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Xing Gao

Publications and source records attributed to Xing Gao.

At least 127 records · Page 7Linked to original sources
arXiv2022

Photometric and spectroscopic studies of the long period low mass ratio deep contact binary KN Per

The photometric analysis and spectroscopic study of the long period low mass ratio deep contact binary KN Per were executed. The light curves of BV(RI)$_c$-band were from the Ningbo Bureau of Education and Xinjiang Observatory Telescope (NEXT) at the Xingming Observatory. Through the analysis of Wilson-Devinney (W-D) program, KN Per was found as an A-type low mass ratio deep contact binary (q=0.236, f=53.4\%). A cool spot applied on the primary component was introduced to explain the unequal maxima of the light curve. Based on the O-C analysis, we found that the rate of the increasing orbital period is $\dot{P}$ = 5.12 $\pm$ (0.30) $\times$ 10$^{-7}$ d/yr, meaning the mass transfer from the secondary component to the primary one. By analyzing the spectroscopic data, we detected chromospheric activity emission line indicators, which is corresponding to the light-curve analysis. 71 long period (P $>$ 0.5 days) contact binaries including our target were collected. The evolutionary states of all collected stars were investigated by the illustrations of mass-radius, mass-luminosity, and log M$_{T}$ - log J$_{o}$. The relations of some physical parameters were also determined. With the instability parameters of KN Per, we determined that it is a stable contact binary system at present.

astro-ph.SR↗
arXiv2022

Incorporating Causal Analysis into Diversified and Logical Response Generation

Although the Conditional Variational AutoEncoder (CVAE) model can generate more diversified responses than the traditional Seq2Seq model, the responses often have low relevance with the input words or are illogical with the question. A causal analysis is carried out to study the reasons behind, and a methodology of searching for the mediators and mitigating the confounding bias in dialogues is provided. Specifically, we propose to predict the mediators to preserve relevant information and auto-regressively incorporate the mediators into generating process. Besides, a dynamic topic graph guided conditional variational autoencoder (TGG-CVAE) model is utilized to complement the semantic space and reduce the confounding bias in responses. Extensive experiments demonstrate that the proposed model is able to generate both relevant and informative responses, and outperforms the state-of-the-art in terms of automatic metrics and human evaluations.

cs.CL↗
arXiv2022

The First Photometric and Orbital Period Investigation of an Extremely Low Mass Ratio Contact Binary with a Sudden Period Change, TYC 4002-2628-1

Photometric observations for the totally eclipsing binary system TYC 4002-2628-1, were obtained between November 2020 and November 2021. To determine the stellar atmospheric parameters, a spectral image was taken with the 2.16 m telescope at National Astronomical Observatory of China (NAOC). TYC 4002-2628-1 is a low-amplitude (about 0.15 mag for $V$ band), short-period (0.3670495 d), contact eclipsing binary with a total secondary eclipse. Intrinsic light curve variations and the reversal of the O'Connell effect are detected in the light curves, which may be due to spot activity. Based on the photometric solutions derived from the multi-band time series light curves, TYC 4002-2628-1 is an extremely low mass ratio contact binary with a mass ratio of $q\sim$ 0.0482 and a fill-out factor of $f\sim5\%$. By analyzing the $O-C$ variations, we find that its orbital period remains unchanged when BJD < 2458321 . Then the orbital period changed suddenly around BJD 2458743 and has an increasing rate of $dP/dt=1.62\times{10^{-5}}day\cdot yr^{-1}=140$ $second\cdot century^{-1}$ . If confirmed, TYC 4002-2628-1 would be the contact binary with the highest orbital period increasing rate so far. By investigating the ratio of orbital angular momentum to the spin angular momentum ( $J_{orb}$/$J_{spin}$ $<3$) , the instability mass ratio ($q_{inst}/q=1.84$) and the instability separation ($A_{inst}/A=1.35$), TYC 4002-2628-1 can be regarded as a merger candidate.

astro-ph.SR↗
arXiv2022

Generating Persuasive Responses to Customer Reviews with Multi-Source Prior Knowledge in E-commerce

Customer reviews usually contain much information about one's online shopping experience. While positive reviews are beneficial to the stores, negative ones will largely influence consumers' decision and may lead to a decline in sales. Therefore, it is of vital importance to carefully and persuasively reply to each negative review and minimize its disadvantageous effect. Recent studies consider leveraging generation models to help the sellers respond. However, this problem is not well-addressed as the reviews may contain multiple aspects of issues which should be resolved accordingly and persuasively. In this work, we propose a Multi-Source Multi-Aspect Attentive Generation model for persuasive response generation. Various sources of information are appropriately obtained and leveraged by the proposed model for generating more informative and persuasive responses. A multi-aspect attentive network is proposed to automatically attend to different aspects in a review and ensure most of the issues are tackled. Extensive experiments on two real-world datasets, demonstrate that our approach outperforms the state-of-the-art methods and online tests prove that our deployed system significantly enhances the efficiency of the stores' dealing with negative reviews.

cs.CL↗
arXiv2022

Free $Ω$-Rota-Baxter systems and Gröbner-Shirshov bases

In this paper, we propose the concept of an $Ω$-Rota-Baxter system, which is a generalization of a Rota-Baxter system and an $Ω$-Rota-Baxter algebra of weight zero. In the framework of operated algebras, we obtain a linear basis of a free $Ω$-Rota-Baxter system for an extended diassociative semigroup $Ω$, in terms of bracketed words and the method of Gröbner-Shirshov bases. As applications, we introduce the concepts of Rota-Baxter system family algebras and matching Rota-Baxter systems as special cases of $Ω$-Rota-Baxter systems, and construct their free objects. Meanwhile, free $Ω$-Rota-Baxter algebras of weight zero, free Rota-Baxter systems, free Rota-Baxter family algebras and free matching Rota-Baxter algebras are reconstructed via new method.

math.RA↗
arXiv2022

Operated groups, differential groups and Rota-Baxter groups with an emphasis on the free objects

Groups with various types of operators, in particular the recently introduced Rota-Baxter groups, have generated renowned interest with close connections to numerical integrals, Yang-Baxter equation, integrable systems and post-Hopf algebras. This paper gives the general notion of operated groups and provides explicit constructions of free operated groups, free differential groups and free Rota-Baxter groups.

math.GR↗
arXiv2022

Extremely low mass ratio contact binaries -- I. the first photometric and spectroscopic investigations of ten systems

The photometric and spectroscopic investigations of ten contact binaries were presented for the first time. It is discovered that the mass ratios of all the ten targets are smaller than 0.15, they are extremely low mass ratio contact binaries. Seven of them are deep contact binaries, two are medium contact binaries, while only one is a shallow contact system. Five of them show O'Connell effect, and a dark spot on one of the two components can lead to a good fit of the asymmetric light curves. The orbital period studies of the ten binaries reveal that they all exhibit long-term period changes, six of them are increasing, while the others are shrinking. The LAMOST spectra were analyzed by the spectral subtraction method, and all the ten targets exhibit excess emissions in the H$_α$ line, indicating chromospheric activity. The evolutionary states of the two components of the ten binaries were studied, and it is found that their evolutionary states are identical to those of the other contact binaries. Based on the study of the relation between orbital angular momentum and total mass, we discovered the ten systems may be at the late evolutionary stage of a contact binary. The initial masses of the two components and the ages of them were obtained. By calculating the instability parameters, we found that the ten contact binaries are relatively stable at present.

astro-ph.SR↗
arXiv2022

MGIMN: Multi-Grained Interactive Matching Network for Few-shot Text Classification

Text classification struggles to generalize to unseen classes with very few labeled text instances per class. In such a few-shot learning (FSL) setting, metric-based meta-learning approaches have shown promising results. Previous studies mainly aim to derive a prototype representation for each class. However, they neglect that it is challenging-yet-unnecessary to construct a compact representation which expresses the entire meaning for each class. They also ignore the importance to capture the inter-dependency between query and the support set for few-shot text classification. To deal with these issues, we propose a meta-learning based method MGIMN which performs instance-wise comparison followed by aggregation to generate class-wise matching vectors instead of prototype learning. The key of instance-wise comparison is the interactive matching within the class-specific context and episode-specific context. Extensive experiments demonstrate that the proposed method significantly outperforms the existing state-of-the-art approaches, under both the standard FSL and generalized FSL settings.

cs.CL↗
arXiv2022

A Unified Analysis of Dynamic Interactive Learning

In this paper we investigate the problem of learning evolving concepts over a combinatorial structure. Previous work by Emamjomeh-Zadeh et al. [2020] introduced dynamics into interactive learning as a way to model non-static user preferences in clustering problems or recommender systems. We provide many useful contributions to this problem. First, we give a framework that captures both of the models analyzed by [Emamjomeh-Zadeh et al., 2020], which allows us to study any type of concept evolution and matches the same query complexity bounds and running time guarantees of the previous models. Using this general model we solve the open problem of closing the gap between the upper and lower bounds on query complexity. Finally, we study an efficient algorithm where the learner simply follows the feedback at each round, and we provide mistake bounds for low diameter graphs such as cliques, stars, and general o(log n) diameter graphs by using a Markov Chain model.

cs.LG↗
arXiv2022

New operated polynomial identities and Gröbner-Shirshov bases

Quite recently, Bremner et al. introduced a new approach to Rota's Classification Problem and classified some (new) operated polynomial identities. In this paper, we prove that all operated polynomial identities classified by Bremner et al. are Gröbner-Shirshov.

math.RA↗
arXiv2022

Weighted infinitesimal bialgebras

As an algebraic meaning of the nonhomogenous associative Yang-Baxter equation, weighted infinitesimal bialgebras play an important role in mathematics and mathematical physics. In this paper, we introduce the concept of weighted infinitesimal Hopf modules and show that any module carries a natural structure of weighted infinitesimal unitary Hopf module over a weighted quasitriangular infinitesimal unitary bialgebra. We decorate planar rooted forests in a new way, and prove that the space of rooted forests, together with a coproduct and a family of grafting operations, is the free $Ω$-cocycle infinitesimal unitary bialgebra of weight zero on a set. A combinatorial description of the coproduct is given. As applications, we obtain the initial object in the category of cocycle infinitesimal unitary bialgebras on undecorated planar rooted forests, which is the object studied in the (noncommutative) Connes-Kreimer Hopf algebra. Finally, we derive two pre-Lie algebras from an arbitrary weighted infinitesimal bialgebra and weighted commutative infinitesimal bialgebra, respectively. The second construction generalizes the Gel'fand-Dorfman Theorem on Novikov algebras.

math.RA↗
arXiv2022

Operator identities on Lie algebras, rewriting systems and Gröbner-Shirshov bases

Motivated by the pivotal role played by linear operators, many years ago Rota proposed to determine algebraic operator identities satisfied by linear operators on associative algebras, later called Rota's program on algebraic operators. Recent progresses on this program have been achieved in the contexts of operated algebra, rewriting systems and Groebner-Shirshov bases. These developments also suggest that Rota's insight can be applied to determine operator identities on Lie algebras, and thus to put the various linear operators on Lie algebras in a uniform perspective. This paper carries out this approach, utilizing operated polynomial Lie algebras spanned by non-associative Lyndon-Shirshov bracketed words. The Lie algebra analog of Rota's program was formulated in terms convergent rewriting systems and equivalently in terms of Groebner-Shirshov bases. This Lie algebra analog is shown to be compatible with Rota's program for associative algebras. As applications, a classification of differential type operators and Rota-Baxter operators are presented.

math.QA↗
arXiv2021

Non-Markovian Stochastic Schrödinger Equation: Matrix Product State Approach to the Hierarchy of Pure States

We derive a stochastic hierarchy of matrix product states (HOMPS) for non-Markovian dynamics in open quantum system at finite temperature, which is numerically exact and efficient. HOMPS is obtained from the recently developed stochastic hierarchy of pure states (HOPS) by expressing HOPS in terms of formal creation and annihilation operators. The resulting stochastic first order differential equation is then formulated in terms of matrix product states and matrix product operators. In this way the exponential complexity of HOPS can be reduced to scale polynomial with the number of particles. The validity and efficiency of HOMPS is demonstrated for the spin-boson model and long chains where each site is coupled to a structured, strongly non-Markovian environment.

quant-ph↗
arXiv2021

Rota's program on algebraic operators, rewriting systems and Gröbner-Shirshov bases

Many years ago, Rota proposed a program on determining algebraic identities that can be satisfied by linear operators. After an extended period of dormant, progress on this program picked up speed in recent years, thanks to perspectives from operated algebras and Gröbner-Shirshov bases. These advances were achieved in a series of papers from special cases to more general situations. These perspectives also indicate that Rota's insight can be manifested very broadly, for other algebraic structures such as Lie algebras, and further in the context of operads. This paper gives a survey on the motivation, early developments and recent advances on Rota's program, for linear operators on associative algebras and Lie algebras. Emphasis will be given to the applications of rewriting systems and Gröbner-Shirshov bases. Problems, old and new, are proposed throughout the paper to prompt further developments on Rota's program.

math.RA↗
arXiv2021

Operator forms of nonhomogeneous associative classical Yang-Baxter equation

This paper studies operator forms of the nonhomogeneous associative classical Yang-Baxter equation (nhacYBe), extending and generalizing such studies for the classical Yang-Baxter equation and associative Yang-Baxter equation that can be tracked back to the works of Semonov-Tian-Shansky and Kupershmidt on Rota-Baxter Lie algebras and $\mathcal{O}$-operators. In general, solutions of the nhacYBe are characterized in terms of generalized $\mathcal{O}$-operators. The characterization can be given by the classical $\mathcal{O}$-operators precisely when the solutions satisfy an invariant condition. When the invariant condition is compatible with a Frobenius algebra, such solutions have close relationships with Rota-Baxter operators on the Frobenius algebra. In general, solutions of the nhacYBe can be produced from Rota-Baxter operators, and then from $\mathcal{O}$-operators when the solutions are taken in semi-direct product algebras. In the other direction, Rota-Baxter operators can be obtained from solutions of the nhacYBe in unitizations of algebras. Finally a classifications of solutions of the nhacYBe satisfying the mentioned invariant condition in all unital complex algebras of dimensions two and three are obtained. All these solutions are shown to come from Rota-Baxter operators.

math.QA↗
arXiv2021

Hopf algebra of multi-decorated rooted forests, free matching Rota-Baxter algebras and Gröbner-Shirshov bases

Recent advances in stochastic PDEs, Hopf algebras of typed trees and integral equations have inspired the study of algebraic structures with replicating operations. To understand their algebraic and combinatorial nature, we first use rooted forests with multiple decoration sets to construct free Hopf algebras with multiple Hochschild 1-cocycle conditions. Applying the universal property of the underlying operated algebras and the method of Gröbner-Shirshov bases, we then construct free objects in the category of matching Rota-Baxter algebras which is a generalization of Rota-Baxter algebras to allow multiple Rota-Baxter operators. Finally the free matching Rota-Baxter algebras are equipped with a cocycle Hopf algebra structure.

math.RA↗
arXiv2021

Message Passing in Graph Convolution Networks via Adaptive Filter Banks

Graph convolution networks, like message passing graph convolution networks (MPGCNs), have been a powerful tool in representation learning of networked data. However, when data is heterogeneous, most architectures are limited as they employ a single strategy to handle multi-channel graph signals and they typically focus on low-frequency information. In this paper, we present a novel graph convolution operator, termed BankGCN, which keeps benefits of message passing models, but extends their capabilities beyond `low-pass' features. It decomposes multi-channel signals on graphs into subspaces and handles particular information in each subspace with an adapted filter. The filters of all subspaces have different frequency responses and together form a filter bank. Furthermore, each filter in the spectral domain corresponds to a message passing scheme, and diverse schemes are implemented via the filter bank. Importantly, the filter bank and the signal decomposition are jointly learned to adapt to the spectral characteristics of data and to target applications. Furthermore, this is implemented almost without extra parameters in comparison with most existing MPGCNs. Experimental results show that the proposed convolution operator permits to achieve excellent performance in graph classification on a collection of benchmark graph datasets.

cs.LG↗