Amplitudes for astrophysicists: known knowns

The use of quantum field theory to understand astrophysical phenomena is not new. However, for the most part, the methods used are those that have been developed decades ago. The intervening years have seen some remarkable developments in computational quantum field theoretic tools. In particle physics, this technology has facilitated calculations that, even ten years ago would have seemed laughably difficult. It is remarkable, then, that most of these new techniques have remained firmly within the domain of high energy physics. We would like to change this. As alluded to in the title, this paper is aimed at showcasing the use of modern on-shell methods in the context of astrophysics and cosmology. In this article, we use the old problem of the bending of light by a compact object as an anchor to pedagogically develop these new computational tools. Once developed, we then illustrate their power and utility with an application to the scattering of gravitational waves.     

Comment on “Questioning the Recent Observation of Quantum Hawking Radiation” [Ann. Phys. (Berlin) 2018, 530, 1700114]

The observation of quantum Hawking radiation and its entanglement in an analogue black hole was recently reported. A subsequent article presented critical comments of the study. The article suffers from technical difficulties which invalidate its claims. These include the misunderstanding of a simple Fourier transform, the unnecessary modification of experimental data, and the assertion that the experiment measured a strictly‐zero population.     

Covalent Template-Directed Synthesis of a Spoked 18-Porphyrin Nanoring**

Rings of porphyrins mimic natural light-harvesting chlorophyll arrays and offer insights into electronic delocalization, providing a motivation for creating larger nanorings with closely spaced porphyrin units. Here, we demonstrate the first synthesis of a macrocycle consisting entirely of 5,15-linked porphyrins. This porphyrin octadecamer was constructed using a covalent six-armed template, made by cobalt-catalyzed cyclotrimerization of an H-shaped tolan with porphyrin trimer ends. The porphyrins around the circumference of the nanoring were linked together by intramolecular oxidative meso-meso coupling and partial β-β fusion, to give a nanoring consisting of six edge-fused zinc(II) porphyrin dimer units and six un-fused nickel(II) porphyrins. STM imaging on a gold surface confirms the size and shape of the spoked 18-porphyrin nanoring (calculated diameter: 4.7 nm).     

Online Prediction with History-Dependent Experts: The General Case

We study the problem of prediction of binary sequences with expert advice in the online setting, which is a classic example of online machine learning. We interpret the binary sequence as the price history of a stock, and view the predictor as an investor, which converts the problem into a stock prediction problem. In this framework, an investor, who predicts the daily movements of a stock, and an adversarial market, who controls the stock, play against each other over N turns. The investor combines the predictions of $n\ge 2$ experts in order to make a decision about how much to invest at each turn, and aims to minimize their regret with respect to the best-performing expert at the end of the game. We consider the problem with history-dependent experts, in which each expert uses the previous d days of history of the market in making their predictions. We prove that the value function for this game, rescaled appropriately, converges as $N\to \mathrm{\infty }$ at a rate of $O\left(N^{-1/6}\right)$ to the viscosity solution of a nonlinear degenerate elliptic PDE, which can be understood as the Hamilton-Jacobi-Issacs equation for the two-person game. As a result, we are able to deduce asymptotically optimal strategies for the investor. Our results extend those established by the first author and R.V. Kohn [14] for $n=2$ experts and $d\le 4$ days of history. © 2022 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.     

Pd‐Catalysed Direct Arylation Polymerisation for Synthesis of Low‐Bandgap Conjugated Polymers and Photovoltaic Performance

Low‐bandgap conjugated copolymers based on a donor–acceptor structure have been synthesised via palladium‐complex catalysed direct arylation polymerisation. Initially, we report the optimisation of the synthesis of poly(cyclopentadithiophene‐alt‐benzothiadiazole) (PCPDTBT) formed between cyclopentadithiophene and dibromobenzothiadiazole units. The polymerisation condition has been optimised, which affords high‐molecular‐weight polymers of up to M _n = 70 k using N‐methylpyrrolidone as a solvent. The polymers are used to fabricate organic photovoltaic devices and the best performing PCPDTBT device exhibits a moderate improvement over devices fabricated using the related polymer via Suzuki coupling. Similar polymerisation conditions have also been applied for other monomer units.     

eHydrogenation: Hydrogen-free Electrochemical Hydrogenation

Hydrogenation reactions are staple transformations commonly used across scientific fields to synthesise pharmaceuticals, natural products, and various functional materials. However, the vast majority of these reactions require the use of a toxic and costly catalyst leading to unpractical, hazardous and often functionally limited conditions. Herein, we report a new, general, practical, efficient, mild and high-yielding hydrogen-free electrochemical method for the reduction of alkene, alkyne, nitro and azido groups. Finally, this method has been applied to deuterium labelling.     

Designs to Improve Capability of Neural Networks to Make Structural Predictions

Chinese Journal of Polymer Science - A deep neural network model generally consists of different modules that play essential roles in performing a task. The optimal design of a module for use in...