arXiv subjects

Lun Zhang

Publications and source records attributed to Lun Zhang.

At least 37 records · Page 2Linked to original sources

arXiv2024

Multi-objective Optimal Roadside Units Deployment in Urban Vehicular Networks

The significance of transportation efficiency, safety, and related services is increasing in urban vehicular networks. Within such networks, roadside units (RSUs) serve as intermediates in facilitating communication. Therefore, the deployment of RSUs is of utmost importance in ensuring the quality of communication services. However, the optimization objectives, such as time delay and deployment cost, are commonly developed from diverse perspectives. As a result, it is possible that conflicts may arise among the objectives. Furthermore, in urban environments, the presence of various obstacles, such as buildings, gardens, lakes, and other infrastructure, poses challenges for the deployment of RSUs. Hence, the deployment encounters significant difficulties due to the existence of multiple objectives, constraints imposed by obstacles, and the necessity to explore a large-scale optimization space. To address this issue, two versions of multi-objective optimization algorithms are proposed in this paper. By utilizing a multi-population strategy and an adaptive exploration technique, the methods efficiently explore a large-scale decision-variable space. In order to mitigate the issue of an overcrowded deployment of RSUs, a calibrating mechanism is adopted to adjust RSU density during the optimization procedures. The proposed methods also take care of data offloading between vehicles and RSUs by setting up an iterative best response sequence game (IBRSG). By comparing the proposed algorithms with several state-of-the-art algorithms, the results demonstrate that our strategies perform better in both high-density and low-density urban scenarios. The results also indicate that the proposed solutions substantially improve the efficiency of vehicular networks.

cs.NE↗

arXiv2023

MuFuzz: Sequence-Aware Mutation and Seed Mask Guidance for Blockchain Smart Contract Fuzzing

As blockchain smart contracts become more widespread and carry more valuable digital assets, they become an increasingly attractive target for attackers. Over the past few years, smart contracts have been subject to a plethora of devastating attacks, resulting in billions of dollars in financial losses. There has been a notable surge of research interest in identifying defects in smart contracts. However, existing smart contract fuzzing tools are still unsatisfactory. They struggle to screen out meaningful transaction sequences and specify critical inputs for each transaction. As a result, they can only trigger a limited range of contract states, making it difficult to unveil complicated vulnerabilities hidden in the deep state space. In this paper, we shed light on smart contract fuzzing by employing a sequence-aware mutation and seed mask guidance strategy. In particular, we first utilize data-flow-based feedback to determine transaction orders in a meaningful way and further introduce a sequence-aware mutation technique to explore deeper states. Thereafter, we design a mask-guided seed mutation strategy that biases the generated transaction inputs to hit target branches. In addition, we develop a dynamic-adaptive energy adjustment paradigm that balances the fuzzing resource allocation during a fuzzing campaign. We implement our designs into a new smart contract fuzzer named MuFuzz, and extensively evaluate it on three benchmarks. Empirical results demonstrate that MuFuzz outperforms existing tools in terms of both branch coverage and bug finding. Overall, MuFuzz achieves higher branch coverage than state-of-the-art fuzzers (up to 25%) and detects 30% more bugs than existing bug detectors.

cs.CR↗

arXiv2023

Empirical Review of Smart Contract and DeFi Security: Vulnerability Detection and Automated Repair

Decentralized Finance (DeFi) is emerging as a peer-to-peer financial ecosystem, enabling participants to trade products on a permissionless blockchain. Built on blockchain and smart contracts, the DeFi ecosystem has experienced explosive growth in recent years. Unfortunately, smart contracts hold a massive amount of value, making them an attractive target for attacks. So far, attacks against smart contracts and DeFi protocols have resulted in billions of dollars in financial losses, severely threatening the security of the entire DeFi ecosystem. Researchers have proposed various security tools for smart contracts and DeFi protocols as countermeasures. However, a comprehensive investigation of these efforts is still lacking, leaving a crucial gap in our understanding of how to enhance the security posture of the smart contract and DeFi landscape. To fill the gap, this paper reviews the progress made in the field of smart contract and DeFi security from the perspective of both vulnerability detection and automated repair. First, we analyze the DeFi smart contract security issues and challenges. Specifically, we lucubrate various DeFi attack incidents and summarize the attacks into six categories. Then, we present an empirical study of 42 state-of-the-art techniques that can detect smart contract and DeFi vulnerabilities. In particular, we evaluate the effectiveness of traditional smart contract bug detection tools in analyzing complex DeFi protocols. Additionally, we investigate 8 existing automated repair tools for smart contracts and DeFi protocols, providing insight into their advantages and disadvantages. To make this work useful for as wide of an audience as possible, we also identify several open issues and challenges in the DeFi ecosystem that should be addressed in the future.

cs.CR↗

arXiv2023

On the gap probability of the tacnode process

The tacnode process is a universal determinantal point process arising from non-intersecting particle systems and tiling problems. It is the aim of this work to explore the integrable structure and large gap asymptotics for the gap probability of the thinned/unthinned tacnode process over $(-s,s)$. We establish an integral representation of the gap probability in terms of the Hamiltonian associated with a system of differential equations. With the aids of some remarkable differential identities for the Hamiltonian, we also compute large gap asymptotics, up to and including the constant term in the thinned case. As direct applications, we obtain expectation, variance and a central limit theorem for the associated counting function.

math-ph↗

arXiv2023

Asymptotics of the deformed higher order Airy-kernel determinants and applications

We study the one-parameter family of Fredholm determinants $\det(I-ρ^2\mathcal{K}_{n,x})$, $ρ\in\mathbb{R}$, where $\mathcal{K}_{n,x}$ stands for the integral operator acting on $L^2(x,+\infty)$ with the higher order Airy kernel. This family of determinants represents a new universal class of distributions which is a higher order analogue of the classical Tracy-Widom distribution. Each of the determinants admits an integral representation in terms of a special real solution to the $n$-th member of the Painlevé II hierarchy. Using the Riemann-Hilbert approach, we establish asymptotics of the determinants and the associated higher order Painlevé II transcendents as $x\to -\infty$ for $0<|ρ|<1$ and $|ρ|>1$, respectively. In the case of $0<|ρ|<1$, we are able to calculate the constant term in the asymptotic expansion of the determinants, while for $|ρ|>1$, the relevant asymptotics exhibit singular behaviors. Applications of our results are also discussed, which particularly include asymptotic statistical properties of the counting function for the random point process defined by the higher order Airy kernel.

math-ph↗

arXiv2022

Asymptotics of the hard edge Pearcey determinant

We study the Fredholm determinant of an integral operator associated to the hard edge Pearcey kernel. This determinant appears in a variety of random matrix and non-intersecting paths models. By relating the logarithmic derivatives of the Fredholm determinant to a $3 \times 3$ Riemann-Hilbert problem, we obtain asymptotics of the determinant, which is also known as the large gap asymptotics for the corresponding point process.

math.PR↗

arXiv2022

Extending combinatorial regulatory network modeling to include activity control and decay modulation

Understanding how the structure of within-system interactions affects the dynamics of the system is important in many areas of science. We extend a network dynamics modeling platform DSGRN, which combinatorializes both dynamics and parameter space to construct finite but accurate summaries of network dynamics, to new types of interactions. While the standard DSGRN assumes that each network edge controls the rate of abundance of the target node, the new edges may control either activity level or a decay rate of its target. While motivated by processes of post-transcriptional modification and ubiquitination in systems biology, our extension is applicable to the dynamics of any signed directed network.

math.DS↗

arXiv2022

Gap probability for the hard edge Pearcey process

The hard edge Pearcey process is universal in random matrix theory and many other stochastic models. This paper deals with the gap probability for the thinned/unthinned hard edge Pearcey process over the interval $(0,s)$ by working on the relevant Fredholm determinants. We establish an integral representation of the gap probability via a Hamiltonian related a system of coupled differential equations. Together with some remarkable differential identities for the Hamiltonian, we derive the large gap asymptotics for the thinned case, up to and including the constant term. As an application, we also obtain the asymptotic statistical properties of the counting function for the hard edge Pearcey process.

math-ph↗

arXiv2022

On the deformed Pearcey determinant

In this paper, we are concerned with the deformed Pearcey determinant $\det\left(I-γK^{\mathrm{Pe}}_{s,ρ}\right)$, where $0 \leq γ<1$ and $K^{\mathrm{Pe}}_{s,ρ}$ stands for the trace class operator acting on $L^2\left(-s, s\right)$ with the classical Pearcey kernel arising from random matrix theory. This determinant corresponds to the gap probability for the Pearcey process after thinning, which means each particle in the Pearcey process is removed independently with probability $1-γ$. We establish an integral representation of the deformed Pearcey determinant involving the Hamiltonian associated with a family of special solutions to a system of nonlinear differential equations. Together with some remarkable differential identities for the Hamiltonian, this allows us to obtain the large gap asymptotics, including the exact calculation of the constant term, which complements our previous work on the undeformed case (i.e., $γ=1$). It comes out that the deformed Pearcey determinant exhibits a significantly different asymptotic behavior from the undeformed case, which suggests a transition will occur as the parameter $γ$ varies. As an application of our results, we obtain the asymptotics for the expectation and variance of the counting function for the Pearcey process, and a central limit theorem as well.

math-ph↗

arXiv2021

A vector Riemann-Hilbert approach to the Muttalib-Borodin ensembles

In this paper, we consider Muttalib-Borodin ensemble of Laguerre type, a determinantal point process over $[0,\infty)$ which depends on the varying weights $x^αe^{-nV(x)}$, $α>-1$, and a parameter $θ$. For $θ$ being a positive integer, we derive asymptotics of the associated biorthogonal polynomials near the origin for a large class of potential functions $V$ as $n\to \infty$. This further allows us to establish the hard edge scaling limit of the correlation kernel, which is previously only known in the special cases and conjectured to be universal. Our proof is based on the Deift/Zhou nonlinear steepest descent analysis of two $1 \times 2$ vector-valued Riemann-Hilbert problems that characterize the biorthogonal polynomials and the explicit constructions of $(θ+1)\times(θ+1)$ local parametrices near the origin in terms of the Meijer G-functions.

math.PR↗

arXiv2021

Higher order Airy and Painlevé asymptotics for the mKdV hierarchy

In this paper, we consider Cauchy problem for the modified Korteweg-de Vries hierarchy on the real line with decaying initial data. Using the Riemann--Hilbert formulation and nonlinear steepest descent method, we derive a uniform asymptotic expansion to all orders in powers of $t^{-1/(2n+1)}$ with smooth coefficients of the variable $(-1)^{n+1}x((2n+1) t)^{-1/(2n+1)}$ in the self-similarity region for the solution of $n$-th member of the hierarchy. It turns out that the leading asymptotics is described by a family of special solutions of the Painlevé II hierarchy, which generalize the classical Ablowitz-Segur solution for the Painelvé II equation and appear in a variety of random matrix and statistical physics models. We establish the connection formulas for this family of solutions. In the special case that the reflection coefficient vanishes at the origin, the solutions of Painlevé II hierarchy in the leading coefficient vanishes as well, the leading and subleading terms in the asymptotic expansion are instead given explicitly in terms of derivatives of the generalized Airy function.

math.AP↗

arXiv2021

Computing linear extensions for polynomial posets subject to algebraic constraints

In this paper we consider the classical problem of computing linear extensions of a given poset which is well known to be a difficult problem. However, in our setting the elements of the poset are multivariate polynomials, and only a small "admissible" subset of these linear extensions, determined implicitly by the evaluation map, are of interest. This seemingly novel problem arises in the study of global dynamics of gene regulatory networks in which case the poset is a Boolean lattice. We provide an algorithm for solving this problem using linear programming for arbitrary partial orders of linear polynomials. This algorithm exploits this additional algebraic structure inherited from the polynomials to efficiently compute the admissible linear extensions. The biologically relevant problem involves multilinear polynomials and we provide a construction for embedding it into an instance of the linear problem.

math.CO↗

arXiv2020

Asymptotics of Fredholm determinant associated with the Pearcey kernel

The Pearcey kernel is a classical and universal kernel arising from random matrix theory, which describes the local statistics of eigenvalues when the limiting mean eigenvalue density exhibits a cusp-like singularity. It appears in a variety of statistical physics models beyond matrix models as well. We consider the Fredholm determinant of a trace class operator acting on $L^2\left(-s, s\right)$ with the Pearcey kernel. Based on a steepest descent analysis for a $3\times 3$ matrix-valued Riemann-Hilbert problem, we obtain asymptotics of the Fredholm determinant as $s\to +\infty$, which is also interpreted as large gap asymptotics in the context of random matrix theory.

math-ph↗

arXiv2020

Analysis of multivariate Gegenbauer approximation in the hypercube

In this paper, we are concerned with multivariate Gegenbauer approximation of functions defined in the $d$-dimensional hypercube. Two new and sharper bounds for the coefficients of multivariate Gegenbauer expansion of analytic functions are presented based on two different extensions of the Bernstein ellipse. We then establish an explicit error bound for the multivariate Gegenbauer approximation associated with an $\ell^q$ ball index set in the uniform norm. We also consider the multivariate approximation of functions with finite regularity and derive the associated error bound on the full grid in the uniform norm. As an application, we extend our arguments to obtain some new tight bounds for the coefficients of tensorized Legendre expansions in the context of polynomial approximation of parameterized PDEs.

math.NA↗

arXiv2020

On integrals of the tronquée solutions and the associated Hamiltonians for the Painlevé II equation

We consider a family of tronquée solutions of the Painelvé II equation \begin{equation*} q''(s)=2q(s)^3+sq(s)-(2α+\frac12), \qquad α> -\frac12, \end{equation*} which is characterized by the Stokes multipliers $$s_1=-e^{-2απi },\quad s_2=ω, \quad s_3=-e^{2 απi} $$ with $ω$ being a free parameter. These solutions include the well-known generalized Hastings-McLeod solution as a special case if $ω=0$. We derive asymptotics of integrals of the tronquée solutions and the associated Hamiltonians over the real axis for $α> -1/2$ and $ω\geq 0$, with the constant terms evaluated explicitly. Our results agree with those already known in the literature if the parameters $α$ and $ω$ are chosen to be special values. Some applications of our results in random matrix theory are also discussed.

math-ph↗

arXiv2019

Large n limit for the product of two coupled random matrices

For a pair of coupled rectangular random matrices we consider the squared singular values of their product, which form a determinantal point process. We show that the limiting mean distribution of these squared singular values is described by the second component of the solution to a vector equilibrium problem. This vector equilibrium problem is defined for three measures with an upper constraint on the first measure and an external field on the second measure. We carry out the steepest descent analysis for a 4 $\times$ 4 matrix-valued Riemann-Hilbert problem, which characterizes the correlation kernel and is related to mixed type multiple orthogonal polynomials associated with the modified Bessel functions. A careful study of the vector equilibrium problem, combined with this asymptotic analysis, ultimately leads to the aforementioned convergence result for the limiting mean distribution, an explicit form of the associated spectral curve, as well as local Sine, Meijer-G and Airy universality results for the squared singular values considered.

math-ph↗

arXiv2019

Gaussian unitary ensembles with pole singularities near the soft edge and a system of coupled Painlevé XXXIV equations

In this paper, we study the singularly perturbed Gaussian unitary ensembles defined by the measure \begin{equation*} \frac{1}{C_n} e^{- n\textrm{tr}\, V(M;λ,\vec{t}\;)}dM, \end{equation*} over the space of $n \times n$ Hermitian matrices $M$, where $V(x;λ,\vec{t}\;):= 2x^2 + \sum_{k=1}^{2m}t_k(x-λ)^{-k}$ with $\vec{t}= (t_1, t_2, \ldots, t_{2m})\in \mathbb{R}^{2m-1} \times (0,\infty)$, in the multiple scaling limit where $λ\to 1$ together with $\vec{t} \to \vec{0}$ as $n\to \infty$ at appropriate related rates. We obtain the asymptotics of the partition function, which is described explicitly in terms of an integral involving a smooth solution to a new coupled Painlevé system generalizing the Painlevé XXXIV equation. The large $n$ limit of the correlation kernel is also derived, which leads to a new universal class built out of the $Ψ$-function associated with the coupled Painlevé system.

math-ph↗

arXiv2018

Neural Abstract Style Transfer for Chinese Traditional Painting

Chinese traditional painting is one of the most historical artworks in the world. It is very popular in Eastern and Southeast Asia due to being aesthetically appealing. Compared with western artistic painting, it is usually more visually abstract and textureless. Recently, neural network based style transfer methods have shown promising and appealing results which are mainly focused on western painting. It remains a challenging problem to preserve abstraction in neural style transfer. In this paper, we present a Neural Abstract Style Transfer method for Chinese traditional painting. It learns to preserve abstraction and other style jointly end-to-end via a novel MXDoG-guided filter (Modified version of the eXtended Difference-of-Gaussians) and three fully differentiable loss terms. To the best of our knowledge, there is little work study on neural style transfer of Chinese traditional painting. To promote research on this direction, we collect a new dataset with diverse photo-realistic images and Chinese traditional paintings. In experiments, the proposed method shows more appealing stylized results in transferring the style of Chinese traditional painting than state-of-the-art neural style transfer methods.

cs.CV↗