arXiv subjects
Publications and source records attributed to Yuan Xu.
Highly localized kernels based on orthogonal polynomials have been studied and utilized over several regular domains. Much of the results deduced via these kernels can be treated uniformly in the framework of localizable spaces of homogeneous type. We clarify the concept of localness and provide a list of such localizable spaces.
Diffusive limit of the one-species Vlasov-Maxwell-Boltzmann system in perturbation framework still remains unsolved, due to the weaker time decay rate compared with the two-species Vlasov-Maxwell-Boltzmann system. By employing the weighted energy method with two newly introduced weight functions and some novel treatments, we solve this problem for the full range of cutoff hard potentials $0\leq γ\leq 1$. Uniform estimate with respect to the Knudsen number $\varepsilon\in (0,1]$ is established globally in time, which eventually leads to the global existence of solutions to the one-species Vlasov-Maxwell-Boltzmann system and hydrodynamic limit to the incompressible Navier-Stokes-Fourier-Maxwell system. To the best of our knowledge, this is the first result on diffusive limit of the one-species Vlasov-Maxwell-Boltzmann system in perturbation framework.
Penetration testing, a crucial industrial practice for ensuring system security, has traditionally resisted automation due to the extensive expertise required by human professionals. Large Language Models (LLMs) have shown significant advancements in various domains, and their emergent abilities suggest their potential to revolutionize industries. In this research, we evaluate the performance of LLMs on real-world penetration testing tasks using a robust benchmark created from test machines with platforms. Our findings reveal that while LLMs demonstrate proficiency in specific sub-tasks within the penetration testing process, such as using testing tools, interpreting outputs, and proposing subsequent actions, they also encounter difficulties maintaining an integrated understanding of the overall testing scenario. In response to these insights, we introduce PentestGPT, an LLM-empowered automatic penetration testing tool that leverages the abundant domain knowledge inherent in LLMs. PentestGPT is meticulously designed with three self-interacting modules, each addressing individual sub-tasks of penetration testing, to mitigate the challenges related to context loss. Our evaluation shows that PentestGPT not only outperforms LLMs with a task-completion increase of 228.6\% compared to the \gptthree model among the benchmark targets but also proves effective in tackling real-world penetration testing challenges. Having been open-sourced on GitHub, PentestGPT has garnered over 4,700 stars and fostered active community engagement, attesting to its value and impact in both the academic and industrial spheres.
Fock states with a well-defined number of photons in an oscillator have shown a wide range of applications in quantum information science. Nonetheless, their usefulness has been marred by single and multiple photon losses due to unavoidable environment-induced dissipation. Though several dissipation engineering methods have been developed to counteract the leading single-photon loss error, averting multiple photon losses remains elusive. Here, we experimentally demonstrate a dissipation engineering method that autonomously stabilizes multi-photon Fock states against losses of multiple photons using a cascaded selective photon-addition operation in a superconducting quantum circuit. Through measuring the photon-number populations and Wigner tomography of the oscillator states, we observe a prolonged preservation of nonclassical Wigner negativities for the stabilized Fock states $\vert N\rangle$ with $N=1,2,3$ for a duration of about 10 ms. Furthermore, the dissipation engineering method demonstrated here also facilitates the implementation of a non-unitary operation for resetting a binomially-encoded logical qubit. These results highlight potential applications in error-correctable quantum information processing against multi-photon-loss errors.
Diffusive limit of the Vlasov-Poisson-Boltzmann system without angular cutoff in the framework of perturbation around global Maxwellian still remains open. By employing the weighted energy method with a newly introduced weight function $w_l(α,β)$ and some novel treatments, we solve this problem for the full range of non-cutoff potentials $γ>-3$ and $0 -3$ and $0<s<1$.
Diffusive limit of the non-cutoff Vlasov-Maxwell-Boltzmann system in perturbation framework still remains open. By employing a new weight function and making full use of the anisotropic dissipation property of the non-cutoff linearized Boltzmann operator, we solve this problem with some novel treatments for non-cutoff potentials $γ> \max\{-3, -\frac{3}{2}-2s\}$, including both strong angular singularity $\frac{1}{2} \leq s <1$ and weak angular singularity $0 < s < \frac{1}{2}$. Uniform estimate with respect to the Knudsen number $\varepsilon\in (0,1]$ is established globally in time, which eventually leads to the global existence of solutions to the non-cutoff Vlasov-Maxwell-Boltzmann system as well as hydrodynamic limit to the two-fluid incompressible Navier-Stokes-Fourier-Maxwell system with Ohm's law. The indicators $γ> \max\{-3, -\frac{3}{2}-2s\}$ and $0 < s <1$ in this paper cover all ranges that can be achieved by the previously established global solutions to the non-cutoff Vlasov-Maxwell-Boltzmann system in perturbation framework.
Millimeter wave (mmWave) has attracted considerable attention due to its wide bandwidth and high frequency. However, it is highly susceptible to blockages, resulting in significant degradation of the coverage and the sum rate. A promising approach is deploying distributed reconfigurable intelligent surfaces (RISs), which can establish extra communication links. In this paper, we investigate the impact of distributed RISs on the coverage probability and the sum rate in mmWave wireless communication systems. Specifically, we first introduce the system model, which includes the blockage, the RIS and the user distribution models, leveraging the Poisson point process. Then, we define the association criterion and derive the conditional coverage probabilities for the two cases of direct association and reflective association through RISs. Finally, we combine the two cases using Campbell's theorem and the total probability theorem to obtain the closed-form expressions for the ergodic coverage probability and the sum rate. Simulation results validate the effectiveness of the proposed analytical approach, demonstrating that the deployment of distributed RISs significantly improves the ergodic coverage probability by 45.4% and the sum rate by over 1.5 times.
In this paper, we investigate the millimeter-wave (mmWave) near-field beam training problem to find the correct beam direction. In order to address the high complexity and low identification accuracy of existing beam training techniques, we propose an efficient hashing multi-arm beam (HMB) training scheme for the near-field scenario. Specifically, we first design a set of sparse bases based on the polar domain sparsity of the near-field channel. Then, the random hash functions are chosen to construct the near-field multi-arm beam training codebook. Each multi-arm beam codeword is scanned in a time slot until all the predefined codewords are traversed. Finally, the soft decision and voting methods are applied to distinguish the signal from different base stations and obtain correctly aligned beams. Simulation results show that our proposed near-field HMB training method can reduce the beam training overhead to the logarithmic level, and achieve 96.4% identification accuracy of exhaustive beam training. Moreover, we also verify applicability under the far-field scenario.
In this paper, we investigate the beam training problem in the multi-user millimeter wave (mmWave) communication system, where multiple reconfigurable intelligent surfaces (RISs) are deployed to improve the coverage and the achievable rate. However, existing beam training techniques in mmWave systems suffer from the high complexity (i.e., exponential order) and low identification accuracy. To address these problems, we propose a novel hashing multi-arm beam (HMB) training scheme that reduces the training complexity to the logarithmic order with the high accuracy. Specifically, we first design a generation mechanism for HMB codebooks. Then, we propose a demultiplexing algorithm based on the soft decision to distinguish signals from different RIS reflective links. Finally, we utilize a multi-round voting mechanism to align the beams. Simulation results show that the proposed HMB training scheme enables simultaneous training for multiple RISs and multiple users, and reduces the beam training overhead to the logarithmic level. Moreover, it also shows that our proposed scheme can significantly improve the identification accuracy by at least 20% compared to existing beam training techniques.
We extend the polynomial Pell's equation satisfied by univariate Chebyshev polynomials on [--1, 1] from one variable to several variables, using orthogonal polynomials on regular domains that include cubes, balls, and simplexes of arbitrary dimension. Moreover, we show that such an equation is strongly connected (i) to a certificate of positivity (from real algebraic geometry) on the domain, as well as (ii) to the Christoffel functions of the equilibrium measure on the domain. In addition, the solution to Pell's equation reflects an extremal property of orthonormal polynomials associated with an entropy-like criterion.
The millimeter wave (mmWave) has received considerable interest due to its expansive bandwidth and high frequency. However, a noteworthy challenge arises from its vulnerability to blockages, leading to reduced coverage and achievable rates. To address these limitations, a potential solution is to deploy distributed reconfigurable intelligent surfaces (RISs), which comprise many low-cost and passively reflected elements, and can facilitate the establishment of extra communication links. In this paper, we leverage stochastic geometry to investigate the ergodic coverage probability and the achievable rate in both distributed RISs-assisted single-cell and multi-cell mmWave wireless communication systems. Specifically, we first establish the system model considering the stochastically distributed blockages, RISs and users by the Poisson point process. Then we give the association criterion and derive the association probabilities, the distance distributions, and the conditional coverage probabilities for two cases of associations between base stations and users without or with RISs. Finally, we use Campbell's theorem and the total probability theorem to obtain the closed-form expressions of the ergodic coverage probability and the achievable rate. Simulation results verify the effectiveness of our analysis method, and demonstrate that by deploying distributed RISs, the ergodic coverage probability is significantly improved by approximately 50%, and the achievable rate is increased by more than 1.5 times.
The rise of mobile devices with abundant sensory data and local computing capabilities has driven the trend of federated learning (FL) on these devices. And personalized FL (PFL) emerges to train specific deep models for each mobile device to address data heterogeneity and varying performance preferences. However, mobile training times vary significantly, resulting in either delay (when waiting for slower devices for aggregation) or accuracy decline (when aggregation proceeds without waiting). In response, we propose a shift towards asynchronous PFL, where the server aggregates updates as soon as they are available. Nevertheless, existing asynchronous protocols are unfit for PFL because they are devised for federated training of a single global model. They suffer from slow convergence and decreased accuracy when confronted with severe data heterogeneity prevalent in PFL. Furthermore, they often exclude slower devices for staleness control, which notably compromises accuracy when these devices possess critical personalized data. Therefore, we propose EchoPFL, a coordination mechanism for asynchronous PFL. Central to EchoPFL is to include updates from all mobile devices regardless of their latency. To cope with the inevitable staleness from slow devices, EchoPFL revisits model broadcasting. It intelligently converts the unscalable broadcast to on-demand broadcast, leveraging the asymmetrical bandwidth in wireless networks and the dynamic clustering-based PFL. Experiments show that compared to status quo approaches, EchoPFL achieves a reduction of up to 88.2% in convergence time, an improvement of up to 46% in accuracy, and a decrease of 37% in communication costs
We define positive and strictly positive definite functions on a domain and study these functions on a list of regular domains. The list includes the unit ball, conic surface, hyperbolic surface, solid hyperboloid, and simplex. Each of these domains is embedded in a quadrant or a union of quadrants of the unit sphere by a distance preserving map, from which characterizations of positive definite and strictly positive definite functions are derived for these regular domains.
This report details the methods of the winning entry of the AVDN Challenge in ICCV CLVL 2023. The competition addresses the Aerial Navigation from Dialog History (ANDH) task, which requires a drone agent to associate dialog history with aerial observations to reach the destination. For better cross-modal grounding abilities of the drone agent, we propose a Target-Grounded Graph-Aware Transformer (TG-GAT) framework. Concretely, TG-GAT first leverages a graph-aware transformer to capture spatiotemporal dependency, which benefits navigation state tracking and robust action planning. In addition,an auxiliary visual grounding task is devised to boost the agent's awareness of referred landmarks. Moreover, a hybrid augmentation strategy based on large language models is utilized to mitigate data scarcity limitations. Our TG-GAT framework won the AVDN Challenge, with 2.2% and 3.0% absolute improvements over the baseline on SPL and SR metrics, respectively. The code is available at https://github.com/yifeisu/TG-GAT.
Adversarial training is an important topic in robust deep learning, but the community lacks attention to its practical usage. In this paper, we aim to resolve a real-world challenge, i.e., training a model on an imbalanced and noisy dataset to achieve high clean accuracy and adversarial robustness, with our proposed Omnipotent Adversarial Training (OAT) strategy. OAT consists of two innovative methodologies to address the imperfection in the training set. We first introduce an oracle into the adversarial training process to help the model learn a correct data-label conditional distribution. This carefully-designed oracle can provide correct label annotations for adversarial training. We further propose logits adjustment adversarial training to overcome the data imbalance issue, which can help the model learn a Bayes-optimal distribution. Our comprehensive evaluation results show that OAT outperforms other baselines by more than 20% clean accuracy improvement and 10% robust accuracy improvement under complex combinations of data imbalance and label noise scenarios. The code can be found in https://github.com/GuanlinLee/OAT.
We study orthogonal polynomials for a weight function defined over a domain of revolution, where the domain is formed from rotating a two-dimensional region and goes beyond the quadratic domains. Explicit constructions of orthogonal bases are provided for weight functions on a number of domains. Particular attention is paid to the setting when an orthogonal basis can be constructed explicitly in terms of known polynomials of either one or two variables. Several new families of orthogonal polynomials are derived, including a few families that are eigenfunctions of a spectral operator and their reproducing kernels satisfy an addition formula.
Controlling the flow of quantum information is a fundamental task for quantum computers, which is unfeasible to realize on classical devices. Coherent devices which can process quantum states are thus required to route the quantum states that encode information. In this paper we demonstrate experimentally the smallest quantum transistor with a superconducting quantum processor which is composed of a collector qubit, an emitter qubit, and a coupler (transistor gate). The interaction strength between the collector and emitter qubits is controlled by the frequency and state of the coupler, effectively implementing a quantum switch. Through the coupler-state-dependent Heisenberg (inherent) interaction between the qubits, a single-step (native) conditional $i$SWAP operation can be applied. To this end, we find that it is important to take into consideration higher energy level for achieving a native and high-fidelity transistor operation. By reconstructing the Quantum Process Tomography, we obtain an operation fidelity of $92.36\%$ when the transistor gate is open ($i$SWAP implementation) and $95.23 \%$ in the case of closed gate (identity gate implementation). The architecture has strong potential in quantum information processing applications with superconducting qubits.
Recent advances in machine learning and natural language processing have fostered the enormous prosperity of smart voice assistants and their services, e.g., Alexa, Google Home, Siri, etc. However, voice spoofing attacks are deemed to be one of the major challenges of voice control security, and never stop evolving such as deep-learning-based voice conversion and speech synthesis techniques. To solve this problem outside the acoustic domain, we focus on head-wearable devices, such as earbuds and virtual reality (VR) headsets, which are feasible to continuously monitor the bone-conducted voice in the vibration domain. Specifically, we identify that air and bone conduction (AC/BC) from the same vocalization are coupled (or concurrent) and user-level unique, which makes them suitable behavior and biometric factors for multi-factor authentication (MFA). The legitimate user can defeat acoustic domain and even cross-domain spoofing samples with the proposed two-stage AirBone authentication. The first stage answers \textit{whether air and bone conduction utterances are time domain consistent (TC)} and the second stage runs \textit{bone conduction speaker recognition (BC-SR)}. The security level is hence increased for two reasons: (1) current acoustic attacks on smart voice assistants cannot affect bone conduction, which is in the vibration domain; (2) even for advanced cross-domain attacks, the unique bone conduction features can detect adversary's impersonation and machine-induced vibration. Finally, AirBone authentication has good usability (the same level as voice authentication) compared with traditional MFA and those specially designed to enhance smart voice security. Our experimental results show that the proposed AirBone authentication is usable and secure, and can be easily equipped by commercial off-the-shelf head wearables with good user experience.