A machine learning pipeline for autonomous numerical analytic continuation of Dyson-Schwinger equations

Dyson-Schwinger equations (DSEs) are a non-perturbative way to express n-point functions in quantum field theory. Working in Euclidean space and in Landau gauge, for example, one can study the quark propagator Dyson-Schwinger equation in the real and complex domain, given that a suitable and tractable truncation has been found. When aiming for solving these equations in the complex domain, that is, for complex external momenta, one has to deform the integration contour of the radial component in the complex plane of the loop momentum expressed in hyper-spherical coordinates. This has to be done in order to avoid poles and branch cuts in the integrand of the self-energy loop. Since the nature of Dyson-Schwinger equations is such, that they have to be solved in a self-consistent way, one cannot analyze the analytic properties of the integrand after every iteration step, as this would not be feasible. In these proceedings, we suggest a machine learning pipeline based on deep learning (DL) approaches to computer vision (CV), as well as deep reinforcement learning (DRL), that could solve this problem autonomously by detecting poles and branch cuts in the numerical integrand after every iteration step and by suggesting suitable integration contour deformations that avoid these obstructions. We sketch out a proof of principle for both of these tasks, that is, the pole and branch cut detection, as well as the contour deformation.

Toward massless and massive event shapes in the large-β0 limit

We present results for SCET and bHQET matching coefficients and jet functions in the large-β0 limit. Our computations exactly predict all terms of the form $$ {\alpha}_s^{n+1}{n}_f^n $$ α s n + 1 n f n for any n ≥ 0, and we find full agreement with the coefficients computed in the full theory up to $$ \mathcal{O}\left({\alpha}_s^4\right) $$ O α s 4 . We obtain all-order closed expressions for the cusp and non-cusp anomalous dimensions (which turn out to be unambiguous) as well as matrix elements (with ambiguities) in this limit, which can be easily expanded to arbitrarily high powers of αs using recursive algorithms to obtain the corresponding fixed-order coefficients. Examining the poles laying on the positive real axis of the Borel-transform variable u we quantify the perturbative convergence of a series and estimate the size of non-perturbative corrections. We find a so far unknown u = 1/2 renormalon in the bHQET hard factor Hm that affects the normalization of the peak differential cross section for boosted top quark pair production. For ambiguous series the so-called Borel sum is defined with the principal value prescription. Furthermore, one can assign an ambiguity based on the arbitrariness of avoiding the poles by contour deformation into the positive or negative imaginary half-plane. Finally, we compute the relation between the pole mass and four low-scale short distance masses in the large-β0 approximation (MSR, RS and two versions of the jet mass), work out their μ- and R-evolution in this limit, and study how their implementation improves the convergence of the position-space bHQET jet function, whose three-loop coefficient in full QCD is numerically estimated.

Optimisation of complex integration contours at higher order

We continue our study of contour deformation as a practical tool for dealing with the sign problem using the d-dimensional Bose gas with non-zero chemical potential as a toy model. We derive explicit expressions for contours up to the second order with respect to a natural small parameter and generalise these contours to an ansatz for which the evaluation of the Jacobian is fast (O(1)). We examine the behaviour of the various proposed contours as a function of space-time dimensionality, the chemical potential, and lattice size and geometry and use the mean phase factor as a measure of the severity of the sign problem. In turns out that this method leads to a substantial reduction of the sign problem and that it becomes more efficient as space-time dimensionality is increased. Correlations among contributions to Im 〈S〉 play a key role in determining the mean phase factor and we examine these correlations in detail.

Hand Side Recognition and Authentication System based on Deep Convolutional Neural Networks

The human hand has been considered a promising component for biometric-based identification and authentication systems for many decades. In this paper, hand side recognition framework is proposed based on deep learning and biometric authentication using the hashing method. The proposed approach performs in three phases: (a) hand image segmentation and enhancement by morphological filtering, automatic thresholding, and active contour deformation, (b) hand side recognition based on deep Convolutional Neural Networks (CNN), and (c) biometric authentication based on the hashing method. The proposed framework is evaluated using a very large hand dataset, which consists of 11076 hand images, including left/ right and dorsal/ palm hand images for 190 persons. Finally, the experimental results show the efficiency of the proposed framework in both dorsal-palm and left-right recognition with an average accuracy of 96.24 and 98.26, respectively, using a completely automated computer program.

Urban Scene Vectorized Modeling Based on Contour Deformation

Modeling urban scenes automatically is an important problem for both GIS and nonGIS specialists with applications like urban planning, autonomous driving, and virtual reality. In this paper, we present a novel contour deformation approach to generate regularized and vectorized 3D building models from the orthophoto and digital surface model (DSM).The proposed method has four major stages: dominant directions extraction, find target align direction, contour deformation, and model generation. To begin with, we extract dominant directions for each building contour in the orthophoto. Then every edge of the contour is assigned with one of the dominant directions via a Markov random field (MRF). Taking the assigned direction as target, we define a deformation energy with the Advanced Most-Isometric ParameterizationS (AMIPS) to align the contour to the dominant directions. Finally, the aligned contour is simplified and extruded to 3D models. Through the alignment deformation, we are able to straighten the contour while keeping the sharp turning corners. Our contour deformation based urban modeling approach is accurate and robust comparing with the state-of-the-arts as shown in experiments on the public dataset.