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Recent advances in digitization have led to the availability of multivariate time series data in various domains, enabling real-time monitoring of operations. Identifying abnormal data patterns and detecting potential failures in these scenarios are important yet rather challenging. In this work, we propose a novel unsupervised anomaly detection method for time series data. The proposed framework jointly learns the observation model and the dynamic model, and model uncertainty is estimated from normal samples. Specifically, a long short-term memory (LSTM)-based encoder-decoder is adopted to represent the mapping between the observation space and the latent space. Bidirectional transitions of states are simultaneously modeled by leveraging backward and forward temporal information. Regularization of the latent space places constraints on the states of normal samples, and Mahalanobis distance is used to evaluate the abnormality level. Empirical studies on synthetic and real-world datasets demonstrate the superior performance of the proposed method in anomaly detection tasks.

For many tasks of data analysis, we may only have the information of the explanatory variable and the evaluation of the response values are quite expensive. While it is impractical or too costly to obtain the responses of all units, a natural remedy is to judiciously select a good sample of units, for which the responses are to be evaluated. In this paper, we adopt the classical criteria in design of experiments to quantify the information of a given sample regarding parameter estimation. Then, we provide a theoretical justification for approximating the optimal sample problem by a continuous problem, for which fast algorithms can be further developed with the guarantee of global convergence. Our results have the following novelties: (i) The statistical efficiency of any candidate sample can be evaluated without knowing the exact optimal sample; (ii) It can be applied to a very wide class of statistical models; (iii) It can be integrated with a broad class of information criteria; (iv) It is much faster than existing algorithms. $(v)$ A geometric interpretation is adopted to theoretically justify the relaxation of the original combinatorial problem to continuous optimization problem.

Pest counting, which predicts the number of pests in the early stage, is very important because it enables rapid pest control, reduces damage to crops, and improves productivity. In recent years, light traps have been increasingly used to lure and photograph pests for pest counting. However, pest images have a wide range of variability in pest appearance owing to severe occlusion, wide pose variation, and even scale variation. This makes pest counting more challenging. To address these issues, this study proposes a new pest counting model referred to as multiscale and deformable attention CenterNet (Mada-CenterNet) for internal low-resolution (LR) and high-resolution (HR) joint feature learning. Compared with the conventional CenterNet, the proposed Mada-CenterNet adopts a multiscale heatmap generation approach in a two-step fashion to predict LR and HR heatmaps adaptively learned to scale variations, that is, changes in the number of pests. In addition, to overcome the pose and occlusion problems, a new between-hourglass skip connection based on deformable and multiscale attention is designed to ensure internal LR and HR joint feature learning and incorporate geometric deformation, thereby resulting in an improved pest counting accuracy. Through experiments, the proposed Mada-CenterNet is verified to generate the HR heatmap more accurately and improve pest counting accuracy owing to multiscale heatmap generation, joint internal feature learning, and deformable and multiscale attention. In addition, the proposed model is confirmed to be effective in overcoming severe occlusions and variations in pose and scale. The experimental results show that the proposed model outperforms state-of-the-art crowd counting and object detection models.

In this article, we introduce parallel-in-time methods for state and parameter estimation in general nonlinear non-Gaussian state-space models using the statistical linear regression and the iterated statistical posterior linearization paradigms. We also reformulate the proposed methods in a square-root form, resulting in improved numerical stability while preserving the parallelization capabilities. We then leverage the fixed-point structure of our methods to perform likelihood-based parameter estimation in logarithmic time with respect to the number of observations. Finally, we demonstrate the practical performance of the methodology with numerical experiments run on a graphics processing unit (GPU).

In this article, an efficient transient electricalthermal co-simulation method based on the finite element method (FEM) and the discontinuous Galerkin time-domain (DGTD) method is developed for electrical-thermal coupling analysis of multiscale structures. Two Independent meshes are adopted by the steady electrical analysis and the transient thermal simulation to avoid redundant overhead. In order to enhance the feasibility and efficiency of solving multiscale and sophisticated structures, a local time stepping (LTS) technique coupled with an interpolation method is incorporated into the co-simulation method. Several numerical examples from simple structures to complex multiscale PDN structures are carried out to demonstrate the accuracy and efficiency of the proposed method by comparing with the COMSOL. Finally, two practical numerical examples are considered to confirm the performance of the proposed method for complex and multiscale structures.

Directed networks are conveniently represented as graphs in which ordered edges encode interactions between vertices. Despite their wide availability, there is a shortage of statistical models amenable for inference, specially when contextual information and degree heterogeneity are present. This paper presents an annotated graph model with parameters explicitly accounting for these features. To overcome the curse of dimensionality due to modelling degree heterogeneity, we introduce a sparsity assumption and propose a penalized likelihood approach with $\ell_1$-regularization for parameter estimation. We study the estimation and selection consistency of this approach under a sparse network assumption, and show that inference on the covariate parameter is straightforward, thus bypassing the need for the kind of debiasing commonly employed in $\ell_1$-penalized likelihood estimation. Simulation and data analysis corroborate our theoretical findings.

Message Passing Neural Networks (MPNNs) are a widely used class of Graph Neural Networks (GNNs). The limited representational power of MPNNs inspires the study of provably powerful GNN architectures. However, knowing one model is more powerful than another gives little insight about what functions they can or cannot express. It is still unclear whether these models are able to approximate specific functions such as counting certain graph substructures, which is essential for applications in biology, chemistry and social network analysis. Motivated by this, we propose to study the counting power of Subgraph MPNNs, a recent and popular class of powerful GNN models that extract rooted subgraphs for each node, assign the root node a unique identifier and encode the root node's representation within its rooted subgraph. Specifically, we prove that Subgraph MPNNs fail to count more-than-4-cycles at node level, implying that node representations cannot correctly encode the surrounding substructures like ring systems with more than four atoms. To overcome this limitation, we propose I$^2$-GNNs to extend Subgraph MPNNs by assigning different identifiers for the root node and its neighbors in each subgraph. I$^2$-GNNs' discriminative power is shown to be strictly stronger than Subgraph MPNNs and partially stronger than the 3-WL test. More importantly, I$^2$-GNNs are proven capable of counting all 3, 4, 5 and 6-cycles, covering common substructures like benzene rings in organic chemistry, while still keeping linear complexity. To the best of our knowledge, it is the first linear-time GNN model that can count 6-cycles with theoretical guarantees. We validate its counting power in cycle counting tasks and demonstrate its competitive performance in molecular prediction benchmarks.

Topologically interlocked materials and structures, which are assemblies of unbonded interlocking building blocks, are promising concepts for versatile structural applications. They have been shown to exhibit exceptional mechanical properties, including outstanding combinations of stiffness, strength, and toughness, beyond those achievable with common engineering materials. Recent work has established a theoretical upper limit for the strength and toughness of beam-like topologically interlocked structures. However, this theoretical limit is only achievable for structures with unrealistically high friction coefficients; therefore, it remains unknown whether it is achievable in actual structures. Here, we demonstrate that a hierarchical approach for topological interlocking, inspired by biological systems, overcomes these limitations and provides a path toward optimized mechanical performance. We consider beam-like topologically interlocked structures that present a sinusoidal surface morphology with controllable amplitude and wavelength and examine the properties of the structures using numerical simulations. The results show that the presence of surface morphologies increases the effective frictional strength of the interfaces and, if well-designed, enables us to reach the theoretical limit of the structural carrying capacity with realistic friction coefficients. Furthermore, we observe that the contribution of the surface morphology to the effective friction coefficient of the interface is well described by a criterion combining the surface curvature and surface gradient. Our study demonstrates the ability to architecture the surface morphology in beam-like topological interlocked structures to significantly enhance its structural performance.

Bayesian clustering typically relies on mixture models, with each component interpreted as a different cluster. After defining a prior for the component parameters and weights, Markov chain Monte Carlo (MCMC) algorithms are commonly used to produce samples from the posterior distribution of the component labels. The data are then clustered by minimizing the expectation of a clustering loss function that favours similarity to the component labels. Unfortunately, although these approaches are routinely implemented, clustering results are highly sensitive to kernel misspecification. For example, if Gaussian kernels are used but the true density of data within a cluster is even slightly non-Gaussian, then clusters will be broken into multiple Gaussian components. To address this problem, we develop Fusing of Localized Densities (FOLD), a novel clustering method that melds components together using the posterior of the kernels. FOLD has a fully Bayesian decision theoretic justification, naturally leads to uncertainty quantification, can be easily implemented as an add-on to MCMC algorithms for mixtures, and favours a small number of distinct clusters. We provide theoretical support for FOLD including clustering optimality under kernel misspecification. In simulated experiments and real data, FOLD outperforms competitors by minimizing the number of clusters while inferring meaningful group structure.

Graph Neural Networks (GNNs), which generalize deep neural networks to graph-structured data, have drawn considerable attention and achieved state-of-the-art performance in numerous graph related tasks. However, existing GNN models mainly focus on designing graph convolution operations. The graph pooling (or downsampling) operations, that play an important role in learning hierarchical representations, are usually overlooked. In this paper, we propose a novel graph pooling operator, called Hierarchical Graph Pooling with Structure Learning (HGP-SL), which can be integrated into various graph neural network architectures. HGP-SL incorporates graph pooling and structure learning into a unified module to generate hierarchical representations of graphs. More specifically, the graph pooling operation adaptively selects a subset of nodes to form an induced subgraph for the subsequent layers. To preserve the integrity of graph's topological information, we further introduce a structure learning mechanism to learn a refined graph structure for the pooled graph at each layer. By combining HGP-SL operator with graph neural networks, we perform graph level representation learning with focus on graph classification task. Experimental results on six widely used benchmarks demonstrate the effectiveness of our proposed model.