相关论文: Multivariate Integral Perturbation Techniques - I …

This paper is devoted to the problem of sampling Gaussian fields in high dimension. Solutions exist for two specific structures of inverse covariance : sparse and circulant. The proposed approach is valid in a more general case and…

We study the semiclassical propagation of coherent states in $d$ dimensions, which in general involves complex classical dynamics. Several simple approximations are derived that depend only on real classical trajectories, among them the…

This work builds upon previous efforts in online incremental learning, namely the Incremental Gaussian Mixture Network (IGMN). The IGMN is capable of learning from data streams in a single-pass by improving its model after analyzing each…

Numerical Stochastic Perturbation Theory (NSPT) has over the years proved to be a valuable tool, in particular being able to reach unprecedented orders for Lattice Gauge Theories, whose perturbative expansions are notoriously cumbersome.…

An expansion method for perturbation of the zero temperature grand canonical density matrix is introduced. The method achieves quadratically convergent recursions that yield the response of the zero temperature density matrix upon variation…

Perturbation theory, the quasiclassical approximation and the quantum surface of section method are combined for the first time. This gives a new solution of the the long standing problem of quantizing the resonances generically appearing…

An integrable theory is developed for the perturbation equations engendered from small disturbances of solutions. It includes various integrable properties of the perturbation equations: hereditary recursion operators, master symmetries,…

Gaussian graphical regressions have emerged as a powerful approach for regressing the precision matrix of a Gaussian graphical model on covariates, which, unlike traditional Gaussian graphical models, can help determine how graphs are…

The path integral for the propagator is expanded into a perturbation series, which can be exactly summed in the case of $\delta$-function perturbations giving a closed expression for the (energy-dependent) Green function. Making the…

The calculation of scalar gravitational and matter perturbations during multiple-field inflation valid to first order in slow roll is discussed. These fields may be the coordinates of a non-trivial field manifold and hence have non-minimal…

We provide a perturbative expansion for the empirical spectral distribution of a Hermitian matrix with large size perturbed by a random matrix with small operator norm whose entries in the eigenvector basis of the first one are independent…

This article explores the optimization of variational approximations for posterior covariances of Gaussian multiway arrays. To achieve this, we establish a natural differential geometric optimization framework on the space using the…

We develop general purpose algorithms for computing and utilizing both the Dyson series and Magnus expansion, with the goal of facilitating numerical perturbative studies of quantum dynamics. To enable broad applications to models with…

We introduce and study a discrete multi-period extension of the classical knapsack problem, dubbed generalized incremental knapsack. In this setting, we are given a set of $n$ items, each associated with a non-negative weight, and $T$ time…

Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…

Perturbation expansions appear to be divergent series in many physically interesting situations, including in quantum field theories like quantum electrodynamics (QED) and quantum chromodynamics (QCD), where the perturbative coefficients…

A late time asymptotic perturbative analysis of curvature coupled complex scalar field models with accelerated cosmological expansion is carried out on the level of formal power series expansions. For this, algebraic analogues of the…

Recently, we presented a unified way of analysing classical cosmological perturbation in generalized gravity theories. In this paper, we derive the perturbation spectrums generated from quantum fluctuations again in unified forms. We…

We study quasi-Newton methods from the viewpoint of information geometry induced associated with Bregman divergences. Fletcher has studied a variational problem which derives the approximate Hessian update formula of the quasi-Newton…

In these lectures I will give an introduction to Feynman integrals. In the first part of the course I review the basics of the perturbative expansion in quantum field theories. In the second part of the course I will discuss more advanced…