We study the Cauchy problem of the Kolmogorov-Fokker-Planck equations and show that the solution enjoys an analytic smoothing effect with L?initial datum for positive time.
Adversarial attacks pose a significant threat to artificial intelligence systems by exposing them to vulnerabilities in deep learning models.Existing defense mechanisms often suffer drawbacks,such as the need for mode...Adversarial attacks pose a significant threat to artificial intelligence systems by exposing them to vulnerabilities in deep learning models.Existing defense mechanisms often suffer drawbacks,such as the need for model retraining,significant inference time overhead,and limited effectiveness against specific attack types.Achieving perfect defense against adversarial attacks remains elusive,emphasizing the importance of mitigation strategies.In this study,we propose a defense mechanism that applies random cropping and Gaussian filtering to input images to mitigate the impact of adversarial attacks.First,the image was randomly cropped to vary its dimensions and then placed at the center of a fixed 299299 space,with the remaining areas filled with zero padding.Subsequently,Gaussian×filtering with a 77 kernel and a standard deviation of two was applied using a convolution operation.Finally,the×smoothed image was fed into the classification model.The proposed defense method consistently appeared in the upperright region across all attack scenarios,demonstrating its ability to preserve classification performance on clean images while significantly mitigating adversarial attacks.This visualization confirms that the proposed method is effective and reliable for defending against adversarial perturbations.Moreover,the proposed method incurs minimal computational overhead,making it suitable for real-time applications.Furthermore,owing to its model-agnostic nature,the proposed method can be easily incorporated into various neural network architectures,serving as a fundamental module for adversarial defense strategies.展开更多
Combining TT* argument and bilinear interpolation,this paper obtains the Strichartz and smoothing estimates of dispersive semigroup e^(-itP(D)) in weighted L^(2) spaces.Among other things,we recover the results in[1]....Combining TT* argument and bilinear interpolation,this paper obtains the Strichartz and smoothing estimates of dispersive semigroup e^(-itP(D)) in weighted L^(2) spaces.Among other things,we recover the results in[1].Moreover,the application of these results to the well-posedness of some equations are shown in the last section.展开更多
We demonstrate a new polarization smoothing(PS)approach utilizing residual stress birefringence in fused silica to create a spatially random polarization control plate(SRPCP),thereby improving target illumination unif...We demonstrate a new polarization smoothing(PS)approach utilizing residual stress birefringence in fused silica to create a spatially random polarization control plate(SRPCP),thereby improving target illumination uniformity in inertial confinement fusion(ICF)laser systems.The fundamental operating mechanism and key fabrication techniques for the SRPCP are systematically developed and experimentally validated.The SRPCP converts a linearly polarized 3ω incident laser beam into an output beam with a spatially randomized polarization distribution.When combined with a continuous phase plate,the SRPCP effectively suppresses high-intensity speckles at all spatial frequencies in the focal spot.The proposed PS technique is specifically designed for high-fluence large-aperture laser systems,enabling novel polarization control regimes in laser-driven ICF.展开更多
基金Supported by NSFC (No.12031006)Fundamental Research Funds for the Central Universities of China。
文摘We study the Cauchy problem of the Kolmogorov-Fokker-Planck equations and show that the solution enjoys an analytic smoothing effect with L?initial datum for positive time.
基金supported by the Glocal University 30 Project Fund of Gyeongsang National University in 2025.
文摘Adversarial attacks pose a significant threat to artificial intelligence systems by exposing them to vulnerabilities in deep learning models.Existing defense mechanisms often suffer drawbacks,such as the need for model retraining,significant inference time overhead,and limited effectiveness against specific attack types.Achieving perfect defense against adversarial attacks remains elusive,emphasizing the importance of mitigation strategies.In this study,we propose a defense mechanism that applies random cropping and Gaussian filtering to input images to mitigate the impact of adversarial attacks.First,the image was randomly cropped to vary its dimensions and then placed at the center of a fixed 299299 space,with the remaining areas filled with zero padding.Subsequently,Gaussian×filtering with a 77 kernel and a standard deviation of two was applied using a convolution operation.Finally,the×smoothed image was fed into the classification model.The proposed defense method consistently appeared in the upperright region across all attack scenarios,demonstrating its ability to preserve classification performance on clean images while significantly mitigating adversarial attacks.This visualization confirms that the proposed method is effective and reliable for defending against adversarial perturbations.Moreover,the proposed method incurs minimal computational overhead,making it suitable for real-time applications.Furthermore,owing to its model-agnostic nature,the proposed method can be easily incorporated into various neural network architectures,serving as a fundamental module for adversarial defense strategies.
基金supported by the NSFC(12071437)the National Key R&D Program of China(2022YFA1005700).
文摘Combining TT* argument and bilinear interpolation,this paper obtains the Strichartz and smoothing estimates of dispersive semigroup e^(-itP(D)) in weighted L^(2) spaces.Among other things,we recover the results in[1].Moreover,the application of these results to the well-posedness of some equations are shown in the last section.
基金supported by the National Natural Science Foundation of China(Grant No.62275235).
文摘We demonstrate a new polarization smoothing(PS)approach utilizing residual stress birefringence in fused silica to create a spatially random polarization control plate(SRPCP),thereby improving target illumination uniformity in inertial confinement fusion(ICF)laser systems.The fundamental operating mechanism and key fabrication techniques for the SRPCP are systematically developed and experimentally validated.The SRPCP converts a linearly polarized 3ω incident laser beam into an output beam with a spatially randomized polarization distribution.When combined with a continuous phase plate,the SRPCP effectively suppresses high-intensity speckles at all spatial frequencies in the focal spot.The proposed PS technique is specifically designed for high-fluence large-aperture laser systems,enabling novel polarization control regimes in laser-driven ICF.
