Knowledge Graphs (KGs) are widely used in many fields of application, and especially play an essential role in recommendation systems. KGs often need to be complete, missing relationships between users and items, data sparsity, weak associations, and difficulties in knowledge inference, resulting in low credibility of recommendation results. Therefore, we propose a novel Knowledge Graph (KG) recommendation algorithms. Due to the availability of interaction data across numerous events, KGs also exhibit dynamics over time. By taking into account the temporal variable, it is possible to organise well-structured external information to connect users and items, thereby expanding user preferences to a certain extent. The proposed algorithm employs GCNs to encode the heterogeneous graph, which includes user-item interactions and the KG. It addresses the challenge of high-dimensional data by using the inner product of users and items. The algorithm uncovers potential alignment relationships and learns the embedding of user-item and relationships by applying convolutional processing to the graph data's features and performing data fusion, the new algorithm uncovers potential alignment relationships, and learns embedding of user-item and relationships. The experimental results on the Mean Reciprocal Rank (MRR) and Hits@k demonstrate that the proposed algorithm outperforms state-of-the-art algorithms in terms of the credibility and accuracy of recommendation results.

We perform a 2D Fourier transform along the horizontal direction on the 3D integration problem for the DC anomalous potential in the spatial domain, transforming it into a 1D integration problem with independent solutions at different wavenumbers. And the resulting 1D integral equation in the wavenumber domain is expressed as a sum of element integrals. We then employ the shape function method, using a quadratic shape function to characterize the scattering current density for each element and compute analytical expressions for the element integrals. Finally, we performed a 2D inverse Fourier transform of the wavenumber-domain anomalous potential and electric field to obtain their values in the spatial domain, which are modified using iterative operators. This approach fully leverages the efficiency of the Fourier transform method and the high accuracy of the shape function integration method to achieve faster and more accurate solutions to the 3D DC resistivity numerical simulation problem. Two examples demonstrate the accuracy and efficiency of our proposed algorithm. Numerical examples were used to analyze the relationship between the number of iterations and the anomaly conductivity difference during the convergence of the algorithm. It is shown that the algorithm converges faster for high resistance anomalies and can be applied to simulate models with significantly different resistivities between the background medium and the anomaly.

It is a key issue to find out all longest common subsequences of multiple sequences over a set of finite alphabets, namely MLCS problem, in computational biology, pattern recognition and information retrieval, to name a few. However, it is very challenging to tackle the large-scale MLCS problem effectively and efficiently due to the high complexity of time and space. To this end, this paper will therefore propose a Branch Elimination based Space and Time efficient algorithm called BEST-MLCS, which includes the following four key strategies: 1) Estimation scheme for the lower bound of the length of MLCS. 2) Estimation scheme for the upper bound of the length of the paths through the current node. 3) Branch elimination strategy by finding all useless match points and removing the branches not on the longest paths. 4) A new Directed Acyclic Graph (DAG) construction method for constructing the smallest DAG among the existing ones. As a result, the proposed algorithm BEST-MLCS can save a lot of space and time and can handle much larger scale MLCS problems than the existing algorithms. Extensive experiments conducted on biological DNA sequences show that the performance of the proposed algorithm BEST-MLCS outperforms three state-of-the-art algorithms in terms of run-time and memory consumption.

Searching Longest Common Subsequences (LCS) of Multi-ple (i.e., three or more) sequences, denoted as MLCS for short, is a fundamental problem in computational biology, pattern recognition, file comparison and information retrieval, to name a few. Basically, an MLCS problem is more challenging than the LCS of two sequences which can be solved by a dynamic programming (DP) method whose running time and memory space are both$O(n^{2})$, where$n$is the length of the sequences.

MOTIVATION: Multiple longest common subsequence (MLCS) problem is searching all longest common subsequences of multiple character sequences. It appears in many fields such as data mining, DNA alignment, bioinformatics, text editing and so on. With the increasing in sequence length and number of sequences, the existing dynamic programming algorithms and the dominant point-based algorithms become ineffective and inefficient, especially for large-scale MLCS problems. RESULTS: In this paper, by considering the characteristics of DNA sequences with many consecutively repeated characters, we first design a character merging scheme which merges the consecutively repeated characters in the sequences. As a result, it shortens the length of sequences considered and saves the space of storing all sequences. To further reduce the space and time costs, we construct a weighted directed acyclic graph which is much smaller than widely used directed acyclic graph for MLCS problems. Based on these techniques, we propose a fast and memory efficient algorithm for MLCS problems. Finally, the experiments are conducted and the proposed algorithm is compared with several state-of-the art algorithms. The experimental results show that the proposed algorithm performs better than the compared state-of-the art algorithms in both time and space costs. AVAILABILITY AND IMPLEMENTATION: https://www.ncbi.nlm.nih.gov/nuccore and https://github.com/liusen1006/MLCS.

MOTIVATION: Searching the Longest Common Subsequences of many sequences is called a Multiple Longest Common Subsequence (MLCS) problem which is a very fundamental and challenging problem in many fields of data mining. The existing algorithms cannot be applicable to problems with long and large-scale sequences due to their huge time and space consumption. To efficiently handle large-scale MLCS problems, a Path Recorder Directed Acyclic Graph (PRDAG) model and a novel Path Recorder Algorithm (PRA) are proposed. RESULTS: In PRDAG, we transform the MLCS problem into searching the longest path from the Directed Acyclic Graph (DAG), where each longest path in DAG corresponds to an MLCS. To tackle the problem efficiently, we eliminate all redundant and repeated nodes during the construction of DAG, and for each node, we only maintain the longest paths from the source node to it but ignore all non-longest paths. As a result, the size of the DAG becomes very small, and the memory space and search time will be greatly saved. Empirical experiments have been performed on a standard benchmark set of both DNA sequences and protein sequences. The experimental results demonstrate that our model and algorithm outperform the related leading algorithms, especially for large-scale MLCS problems. AVAILABILITY AND IMPLEMENTATION: This program code is written by the first author and can be available at https://www.ncbi.nlm.nih.gov/nuccore and https://blog.csdn.net/wswguilin. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Currently, there are four drawbacks for filled function methods: (1) too many local optimal solutions result in huge difficulty to search global optimal solutions; (2) difficult to control the parameter(s); (3) difficult to determine the initial point for minimization of filled function; (4) the shallow basins will affect the solution precision during the minimization of the filled function. To overcome these drawbacks, in this paper, we adopt a flatten function to eliminate many local optimal solutions first, and then a new filled function with one parameter is proposed, and its parameter is easy to control. Furthermore, we propose an efficient method for determining initial point of the filled function by using adaptive step size. Moreover, when some basins of the filled function are shallow ones, it will result in inefficiency of searching these basins during the minimization of the filled function. To tackle this issue and make the search for global optimal solutions much easier, we propose a strategy of basin deepening. By integrating these schemes, we propose a new efficient filled flatten function method. Numerical results indicate the efficiency and effectiveness of the proposed filled function methods.