A note on connected formula for form factors

In this note we study the connected prescription, originally derived from Witten's twistor string theory, for tree-level form factors in ${\cal N}=4$ super-Yang-Mills theory. The construction is based on the recently proposed four-dimensional scattering equations with $n$ massless on-shell states and one off-shell state, which we expect to work for form factors of general operators. To illustrate the universality of the prescription, we propose compact formulas for super form factors with chiral stress-tensor multiplet operator, and bosonic ones with scalar operators ${\rm Tr}(\phi^m)$ for arbitrary $m$.Comment: 13 page

Scattering Equations, Twistor-string Formulas and Double-soft Limits in Four Dimensions

We study scattering equations and formulas for tree amplitudes of various theories in four dimensions, in terms of spinor helicity variables and on-shell superspace for supersymmetric theories. As originally obtained in Witten's twistor string theory and other twistor-string models, the equations can take either polynomial or rational forms, and we clarify the simple relation between them. We present new, four-dimensional formulas for all tree amplitudes in the non-linear sigma model, a special Galileon theory and the maximally supersymmetric completion of the Dirac-Born-Infeld theory. Furthermore, we apply the formulas to study various double-soft theorems in these theories, including the emissions of a pair of soft photons, fermions and scalars for super-amplitudes in super-DBI theory.Comment: 22 pages, 2 tables; v2: ref added, minor typos fixe

A Location-Inventory-Routing Problem in Forward and Reverse Logistics Network Design

We study a new problem of location-inventory-routing in forward and reverse logistic (LIRP-FRL) network design, which simultaneously integrates the location decisions of distribution centers (DCs), the inventory policies of opened DCs, and the vehicle routing decision in serving customers, in which new goods are produced and damaged goods are repaired by a manufacturer and then returned to the market to satisfy customers’ demands as new ones. Our objective is to minimize the total costs of manufacturing and remanufacturing goods, building DCs, shipping goods (new or recovered) between the manufacturer and opened DCs, and distributing new or recovered goods to customers and ordering and storage costs of goods. A nonlinear integer programming model is proposed to formulate the LIRP-FRL. A new tabu search (NTS) algorithm is developed to achieve near optimal solution of the problem. Numerical experiments on the benchmark instances of a simplified version of the LIRP-FRL, the capacitated location routing problem, and the randomly generated LIRP-FRL instances demonstrate the effectiveness and efficiency of the proposed NTS algorithm in problem resolution

Design of a Multiobjective Reverse Logistics Network Considering the Cost and Service Level

Reverse logistics, which is induced by various forms of used products and materials, has received growing attention throughout this decade. In a highly competitive environment, the service level is an important criterion for reverse logistics network design. However, most previous studies about product returns only focused on the total cost of the reverse logistics and neglected the service level. To help a manufacturer of electronic products provide quality postsale repair service for their consumer, this paper proposes a multiobjective reverse logistics network optimisation model that considers the objectives of the cost, the total tardiness of the cycle time, and the coverage of customer zones. The Nondominated Sorting Genetic Algorithm II (NSGA-II) is employed for solving this multiobjective optimisation model. To evaluate the performance of NSGA-II, a genetic algorithm based on weighted sum approach and Multiobjective Simulated Annealing (MOSA) are also applied. The performance of these three heuristic algorithms is compared using numerical examples. The computational results show that NSGA-II outperforms MOSA and the genetic algorithm based on weighted sum approach. Furthermore, the key parameters of the model are tested, and some conclusions are drawn

Towards Efficient SDRTV-to-HDRTV by Learning from Image Formation

Modern displays are capable of rendering video content with high dynamic range (HDR) and wide color gamut (WCG). However, the majority of available resources are still in standard dynamic range (SDR). As a result, there is significant value in transforming existing SDR content into the HDRTV standard. In this paper, we define and analyze the SDRTV-to-HDRTV task by modeling the formation of SDRTV/HDRTV content. Our analysis and observations indicate that a naive end-to-end supervised training pipeline suffers from severe gamut transition errors. To address this issue, we propose a novel three-step solution pipeline called HDRTVNet++, which includes adaptive global color mapping, local enhancement, and highlight refinement. The adaptive global color mapping step uses global statistics as guidance to perform image-adaptive color mapping. A local enhancement network is then deployed to enhance local details. Finally, we combine the two sub-networks above as a generator and achieve highlight consistency through GAN-based joint training. Our method is primarily designed for ultra-high-definition TV content and is therefore effective and lightweight for processing 4K resolution images. We also construct a dataset using HDR videos in the HDR10 standard, named HDRTV1K that contains 1235 and 117 training images and 117 testing images, all in 4K resolution. Besides, we select five metrics to evaluate the results of SDRTV-to-HDRTV algorithms. Our final results demonstrate state-of-the-art performance both quantitatively and visually. The code, model and dataset are available at https://github.com/xiaom233/HDRTVNet-plus.Comment: Extended version of HDRTVNe

Density Functional Theory Study on the Mechanism of Biochar Gasification in CO2 Environment

This work presents a comprehensive analysis on the CO2 gasification of miscanthus derived biochar by using combined experimental and computational methods. The empirical formula and the 2D molecular model of the biochar were proposed based on the results from elemental analysis, Fourier infrared spectroscopy, and solid-state 13C NMR spectroscopy. The density functional theory (DFT) method was used to study the conversion of biochar to gaseous products under the CO2 condition at the B3LYP/6-31G(d,p) level. The reactants, intermediates, transition states, and products during the CO2 gasification process were analyzed, and the activation energy (ΔE) of each reaction step and thermodynamic parameters (Gibbs free energy, ΔG, and enthalpy, ΔH) were obtained. By comparison of the kinetic and thermodynamic parameters of different reaction paths, it was found that the proposed path 1 and path 5 could occur spontaneously with the changes in Gibbs free energy (ΔG) being -182.6 and -170.6 kJ/mol, respectively. The order of the reaction path was path 1 < path 5 < path 3 < path 4 < path 2, in terms of the degree of difficulty. It was also found that, for the benzene ring having a ring-opening reaction, when the substituents were located in the 2 and 3 carbon atoms or the 2, 3, and 5 carbon atoms, the C-C bond between the 1 and 6 carbon atoms was more prone to homolytic reaction than that between the 1 and 2 carbon atoms