arXiv subjects

Qinglin Yang

Publications and source records attributed to Qinglin Yang.

At least 37 records · Page 2Linked to original sources

arXiv2024

Differential equations and recursive solutions for cosmological amplitudes

Recently considerable efforts have been devoted to computing cosmological correlators and the corresponding wavefunction coefficients, as well as understanding their analytical structures. In this note, we revisit the computation of these ``cosmological amplitudes" associated with any tree or loop graph for conformal scalars with time-dependent interactions in the power-law FRW universe, directly in terms of iterated time integrals. We start by decomposing any such cosmological amplitude (for loop graph, the ``integrand" prior to loop integrations) as a linear combination of {\it basic time integrals}, one for each {\it directed graph}. We derive remarkably simple first-order differential equations involving such time integrals with edges ``contracted" one at a time, which can be solved recursively and the solution takes the form of Euler-Mellin integrals/generalized hypergeometric functions. By combining such equations, we then derive a complete system of differential equations for all time integrals needed for a given graph. Our method works for any graph: for a tree graph with $n$ nodes, this system can be transformed into the {\it canonical differential equations} of size $4^{n{-}1}$ quivalent to the graphic rules derived recently%so-called ``kinematic flow", and we also derive the system of differential equations for loop integrands {\it e.g.} of all-loop two-site graphs and one-loop $n$-gon graphs. Finally, we show how the differential equations truncate for the de Sitter (dS) case (in a way similar to differential equations for Feynman integrals truncate for integer dimensions), which immediately yields the complete symbol for the dS amplitude with interesting structures {\it e.g.} for $n$-site chains and $n$-gon cases.

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arXiv2024

Efficient Model Compression for Hierarchical Federated Learning

Federated learning (FL), as an emerging collaborative learning paradigm, has garnered significant attention due to its capacity to preserve privacy within distributed learning systems. In these systems, clients collaboratively train a unified neural network model using their local datasets and share model parameters rather than raw data, enhancing privacy. Predominantly, FL systems are designed for mobile and edge computing environments where training typically occurs over wireless networks. Consequently, as model sizes increase, the conventional FL frameworks increasingly consume substantial communication resources. To address this challenge and improve communication efficiency, this paper introduces a novel hierarchical FL framework that integrates the benefits of clustered FL and model compression. We present an adaptive clustering algorithm that identifies a core client and dynamically organizes clients into clusters. Furthermore, to enhance transmission efficiency, each core client implements a local aggregation with compression (LC aggregation) algorithm after collecting compressed models from other clients within the same cluster. Simulation results affirm that our proposed algorithms not only maintain comparable predictive accuracy but also significantly reduce energy consumption relative to existing FL mechanisms.

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arXiv2023

On symbology and differential equations of Feynman integrals from Schubert analysis

We take the first step in generalizing the so-called "Schubert analysis", originally proposed in twistor space for four-dimensional kinematics, to the study of symbol letters and more detailed information on canonical differential equations for Feynman integral families in general dimensions with general masses. The basic idea is to work in embedding space and compute possible cross-ratios built from (Lorentz products of) maximal cut solutions for all integrals in the family. We demonstrate the power of the method using the most general one-loop integrals, as well as various two-loop planar integral families (such as sunrise, double-triangle and double-box) in general dimensions. Not only can we obtain all symbol letters as cross-ratios from maximal-cut solutions, but we also reproduce entries in the canonical differential equations satisfied by a basis of dlog integrals.

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arXiv2023

MetaOpera: A Cross-Metaverse Interoperability Protocol

With the rapid evolution of metaverse technologies, numerous metaverse applications have arisen for various purposes and scenarios. This makes interoperability across metaverses becomes one of the fundamental technology enablers in the metaverse space. The aim of interoperability is to provide a seamless experience for users to interact with metaverses. However, the development of cross-metaverse interoperability is still in its initial stage in both industry and academia. In this paper, we review the state-of-the-art cross-metaverse interoperability schemes. These schemes are designed for specific interoperating scenarios and do not generalize for all types of metaverses. To this end, we propose MetaOpera, a generalized cross-metaverse interoperability protocol. By connecting to the MetaOpera, users, and objects in metaverses that rely on centralized servers or decentralized blockchains are able to interoperate with each other. We also develop a proof-of-concept implementation for MetaOpera, evaluate its performance, and compare it with a state-of-the-art cross-metaverse scheme based on Sidechains. Simulation results demonstrate that the size of cross-metaverse proof and the average time of cross-metaverse transactions using the proposed solution are respectively about eight times and three times smaller than the Sidechains scheme. This paper also suggests a number of open issues and challenges faced by cross-metaverse interoperability that may inspire future research.

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arXiv2022

Bootstrapping elliptic Feynman integrals using Schubert analysis

The symbol bootstrap has proven to be a powerful tool for calculating polylogarithmic Feynman integrals and scattering amplitudes. In this letter, we initiate the symbol bootstrap for elliptic Feynman integrals. Concretely, we bootstrap the symbol of the twelve-point two-loop double-box integral in four dimensions, which depends on nine dual-conformal cross ratios. We obtain the symbol alphabet, which contains 100 logarithms as well as 9 simple elliptic integrals, via a Schubert-type analysis, which we equally generalize to the elliptic case. In particular, we find a compact, one-line formula for the (2,2)-coproduct of the result.

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arXiv2022

Economic Systems in Metaverse: Basics, State of the Art, and Challenges

Economic systems play pivotal roles in the metaverse. However, we have not yet found an overview that systematically introduces economic systems for the metaverse. Therefore, we review the state-of-the-art solutions, architectures, and systems related to economic systems. When investigating those state-of-the-art studies, we keep two questions in our mind: (1) what is the framework of economic systems in the context of the metaverse, and (2) what activities would economic systems engage in the metaverse? This article aims to disclose insights into the economic systems that work for both the current and the future metaverse. To have a clear overview of the economic-system framework, we mainly discuss the connections among three fundamental elements in the metaverse, i.e., digital creation, digital assets, and the digital trading market. After that, we elaborate on each topic of the proposed economic-system framework. Those topics include incentive mechanisms, monetary systems, digital wallets, decentralized finance (DeFi) activities, and cross-platform interoperability for the metaverse. For each topic, we mainly discuss three questions: a) the rationale of this topic, b) why the metaverse needs this topic, and c) how this topic will evolve in the metaverse. Through this overview, we wish readers can better understand what economic systems the metaverse needs, and the insights behind the economic activities in the metaverse.

cs.CY↗

arXiv2022

The symbology of Feynman integrals from twistor geometries

We study the symbology of planar Feynman integrals in dimensional regularization by considering geometric configurations in momentum twistor space corresponding to their leading singularities (LS). Cutting propagators in momentum twistor space amounts to intersecting lines associated with loop and external dual momenta, including the special line associated with the point at infinity, which breaks dual conformal symmetry. We show that cross-ratios of intersection points on these lines, especially those on the infinity line, naturally produce symbol letters for Feynman integrals in $D=4-2ε$, which include and generalize their LS. At one loop, we obtain all symbol letters using intersection points from quadruple cuts for integrals up to pentagon kinematics with two massive corners, which agree perfectly with canonical differential equation (CDE) results. We then obtain all two-loop letters, for up to four-mass box and one-mass pentagon kinematics, by considering more intersections arising from two-loop cuts. Finally we comment on how cluster algebras appear from this construction, and importantly how we may extend the method to non-planar integrals.

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arXiv2022

A study of Feynman integrals with uniform transcendental weights and the symbology from dual conformal symmetry

Multi-loop Feynman integrals are key objects for the high-order correction computations in high energy phenomenology. These integrals with multiple scales, may have complicated symbol structures. We show that the dual conformal symmetry sheds light on the alphabet and symbol structures of multi-loop Feynman integrals. In this paper, first, as a cutting-edge example, we derive the two-loop four-external-mass Feynman integrals with uniform transcendental (UT) weights, based on the latest developments on UT integrals. Then we show that all the symbol letters can be nicely obtained from those of closely-related dual conformal integrals, by sending a dual point to infinity. Certain properties of the symbol such as first two entries and extended Steinmann relations are also studied from analogous properties of dual conformal integrals.

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arXiv2022

Fusing Blockchain and AI with Metaverse: A Survey

Metaverse as the latest buzzword has attracted great attention from both industry and academia. Metaverse seamlessly integrates the real world with the virtual world and allows avatars to carry out rich activities including creation, display, entertainment, social networking, and trading. Thus, it is promising to build an exciting digital world and to transform a better physical world through the exploration of the metaverse. In this survey, we dive into the metaverse by discussing how Blockchain and Artificial Intelligence (AI) fuse with it through investigating the state-of-the-art studies across the metaverse components, digital currencies, AI applications in the virtual world, and blockchain-empowered technologies. Further exploitation and interdisciplinary research on the fusion of AI and Blockchain towards metaverse will definitely require collaboration from both academia and industries. We wish that our survey can help researchers, engineers, and educators build an open, fair, and rational future metaverse.

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arXiv2022

Schubert Problems, Positivity and Symbol Letters

We propose a geometrical approach to generate symbol letters of amplitudes/integrals in planar $\mathcal{N}=4$ Super Yang-Mills theory, known as {\it Schubert problems}. Beginning with one-loop integrals, we find that intersections of lines in momentum twistor space are always ordered on a given line, once the external kinematics $\mathbf{Z}$ is in the positive region $G_+(4,n)$. Remarkably, cross-ratios of these ordered intersections on a line, which are guaranteed to be positive now, nicely coincide with symbol letters of corresponding Feynman integrals, whose positivity is then concluded directly from such geometrical configurations. In particular, we reproduce from this approach the $18$ multiplicative independent algebraic letters for $n=8$ amplitudes up to three loops. Finally, we generalize the discussion to two-loop Schubert problems and, again from ordered points on a line, generate a new kind of algebraic letters which mix two distinct square roots together. They have been found recently in the alphabet of two-loop double-box integral with $n\geq9$, and they are expected to appear in amplitudes at $k+\ell\geq4$.

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arXiv2021

WebFed: Cross-platform Federated Learning Framework Based on Web Browser with Local Differential Privacy

For data isolated islands and privacy issues, federated learning has been extensively invoking much interest since it allows clients to collaborate on training a global model using their local data without sharing any with a third party. However, the existing federated learning frameworks always need sophisticated condition configurations (e.g., sophisticated driver configuration of standalone graphics card like NVIDIA, compile environment) that bring much inconvenience for large-scale development and deployment. To facilitate the deployment of federated learning and the implementation of related applications, we innovatively propose WebFed, a novel browser-based federated learning framework that takes advantage of the browser's features (e.g., Cross-platform, JavaScript Programming Features) and enhances the privacy protection via local differential privacy mechanism. Finally, We conduct experiments on heterogeneous devices to evaluate the performance of the proposed WebFed framework.

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arXiv2021

Bootstrapping octagons in reduced kinematics from $A_2$ cluster algebras

Multi-loop scattering amplitudes/null polygonal Wilson loops in ${\mathcal N}=4$ super-Yang-Mills are known to simplify significantly in reduced kinematics, where external legs/edges lie in an $1+1$ dimensional subspace of Minkowski spacetime (or boundary of the $\rm AdS_3$ subspace). Since the edges of a $2n$-gon with even and odd labels go along two different null directions, the kinematics is reduced to two copies of $G(2,n)/T \sim A_{n{-}3}$. In the simplest octagon case, we conjecture that all loop amplitudes and Feynman integrals are given in terms of two overlapping $A_2$ functions (a special case of two-dimensional harmonic polylogarithms): in addition to the letters $v, 1+v, w, 1+w$ of $A_1 \times A_1$, there are two letters $v-w, 1- v w$ mixing the two sectors but they never appear together in the same term; these are the reduced version of four-mass-box algebraic letters. Evidence supporting our conjecture includes all known octagon amplitudes as well as new computations of multi-loop integrals in reduced kinematics. By leveraging this alphabet and conditions on first and last entries, we initiate a bootstrap program in reduced kinematics: within the remarkably simple space of overlapping $A_2$ functions, we easily obtain octagon amplitudes up to two-loop NMHV and three-loop MHV. We also briefly comment on the generalization to $2n$-gons in terms of $A_2$ functions and beyond.

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arXiv2021

Comments on all-loop constraints for scattering amplitudes and Feynman integrals

We comment on the status of "Steinmann-like" constraints, i.e. all-loop constraints on consecutive entries of the symbol of scattering amplitudes and Feynman integrals in planar ${\cal N}=4$ super-Yang-Mills, which have been crucial for the recent progress of the bootstrap program. Based on physical discontinuities and Steinmann relations, we first summarize all possible double discontinuities (or first-two-entries) for (the symbol of) amplitudes and integrals in terms of dilogarithms, generalizing well-known results for $n=6,7$ to all multiplicities. As our main result, we find that extended-Steinmann relations hold for all finite integrals that we have checked, including various ladder integrals, generic double-pentagon integrals, as well as finite components of two-loop NMHV amplitudes for any $n$; with suitable normalization such as minimal subtraction, they hold for $n=8$ MHV amplitudes at three loops. We find interesting cancellation between contributions from rational and algebraic letters, and for the former we have also tested cluster-adjacency conditions using the so-called Sklyanin brackets. Finally, we propose a list of possible last-two-entries for $n$-point MHV amplitudes derived from $\bar{Q}$ equations, which can be used to reduce the space of functions for higher-point MHV amplitudes.

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arXiv2021

Truncated cluster algebras and Feynman integrals with algebraic letters

We propose that the symbol alphabet for classes of planar, dual-conformal-invariant Feynman integrals can be obtained as truncated cluster algebras purely from their kinematics, which correspond to boundaries of (compactifications of) $G_+(4,n)/T$ for the $n$-particle massless kinematics. For one-, two-, three-mass-easy hexagon kinematics with $n=7,8,9$, we find finite cluster algebras $D_4$, $D_5$ and $D_6$ respectively, in accordance with previous result on alphabets of these integrals. As the main example, we consider hexagon kinematics with two massive corners on opposite sides and find a truncated affine $D_4$ cluster algebra whose polytopal realization is a co-dimension 4 boundary of that of $G_+(4,8)/T$ with 39 facets; the normal vectors for 38 of them correspond to g-vectors and the remaining one gives a limit ray, which yields an alphabet of $38$ rational letters and $5$ algebraic ones with the unique four-mass-box square root. We construct the space of integrable symbols with this alphabet and physical first-entry conditions, whose dimension can be reduced using conditions from a truncated version of cluster adjacency. Already at weight $4$, by imposing last-entry conditions inspired by the $n=8$ double-pentagon integral, we are able to uniquely determine an integrable symbol that gives the algebraic part of the most generic double-pentagon integral. Finally, we locate in the space the $n=8$ double-pentagon ladder integrals up to four loops using differential equations derived from Wilson-loop $d\log$ forms, and we find a remarkable pattern about the appearance of algebraic letters.

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arXiv2021

Notes on cluster algebras and some all-loop Feynman integrals

We study cluster algebras for some all-loop Feynman integrals, including box-ladder, penta-box-ladder, and (seven-point) double-penta-ladder integrals. In addition to the well-known box ladder whose symbol alphabet is $D_2\simeq A_1^2$, we show that penta-box ladder has an alphabet of $D_3\simeq A_3$ and provide strong evidence that the alphabet of double-penta ladder can be identified with a $D_4$ cluster algebra. We relate the symbol letters to the ${\bf u}$ variables of cluster configuration space, which provide a gauge-invariant description of the cluster algebra, and we find various sub-algebras associated with limits of the integrals. We comment on constraints similar to extended-Steinmann relations or cluster adjacency conditions on cluster function spaces. Our study of the symbol and alphabet is based on the recently proposed Wilson-loop ${\rm d}\log$ representation, which allows us to predict higher-loop alphabet recursively; by applying such recursions to six-dimensional hexagon integrals, we also find $D_5$ and $D_6$ cluster functions for the two-mass-easy and three-mass-easy case, respectively.

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arXiv2021

The Wilson-loop $d \log$ representation for Feynman integrals

We introduce and study the Wilson-loop ${\rm d}\log$ representation of certain Feynman integrals for scattering amplitudes in ${\cal N}=4$ SYM and beyond, which makes their evaluation completely straightforward. Such a representation was motivated by the dual Wilson loop picture, and it can also be derived by partial Feynman parametrization of loop integrals. We first introduce it for the simplest one-loop examples, the chiral pentagon in four dimensions and the three-mass-easy hexagon in six dimensions, which are represented by two- and three-fold ${\rm d}\log$ integrals that are nicely related to each other. For multi-loop examples, we write the $L$-loop generalized penta-ladders as $2(L{-}1)$-fold ${\rm d}\log$ integrals of some one-loop integral, so that once the latter is known, the integration can be performed in a systematic way. In particular, we write the eight-point penta-ladder as a $2L$-fold ${\rm d}\log$ integral whose symbol can be computed without performing the integration; we also obtain the last entries and the symbol alphabet of these integrals. Similarly we compute and study the symbol of the seven-point double-penta-ladder, which is represented by a $2(L{-}1)$-fold integral of a hexagon; the latter can be written as a two-fold ${\rm d}\log$ integral plus a boundary term. We comment on the relation of our representation to differential equations and resum the ladders by solving certain integral equations.

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arXiv2021

Feynman Integrals and Scattering Amplitudes from Wilson Loops

We study Feynman integrals and scattering amplitudes in ${\cal N}=4$ super-Yang-Mills by exploiting the duality with null polygonal Wilson loops. Certain Feynman integrals, including one-loop and two-loop chiral pentagons, are given by Feynman diagrams of a supersymmetric Wilson loop, where one can perform loop integrations and be left with simple integrals along edges. As the main application, we compute analytically for the first time, the symbol of the generic ($n\geq 12$) double pentagon, which gives two-loop MHV amplitudes and components of NMHV amplitudes to all multiplicities. We represent the double pentagon as a two-fold $\mathrm{d} \log$ integral of a one-loop hexagon, and the non-trivial part of the integration lies at rationalizing square roots contained in the latter. We obtain a remarkably compact "algebraic words" which contain $6$ algebraic letters for each of the $16$ square roots, and they all nicely cancel in combinations for MHV amplitudes and NMHV components which are free of square roots. In addition to $96$ algebraic letters, the alphabet consists of $152$ dual conformal invariant combinations of rational letters.

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arXiv2020

Triangulations for ABHY Polytopes and Recursions for Tree and Loop Amplitudes

In this note we make a field-theoretical derivation of a series of new recursion relations by a one-parameter deformation of kinematic variables for tree and one-loop amplitudes of bi-adjoint $ϕ^3$ theory. Tree amplitudes are given by canonical forms/functions of associahedra realized in kinematic space by Arkani-Hamed, Bai, He and Yan (ABHY); the construction has been extended to generalized associahedra, where type $\mathcal{B}$/$\mathcal{C}$ polytopes compute tadpole diagrams and type $\mathcal{D}$ polytopes compute one-loop planar $ϕ^3$ amplitudes. The new recursions are natural generalizations of the formula we found in 1810.08508, and are shown to work for all "C-independent" ABHY polytopes. Geometrically, the formula indicates triangulation of the generalized associahedron by projecting the whole polytope onto its boundary determined by the deformation. When projecting onto one facet, our recursion gives, e.g. "soft-limit triangulation" and "forward-limit triangulation" for tree and one-loop level. But we also find a lot of new formulae from our recursion relation, by projecting onto lower dimensional facets.

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