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Multivariate time series usually have entangled temporal patterns and various anomaly types. Meanwhile, they often contain both continuous and discrete features. Many existing methods directly model correlations in complex multivariate time series to conduct anomaly detection. Decomposing time series into different components, such as the overall trend and fluctuations, can contribute to better extracting semantic information and detecting anomalies. Existing decomposition-based anomaly detection methods still have several limitations. First, they directly decompose all features without considering that discrete features are unsuitable for decomposition because they do not have trends or fluctuations. Second, they adopt the same networks for different components with different characteristics, limiting their ability to extract semantic information. Moreover, due to the nature of Transformers, existing reconstruction-based methods using Transformers rarely form information bottlenecks, reducing the differentiation between the reconstruction errors of normal data and anomalies. This paper proposes a multivariate time series anomaly detection method with separation, decomposition, and dual Transformer-based autoencoder (SDDformer). Different from existing methods, SDDformer separates continuous and discrete features and only decomposes continuous features into trend and residual components. Considering the different characteristics of different components, SDDformer adopts Crossformer and the vanilla Transformer as the backbone of two different autoencoders to reconstruct the trend and residual components. Information bottlenecks are better formed using an extra token as the latent variable between the encoder and the decoder. SDDformer regards reconstructing a discrete feature as a classification task and calculates Cross-Entropy as its reconstruction error. Three different metrics are adopted in this paper to compare SDDformer with a variety of typical anomaly detection methods on public data sets, and the experimental results prove that SDDformer can achieve state-of-the-art performance. • A two-stream multivariate time series anomaly detection method is proposed. • Continuous and discrete features are separated before decomposition. • Only continuous features are decomposed into the trend and residual components. • Two different autoencoders are proposed to reconstruct different components. • The reconstruction of a discrete feature is regarded as a classification task. [ABSTRACT FROM AUTHOR]

This paper is concerned with the stability and stabilization problems for T-S fuzzy systems with two additive time-varying delays. Firstly, a novel Lyapounov-Krasovskii functional (LKF) is constructed by delay-product-type functional method together with the state vector augmentation. In order to handle time-delay square terms introduced into the derivative of LKF, an extended binary quadratic function negative-determination lemma is proposed. A less conservative delay-dependent stability condition is developed since not only some new bounding technologies are employed to deal with integral terms, but also the proposed lemma is employed to dispose nonlinear time-delay terms in derivative of constructed function. Then, the corresponding controller design method for closed-loop delayed fuzzy system is derived based on parallel distributed compensation scheme. Finally, four numerical examples are given to illustrate the superiority and effectiveness of the proposed criteria. [ABSTRACT FROM AUTHOR]

Let G = (V , E) be a simple graph with vertex set as V and edge set as E. Within the framework of graph-based binary coding, a graph G is a threshold graph if and only if it can be generated by a binary code of the type 0 s 1 1 t 1 ... 0 s k 1 t k , where s i and t i are positive integers with 1 ≤ i ≤ k. This type of binary code is called a binary generating code of G. In this paper, we address a problem originally posed by Harary and Schwenk in [10] titled "Which graphs have integral spectra?" in which the main focus of our investigations lies in the Seidel Laplacian spectrum of G generated by 0 s 1 1 t 1 ... 0 s k 1 t k . We establish that all eigenvalues of G are integers and multiplicities of eigenvalues are equal to powers of bits 0 and 1 (sizes of strings of 0's and 1's) involved in a binary generating code of G. We exhibit a necessary and sufficient condition in terms of eigenvalues of the matrix associated with a graph-based G binary code to be Seidel Laplacian integral. Furthermore, for any prime p , we explore the Seidel Laplacian spectrum of zero-divisor graphs associated with the ring Z p m (where m is a positive integer) and the polynomial ring Z p [ x ] / (x p). [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel surface reconstruction method for unoriented points by establishing and solving a nonlinear equation system. By treating normals as unknown parameters and imposing the conditions that the implicit field is constant and its gradients parallel to the normals on the input point cloud, we establish a nonlinear equation system involving the oriented normals. To simplify the system, we transform it into a 0-1 integer programming problem solely focusing on orientation by incorporating inconsistent oriented normal information through PCA. We solve the simplified problem using flipping-based iterative algorithms and propose two novel criteria for flipping based on theoretical analysis. Extensive experiments on renowned datasets demonstrate that our flipping-based method with wavelet surface reconstruction achieves state-of-the-art results in orientation and reconstruction. Furthermore, it exhibits linear computational and storage complexity by leveraging the orthogonality and compact support properties of wavelet bases. The source code is available at https://github.com/mayueji/FISR_code. • We propose a novel surface reconstruction method by establishing and solving nonlinear equation systems numerically. • To tackle the nonlinear equation system, we innovatively propose the gradient-based criterion and value-based criterion. • Our method achieves state-of-the-art performance in orientation and reconstruction. Its linear complexity overcomes computational and storage bottlenecks. [ABSTRACT FROM AUTHOR]

Cross-modal hashing has attracted a lot of attention and achieved remarkable success in large-scale cross-media similarity retrieval applications because of its superior computational efficiency and low storage overhead. However, constructing similarity relationship among samples in cross-modal unsupervised hashing is challenging because of the lack of manual annotation. Most existing unsupervised methods directly use the representations extracted from the backbone of their respective modality to construct instance similarity matrices, leading to inaccurate similarity matrices and resulting in suboptimal hash codes. To address this issue, a novel unsupervised hashing model, named Structure-aware Contrastive Hashing for Unsupervised Cross-modal Retrieval (SACH), is proposed in this paper. Specifically, we concurrently employ both high-dimensional representations and discriminative representations learned by the network to construct a more informative semantic correlative matrix across modalities. Moreover, we design a multimodal structure-aware alignment network to minimize heterogeneous gap in the high-order semantic space of each modality, effectively reducing disparities within heterogeneous data sources and enhancing the consistency of semantic information across modalities. Extensive experimental results on two widely utilized datasets demonstrate the superiority of our proposed SACH method in cross-modal retrieval tasks over existing state-of-the-art methods. • We propose an informative multimodal correlation matrix construction approach. • We propose a multimodal structure-aware alignment network to bridge heterogeneous gaps. • Extensive experiments show SACH's superiority in cross-modal retrieval. [ABSTRACT FROM AUTHOR]

Session-based recommendations (SBR) aim to predict the user's next choice of items based on historical data. It is hard to access the interaction information between users and we can only analyze the user's behavioral preferences based on the current session characteristics, which makes the recommendation task in this field quite challenging. Recently, considerable research has grown up around the theme of SBR. Previous works apply attention mechanisms and Graph Neural Networks (GNN) to achieve remarkable results. However, these methods ignore two main points: one is losing sight of the specific position of items in the session; the other is to drive global preference with local preference without considering the offset of the target preference among items in the session. This paper proposes a Global Target Preference Attention Network (GTPAN) Model with position information for the session-based recommendation. We introduce a position-aware embedding module to eliminate the effect of position missing. Considering that each item in the session is potentially rich in latent information of target preference, we use a target preference attention layer to learn the target preference vector of the session. Extensive experiments on three real datasets show that the proposed GTPAN model outperforms state-of-the-art session-based recommendation methods, especially on datasets with long sessions. [ABSTRACT FROM AUTHOR]

This paper constructs a class of lattices whose discrete analogues are variable-length non-linear codes. The well-known discrete analogue of lattices and linear codes inspires our approach. We next design a variable length binary non-linear code called automorphism orbit code from a finite abelian p -group of rank greater than 1, where p is a prime. For each finite abelian p -group, codewords of the automorphism orbit code are variable-length codewords called automorphism orbit codewords. The homomorphisms between groups determine homomorphism codes , whereas automorphism orbit codes are specified by partitions of a number, orbits of group action, homomorphisms and automorphisms of groups. For some groups G and H , we shall use elements of H o m (G , H) to create a cover relation for bit strings of codewords of an automorphism orbit code and formulate a lattice of variable length non-linear codes. [ABSTRACT FROM AUTHOR]

In two previous papers we constructed new families of completely regular codes by concatenation methods. Here we determine cases in which the new codes are completely transitive. For these cases we also find the automorphism groups of such codes. For the remaining cases, we show that the codes are not completely transitive assuming an upper bound on the order of the monomial automorphism groups, according to computational results. [ABSTRACT FROM AUTHOR]

In this paper, we propose intra- and inter-feature orthogonal fusion (IIOF) of local and global features obtained from MS-SincResNet or MS-SSincResNet (a variant of MS-SincResNet) for music emotion recognition (MER). Given a raw waveform of music signal, MS-SincResNet/MS-SSincResNet is first used to learn several 2D representations having different receptive fields and obtain embeddings with time-frequency information from different layers. Then, local and global features are extracted from these embeddings. IIOF consisting of intra-feature OF and inter-feature OF is further employed to integrate both local and global features to obtain a discriminative descriptor for MER. The intra-feature OF is used to enhance the diversity of the global feature, and the inter-feature OF is utilized to reduce redundancies and produce complementary information between local and global features. The experimental results have demonstrated that the representation discriminability can be enhanced by IIOF considering the feature orthogonality. Furthermore, extensive experimental results have shown that the proposed method outperforms other state-of-the-art methods in terms of regression and classification tasks on the well-known MER datasets, including the DEAM dataset and the PMEmo dataset. The codes are available at https://github.com/PeiChunChang/MS-SSincResNet_with_IIOF. • We propose IIOF approach to effectively integrating local and global features. • IIOF is combined with MS-SincResNet and MS-SSincResNet for music emotion recognition. • The proposed method outperforms other state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Based on good algebraic structures and practicabilities, generalized quasi-cyclic (GQC) codes play important roles in coding theory. In this paper, we study some results on GQC codes over Z 4 including normalized generating sets, minimal generating sets and normalized generating sets of their dual codes. As an application, new Z 4 -linear codes and good binary nonlinear codes are constructed from GQC codes over Z 4. [ABSTRACT FROM AUTHOR]

The Internet of Things (IoT) has experienced phenomenal expansion over the past few years and has emerged as one of the most dynamic sectors of the international market. Android has become the driving force behind the rapid development of the IoT, and malware is one of the most severe concerns. Android is an open-source platform with a significant number of users. The identification of Android malware has become more critical in cybersecurity due to the meteoric rise of Android malware over the past few years and the severity of the damage it inflicts on smartphone users. Existing traditional Android malware detection methods based on machine learning have achieved encouraging performance. Still, the solution requires a massive workforce of feature engineering to build dynamic or static features and continuous learning through pre-extracted features to maintain high performance in identifying malware. Therefore, technologies for end-to-end malware detection without human interaction are necessary. In response to the rapid evolution of Android malware, a convolutional neural network that can acquire knowledge without requiring feature extraction is ideally suited. This paper offers a unique classification approach for malware based on a convolutional neural network, with feature extraction selected from the current pre-trained models DenseNet169, Xception, InceptionV3, ResNet50, and VGG16. The proposed methods have an advantage over existing detection methods due to their end-to-end learning process. Our suggested approaches convert Android APK files to binary codes and RGB images for usage as inputs to deep learning models. These models are trained and evaluated using the CICInvesAndMal2019 dataset, which consists of 333 benign and 428 malicious applications. Experiments demonstrate that the proposed approaches achieve a classification accuracy of 95.24%, 95.24%, and 95.83% for DenseNet169, InceptionV3, and VGG16, respectively, on a 761-sample dataset of malware, which is superior to other compared algorithms. Compared to previous methods, our suggested methods are more applicable to Android IoT devices since they do not require manual feature engineering and consume fewer resources. [ABSTRACT FROM AUTHOR]

In this paper, we always assume that p and n > 3 are two distinct odd primes, m ≥ 2 is a positive integer, and gcd ⁡ (p m , 2 n (2 2 n − 1)) ≠ 1. Set r = p 2 or r = p 3 , we determine upper bounds on the number of inequivalent extended binary irreducible Goppa codes Γ (L , g) of degree r and length 2 n + 1 , where L = F 2 n ∪ { ∞ } is the support set and each g (x) is an irreducible polynomial of degree r over F 2 n . [ABSTRACT FROM AUTHOR]