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
In this paper, we present a new method for reducing seismic noise while preserving structural and stratigraphic discontinuities. Structure-oriented edge-preserving smoothing requires information such as the local orie...In this paper, we present a new method for reducing seismic noise while preserving structural and stratigraphic discontinuities. Structure-oriented edge-preserving smoothing requires information such as the local orientation and edge of the reflections. The information is usually estimated from seismic data with full frequency bandwidth. When the data has a very low signal to noise ratio （SNR）, the noise usually reduces the estimation accuracy. For seismic data with extremely low SNR, the dominant frequency has higher SNR than other frequencies, so it can provide orientation and edge information more reliably than other frequencies. Orientation and edge are usually described in terms of apparent reflection dips and coherence differences, respectively. When frequency changes, both dip and coherence difference change more slowly than the seismogram itself. For this reason, dip and coherence estimated from dominant frequency data can approximately represent those of other frequency data. Ricker wavelet are widely used in seismic modeling. The Marr wavelet has the same shape as Ricker wavelets in both time and frequency domains, so the Marr wavelet transform is selected to divide seismic data into several frequency bands. Reflection apparent dip as well as the edge information can be obtained by scanning the dominant frequency data. This information can be used to selectively smooth the frequency bands （dominant, low, and high frequencies） separately by structure-oriented edge-preserving smoothing technology. The ultimate noise-suppressed seismic data is the combination of the smoothed frequency band data. Application to synthetic and real data shows the method can effectively reduce noise, preserve edges, improve trackable reflection continuity, and maintain useful information in seismic data.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.
基金supported by China National Petroleum Corporation (CNPC) Innovation Fund (Grant No.07E1019)Specialized Research Fund for the Doctoral Program of Higher Education (SRFDP) (Grant No.200804251502)
文摘In this paper, we present a new method for reducing seismic noise while preserving structural and stratigraphic discontinuities. Structure-oriented edge-preserving smoothing requires information such as the local orientation and edge of the reflections. The information is usually estimated from seismic data with full frequency bandwidth. When the data has a very low signal to noise ratio （SNR）, the noise usually reduces the estimation accuracy. For seismic data with extremely low SNR, the dominant frequency has higher SNR than other frequencies, so it can provide orientation and edge information more reliably than other frequencies. Orientation and edge are usually described in terms of apparent reflection dips and coherence differences, respectively. When frequency changes, both dip and coherence difference change more slowly than the seismogram itself. For this reason, dip and coherence estimated from dominant frequency data can approximately represent those of other frequency data. Ricker wavelet are widely used in seismic modeling. The Marr wavelet has the same shape as Ricker wavelets in both time and frequency domains, so the Marr wavelet transform is selected to divide seismic data into several frequency bands. Reflection apparent dip as well as the edge information can be obtained by scanning the dominant frequency data. This information can be used to selectively smooth the frequency bands （dominant, low, and high frequencies） separately by structure-oriented edge-preserving smoothing technology. The ultimate noise-suppressed seismic data is the combination of the smoothed frequency band data. Application to synthetic and real data shows the method can effectively reduce noise, preserve edges, improve trackable reflection continuity, and maintain useful information in seismic data.
