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A bstract In this paper, we develop an improved method for directly calculating double-copy-compatible tree numerators in (super-)Yang-Mills and Yang-Mills-scalar theories. Our new scheme gets rid of any explicit dependence on reference orderings , restoring a form of crossing symmetry to the numerators. This in turn improves the computational efficiency of the algorithm, allowing us to go well beyond the number of external particles accessible with the reference order based methods. Motivated by a parallel study of one-loop BCJ numerators from forward limits, we explore the generalization to include a pair of fermions. To improve the accessibility of the new algorithm, we provide a M athematica package that implements the numerator construction. The structure of the computation also provides for a straightforward introduction of minimally-coupled massive particles potentially useful for future computations in both classical and quantum gravity.

A bstract In this paper we derive for the first time the complete gravitational quartic-in-spin interaction of generic compact binaries at the next-to-leading order in the post-Newtonian (PN) expansion. The derivation builds on the effective field theory for gravitating spinning objects, and its recent extensions, in which new type of worldline couplings should be considered, as well as on the extension of the effective action of a spinning particle to quadratic order in the curvature. The latter extension entails a new Wilson coefficient that appears in this sector. This work pushes the precision frontier with spins at the fifth PN (5PN) order for maximally-spinning compact objects, and at the same time informs us of the gravitational Compton scattering with higher spins.

Extracellular vesicles (EVs) are biocompatible, nano‐sized secreted vesicles containing many types of biomolecules, including proteins, RNAs, DNAs, lipids, and metabolites. Their low immunogenicity and ability to functionally modify recipient cells by transferring diverse bioactive constituents make them an excellent candidate for a next‐generation drug delivery system. Here, the recent advances in EV biology and emerging strategies of EV bioengineering are summarized, and the prospects for clinical translation of bioengineered EVs and the challenges to be overcome are discussed. Extracellular vesicles (EVs) managing diverse intercellular communication networks are attracting increasing interest in developing next‐generation drug delivery systems. This review provides a comprehensive state‐of‐the‐art coverage of EV biogenesis, transport, release, and uptake as well as cargo sorting and discusses the progress and challenges of engineering EVs for therapeutic applications.

Due to rapid information technology growth, teaching Chinese in higher education has changed, and Chinese literary majors have vigorously evolved. The key teaching difficulties are scalability, individualized teaching, and a lack of resources and methodologies. Research shows individualized education improves topic comprehension, cultural engagement, and learner interest. Fuzzy association rule mining uses fuzzy linguistic values and membership functions to provide more realistic results. Hence, an algorithm, EF-PCL2T, has been proposed to improve personalized Chinese language and literature teaching (PCL2T) using enhanced fuzzy (EF) Apriori association rule mining integrated with the genetic algorithm. Fuzzy Apriori association rule mining identified frequent itemsets with relevant learning patterns and produced applicable association rules from datasets with fuzzy or unclear information, capturing fluctuating itemset importance and providing a flexible representation of relationships to determine student preferences. From fuzzy-related data, a genetic algorithm optimizes skill sets and creates individualized lesson plans considering each student’s competency and preferences for adjusting to personalized teaching tactics. Testing shows that fuzzy enhancement association rule mining for the PCL2T model improves student retention, PET (personalized teaching efficiency), minimal support and confidence update with fuzzy rules, and student involvement compared to other state-of-the-art methods. Students agree that tailored Chinese language and literary instruction is possible. The improvement results show fuzzy rules with minimum confidence levels of 50% to 100%, highly correlated in this model, student retention ratio of 96%, improved assessment grade of various language skills by 40 marks, PTE analysis of 93%, and student involvement ratio of 97%.

A bstract We compute the next-to-leading order term in the scattering waveform of uncharged black holes in classical general relativity and of half-BPS black holes in N = 8 supergravity. We propose criteria, generalizing explicit calculations at next-to-leading order, for determining the terms in amplitudes that contribute to local observables. For general relativity, we construct the relevant classical integrand through generalized unitarity in two distinct ways, (1) in a heavy-particle effective theory and (2) in general relativity minimally-coupled to scalar fields. With a suitable prescription for the matter propagator in the former, we find agreement between the two methods, thus demonstrating the absence of interference of quantum and classically-singular contributions. The classical N = 8 integrand for massive scalar fields is constructed through dimensional reduction of the known five-point one-loop integrand. Our calculation exhibits novel features compared to conservative calculations and inclusive observables, such as the appearance of master integrals with intersecting matter lines and the appearance of a classical infrared divergence whose absence from classical observables requires a suitable definition of the retarded time.

A bstract By expanding the reduced Pfaffian in the tree level Cachazo-He-Yuan (CHY) integrands for Yang-Mills (YM) and nonlinear sigma model (NLSM), we can get the Bern-Carrasco-Johansson (BCJ) numerators in Del Duca-Dixon-Maltoni (DDM) form for arbitrary number of particles in any spacetime dimensions. In this work, we give a set of very straightforward graphic rules based on spanning trees for a direct evaluation of the BCJ numerators for YM and NLSM. Such rules can be derived from the Laplace expansion of the corresponding reduced Pfaffian. For YM, the each one of the ( n − 2)! DDM form BCJ numerators contains exactly ( n − 1)! terms, corresponding to the increasing trees with respect to the color order. For NLSM, the number of nonzero numerators is at most ( n − 2)! − ( n − 3)!, less than those of several previous constructions.

A bstract We generalize the color/kinematics duality of flat-space scattering amplitudes to the embedding space formulation of AdS boundary correlators. Kinematic numerators and propagators are replaced with differential operators acting on a scalar contact diagram that is the AdS generalization of the momentum conserving delta function of flat space scattering amplitudes. We show that color/kinematics duality implies differential relations among AdS boundary correlators that naturally generalize the flat space BCJ amplitude relations and verify them for the correlators of Yang-Mills theory and of the Nonlinear Sigma Model through four- and six-points, respectively. For the latter we also find representations of the four- and six-point correlator that manifest the duality. Possible double-copy procedures in AdS space are also discussed.

A bstract Using the Cachazo-He-Yuan (CHY) formalism, we prove a recursive expansion of tree level single trace Einstein-Yang-Mills (EYM) amplitudes with an arbitrary number of gluons and gravitons, which is valid for general spacetime dimensions and any helicity configurations. The recursion is written in terms of fewer-graviton EYM amplitudes and pure Yang-Mills (YM) amplitudes, which can be further carried out until we reach an expansion in terms of pure YM amplitudes in Kleiss-Kuijf (KK) basis. Our expansion then generates naturally a spanning tree structure rooted on gluons whose vertices are gravitons. We further propose a set of graph theoretical rules based on spanning trees that evaluate directly the pure YM expansion coefficients.

A bstract The AdS boundary correlators and their dual correlation functions of boundary operators have been the main dynamic observables of the holographic duality relating a bulk AdS theory and a boundary conformal field theory. We show that tree-level AdS boundary correlators for generic states can be expressed as nonlocal differential operators of a certain structure acting on contact Witten diagrams. We further write the boundary correlators in a form that is very similar to flat space amplitudes, with Mandelstam variables replaced by certain combinations of single-state conformal generators, prove that all tree-level AdS boundary correlators have a differential representation, and detail the conversion of such differential expressions to position space. We illustrate the construction through the computation of the boundary correlators of scalars coupled to gluons and gravitons; when converted to position space, they reproduce known results. Color-kinematics duality and BCJ relations can be defined in analogy with their flat space counterparts, and are respected by the scalar correlators with a gluon exchange. We also discuss potential approaches to the double copy and find that its direct generalization may require nontrivial extensions.

A bstract Kinematic numerators of Yang-Mills scattering amplitudes possess a rich Lie algebraic structure that suggest the existence of a hidden infinite-dimensional kinematic algebra. Explicitly realizing such a kinematic algebra is a longstanding open problem that only has had partial success for simple helicity sectors. In past work, we introduced a framework using tensor currents and fusion rules to generate BCJ numerators of a special subsector of NMHV amplitudes in Yang-Mills theory. Here we enlarge the scope and explicitly realize a kinematic algebra for all NMHV amplitudes. Master numerators are obtained directly from the algebraic rules and through commutators and kinematic Jacobi identities other numerators can be generated. Inspecting the output of the algebra, we conjecture a closed-form expression for the master BCJ numerator up to any multiplicity. We also introduce a new method, based on group algebra of the permutation group, to solve for the generalized gauge freedom of BCJ numerators. It uses the recently introduced binary BCJ relations to provide a complete set of NMHV kinematic numerators that consist of pure gauge .