arXiv subjects

Xing Gao

Publications and source records attributed to Xing Gao.

At least 91 records · Page 5Linked to original sources

arXiv2024

Free Novikov algebras and the Hopf algebra of decorated multi-indices

We propose a combinatorial formula for the coproduct in a Hopf algebra of decorated multi-indices that recently appeared in the literature, which can be briefly described as the graded dual of the enveloping algebra of the free Novikov algebra generated by the set of decorations. Similarly to what happens for the Hopf algebra of rooted forests, the formula can be written in terms of admissible cuts. We also prove a combinatorial formula for the extraction-contraction coproduct for undecorated multi-indices, in terms of a suitable notion of covering subforest.

math.CO↗

arXiv2024

Multi-quasisymmetric functions with semigroup exponents, Hopf algebras and Rota-Baxter algebras

Many years ago, G.-C.~Rota discovered a close connection between symmetric functions and Rota-Baxter algebras, and proposed to study generalizations of symmetric functions in the framework of Rota-Baxter algebras. Guided by this proposal, quasisymmetric functions from weak composition (instead of just compositions) were obtained from free Rota-Baxter algebras on one generator. This paper aims to generalize this approach to free Rota-Baxter algebras on multiple generators in order to obtain further generalizations of quasisymmetric functions. For this purpose and also for its independent interest, the space $\mathrm{MQSym}$ of quasisymmetric functions on multiple sequences of variables is defined, generalizing quasisymmetric functions and diagonally quasisymmetric functions of Aval, Bergeron and Bergeron. Linear bases of such multi-quasisymmetric functions are given by monomial multi-quasisymmetric functions and fundamental multi-quasisymmetric functions, the latter recover the fundamental $G^m$-quasisymmetric functions of Aval and Chapoton. Next introduced is the even more general notion of multi-quasisymmetric functions $\mathrm{MQSym}^E$ with exponents in a semigroup $E$, which also generalizes the quasisymmetric functions with semigroup exponents in a recent work. Through this approach, a natural Hopf algebraic structure is obtained on $\mathrm{MQSym}^E$. Finally, in support of Rota's proposal, the free commutative unitary Rota-Baxter algebra on a finite set is shown to be isomorphic to a scalar extension of $\mathrm{MQSym}^E$, a fact which in turn equips the free Rota-Baxter algebra with a Hopf algebra structure.

math.CO↗

arXiv2024

Photometric and Spectroscopic analysis of eight totally eclipsing contact binaries with small mass ratios

This paper selected eight totally eclipsing contact binaries for photometric and spectroscopic studies, spectral data were analyzed by ULySS, and photometric data were analyzed using PHOEBE through MCMC sampling. We used two methods to calculate the initial values for running MCMC: one method is a new approach proposed by ourselves to model light curves without spots, while the other method is the genetic algorithm (GA) which can determine physical parameters with spot. Due to the results, these eight targets are all small mass ratio contact binary stars with a mass ratio below 0.25. There are four systems exhibiting O'Connell effect. By adding a dark spot on the primary component, the ideal fitting can be obtained. Meanwhile, it was found that two systems are shallow contact binaries, while the remaining six are moderate contact binaries. An O-C analysis of the eight eclipsing binary stars revealed that seven of them exhibit long-term changes. Four of them display a long-term decreasing trend, while the other three show a long-term increasing trend, and two targets exhibit periodic variations. The decrease in period may be caused by the transfer of matter from the more massive component to the less massive component, while the increase in period may be caused by the transfer of matter from the less massive component to the more massive component. The absolute physical parameters, orbital angular momentum, initial masses, and ages of these eight systems were calculated. Additionally, their mass-luminosity and mass-radius distributions were analyzed.

astro-ph.SR↗

arXiv2024

Compatible structures of operads by polarization, their Koszul duality and Manin products

Algebraic structures with multiple copies of a given type of operations interrelated by various compatibility conditions have long being studied in mathematics and mathematical physics. They are broadly referred as linearly compatible, matching, and totally compatible structures. This paper gives a unified approach to these structures in the context of operads. We first generalize the process of polarization for polynomials in invariant theory to the one for operads, leading to the general notion of linearly compatible operads. Refining the polarization by partitioning it into foliations, we obtain a notion of matching operads consolidating those appeared recently from applications of regularity structures, and Volterra integral equations. Distinguished among them is the leveled matching compatibility, which is unique with respect to a fix ordering of the vertices in tree monomials. Equating all matching compatibilities of a given operad leads to the totally compatible operad of this operad. For unary/binary quadratic operads, the linear compatibility and the total compatibility are in Koszul dual to each other, and there is a Koszul self-duality among the matching compatibilities. In particular, the leveled matching compatibility is Koszul self-dual. For binary quadratic operads, these three compatible operads can also be obtained by taking Manin black and white products. For some finitely generated binary quadratic operad, Koszulity is preserved under taking the compatibilities.

math.CT↗

arXiv2024

Rota-Baxter operators, differential operators, pre- and Novikov structures on groups and Lie algebras

Rota-Baxter operators on various structures have found important applications in diverse areas, from renormalization of quantum field theory to Yang-Baxter equations. Relative Rota-Baxter operators on Lie algebras are closely related to pre-Lie algebras and post-Lie algebras. Some of their group counterparts have been introduced to study post-groups, skew left braces and set-theoretic solutions of Yang-Baxter equations, but searching suitable notions of relative Rota-Baxter operators on groups with weight zero and pre-groups has been challenging and has been the focus of recent studies, by provisionally imposing an abelian condition. Arising from the works of Balinsky-Novikov and Gelfand-Dorfman, Novikov algebras and their constructions from differential commutative algebras have led to broad applications. Finding their suitable counterparts for groups and Lie algebras has also attracted quite much recent attention. This paper uses one-sided-inverse pairs of maps to give a perturbative approach to a general notion of relative Rota-Baxter operators and differential operators on a group and a Lie algebra with limit-weight. With the extra condition of limit-abelianess on the group or Lie algebra, we give an interpretation of relative Rota-Baxter and differential operators with weight zero. These operators motivate us to define pre-groups and Novikov groups respectively as the induced structures. The tangent maps of these operators are shown to give Rota-Baxter and differential operators with weight zero on Lie algebras. The tangent spaces of the pre-Lie and Novikov Lie groups are pre-Lie algebras and Novikov Lie algebras, fulfilling the expected property. Furthermore, limit-weight relative Rota-Baxter operators on groups give rise to skew left braces and then set-theoretic solutions of the Yang-Baxter equation.

math.QA↗

arXiv2024

SocialBench: Sociality Evaluation of Role-Playing Conversational Agents

Large language models (LLMs) have advanced the development of various AI conversational agents, including role-playing conversational agents that mimic diverse characters and human behaviors. While prior research has predominantly focused on enhancing the conversational capability, role-specific knowledge, and stylistic attributes of these agents, there has been a noticeable gap in assessing their social intelligence. In this paper, we introduce SocialBench, the first benchmark designed to systematically evaluate the sociality of role-playing conversational agents at both individual and group levels of social interactions. The benchmark is constructed from a variety of sources and covers a wide range of 500 characters and over 6,000 question prompts and 30,800 multi-turn role-playing utterances. We conduct comprehensive evaluations on this benchmark using mainstream open-source and closed-source LLMs. We find that agents excelling in individual level does not imply their proficiency in group level. Moreover, the behavior of individuals may drift as a result of the influence exerted by other agents within the group. Experimental results on SocialBench confirm its significance as a testbed for assessing the social interaction of role-playing conversational agents. The benchmark is publicly accessible at https://github.com/X-PLUG/SocialBench.

cs.CL↗

arXiv2024

Caching Aided Multi-Tenant Serverless Computing

One key to enabling high-performance serverless computing is to mitigate cold-starts. Current solutions utilize a warm pool to keep function alive: a warm-start can be analogous to a CPU cache-hit. However, modern cache has multiple hierarchies and the last-level cache is shared among cores, whereas the warm pool is limited to a single tenant for security concerns. Also, the warm pool keep-alive policy can be further optimized using cache replacement algorithms. In this paper, we borrow practical optimizations from caching, and design FaasCamp, a caching-aided multi-tenant serverless computing framework. FaasCamp extends the single-tier warm pool into multi-tiers, with a reclaim pool introduced enabling secure function instance sharing among tenants. Also, FaasCamp leverages machine learning to approximate the optimal cache replacement policy to improve the warm rate. We have implemented a prototype and conducted extensive experiments under multiple scenarios. The results show that FaasCamp can outperform existing platforms with minimal overhead.

cs.DC↗

arXiv2024

Free weighted differential ($q$-tri)dendriform algebras

In the present paper, we propose the concepts of weighted differential ($q$-tri)dendriform algebras and give some basic properties of them. The corresponding free objects are constructed, in both the commutative and noncommutative contexts.

math.RA↗

arXiv2024

Game Theory in Distributed Systems Security: Foundations, Challenges, and Future Directions

Many of our critical infrastructure systems and personal computing systems have a distributed computing systems structure. The incentives to attack them have been growing rapidly as has their attack surface due to increasing levels of connectedness. Therefore, we feel it is time to bring in rigorous reasoning to secure such systems. The distributed system security and the game theory technical communities can come together to effectively address this challenge. In this article, we lay out the foundations from each that we can build upon to achieve our goals. Next, we describe a set of research challenges for the community, organized into three categories -- analytical, systems, and integration challenges, each with "short term" time horizon (2-3 years) and "long term" (5-10 years) items. This article was conceived of through a community discussion at the 2022 NSF SaTC PI meeting.

cs.CR↗

arXiv2024

Rota-Baxter groups with weight zero and integration on topological groups

Rota-Baxter groups with weights $\pm 1$ have attracted quite much attention since their recent introduction, thanks to their connections with Rota-Baxter Lie algebras, factorizations of Lie groups, post- and pre-Lie algebras, braces and set-theoretic solutions of the Yang-Baxter equation. Despite their expected importance from integrals on groups to pre-groups and Yang-Baxter equations, Rota-Baxter groups with weight zero and other weights has been a challenge to define and their search has been the focus of several attempts. By composing an operator with a section map as a perturbation device, we first generalize the notion of a Rota-Baxter operator on a group from the existing case of weight $\pm 1$ to the case where the weight is given by a pair of maps and then a sequence limit of such pairs. From there, two candidates of Rota-Baxter operators with weight zero are given. One of them is the Rota-Baxter operator with limit-weight zero detailed here, with the other candidate introduced in a companion work. This operator is shown to have its tangent map the Rota-Baxter operator with weight zero on Lie algebras. It also gives concrete applications in integrals of maps with values in a class of topological groups called $\RR$-groups, satisfying a multiplicative version of the integration-by-parts formula. In parallel, differential groups in this framework is also developed and a group formulation of the First Fundamental Theorem of Calculus is obtained.

math.QA↗

arXiv2024

Weighted differential ($q$-tri)dendriform algebras

In this paper, we first introduce a weighted derivation on algebras over an operad $\cal P$, and prove that for the free $\cal P$-algebra, its weighted derivation is determined by the restriction on the generators. As applications, we propose the concept of weighted differential ($q$-tri)dendriform algebras and study some basic properties of them. Then Novikov-(tri)dendriform algebras are initiated, which can be induced from differential ($q$-tri) dendriform of weight zero. Finally, the corresponding free objects are constructed, in both the commutative and noncommutative contexts.

math.RA↗

arXiv2024

Quantum Simulation of Open Quantum Dynamics via Non-Markovian Quantum State Diffusion

Quantum simulation of non-Markovian open quantum dynamics is essential but challenging for standard quantum computers due to their non-Hermitian nature, leading to non-unitary evolution, and the limitations of available quantum resources. Here we introduce a hybrid quantum-classical algorithm designed for simulating dissipative dynamics in system with non-Markovian environment. Our approach includes formulating a non-Markovian Stochastic Schrödinger equation with complex frequency modes (cNMSSE) where the non-Markovianity is characterized by the mode excitation. Following this, we utilize variational quantum simulation to capture the non-unitary evolution within the cNMSSE framework, leading to a substantial reduction in qubit requirements. To demonstrate our approach, we investigated the spin-boson model and dynamic quantum phase transitions (DQPT) within transverse field Ising model (TFIM). Significantly, our findings reveal the enhanced DQPT in TFIM due to non-Markovian behavior.

quant-ph↗

arXiv2024

A Shock Flash Breaking Out of a Dusty Red Supergiant

Shock breakout emission is light that arises when a shockwave, generated by core-collapse explosion of a massive star, passes through its outer envelope. Hitherto, the earliest detection of such a signal was at several hours after the explosion, though a few others had been reported. The temporal evolution of early light curves should reveal insights into the shock propagation, including explosion asymmetry and environment in the vicinity, but this has been hampered by the lack of multiwavelength observations. Here we report the instant multiband observations of a type II supernova (SN 2023ixf) in the galaxy M101 (at a distance of 6.85+/-0.15 Mpc), beginning at about 1.4 hours after the explosion. The exploding star was a red supergiant with a radius of about 440 solar radii. The light curves evolved rapidly, on timescales of 1-2 hours, and appeared unusually fainter and redder than predicted by models within the first few hours, which we attribute to an optically thick dust shell before it was disrupted by the shockwave. We infer that the breakout and perhaps the distribution of the surrounding dust were not spherically symmetric.

astro-ph.HE↗

arXiv2024

New constraints on Triton's atmosphere from the 6 October 2022 stellar occultation

The atmosphere of Triton was probed directly by observing a ground-based stellar occultation on 6 October 2022. This rare event yielded 23 positive light curves collected from 13 separate observation stations contributing to our campaign. The significance of this event lies in its potential to directly validate the modest pressure fluctuation on Triton, a phenomenon not definitively verified by previous observations, including only five stellar occultations, and the Voyager 2 radio occultation in 1989. Using an approach consistent with a comparable study, we precisely determined a surface pressure of $14.07_{-0.13}^{+0.21}~\mathrm{μbar}$ in 2022. This new pressure rules out any significant monotonic variation in pressure between 2017 and 2022 through direct observations, as it is in alignment with the 2017 value. Additionally, both the pressures in 2017 and 2022 align with the 1989 value. This provides further support for the conclusion drawn from the previous volatile transport model simulation, which is consistent with the observed alignment between the pressures in 1989 and 2017; that is to say, the pressure fluctuation is modest. Moreover, this conclusion suggests the existence of a northern polar cap extended down to at least $45^\circ$N$-60^\circ$N and the presence of nitrogen between $30^\circ$S and $0^\circ$.

astro-ph.EP↗

arXiv2024

Applying Self-supervised Learning to Network Intrusion Detection for Network Flows with Graph Neural Network

Graph Neural Networks (GNNs) have garnered intensive attention for Network Intrusion Detection System (NIDS) due to their suitability for representing the network traffic flows. However, most present GNN-based methods for NIDS are supervised or semi-supervised. Network flows need to be manually annotated as supervisory labels, a process that is time-consuming or even impossible, making NIDS difficult to adapt to potentially complex attacks, especially in large-scale real-world scenarios. The existing GNN-based self-supervised methods focus on the binary classification of network flow as benign or not, and thus fail to reveal the types of attack in practice. This paper studies the application of GNNs to identify the specific types of network flows in an unsupervised manner. We first design an encoder to obtain graph embedding, that introduces the graph attention mechanism and considers the edge information as the only essential factor. Then, a self-supervised method based on graph contrastive learning is proposed. The method samples center nodes, and for each center node, generates subgraph by it and its direct neighbor nodes, and corresponding contrastive subgraph from the interpolated graph, and finally constructs positive and negative samples from subgraphs. Furthermore, a structured contrastive loss function based on edge features and graph local topology is introduced. To the best of our knowledge, it is the first GNN-based self-supervised method for the multiclass classification of network flows in NIDS. Detailed experiments conducted on four real-world databases (NF-Bot-IoT, NF-Bot-IoT-v2, NF-CSE-CIC-IDS2018, and NF-CSE-CIC-IDS2018-v2) systematically compare our model with the state-of-the-art supervised and self-supervised models, illustrating the considerable potential of our method. Our code is accessible through https://github.com/renj-xu/NEGSC.

cs.LG↗

arXiv2024

Characterizing Ethereum Upgradable Smart Contracts and Their Security Implications

Upgradeable smart contracts (USCs) have been widely adopted to enable modifying deployed smart contracts. While USCs bring great flexibility to developers, improper usage might introduce new security issues, potentially allowing attackers to hijack USCs and their users. In this paper, we conduct a large-scale measurement study to characterize USCs and their security implications in the wild. We summarize six commonly used USC patterns and develop a tool, USCDetector, to identify USCs without needing source code. Particularly, USCDetector collects various information such as bytecode and transaction information to construct upgrade chains for USCs and disclose potentially vulnerable ones. We evaluate USCDetector using verified smart contracts (i.e., with source code) as ground truth and show that USCDetector can achieve high accuracy with a precision of 96.26%. We then use USCDetector to conduct a large-scale study on Ethereum, covering a total of 60,251,064 smart contracts. USCDetecor constructs 10,218 upgrade chains and discloses multiple real-world USCs with potential security issues.

cs.CR↗

arXiv2024

OASim: an Open and Adaptive Simulator based on Neural Rendering for Autonomous Driving

With deep learning and computer vision technology development, autonomous driving provides new solutions to improve traffic safety and efficiency. The importance of building high-quality datasets is self-evident, especially with the rise of end-to-end autonomous driving algorithms in recent years. Data plays a core role in the algorithm closed-loop system. However, collecting real-world data is expensive, time-consuming, and unsafe. With the development of implicit rendering technology and in-depth research on using generative models to produce data at scale, we propose OASim, an open and adaptive simulator and autonomous driving data generator based on implicit neural rendering. It has the following characteristics: (1) High-quality scene reconstruction through neural implicit surface reconstruction technology. (2) Trajectory editing of the ego vehicle and participating vehicles. (3) Rich vehicle model library that can be freely selected and inserted into the scene. (4) Rich sensors model library where you can select specified sensors to generate data. (5) A highly customizable data generation system can generate data according to user needs. We demonstrate the high quality and fidelity of the generated data through perception performance evaluation on the Carla simulator and real-world data acquisition. Code is available at https://github.com/PJLab-ADG/OASim.

cs.CV↗

arXiv2024

M31N 2013-10c: A Newly Identified Recurrent Nova in M31

The nova M31N 2023-11f (2023yoa) has been recently identified as the second eruption of a previously recognized nova, M31N 2013-10c, establishing the latter object as the 21st recurrent nova system thus far identified in M31. Here we present well sampled $R$-band lightcurves of both the 2013 and 2023 eruptions of this system. The photometric evolution of each eruption was quite similar as expected for the same progenitor system. The 2013 and 2023 eruptions each reached peak magnitudes just brighter than $R\sim16$, with fits to the declining branches of the eruptions yielding times to decline by two magnitudes of $t_2(R)=5.5\pm1.7$ and $t_2(R)=3.4\pm1.5$ days, respectively. M31N 2013-10c has an absolute magnitude at peak, $M_R=-8.8\pm0.2$, making it the most luminous known recurrent nova in M31.

astro-ph.SR↗