Hermite-Hadamard, Hermite-Hadamard-Fejer, Dragomir-Agarwal and Pachpatte Type Inequalities for Convex Functions via Fractional Integrals

The aim of this paper is to establish Hermite-Hadamard, Hermite-Hadamard-Fej\'er, Dragomir-Agarwal and Pachpatte type inequalities for new fractional integral operators with exponential kernel. These results allow us to obtain a new class of functional inequalities which generalizes known inequalities involving convex functions. Furthermore, the obtained results may act as a useful source of inspiration for future research in convex analysis and related optimization fields.Comment: 14 pages, to appear in Journal of Computational and Applied Mathematic

Constructing the fermion-boson vertex in QED3

We derive perturbative constraints on the transverse part of the fermion-boson vertex in massive QED3 through its one loop evaluation in an arbitrary covariant gauge. Written in a particular form, these constraints naturally lead us to the first non-perturbative construction of the vertex, which is in complete agreement with its one loop expansion in all momentum regimes. Without affecting its one-loop perturbative properties, we also construct an effective vertex in such a way that the unknown functions defining it have no dependence on the angle between the incoming and outgoing fermion momenta. Such a vertex should be useful for the numerical study of dynamical chiral symmetry breaking, leading to more reliable results.Comment: 13 pages, 2 figure

A shared latent space matrix factorisation method for recommending new trial evidence for systematic review updates

Clinical trial registries can be used to monitor the production of trial evidence and signal when systematic reviews become out of date. However, this use has been limited to date due to the extensive manual review required to search for and screen relevant trial registrations. Our aim was to evaluate a new method that could partially automate the identification of trial registrations that may be relevant for systematic review updates. We identified 179 systematic reviews of drug interventions for type 2 diabetes, which included 537 clinical trials that had registrations in ClinicalTrials.gov. We tested a matrix factorisation approach that uses a shared latent space to learn how to rank relevant trial registrations for each systematic review, comparing the performance to document similarity to rank relevant trial registrations. The two approaches were tested on a holdout set of the newest trials from the set of type 2 diabetes systematic reviews and an unseen set of 141 clinical trial registrations from 17 updated systematic reviews published in the Cochrane Database of Systematic Reviews. The matrix factorisation approach outperformed the document similarity approach with a median rank of 59 and recall@100 of 60.9%, compared to a median rank of 138 and recall@100 of 42.8% in the document similarity baseline. In the second set of systematic reviews and their updates, the highest performing approach used document similarity and gave a median rank of 67 (recall@100 of 62.9%). The proposed method was useful for ranking trial registrations to reduce the manual workload associated with finding relevant trials for systematic review updates. The results suggest that the approach could be used as part of a semi-automated pipeline for monitoring potentially new evidence for inclusion in a review update.Comment: Journal of Biomedical Informatics Vol. 79, March 2018, p. 32-4

A fresh look at the (non-)Abelian Landau-Khalatnikov-Fradkin transformations

The Landau-Khalatnikov-Fradkin transformations (LKFTs) allow to interpolate $n$-point functions between different gauges. We first offer an alternative derivation of these LKFTs for the gauge and fermions field in the Abelian (QED) case when working in the class of linear covariant gauges. Our derivation is based on the introduction of a gauge invariant transversal gauge field, which allows a natural generalization to the non-Abelian (QCD) case of the LKFTs. To our knowledge, within this rigorous formalism, this is the first construction of the LKFTs beyond QED. The renormalizability of our setup is guaranteed to all orders. We also offer a direct path integral derivation in the non-Abelian case, finding full consistency.Comment: 16 page

Landau-Khalatnikov-Fradkin Transformations and the Fermion Propagator in Quantum Electrodynamics

We study the gauge covariance of the massive fermion propagator in three as well as four dimensional Quantum Electrodynamics (QED). Starting from its value at the lowest order in perturbation theory, we evaluate a non-perturbative expression for it by means of its Landau-Khalatnikov-Fradkin (LKF) transformation. We compare the perturbative expansion of our findings with the known one loop results and observe perfect agreement upto a gauge parameter independent term, a difference permitted by the structure of the LKF transformations.Comment: 9 pages, no figures, uses revte

Infrared behaviour of massless QED in space-time dimensions 2 < d < 4

We show that the logarithmic infrared divergences in electron self-energy and vertex function of massless QED in 2+1 dimensions can be removed at all orders of 1/N by an appropriate choice of a non-local gauge. Thus the infrared behaviour given by the leading order in 1/N is not modified by higher order corrections. Our analysis gives a computational scheme for the Amati-Testa model, resulting in a non-trivial conformal invariant field theory for all space-time dimensions 2 < d < 4.Comment: 12 pages, uses axodraw.sty; added comments at the end, and one reference; to appear in Phys. Lett.