paper we first compute the asymptotics of…
The correlation length-scale next to the noise variance are the most used hyperparameters for the Gaussian processes. Typically, stationary covariance functions are used, which are only dependent on the distances between input points and…