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In this paper, we consider the following Choquard type equation \begin{equation} \left\{\begin{aligned} &-\Delta u+\lambda u=\gamma(\Phi_N(|x|)\ast|u|^p)u \ \ \mbox{in $\mathbb{R}^N$}, \\ &\lim\limits_{|x|\to\infty}u(x)=0,\\ \end{aligned}\right. \end{equation} where $N\geq2,\lambda>0,\gamma>0, p\in[1,2]$ and $\Phi_N(|x|)$ denotes the fundamental solution of the Laplacian $-\Delta$ on $\mathbb{R}^N$. This equation does not have a variational frame when $p\neq 2.$ Instead of variational methods, we prove the existence and uniqueness of positive radial solutions of the above equation via the shooting method by establishing some new differential inequalities. The proofs are based on an analysis of the corresponding system of second-order differential equations, and our results extend the existing ones in the literature from $p=2$ to $p\in[1,2]$., Comment: 18pages

Topological superconductivity (TSC) is a promising platform to host Majorana zero mode (MZM) for topological quantum computing. Recently, the noble metal alloy AuSn$_{4}$ has been identified as an intrinsic surface TSC. However, the atomic visualization of its nontrivial surface states and MZM remains elusive. Here, we report the direct observation of unconventional surface states and vortex zero mode at the gold (Au) terminated surfaces of AuSn$_{4}$, by ultra-low scanning tunneling microscope/spectroscopy. Distinct from the trivial metallic bulk states at tin (Sn) surfaces, the Au terminated surface exhibits pronounced surface states near Fermi level. Our density functional theory calculations indicate that these states arise from unconventional Rashba bands, where two Fermi circles from different bands share identical helical spin textures, chiralities, and group velocities in the same direction. Furthermore, we find that although the superconducting gap, critical temperature, anisotropic in-plane critical field are almost identical on Au and Sn terminated surfaces, the in-gap bound states inside Abrikosov vortex cores show significant differences. The vortex on Sn terminated surfaces exhibits a conventional Caroli-de Gennes-Matricon bound state while the Au surface shows a sharp zero-energy core state with a long non-splitting distance, resembling an MZM in a non-quantum-limit condition. This distinction may result from the dominant contribution of unconventional Rashba bands near Fermi energy from Au terminated surface. Our results provide a new platform for studying unconventional Rashba band and MZM in superconductors., Comment: 17 pages, 4 figures

This paper is concerned with the existence and qualitative properties of positive ground state solutions for the planar Schr\"odinger-Newton equation on the disc. First, we prove the existence and radial symmetry of all the positive ground state solutions by employing the symmetric decreasing rearrangement and Talenti's inequality. Next, we develop Newton's theorem and then use the contraction mapping principle to establish the uniqueness of the positive ground state solution for the Schr\"odinger-Newton equation on the disc in the two dimensional case. Finally, we show that the unique positive ground state solution converges to the trivial solution as the radius $R$ tending to infinity, which is totally different from the higher dimensional case in \cite{Guo-Wang-Yi}., Comment: 16 pages

Connected and Autonomous Vehicles (CAVs) technology facilitates the advancement of intelligent transportation. However, intelligent control techniques for mixed traffic flow at signalized intersections involving both CAVs and Human-Driven Vehicles (HDVs) require further investigation into the impact of backward-looking effect. This paper proposes the concept of 1+n+1 mixed platoon considering the backward-looking effect, consisting of one leading CAV, n following HDVs, and one trailing CAV. The leading and trailing CAVs collectively guide the movement of intermediate HDVs at intersections, forming an optimal control framework for platoon-based CAVs at signalized intersections. Initially, a linearized dynamic model for the 1+n+1 mixed platoon is established and compared with a benchmark model focusing solely on controlling the lead vehicle. Subsequently, constraints are formulated for the optimal control framework, aiming to enhance overall intersection traffic efficiency and fuel economy by directly controlling the leading and trailing CAVs in the platoon. Finally, extensive numerical simulations compare vehicle throughput and fuel consumption at signalized intersections under different mixed platoon control methods, validating that considering both front and backward-looking effects in the mixed platoon control method outperforms traditional methods focusing solely on the lead CAV.

Thermophoresis is an effective method to drive the motion of nanoparticles in fluids. The transport of nanoparticles in polymer networks has significant fundamental and applied importance in biology and medicine, and can be described as Brownian particles crossing entropic barriers. This study proposes a novel extension of dissipative particle dynamics (DPD), called the single-particle energy-conserving dissipative particle dynamics (seDPD), which combines the features of single-particle dissipative particle dynamics (sDPD) and energy-conserving dissipative particle dynamics (eDPD) to simulate the thermophoresis of nanoparticles under temperature gradients. The reliability of the seDPD method is verified by considering the viscosity, thermal diffusivity, and hydrodynamic drag force on the nanoparticles. Using this method, the transport of nanoparticles driven by the thermophoretic force across the polymer network is simulated. The results show that the nanoparticles exhibit the phenomenon of giant acceleration of diffusion (GAD) in the polymer network, indicating that Brownian particles can exhibit GAD when crossing entropic barriers.

Providing explanations within the recommendation system would boost user satisfaction and foster trust, especially by elaborating on the reasons for selecting recommended items tailored to the user. The predominant approach in this domain revolves around generating text-based explanations, with a notable emphasis on applying large language models (LLMs). However, refining LLMs for explainable recommendations proves impractical due to time constraints and computing resource limitations. As an alternative, the current approach involves training the prompt rather than the LLM. In this study, we developed a model that utilizes the ID vectors of user and item inputs as prompts for GPT-2. We employed a joint training mechanism within a multi-task learning framework to optimize both the recommendation task and explanation task. This strategy enables a more effective exploration of users' interests, improving recommendation effectiveness and user satisfaction. Through the experiments, our method achieving 1.59 DIV, 0.57 USR and 0.41 FCR on the Yelp, TripAdvisor and Amazon dataset respectively, demonstrates superior performance over four SOTA methods in terms of explainability evaluation metric. In addition, we identified that the proposed model is able to ensure stable textual quality on the three public datasets.

As large-scale text-to-image generation models have made remarkable progress in the field of text-to-image generation, many fine-tuning methods have been proposed. However, these models often struggle with novel objects, especially with one-shot scenarios. Our proposed method aims to address the challenges of generalizability and fidelity in an object-driven way, using only a single input image and the object-specific regions of interest. To improve generalizability and mitigate overfitting, in our paradigm, a prototypical embedding is initialized based on the object's appearance and its class, before fine-tuning the diffusion model. And during fine-tuning, we propose a class-characterizing regularization to preserve prior knowledge of object classes. To further improve fidelity, we introduce object-specific loss, which can also use to implant multiple objects. Overall, our proposed object-driven method for implanting new objects can integrate seamlessly with existing concepts as well as with high fidelity and generalization. Our method outperforms several existing works. The code will be released.

Diffusion of Brownian particles in the tilted periodic potential, usually referred to the washboard potential (WBP), is a well-known model to describe physical systems out of equilibrium. Considering that the biological medium is flexible and thermally fluctuating, a new model, namely the soft matter potential (SMP), is proposed to describe the biological medium. Compared to the washboard potential (WBP), SMP allows Brownian particles to actively modify the structure of the biological medium. Brenner's homogenization theory is applied to predict the diffusivity and velocity of Brownian particles driven by external forces in SMP. Thermodynamic uncertainty relation (TUR) is analyzed for Brownian particles in SMP. It is found that, compared to WBP, Brownian particles in SMP require a lower energy cost $\langle q \rangle$ to achieve accuracy $\mathcal{A}$, i.e. Brownian particles in SMP have higher transport efficiency when driven by external forces.

Deepfake technology poses a significant threat to security and social trust. Although existing detection methods have shown high performance in identifying forgeries within datasets that use the same deepfake techniques for both training and testing, they suffer from sharp performance degradation when faced with cross-dataset scenarios where unseen deepfake techniques are tested. To address this challenge, we propose a Deep Information Decomposition (DID) framework to enhance the performance of Cross-dataset Deepfake Detection (CrossDF). Unlike most existing deepfake detection methods, our framework prioritizes high-level semantic features over specific visual artifacts. Specifically, it adaptively decomposes facial features into deepfake-related and irrelevant information, only using the intrinsic deepfake-related information for real/fake discrimination. Moreover, it optimizes these two kinds of information to be independent with a de-correlation learning module, thereby enhancing the model's robustness against various irrelevant information changes and generalization ability to unseen forgery methods. Our extensive experimental evaluation and comparison with existing state-of-the-art detection methods validate the effectiveness and superiority of the DID framework on cross-dataset deepfake detection.