Related papers: SecDec: A general program for sector decomposition
We propose new algorithms for computing triangular decompositions of polynomial systems incrementally. With respect to previous works, our improvements are based on a {\em weakened} notion of a polynomial GCD modulo a regular chain, which…
We present a closed-form finite-dimensional projection method for regularizing a function defined by a discrete set of measurement data, which have been contaminated by random, zero mean errors, and for estimating the derivative and…
We describe in detail the constrained procedure of differential renormalization and develop the techniques required for one-loop calculations. As an illustration we renormalize Scalar QED and show that the two-, three- and four-point Ward…
We re-evaluate universal computation based on the synthesis of Turing machines. This leads to a view of programs as singularities of analytic varieties or, equivalently, as phases of the Bayesian posterior of a synthesis problem. This new…
We present a method for the analysis of singularities of Feynman amplitudes based on the Speer sector decomposition of the Schwinger parametric integrals combined with the Mellin-Barnes transform. The sector decomposition method is…
We introduce a novel stochastic regularization technique for deep neural networks, which decomposes a layer into multiple branches with different parameters and merges stochastically sampled combinations of the outputs from the branches…
We propose a new method to calculate the 4-dimensional divergent integrals. By calculating the one loop integral as an example, the regularization of the integrals in 3-dimension momentum space are given in details. We find that the new…
The purely numerical evaluation of multi-loop integrals and amplitudes can be a viable alternative to analytic approaches, in particular in the presence of several mass scales, provided sufficient accuracy can be achieved in an acceptable…
We propose several improvements for Linear Programming (LP) decoding algorithms for High Density Parity Check (HDPC) codes. First, we use the automorphism groups of a code to create parity check matrix diversity and to generate valid cuts…
Procedural modeling is now the de facto standard of material modeling in industry. Procedural models can be edited and are easily extended, unlike pixel-based representations of captured materials. In this paper, we present a semi-automatic…
The analogue of polar coordinates in the Euclidean space, a polar decomposition in a metric space, if well-defined, can be very useful in dealing with integrals with respect to a sufficiently regular measure. In this note we handle the…
High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless $p/n\rightarrow0$, a…
The state of art of electromagnetic integral equations has seen significant growth over the past few decades, overcoming some of the fundamental bottlenecks: computational complexity, low frequency and dense discretization breakdown,…
The problem of replacing an integral norm with respect to a given probability measure by the corresponding integral norm with respect to a discrete measure is discussed in the paper. The above problem is studied for elements of finite…
We present recent developments on the topic of the integrand reduction of scattering amplitudes. Integrand-level methods allow to express an amplitude as a linear combination of Master Integrals, by performing operations on the…
Many problems give rise to polynomial systems. These systems often have several parameters and we are interested to study how the solutions vary when we change the values for the parameters. Using predictor-corrector methods we track the…
In this paper, we present several algorithms for dealing with graded components of Laurent polynomial rings. To be more precise, let $S$ be the Laurent polynomial ring $k[x_1,...,x_{r},x_{r+1}^{\pm 1},..., x_n^{\pm 1}]$, $k$ algebraicaly…
We present a convex approach to probabilistic segmentation and modeling of time series data. Our approach builds upon recent advances in multivariate total variation regularization, and seeks to learn a separate set of parameters for the…
Numerous interesting properties in nonlinear systems analysis can be written as polynomial optimization problems with nonconvex sum-of-squares problems. To solve those problems efficiently, we propose a sequential approach of local…
The paper addresses the study and applications of a broad class of extended-real-valued functions, known as optimal value or marginal functions, which are frequently appeared in variational analysis, parametric optimization, and a variety…