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Qi Bao

Publications and source records attributed to Qi Bao.

12 recordsLinked to original sources
arXiv2026

OmegaUse-OfficeVal: Benchmarking LLM Agents on Long-Horizon Office-Suite Tasks with Economic Grounding

Large language model (LLM) agents are increasingly expected to assist users in completing tasks. However, existing benchmarks provide limited support for evaluating whether agents can carry out office-suite workflows at a reasonable cost. We introduce OmegaUse-OfficeVal, a benchmark for evaluating LLM agents on long-horizon office-suite tasks with task-level economic grounding. The benchmark comprises 100 tasks derived from office-suite requests proposed by practitioners and adapted through a privacy-preserving process. On average, these tasks require 2.32 hours of human labor to complete. An important feature of the benchmark is that each task is paired with two economic signals: human labor time and task price proxy. These signals enable direct comparisons between human costs and LLM inference costs, as well as value-weighted evaluation. To support stable evaluation, we develop code-based verifiers from fine-grained rubrics. We evaluate several frontier LLMs together with a human baseline. Although all evaluated LLMs are substantially cheaper and faster than human workers, they have not yet approached human-level deliverable quality. The code and dataset are fully open-sourced, and more information is available on our project website: https://omegause-officeval.github.io.

cs.AI↗
arXiv2024

Role Similarity Metric Based on Spanning Rooted Forest

As a fundamental issue in network analysis, structural node similarity has received much attention in academia and is adopted in a wide range of applications. Among these proposed structural node similarity measures, role similarity stands out because of satisfying several axiomatic properties including automorphism conformation. Existing role similarity metrics cannot handle top-k queries on large real-world networks due to the high time and space cost. In this paper, we propose a new role similarity metric, namely \textsf{ForestSim}. We prove that \textsf{ForestSim} is an admissible role similarity metric and devise the corresponding top-k similarity search algorithm, namely \textsf{ForestSimSearch}, which is able to process a top-k query in $O(k)$ time once the precomputation is finished. Moreover, we speed up the precomputation by using a fast approximate algorithm to compute the diagonal entries of the forest matrix, which reduces the time and space complexity of the precomputation to $O(ε^{-2}m\log^5{n}\log{\frac{1}ε})$ and $O(m\log^3{n})$, respectively. Finally, we conduct extensive experiments on 26 real-world networks. The results show that \textsf{ForestSim} works efficiently on million-scale networks and achieves comparable performance to the state-of-art methods.

cs.SI↗
arXiv2023

Measures and Optimization for Robustness and Vulnerability in Disconnected Networks

The function or performance of a network is strongly dependent on its robustness, quantifying the ability of the network to continue functioning under perturbations. While a wide variety of robustness metrics have been proposed, they have their respective limitations. In this paper, we propose to use the forest index as a measure of network robustness, which overcomes the deficiencies of existing metrics. Using such a measure as an optimization criterion, we propose and study the problem of breaking down a network by attacking some key edges. We show that the objective function of the problem is monotonic but not submodular, which impose more challenging on the problem. We thus resort to greedy algorithms extended for non-submodular functions by iteratively deleting the most promising edges. We first propose a simple greedy algorithm with a proved bound for the approximation ratio and cubic-time complexity. To confront the computation challenge for large networks, we further propose an improved nearly-linear time greedy algorithm, which significantly speeds up the process for edge selection but sacrifices little accuracy. Extensive experimental results for a large set of real-world networks verify the effectiveness and efficiency of our algorithms, demonstrating that our algorithms outperform several baseline schemes.

cs.SI↗
arXiv2023

Notes on $q$-partial differential equations for $q$-Laguerre polynomials and little $q$-Jacobi polynomials

We define two common $q$-orthogonal polynomials: homogeneous $q$-Laguerre polynomials and homogeneous little $q$-Jacobi polynomials. They can be viewed separately as solutions to two $q$-partial differential equations. Then, we proved that if an analytic function satisfies a certain system of $q$-partial differential equations, if and only if it can be expanded in terms of homogeneous $q$-Laguerre polynomials or homogeneous little $q$-Jacobi polynomials. As applications, we obtain generalizations of the Ramanujan $q$-beta integrals and Andrews-Askey integrals. Additionally, we present an operator representation of $q$-Laguerre polynomials that facilitates the computation of identities involving $q$-Laguerre polynomials.

math.CA↗
arXiv2022

Two $q$-operational equations and Hahn polynomials

Motivated by Liu's recent work in \cite{Liu2022}. We shall reveal the essential feature of Hahn polynomials by presenting two new $q$-exponential operators. These lead us to use a systematic method to study identities involving Hahn polynomials. As applications, we use the method of $q$-exponential operator to prove the bilinear generating function of Hahn polynomials and Heine's second transformation formula. Moreover, a generalization of $q$-Gaussian summation is given, too.

math.CA↗
arXiv2022

A Generalization of q-Binomial Theorem

By using Liu's $q$-partial differential equations theory, we prove that if an analytic function in several variables satisfies a system of $q$-partial differential equations, if and only if it can be expanded in terms of homogeneous $(q,c)$-Al-Salam-Carlitz polynomials. As an application, we proved that for $c\neq0$ and $\max \{|cq|,|x|\}<1$, \begin{align*} \sum_{n=0}^{\infty} \frac{ (a;q)_n }{(cq;q)_n}x^n=(ax/c;q)_{\infty} \sum_{n=0}^{\infty} \frac{x^n}{(cq;q)_n}, \end{align*} which is a generalization of famous $q$-binomial theorem or so-called Cauchy theorem.

math.CA↗
arXiv2022

Notes on Generalized Gr\"otzsch Ring Function and Generalized Hersch-Pfluger Distortion Function

For $a\in(0,1)$, $r\in(0,1)$ and $K\in(1,\infty)$, let $\mu_{a}(r)$ and $\varphi_{K}^{a}(r)$ be the generalized Gr\"{o}tzsch ring function and generalized Hersch-Pfluger distortion function. In the past few years, the functions $\mu_{a}(r)$ and $\varphi_{K}^{a}(r)$, and their special cases $\mu_{1/2}(r)$ and $\varphi_{K}^{1/2}(r)$ have been playing the very important role on the theory of quasiconformal mappings and (generalized) Ramanujan's modular equations. In this paper, we present a series expansion of $\mu_{a}(r)$, and thus prove that the function $r\mapsto -[\mu_{a}(r)-\log{(e^{R(a)/2})/r}]$ is absolutely monotonic on $(0,1)$. Here $R(a)$ is the Ramanujan constant. In addition, we also investigate the submultiplicative and power submultiplicative properties of $\varphi_{K}^{a}(r)$, and establish some new inequalities for $\varphi_{K}^{a}(r)$ in terms of elementary functions.

math.CA↗
arXiv2021

Monotonicity Properties of Gaussian Hypergeometric Functions with Respect to the Parameter

The authors establish the necessary and sufficient conditions under which certain combinations of Gaussian hypergeometric function and elementary function are monotone in the parameter, which generalize the recent results of generalized elliptic integrals of the first and second kinds obtained by Qiu et al. Moreover, the authors also prove two monotonicity theorems of generalized elliptic integrals from another point of view.

math.CA↗
arXiv2021

Fast Evaluation for Relevant Quantities of Opinion Dynamics

One of the main subjects in the field of social networks is to quantify conflict, disagreement, controversy, and polarization, and some quantitative indicators have been developed to quantify these concepts. However, direct computation of these indicators involves the operations of matrix inversion and multiplication, which make it computationally infeasible for large-scale graphs with millions of nodes. In this paper, by reducing the problem of computing relevant quantities to evaluating $\ell_2$ norms of some vectors, we present a nearly linear time algorithm to estimate all these quantities. Our algorithm is based on the Laplacian solvers, and has a proved theoretical guarantee of error for each quantity. We execute extensive numerical experiments on a variety of real networks, which demonstrate that our approximation algorithm is efficient and effective, scalable to large graphs having millions of nodes.

cs.SI↗
arXiv2021

On a Conjecture Concerning the Approximates of Complete Elliptic Integral of the First Kind by Inverse Hyperbolic Tangent

Let $\K$ be the complete elliptic integral of the first kind. In this paper, the authors prove that the function $r\mapsto r^{-2}\{[\log(2\K(r)/π)]/\log((\arth r)/r)-3/4\}$ is strictly increasing from $(0,1)$ onto $(1/320,1/4)$, so that $[(\arth r)/r]^{3/4+r^2/320}<2\K(r)/π<[(\arth r)/r]^{3/4+r^2/4}$ for $r\in(0,1)$, in which all the coefficients of the exponents of the two bounds are best possible, thus proving a conjecture raised by Alzer and Qiu to be true, and giving better bounds of $\K(r)$ than those they conjectured and put in an open problem. Some other analytic properties of the complete elliptic integrals, including other kind of approximates for $\K(r)$, are obtained, too.

math.CA↗
arXiv2019

The k-Power Domination Number in Some Self-Similar Graphs

The $k$-power domination problem is a problem in graph theory, which has applications in many areas. However, it is hard to calculate the exact $k$-power domination number since determining k-power domination number of a generic graph is a NP-complete problem. We determine the exact $k$-power domination number in two graphs which have the same number of vertices and edges: pseudofractal scale-free web and Sierpiński gasket. The $k$-power domination number becomes 1 for $k\ge2$ in the Sierpiński gasket, while the $k$-power domination number increases at an exponential rate with regard to the number of vertices in the pseudofractal scale-free web. The scale-free property may account for the difference in the behavior of two graphs.

math.CO↗