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In this paper, we study the coupled Schr\"odinger-KdV system \begin{align*} \begin{cases} -\Delta u +\lambda_1 u=u^3+\beta uv~~&\text{in}~~\mathbb{R}^{3}, \\-\Delta v +\lambda_2 v=\frac{1}{2}v^2+\frac{1}{2}\beta u^2~~&\text{in}~~\mathbb{R}^{3} \end{cases} \end{align*} subject to the mass constraints \begin{equation*} \int_{\mathbb{R}^{3}}|u|^2 dx=a,\quad \int_{\mathbb{R}^{3}}|v|^2 dx=b, \end{equation*} where $a, b>0$ are given constants, $\beta>0$, and the frequencies $\lambda_1,\lambda_2$ arise as Lagrange multipliers. The system exhibits $L^2$-supercritical growth. Using a novel constraint minimization approach, we demonstrate the existence of a local minimum solution to the system. Furthermore, we establish the existence of normalized ground state solutions., Comment: 17 pages, accepted by Z. Angew. Math. Phys

Graph Neural Networks have been widely applied in critical decision-making areas that demand interpretable predictions, leading to the flourishing development of interpretability algorithms. However, current graph interpretability algorithms tend to emphasize generality and often overlook biological significance, thereby limiting their applicability in predicting cancer drug responses. In this paper, we propose a novel post-hoc interpretability algorithm for cancer drug response prediction, CETExplainer, which incorporates a controllable edge-type-specific weighting mechanism. It considers the mutual information between subgraphs and predictions, proposing a structural scoring approach to provide fine-grained, biologically meaningful explanations for predictive models. We also introduce a method for constructing ground truth based on real-world datasets to quantitatively evaluate the proposed interpretability algorithm. Empirical analysis on the real-world dataset demonstrates that CETExplainer achieves superior stability and improves explanation quality compared to leading algorithms, thereby offering a robust and insightful tool for cancer drug prediction.

Predicting the response of a cancer cell line to a therapeutic drug is pivotal for personalized medicine. Despite numerous deep learning methods that have been developed for drug response prediction, integrating diverse information about biological entities and predicting the directional response remain major challenges. Here, we propose a novel interpretable predictive model, DRExplainer, which leverages a directed graph convolutional network to enhance the prediction in a directed bipartite network framework. DRExplainer constructs a directed bipartite network integrating multi-omics profiles of cell lines, the chemical structure of drugs and known drug response to achieve directed prediction. Then, DRExplainer identifies the most relevant subgraph to each prediction in this directed bipartite network by learning a mask, facilitating critical medical decision-making. Additionally, we introduce a quantifiable method for model interpretability that leverages a ground truth benchmark dataset curated from biological features. In computational experiments, DRExplainer outperforms state-of-the-art predictive methods and another graph-based explanation method under the same experimental setting. Finally, the case studies further validate the interpretability and the effectiveness of DRExplainer in predictive novel drug response. Our code is available at: https://github.com/vshy-dream/DRExplainer.

WiFi human sensing is highly regarded for its low-cost and privacy advantages in recognizing human activities. However, its effectiveness is largely confined to controlled, single-user, line-of-sight settings, limited by data collection complexities and the scarcity of labeled datasets. Traditional cross-modal methods, aimed at mitigating these limitations by enabling self-supervised learning without labeled data, struggle to extract meaningful features from amplitude-phase combinations. In response, we introduce AutoSen, an innovative automatic WiFi sensing solution that departs from conventional approaches. AutoSen establishes a direct link between amplitude and phase through automated cross-modal autoencoder learning. This autoencoder efficiently extracts valuable features from unlabeled CSI data, encompassing amplitude and phase information while eliminating their respective unique noises. These features are then leveraged for specific tasks using few-shot learning techniques. AutoSen's performance is rigorously evaluated on a publicly accessible benchmark dataset, demonstrating its exceptional capabilities in automatic WiFi sensing through the extraction of comprehensive cross-modal features.

Carbon allotropes have vast potential in various applications, including superconductivity, energy storage, catalysis, and photoelectric semiconductor devices. Recently, there has been significant research interest in exploring new carbon materials that exhibit unique electronic structures. Here, we propose a novel two-dimensional (2D) carbon allotrope called TCH-SSH-2D, which possesses a Dirac node-line (DNL) semimetallic state. The structure of TCH-SSH-2D is derived from the TCH-type Archimedean polyhedral carbon cluster units, combined with the SSH lattice model, possessing a space group of tetragonal P4/mmm. Using first-principles calculations, we demonstrate that the system is dynamically, thermodynamically, and mechanically stable. It exhibits an energetically favorable structure with no imaginary frequency in the phonon dispersion curves and elastic constants satisfying the Born-Huang stability criterion. Our findings not only contribute to a deeper understanding of the carbon allotrope family but also provide an opportunity to explore unique Dirac states in two-dimensional pure carbon systems.

The appearance of van Hove singularities near the Fermi level leads to prominent phenomena, including superconductivity, charge density wave, and ferromagnetism. Here a bilayer Kagome lattice with multiple van Hove singularities is designed and a novel borophene with such lattice (BK-borophene) is proposed by the first-principles calculations. BK-borophene, which is formed via three-center two-electron (3c-2e) sigma-type bonds, is predicted to be energetically, dynamically, thermodynamically, and mechanically stable. The electronic structure hosts both conventional and high-order van Hove singularities in one band. The conventional van Hove singularity resulting from the horse saddle is 0.065 eV lower than the Fermi level, while the high-order one resulting from the monkey saddle is 0.385 eV below the Fermi level. Both the singularities lead to the divergence of electronic density of states. Besides, the high-order singularity is just intersected to a Dirac-like cone, where the Fermi velocity can reach 1340000 m/s. The interaction between the two Kagome lattices is critical for the appearance of high-order van Hove singularities. The novel bilayer Kagome borophene with rich and intriguing electronic structure offers an unprecedented platform for studying correlation phenomena in quantum material systems and beyond.