arXiv subjects

Xiaofan Li

Publications and source records attributed to Xiaofan Li.

At least 91 records · Page 5Linked to original sources

arXiv2023

Quantum Algorithm for Maximum Biclique Problem

Identifying a biclique with the maximum number of edges bears considerable implications for numerous fields of application, such as detecting anomalies in E-commerce transactions, discerning protein-protein interactions in biology, and refining the efficacy of social network recommendation algorithms. However, the inherent NP-hardness of this problem significantly complicates the matter. The prohibitive time complexity of existing algorithms is the primary bottleneck constraining the application scenarios. Aiming to address this challenge, we present an unprecedented exploration of a quantum computing approach. Efficient quantum algorithms, as a crucial future direction for handling NP-hard problems, are presently under intensive investigation, of which the potential has already been proven in practical arenas such as cybersecurity. However, in the field of quantum algorithms for graph databases, little work has been done due to the challenges presented by the quantum representation of complex graph topologies. In this study, we delve into the intricacies of encoding a bipartite graph on a quantum computer. Given a bipartite graph with n vertices, we propose a ground-breaking algorithm qMBS with time complexity O^*(2^(n/2)), illustrating a quadratic speed-up in terms of complexity compared to the state-of-the-art. Furthermore, we detail two variants tailored for the maximum vertex biclique problem and the maximum balanced biclique problem. To corroborate the practical performance and efficacy of our proposed algorithms, we have conducted proof-of-principle experiments utilizing IBM quantum simulators, of which the results provide a substantial validation of our approach to the extent possible to date.

quant-ph↗

arXiv2023

Directed Greybox Fuzzing with Stepwise Constraint Focusing

Dynamic data flow analysis has been widely used to guide greybox fuzzing. However, traditional dynamic data flow analysis tends to go astray in the massive path tracking and requires to process a large volume of data, resulting in low efficiency in reaching the target location. In this paper, we propose a directed greybox fuzzer based on dynamic constraint filtering and focusing (CONFF). First, all path constraints are tracked, and those with high priority are filtered as the next solution targets. Next, focusing on a single path constraint to be satisfied, we obtain its data condition and probe the mapping relationship between it and the input bytes through multi-byte mapping and single-byte mapping. Finally, various mutation strategies are utilized to solve the path constraint currently focused on, and the target location of the program is gradually approached through path selection. The CONFF fuzzer can reach a specific location faster in the target program, thus efficiently triggering the crash. We designed and implemented a prototype of the CONFF fuzzer and evaluated it with the LAVA-1 dataset and some real-world vulnerabilities. The results show that the CONFF fuzzer can reproduce crashes on the LAVA-1 dataset and most of the real-world vulnerabilities. For most vulnerabilities, the CONFF fuzzer reproduced the crashes with significantly reduced time compared to state-of-the-art fuzzers. On average, the CONFF fuzzer was 23.7x faster than the state-of-the-art code coverage-based fuzzer Angora and 27.3x faster than the classical directed greybox fuzzer AFLGo.

cs.CR↗

arXiv2022

A Modified Trapezoidal Rule for a Class of Weakly Singular Integrals in n Dimensions

In this paper we propose and analyze a general arbitrarily high-order modified trapezoidal rule for a class of weakly singular integrals of the forms $I = \int_{\mathbb{R}^n}ϕ(x)s(x)dx$ in $n$ dimensions, where $ϕ\in C_c^N(\mathbb{R}^n)$ for some sufficiently large $N$ and $s$ is the weakly singular kernel. The admissible class of weakly singular kernel requires $s$ satisfies dilation and symmetry properties and is large enough to contain functions of the form $\frac{P(x)}{|x|^r}$ where $r > 0$ and $P(x)$ is any monomials such that $\text{deg} P < r < \text{deg} P + n$. The modified trapezoidal rule is the singularity-punctured trapezoidal rule added by correction terms involving the correction weights for grid points around singularity. Correction weights are determined by enforcing the quadrature rule exactly evaluates some monomials and solving corresponding linear systems. A long-standing difficulty of these type of methods is establishing the non-singularity of the linear system, despite strong numerical evidences. By using an algebraic-combinatorial argument, we show the non-singularity always holds and prove the general order of convergence of the modified quadrature rule. We present numerical experiments to validate the order of convergence.

math.NA↗

arXiv2022

Numerical integration of stochastic contact Hamiltonian systems via stochastic Herglotz variational principle

In this work we construct a stochastic contact variational integrator and its discrete version via stochastic Herglotz variational principle for stochastic contact Hamiltonian systems. A general structure-preserving stochastic contact method is devised, and the stochastic contact variational integrators are established. The implementation of this approach is validated by the numerical experiments.

math.NA↗

arXiv2022

Solving Non-local Fokker-Planck Equations by Deep Learning

Physics-informed neural networks (PiNNs) recently emerged as a powerful solver for a large class of partial differential equations under various initial and boundary conditions. In this paper, we propose trapz-PiNNs, physics-informed neural networks incorporated with a modified trapezoidal rule recently developed for accurately evaluating fractional laplacian and solve the space-fractional Fokker-Planck equations in 2D and 3D. We describe the modified trapezoidal rule in detail and verify the second-order accuracy. We demonstrate trapz-PiNNs have high expressive power through predicting solution with low $\mathcal{L}^2$ relative error on a variety of numerical examples. We also use local metrics such as pointwise absolute and relative errors to analyze where could be further improved. We present an effective method for improving performance of trapz-PiNN on local metrics, provided that physical observations of high-fidelity simulation of the true solution are available. Besides the usual advantages of the deep learning solvers such as adaptivity and mesh-independence, the trapz-PiNN is able to solve PDEs with fractional laplacian with arbitrary $α\in (0,2)$ and specializes on rectangular domain. It also has potential to be generalized into higher dimensions.

physics.comp-ph↗

arXiv2022

High-order Corrected Trapezoidal Rules for Functions with Fractional Singularities

In this paper, we introduce and analyze arbitrarily high-order quadrature rules for evaluating the two-dimensional singular integrals of the forms \begin{align} I_{i,j} = \int_{\mathbb{R}^2}ϕ(x)\frac{x_ix_j}{|x|^{2+α}} \d x, \quad 0< α< 2 \end{align} where $i,j\in\{1,2\}$ and $ϕ\in C_c^N$ for $N\geq 2$. This type of singular integrals and its quadrature rule appear in the numerical discretization of fractional Laplacian in non-local Fokker-Planck Equations in 2D. The quadrature rules are trapezoidal rules equipped with correction weights for points around singularity. We prove the order of convergence is $2p+4-α$, where $p\in\mathbb{N}_{0}$ is associated with total number of correction weights. Although we work in 2D setting, we formulate definitions and theorems in $n\in\mathbb{N}$ dimensions when appropriate for the sake of generality. We present numerical experiments to validate the order of convergence of the proposed modified quadrature rules.

math.NA↗

arXiv2021

Over-the-Air Aggregation for Federated Learning: Waveform Superposition and Prototype Validation

In this paper, we develop an orthogonal-frequency-division-multiplexing (OFDM)-based over-the-air (OTA) aggregation solution for wireless federated learning (FL). In particular, the local gradients in massive IoT devices are modulated by an analog waveform and are then transmitted using the same wireless resources. To this end, achieving perfect waveform superposition is the key challenge, which is difficult due to the existence of frame timing offset (TO) and carrier frequency offset (CFO). In order to address these issues, we propose a two-stage waveform pre-equalization technique with a customized multiple access protocol that can estimate and then mitigate the TO and CFO for the OTA aggregation. Based on the proposed solution, we develop a hardware transceiver and application software to train a real-world FL task, which learns a deep neural network to predict the received signal strength with global positioning system information. Experiments verify that the proposed OTA aggregation solution can achieve comparable performance to offline learning procedures with high prediction accuracy.

eess.SP↗

arXiv2020

Efficiently Finding a Maximal Clique Summary via Effective Sampling

Maximal clique enumeration (MCE) is a fundamental problem in graph theory and is used in many applications, such as social network analysis, bioinformatics, intelligent agent systems, cyber security, etc. Most existing MCE algorithms focus on improving the efficiency rather than reducing the output size. The output unfortunately could consist of a large number of maximal cliques. In this paper, we study how to report a summary of less overlapping maximal cliques. The problem was studied before, however, after examining the pioneer approach, we consider it still not satisfactory. To advance the research along this line, our paper attempts to make four contributions: (a) we propose a more effective sampling strategy, which produces a much smaller summary but still ensures that the summary can somehow witness all the maximal cliques and the expectation of each maximal clique witnessed by the summary is above a predefined threshold; (b) we prove that the sampling strategy is optimal under certain optimality conditions; (c) we apply clique-size bounding and design new enumeration order to approach the optimality conditions; and (d) to verify experimentally, we test eight real benchmark datasets that have a variety of graph characteristics. The results show that our new sampling strategy consistently outperforms the state-of-the-art approach by producing smaller summaries and running faster on all the datasets.

cs.DB↗

arXiv2020

Symplectic method for Hamiltonian stochastic differential equations with multiplicative Lévy noise in the sense of Marcus

A class of Hamiltonian stochastic differential equations with multiplicative Lévy noise in the sense of Marcus, and the construction and numerical implementation methods of symplectic Euler scheme, are considered. A general symplectic Euler scheme for this kind of Hamiltonian stochastic differential equations is devised, and its convergence theorem is proved. The second part presents realizable numerical implementation methods for this scheme in details. Some numerical experiments are conducted to demonstrate the effectiveness and superiority of the proposed method by the simulations of its orbits, Hamlitonian,and convergence order over a long time interval.

math.NA↗

arXiv2020

Symplectic Euler scheme for Hamiltonian stochastic differential equations driven by Levy noise

This paper proposes a general symplectic Euler scheme for a class of Hamiltonian stochastic differential equations driven by L$\acute{e}$vy noise in the sense of Marcus form. The convergence of the symplectic Euler scheme for this Hamiltonian stochastic differential equations is investigated. Realizable numerical implementation of this scheme is also provided in details. Numerical experiments are presented to illustrate the effectiveness and superiority of the proposed method by the simulations of its orbits, symplectic structure and Hamlitonian.

math.NA↗

arXiv2019

Most Probable Evolution Trajectories in a Genetic Regulatory System Excited by Stable Lévy Noise

We study the most probable trajectories of the concentration evolution for the transcription factor activator in a genetic regulation system, with non-Gaussian stable Lévy noise in the synthesis reaction rate taking into account. We calculate the most probable trajectory by spatially maximizing the probability density of the system path, i.e., the solution of the associated nonlocal Fokker-Planck equation. We especially examine those most probable trajectories from low concentration state to high concentration state (i.e., the likely transcription regime) for certain parameters, in order to gain insights into the transcription processes and the tipping time for the transcription likely to occur. This enables us: (i) to visualize the progress of concentration evolution (i.e., observe whether the system enters the transcription regime within a given time period); (ii) to predict or avoid certain transcriptions via selecting specific noise parameters in particular regions in the parameter space. Moreover, we have found some peculiar or counter-intuitive phenomena in this gene model system, including (a) a smaller noise intensity may trigger the transcription process, while a larger noise intensity can not, under the same asymmetric Lévy noise. This phenomenon does not occur in the case of symmetric Lévy noise; (b) the symmetric Lévy motion always induces transition to high concentration, but certain asymmetric Lévy motions do not trigger the switch to transcription. These findings provide insights for further experimental research, in order to achieve or to avoid specific gene transcriptions, with possible relevance for medical advances.

q-bio.MN↗

arXiv2018

Most probable dynamics of a genetic regulatory network under stable Lévy noise

Numerous studies have demonstrated the important role of noise in the dynamical behaviour of a complex system. The most probable trajectories of nonlinear systems under the influence of Gaussian noise have recently been studied already. However, there has been only a few works that examine how most probable trajectories in the two-dimensional system (MeKS network) are influenced under non-Gaussian stable Lévy noise. Therefore, we discuss the most probable trajectories of a two-dimensional model depicting the competence behaviour in B. subtilis under the influence of stable Lévy noise. On the basis of the Fokker-Planck equation, we describe the noise-induced most probable trajectories of the MeKS network from the low ComK protein concentration (vegetative state) to the high ComK protein concentration (competence state) under stable Lévy noise. We demonstrate choices of the non-Gaussianity index $α$ and the noise intensity $ε$ which generate the ComK protein escape from the low concentration to the high concentration. We also reveal the optimal combination of both parameters $α$ and $ε$ making the tipping time shortest. Moreover, we find that different initial concentrations around the low ComK protein concentration evolve to a metastable state, and provide the optimal $α$ and $ε$ such that the distance between the deterministic competence state and the metastable state is smallest.

math.DS↗

arXiv2018

Fokker-Planck equation driven by asymmetric Lévy motion

Non-Gaussian Lévy noises are present in many models for understanding underlining principles of physics, finance, biology and more. In this work, we consider the Fokker-Planck equation(FPE) due to one-dimensional asymmetric Lévy motion, which is a nonlocal partial differential equation. We present an accurate numerical quadrature for the singular integrals in the nonlocal FPE and develop a fast summation method to reduce the order of the complexity from $O(J^2)$ to $O(J\log J)$ in one time-step, where $J$ is the number of unknowns. We also provide conditions under which the numerical schemes satisfy maximum principle. Our numerical method is validated by comparing with exact solutions for special cases. We also discuss the properties of the probability density functions and the effects of various factors on the solutions, including the stability index, the skewness parameter, the drift term, the Gaussian and non-Gaussian noises and the domain size.

math.DS↗

arXiv2018

Likelihood for transcriptions in a genetic regulatory system under asymmetric stable Lévy noise

This work is devoted to investigating the evolution of concentration in a genetic regulation system, when the synthesis reaction rate is under additive and multiplicative asymmetric stable Lévy fluctuations. By focusing on the impact of skewness (i.e., non-symmetry) in the probability distributions of noise, we find that via examining the mean first exit time (MFET) and the first escape probability (FEP), the asymmetric fluctuations, interacting with nonlinearity in the system, lead to peculiar likelihood for transcription. This includes, in the additive noise case, realizing higher likelihood of transcription for larger positive skewness (i.e., asymmetry) index $β$, causing a stochastic bifurcation at the non-Gaussianity index value $α=1$ (i.e., it is a separating point or line for the likelihood for transcription), and achieving a turning point at the threshold value $β\approx -0.5$ (i.e., beyond which the likelihood for transcription suddenly reversed for $α$ values). The stochastic bifurcation and turning point phenomena do not occur in the symmetric noise case ($β=0$). While in the multiplicative noise case, non-Gaussianity index value $α=1$ is a separating point or line for both the mean first exit time (MFET) and the first escape probability (FEP). We also investigate the noise enhanced stability phenomenon. Additionally, we are able to specify the regions in the whole parameter space for the asymmetric noise, in which we attain desired likelihood for transcription. We have conducted a series of numerical experiments in `regulating' the likelihood of gene transcription by tuning asymmetric stable Lévy noise indexes. This work offers insights for possible ways of achieving gene regulation in experimental research.

physics.bio-ph↗

arXiv2018

Data assimilation and parameter estimation for a multiscale stochastic system with alpha-stable Levy noise

This work is about low dimensional reduction for a slow-fast data assimilation system with non-Gaussian $α-$stable Lévy noise via stochastic averaging. When the observations are only available for slow components, we show that the averaged, low dimensional filter approximates the original filter, by examining the corresponding Zakai stochastic partial differential equations. Furthermore, we demonstrate that the low dimensional slow system approximates the slow dynamics of the original system, by examining parameter estimation and most probable paths.

math.DS↗

arXiv2017

Lévy noise-induced transitions in gene regulatory networks

Important effects of noise on a one-dimensional gene expression model involving a single gene have recently been discussed. However, few works have been devoted to the transition in two-dimensional models which include the interaction of genes. Therefore, we investigate here, a quantitative two-dimensional model (MeKS network) of gene expression dynamics describing the competence development in the B. subtilis under the influence of Lévy as well as Brownian motions, where noises can do the B. subtilis a favor in nutrient depletion. To analyze the transitions between the vegetative and the competence regions therein, two deterministic quantities, the mean first exit time (MFET) and the first escape probability (FEP) from a microscopic perspective, as well as their averaged versions from a macroscopic perspective, are applied. The relative contribution factor (RCF), the ratio of non-Gaussian and Gaussian noise strengths, is adopted to implement optimal control in these transitions. Schematic representations indicate that there exists an optimum choice that makes the transition occurring at the highest probability. Additionally, we use a geometric concept, the stochastic basin of attraction, to exhibit a pictorial comprehension about the influence of the Lévy motion on the basin stability of the competence state.

q-bio.MN↗

arXiv2017

Hybrid Beamforming via the Kronecker Decomposition for the Millimeter-Wave Massive MIMO Systems

Despite its promising performance gain, the realization of mmWave massive MIMO still faces several practical challenges. In particular, implementing massive MIMO in the digital domain requires hundreds of RF chains matching the number of antennas. Furthermore, designing these components to operate at the mmWave frequencies is challenging and costly. These motivated the recent development of hybrid-beamforming where MIMO processing is divided for separate implementation in the analog and digital domains, called the analog and digital beamforming, respectively. Analog beamforming using a phase array introduces uni-modulus constraints on the beamforming coefficients, rendering the conventional MIMO techniques unsuitable and call for new designs. In this paper, we present a systematic design framework for hybrid beamforming for multi-cell multiuser massive MIMO systems over mmWave channels characterized by sparse propagation paths. The framework relies on the decomposition of analog beamforming vectors and path observation vectors into Kronecker products of factors being uni-modulus vectors. Exploiting properties of Kronecker mixed products, different factors of the analog beamformer are designed for either nulling interference paths or coherently combining data paths. Furthermore, a channel estimation scheme is designed for enabling the proposed hybrid beamforming. The scheme estimates the AoA of data and interference paths by analog beam scanning and data-path gains by analog beam steering. The performance of the channel estimation scheme is analyzed. In particular, the AoA spectrum resulting from beam scanning, which displays the magnitude distribution of paths over the AoA range, is derived in closed-form. It is shown that the inter-cell interference level diminishes inversely with the array size, the square root of pilot sequence length and the spatial separation between paths.

cs.IT↗

arXiv2017

Numerical algorithms for mean exit time and escape probability of stochastic systems with asymmetric Lévy motion

For non-Gaussian stochastic dynamical systems, mean exit time and escape probability are important deterministic quantities, which can be obtained from integro-differential (nonlocal) equations. We develop an efficient and convergent numerical method for the mean first exit time and escape probability for stochastic systems with an asymmetric Lévy motion, and analyze the properties of the solutions of the nonlocal equations. We also investigate the effects of different system factors on the mean exit time and escape probability, including the skewness parameter, the size of the domain, the drift term and the intensity of Gaussian and non-Gaussian noises. We find that the behavior of the mean exit time and the escape probability has dramatic difference at the boundary of the domain when the index of stability crosses the critical value of one.

math.DS↗