arXiv subjects

Liyan Song

Publications and source records attributed to Liyan Song.

6 recordsLinked to original sources

arXiv2026

A fractional attraction-repulsion chemotaxis system with generalized logistic source and nonlinear productions

This paper studies a fractional attraction-repulsion system with generalized logistic source and nonlinear productions: \begin{equation*} \left\{ \begin{aligned} &u_t = -(-\Delta)^\alpha u - \chi_1 \nabla \cdot (u \nabla v) + \chi_2 \nabla \cdot (u \nabla w) + au - bu^\gamma, &x \in \mathbb{R}^N, \, t > 0, \\ &0 = \Delta v - \lambda_1 v + \mu_1 u^k, &x \in \mathbb{R}^N, \, t > 0, \\ &0 = \Delta w - \lambda_2 w + \mu_2 u^k, &x \in \mathbb{R}^N, \, t > 0. \end{aligned} \right. \end{equation*} We first establish the global boundedness of classical solutions with nonnegative bounded and uniformly continuous initial data in two different cases: $\gamma \geq k + 1$ and $\gamma < k + 1$, respectively. Next, we show the asymptotic behavior of the global solutions for both cases $\gamma = k + 1$ and $\gamma \neq k + 1$. Finally, we obtain the spreading speed of solutions. In particular, when $\gamma = k + 1$, the upper bound of the spreading speed increases monotonically with $k$. If the condition of balanced attraction-repulsion intensities is further specified, the spreading speed will be equal to $\frac{a}{N + 2\alpha}$.

math.AP↗

arXiv2026

A fractional attraction-repulsion chemotaxis system with time-space dependent growth source and nonlinear productions

This paper studies a fractional attraction-repulsion system with time-space dependent growth source and nonlinear productions: \begin{equation*} \left\{ \begin{aligned}\label{1.1} &u_t = -(-\Delta)^\alpha u - \chi_1 \nabla \cdot (u \nabla v_1) + \chi_2 \nabla \cdot (u \nabla v_2) + a(x,t)u - b(x,t)u^\gamma, &x \in \mathbb{R}^N, \, t > 0, \\ &0 = \Delta v_1 - \lambda_1 v_1 + \mu_1 u^k, &x \in \mathbb{R}^N, \, t > 0, \\ &0 = \Delta v_2 - \lambda_2 v_2 + \mu_2 u^k, &x \in \mathbb{R}^N, \, t > 0. \end{aligned} \right. \end{equation*} We first establish the global boundedness of classical solutions with nonnegative bounded and uniformly continuous initial data in two different cases: $\gamma \geq k + 1$ and $\gamma < k + 1$, respectively. For a fixed $\gamma$, when $k$ exceeds the critical value $\gamma - 1$, a larger $b$ must be chosen to suppress the blow-up of the solution. Moreover, we show the persistence of the global solutions for both cases $\gamma = k + 1$ and $\gamma \neq k + 1$.

math.AP↗

arXiv2024

Comprehensive Review and Empirical Evaluation of Causal Discovery Algorithms for Numerical Data

Causal analysis has become an essential component in understanding the underlying causes of phenomena across various fields. Despite its significance, existing literature on causal discovery algorithms is fragmented, with inconsistent methodologies, i.e., there is no universal classification standard for existing methods, and a lack of comprehensive evaluations, i.e., data characteristics are often ignored to be jointly analyzed when benchmarking algorithms. This study addresses these gaps by conducting an exhaustive review and empirical evaluation for causal discovery methods on numerical data, aiming to provide a clearer and more structured understanding of the field. Our research begins with a comprehensive literature review spanning over two decades, analyzing over 200 academic articles and identifying more than 40 representative algorithms. This extensive analysis leads to the development of a structured taxonomy tailored to the complexities of causal discovery, categorizing methods into six main types. To address the lack of comprehensive evaluations, our study conducts an extensive empirical assessment of 29 causal discovery algorithms on multiple synthetic and real-world datasets. We categorize synthetic datasets based on size, linearity, and noise distribution, employing five evaluation metrics, and summarize the top-3 algorithm recommendations, providing guidelines for users in various data scenarios. Our results highlight a significant impact of dataset characteristics on algorithm performance. Moreover, a metadata extraction strategy with an accuracy exceeding 80% is developed to assist users in algorithm selection on unknown datasets. Based on these insights, we offer professional and practical guidelines to help users choose the most suitable causal discovery methods for their specific dataset.

cs.AI↗

arXiv2023

ItoV: Efficiently Adapting Deep Learning-based Image Watermarking to Video Watermarking

Robust watermarking tries to conceal information within a cover image/video imperceptibly that is resistant to various distortions. Recently, deep learning-based approaches for image watermarking have made significant advancements in robustness and invisibility. However, few studies focused on video watermarking using deep neural networks due to the high complexity and computational costs. Our paper aims to answer this research question: Can well-designed deep learning-based image watermarking be efficiently adapted to video watermarking? Our answer is positive. First, we revisit the workflow of deep learning-based watermarking methods that leads to a critical insight: temporal information in the video may be essential for general computer vision tasks but not for specific video watermarking. Inspired by this insight, we propose a method named ItoV for efficiently adapting deep learning-based Image watermarking to Video watermarking. Specifically, ItoV merges the temporal dimension of the video with the channel dimension to enable deep neural networks to treat videos as images. We further explore the effects of different convolutional blocks in video watermarking. We find that spatial convolution is the primary influential component in video watermarking and depthwise convolutions significantly reduce computational cost with negligible impact on performance. In addition, we propose a new frame loss to constrain that the watermark intensity in each video clip frame is consistent, significantly improving the invisibility. Extensive experiments show the superior performance of the adapted video watermarking method compared with the state-of-the-art methods on Kinetics-600 and Inter4K datasets, which demonstrate the efficacy of our method ItoV.

cs.CR↗

arXiv2013

Direct femtosecond pulse compression with miniature-sized Bragg cholesteric liquid crystal

Direct compression of femtosecond optical pulses from a Ti:sapphire laser oscillator was realized with a cholesteric liquid crystal acting as a nonlinear 1D periodic Bragg grating. With a 6-um thick sample, the pulse duration could be compressed from 100 to 48 femtoseconds. Coupled-mode equations for forward and backward waves were employed to simulate the dynamics therein and good agreement between theory and experiment was obtained.

physics.optics↗

arXiv2013

Buffering and Trapping Ultrashort Optical Pulses in Concatenated Bragg Gratings

Strong retardation of ultrashort optical pulses, including their deceleration and stoppage in the form of Bragg solitons in a cascaded Bragg-grating (BG) structure, is proposed. The manipulations of the pulses are carried out, using nonlinear effects, in a chirped BG segment which is linked, via a defect, to a uniform grating. The storage of the ultrashort pulses is shown to be very robust with respect to variations of the input field intensity, suggesting the feasibility of storing ultrafast optical pulses in such a structure. Physical estimates are produced for the BGs written in silicon.

nlin.PS↗