Evaluating Feynman integrals by the hypergeometry

The hypergeometric function method naturally provides the analytic expressions of scalar integrals from concerned Feynman diagrams in some connected regions of independent kinematic variables, also presents the systems of homogeneous linear partial differential equations satisfied by the corresponding scalar integrals. Taking examples of the one-loop $B_{_0}$ and massless $C_{_0}$ functions, as well as the scalar integrals of two-loop vacuum and sunset diagrams, we verify our expressions coinciding with the well-known results of literatures. Based on the multiple hypergeometric functions of independent kinematic variables, the systems of homogeneous linear partial differential equations satisfied by the mentioned scalar integrals are established. Using the calculus of variations, one recognizes the system of linear partial differential equations as stationary conditions of a functional under some given restrictions, which is the cornerstone to perform the continuation of the scalar integrals to whole kinematic domains numerically with the finite element methods. In principle this method can be used to evaluate the scalar integrals of any Feynman diagrams.Comment: 39 pages, including 2 ps figure

Realization of Zero-Refractive-Index Lens with Ultralow Spherical Aberration

Optical complex materials offer unprecedented opportunity to engineer fundamental band dispersion which enables novel optoelectronic functionality and devices. Exploration of photonic Dirac cone at the center of momentum space has inspired an exceptional characteristic of zero-index, which is similar to zero effective mass in fermionic Dirac systems. Such all-dielectric zero-index photonic crystals provide an in-plane mechanism such that the energy of the propagating waves can be well confined along the chip direction. A straightforward example is to achieve the anomalous focusing effect without longitudinal spherical aberration, when the size of zero-index lens is large enough. Here, we designed and fabricated a prototype of zero-refractive-index lens by comprising large-area silicon nanopillar array with plane-concave profile. Near-zero refractive index was quantitatively measured near 1.55 um through anomalous focusing effect, predictable by effective medium theory. The zero-index lens was also demonstrated to perform ultralow longitudinal spherical aberration. Such IC compatible device provides a new route to integrate all-silicon zero-index materials into optical communication, sensing, and modulation, and to study fundamental physics on the emergent fields of topological photonics and valley photonics.Comment: 14 pages, 4 figure

DeepCF: A Unified Framework of Representation Learning and Matching Function Learning in Recommender System

In general, recommendation can be viewed as a matching problem, i.e., match proper items for proper users. However, due to the huge semantic gap between users and items, it's almost impossible to directly match users and items in their initial representation spaces. To solve this problem, many methods have been studied, which can be generally categorized into two types, i.e., representation learning-based CF methods and matching function learning-based CF methods. Representation learning-based CF methods try to map users and items into a common representation space. In this case, the higher similarity between a user and an item in that space implies they match better. Matching function learning-based CF methods try to directly learn the complex matching function that maps user-item pairs to matching scores. Although both methods are well developed, they suffer from two fundamental flaws, i.e., the limited expressiveness of dot product and the weakness in capturing low-rank relations respectively. To this end, we propose a general framework named DeepCF, short for Deep Collaborative Filtering, to combine the strengths of the two types of methods and overcome such flaws. Extensive experiments on four publicly available datasets demonstrate the effectiveness of the proposed DeepCF framework

Longitudinal optical conductivities in tilted Dirac bands

We report a unified theory based on linear response, for analyzing the longitudinal optical conductivity (LOC) of materials with tilted Dirac cones. Depending on the tilt parameter $t$, the Dirac electrons have four phases, untilted, type-I, type-II, and type-III; the Dirac dispersion can be isotropic or anisotropic; the spatial dimension of the material can be one-, two-, or three-dimensions. The interband LOCs and intraband LOCs in $d$ dimension (with $d\ge2$) are found to scale as to $\sigma_{0}\omega^{d-2}$ and $\sigma_{0}|\mu|^{d-1}\delta(\omega)$, respectively, where $\omega$ is the frequency and $\mu$ the chemical potential. The interband LOCs always vanish in one dimension due to lacking of extra spatial dimension. The angular dependence of LOCs is found to characterize the band tilting, and the constant asymptotic background values of LOC reflect features of the Dirac bands. The LOCs in the anisotropic tilted Dirac cone can be connected to its isotropic counterpart by a ratio that consists of Fermi velocities. The findings are valid for a great many Dirac materials in the spatial dimensions of physical interests.Comment: 11 pages, 3 figure

Advances in the Study of Magnesium Alloys and Their Use in Bone Implant Material

Magnesium and magnesium alloys have great application potential in the field of orthopaedics. Compared with traditional inorganic nonmetallic materials and medical polymer materials, magnesium alloys have many advantages, such as better strength, toughness, fatigue resistance, and easy processing. Its mechanical properties are suitable and controllable. It can meet the same elastic modulus, cell compatibility, and biodegradability as human cortical bone. There are also some drawbacks for biodegradability, as magnesium and its alloys, with their high degradation rate, can cause insufficient integrity of the mechanical properties. This paper summarises the research on magnesium and its magnesium alloy materials in the field of bone implantation, looking at what magnesium and its magnesium alloys are, the history of magnesium alloys in bone implant materials, the manufacturing of magnesium alloys, the mechanical properties of magnesium alloys, the bio-compatibility and clinical applications of magnesium alloys, the shortcomings, and the progress of research in recent years

A new stripe rust resistance gene transferred from Thinopyrum intermedium to hexaploid wheat (Triticum aestivum)

Wheat stripe rust (Puccinia striiforis f. sp. tritici) races CYR31 and CYR32, prevalent in China, are virulent to many wheat stripe rust resistance genes (Yr genes). To expand the availability of effective resistance to CYR31 and CYR32, stripe rust resistance was transferred from intermediate wheatgrass (Thinopyrum intermedium) to common wheat (Triticum aestivum). The susceptible wheat cultivar CM107 was crossed with amphiploid TAI7047, derived from the wide cross Taiyuan768/Thinopyrum intermedium//76(64). Two wheat lines originating from the cross, YU24 and YU25, were resistant to CYR31 and CYR32. Pedigree analysis showed that the resistance to stripe rust in YU24 and YU25 originated from intermediate wheatgrass. Genetic analyses indicated that the resistance to stripe rust is controlled by a single dominant gene. Allelic tests determined that the resistance gene(s) in YU24 and YU25 are identical. The new gene has temporarily been designated as YrYU25. SSR and RAPD analyses showed that YrYU25 was introduced by cryptic translocation into common wheat.Les races CYR31 et CYR32 de la rouille jaune du blé (Puccinia striiforis f. sp. tritici), très répandues en Chine, sont virulentes pour plusieurs gènes de résistance à cette maladie (gènes Yr). Afin d'accroître la disponibilité d'une résistance efficace aux races CYR31 et CYR32, la résistance à la rouille jaune du blé a été transférée de l'agropyre intermédiaire (Thinopyrum intermedium) au blé tendre (Triticum aestivum). CM107, un cultivar de blé sensible, a été croisé avec l'amphiploïde AI7047 dérivé du croisement éloigné Taiyuan768/Thinopyrum intermedium//76(64). Deux lignées de blé provenant de ce croisement, soit YU24 et YU25, étaient résistantes aux races CYR31 et CYR32. Une analyse généalogique a démontré que la résistance à la rouille jaune du blé chez les lignées YU24 et YU25 provenait de l'agropyre intermédiaire. Des analyses génétiques ont indiqué que cette résistance était contrôlée par un seul gène dominant. Des tests d'allélisme ont révélé que le(s) gène(s) de résistance dans les lignées YU24 et YU25 étaient identiques. Le nouveau gène a temporairement été nommé YrYU25. Des analyses SSR et RAPD ont démontré que le gène YrYU25 avait été introduit dans le blé tendre par translocation cryptique

QED contribution to the production of J/\psi+c\bar{c}+X at the Tevatron and LHC

We calculate \alpha^{2}\alpha_{s}^{2} order QED contribution to J/\psi production in pp(\bar{p})\to J/\psi+c\bar{c} color-singlet process at the Tevatron and LHC in the framework of non-relativistic QCD. The contribution of the interference between the \alpha^{2}\alpha_{s}^{2} QED and \alpha_{s}^{4} QCD is also taken into account. The J/\psi production associated with a charm quark pair could be a measurable signal at hadron collider experiment. Our calculations show that by including the QED contribution, the p_{t} distribution is enhanced by a factor of 1.5 (1.9) at the Tevatron (LHC) at p_{t}=50 (100) GeV. In addition, the polarization of J/\psi turns from unpolarized in all region to increasingly transverse when p_{t} becomes larger.Comment: 14 pages, 6 figures, version accepted for publication in Phys Rev