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The Belief Rule-Based (BRB) system faces the rule combination explosion issue, making it challenging to construct the rule base efficiently. The Extended Belief Rule-Based (EBRB) system offers a solution to this problem by using data-driven methods. However, using EBRB system requires the traversal of the entire rule base, which can be time-consuming and result in the activation of many irrelevant rules, leading to an incorrect decision. Existing search optimization methods can somewhat solve this issue, but they have limitations. Moreover, the calculation of the rule activation weight only considers the similarity between input data and a single rule, ignoring the influence of the rule linkage. To address these problems, we propose a new EBRB system based on the K-Nearest Neighbor graph index (Graph-EBRB). We introduce the Hierarchical Navigable Small World (HNSW) algorithm to create the K-Nearest Neighbor graph index of the EBRB system. This index allows us to efficiently search and activate a set of key rules. We also propose a new activation weight calculation method based on the Graph Convolution Neural Network (GCN), and we optimize the system performance using a parameter learning strategy. We conduct a comprehensive experiment on 14 commonly used public data sets, and the results show that Graph-EBRB system significantly improves the reasoning efficiency and accuracy of the EBRB system. Finally, we apply the Graph-EBRB system to tree disease identification and achieve excellent classification performance, identifying over 90% of the diseased trees on the complete dataset. [ABSTRACT FROM AUTHOR]

• An improved multi-bubble algorithm for the free surface lattice Boltzmann method (FSLBM) is provided. • The algorithm can efficiently simulate the bubble splitting and merging process. • As an extension of FSLBM, it can be used to solve a wider range of two-phase flow more efficiently. • The algorithm is validated by using analytical solution and experimental results. Flow with bubbles is a commonly occurring phenomenon in nature and industrial applications. This study provides a multi-bubble model for the free surface lattice Boltzmann method (FSLBM) which can be used to simulate fluid flow with bubbles as well as their splitting and merging processes. FSLBM neglects the flow of gas and considers only the gas pressure, and thus simplifies the gas-liquid two-phase flow to a single-phase free surface. The compression of the bubble will influence its pressure and lead to movement, splitting, or merging processes within the bubble flow. The multi-bubble model considers the evolution of bubble's pressure by enhancing the model for free surface which simulates the behavior of gas-liquid interface inside the liquid. The Smagorinsky subgrid-scale model (SGS) and the more advanced multiple-relaxation-time (MRT) collision model is used for high Reynolds number. In this study, a bubble algorithm to handle the bubble splitting and merging without incurring significant computational costs is provided. The verification and analysis of this model are given by a comparison between both analytical solution and an experiment. Therefore, the multi-bubble as an extension of FSLBM can be used to solve a wider range of two-phase flow problems more efficiently, such as bubble formation, metal foaming process, and development in chemical reactors. [ABSTRACT FROM AUTHOR]

Multiobjective optimization problems (MOPs) are the optimization problem with multiple conflicting objectives. Generally, an optimization algorithm can find a large number of optimal solutions for MOPs, which easily overwhelm decision makers (DMs) and make it difficult for decision-making. Preference-based evolutionary multiobjective optimization (EMO) aims to find the partial optima in the regions preferred by the DM. Although it narrows the scope of the optimal solutions, it usually still returns a population of optimal solutions (typically 100 or larger in EMO) with a small distance between adjacent optima. Top-K, which is a well-established research subject in many fields to find the best K solutions, may be a direction to reduce the number of optimal solutions. In this paper, first, we introduce the top-K notion into preference-based EMO and propose the top-K model to obtain the best K individuals of multiobjective optimization problems (MOPs). Then, with the top-K model, we propose NSGA-II-TopK and SPEA2-TopK to search for the top-K preferred solutions for preference-based continuous and combinatorial MOPs, respectively. Finally, the proposed algorithms with several representative preference-based EMO algorithms are compared in different preference situations for MOPs. Experimental results show the proposed algorithms have strong performances against the compared algorithms. [ABSTRACT FROM AUTHOR]

To solve constrained optimization problems (COPs), it is crucial to guide the infeasible solution to a feasible region. Gradient-based repair (GR) is a successful repair strategy, where the forward difference is often used to estimate the gradient. However, GR has major deficiencies. First, it is difficult to deal with individuals falling into the local optima. Second, large amounts of fitness evaluations are required to estimate the gradient. In this paper, we proposed a new repair strategy, random direction repair (RDR). RDR generates a set of random directions, and calculates the repair direction and the repair step size of infeasible individual to reduce its constraint violation. Since the introduction of randomness, RDR could deal with individuals falling into the local optima. Furthermore, RDR only requires a few number of fitness evaluation. To demonstrate the performance of RDR, RDR was embedded into two state-of-the-art evolutionary continuous constrained optimization algorithms, tested on the Congress on Evolutionary Computation 2017 constrained real-parameter optimization benchmark. Experimental results demonstrated that RDR combined with evolutionary algorithms are highly competitive. [ABSTRACT FROM AUTHOR]

Large language models have revolutionized natural language processing, leading to the emergence of Embedding as a Service (EaaS). While EaaS facilitates access to advanced embedding models, it also presents challenges in copyright protection. Current research primarily relies on single-target watermarking frameworks, where a predefined vector is integrated as a watermark into text embeddings. However, these approaches are vulnerable to watermark information leakage. To investigate this issue, we introduce the Embedding Similarity Shift Attack (ESSA), an innovative attack algorithm designed to detect trigger instances in single-target watermarking systems by analyzing similarity shifts among constructed reference sentence pairs. Additionally, to defend against such an attack, we propose Adaptive Multi-Target Watermarking (AMT-WM). AMT-WM stands as the pioneering multi-target watermarking method aimed at safeguarding the copyright of EaaS. Specifically, AMT-WM constructs multiple watermarks through the utilization of orthogonal vectors to mitigate selection bias towards a particular vector. Furthermore, it incorporates a randomly selected sentence embedding as the base embedding to enhance the confidentiality of backdoored embeddings. For multi-target watermarking, we implement adaptive watermark injection and validation based on similarity. Comprehensive experiments conducted on various datasets validate the effectiveness of ESSA in trigger detection performance and the efficacy of AMT-WM in copyright protection. Our code will be available soon. [ABSTRACT FROM AUTHOR]

For H2+ at the critical internuclear distance where the charge-resonance-enhanced ionization is most prominent, the lateral photoelectron momentum distribution presents the Fraunhofer-like diffraction pattern: a central disk surrounded by one or more rings. We study this phenomenon by simulating the time-dependent Schrödinger equation and unveil the mechanism: the stretched molecule constructs an interatomic Coulomb potential, which works as a circular aperture and diffracts the electron when it travels between two nuclei. This distinct lateral photoelectron momentum distribution offers another perspective to look into molecular structures. [ABSTRACT FROM AUTHOR]