Related papers: SecDec: A general program for sector decomposition
We propose a multi-index algorithm for the Monte Carlo (MC) discretization of a linear, elliptic PDE with affine-parametric input. We prove an error vs. work analysis which allows a multi-level finite-element approximation in the physical…
A unified scheme for treating generalized superselection sectors is proposed on the basis of the notion of selection criteria to characterize states of relevance to each specific domain in quantum physics, ranging from the relativistic…
Scattering amplitudes at loop level can be expressed in terms of Feynman integrals. The latter satisfy partial differential equations in the kinematical variables. We argue that a good choice of basis for (multi-)loop integrals can lead to…
We present a new method for the decomposition of multi-loop Euclidean Feynman integrals into quasi-finite Feynman integrals. These are defined in shifted dimensions with higher powers of the propagators, make explicit both infrared and…
We develop a practical approach to semidefinite programming (SDP) that includes the von Neumann entropy, or an appropriate variant, as a regularization term. In particular we solve the dual of the regularized program, demonstrating how a…
Insightful visualization of multidimensional scalar fields, in particular parameter spaces, is key to many fields in computational science and engineering. We propose a principal component-based approach to visualize such fields that…
We describe a recursive algorithm that decomposes an algebraic set into locally closed equidimensional sets, i.e. sets which each have irreducible components of the same dimension. At the core of this algorithm, we combine ideas from the…
It was recently shown that the phase retrieval imaging of a sample can be modeled as a simple convolution process. Sometimes, such a convolution depends on physical parameters of the sample which are difficult to estimate a priori. In this…
I propose an orthogonalization procedure preserving the grading of the initial graded set of linearly independent vectors. In particular, this procedure is applicable for orthonormalization of any countable set of polynomials in several…
We introduce a discretization scheme for continuous localized frames using quasi-Monte Carlo integration and discrepancy theory. By generalizing classical concepts, we define a discrepancy measure on the entire phase space $\mathbb{R}^2$…
Diagonalization, or eigenvalue decomposition, is very useful in many areas of applied mathematics, including signal processing and quantum physics. Matrix decomposition is also a useful tool for approximating matrices as the product of a…
This paper describes applications of extrapolation for the computation of coefficients in an expansion of infrared divergent integrals. An extrapolation procedure is performed with respect to a parameter introduced by dimensional…
We introduce a generalization of the conventional renormalization schemes used in dimensional regularization, which illuminates the renormalization scheme and scale ambiguities of pQCD predictions, exposes the general pattern of…
One of the two existing strategies of resolving singularities of multifold Mellin-Barnes integrals in the dimensional regularization parameter, or a parameter of the analytic regularization, is formulated in a modified form. The…
A method is introduced to calculate the UV-divergent parts at one-loop level in dimensional regularization. The method is based on the recursion, and the basic integrals are just the scaleless integrals after the recursive reduction, which…
One of the challenges with functional data is incorporating spatial structure, or local correlation, into the analysis. This structure is inherent in the output from an increasing number of biomedical technologies, and a functional linear…
Tensor decomposition methods allow us to learn the parameters of latent variable models through decomposition of low-order moments of data. A significant limitation of these algorithms is that there exists no general method to regularize…
We investigate continuous regularization methods for linear inverse problems of static and dynamic type. These methods are based on dynamic programming approaches for linear quadratic optimal control problems. We prove regularization…
We consider the problem of numerically integrating functions with hyperplane discontinuities over the entire Euclidean space in many dimensions. We describe a simple process through which the Euclidean space is partitioned into simplices on…
We give systematic method to evaluate a large class of one-dimensional integral relating to multiple zeta values (MZV) and colored MZV. We also apply the technique of iterated integrals and regularization to elucidate the nature of some…