On non-stationary threshold autoregressive models

In this paper we study the limiting distributions of the least-squares estimators for the non-stationary first-order threshold autoregressive (TAR(1)) model. It is proved that the limiting behaviors of the TAR(1) process are very different from those of the classical unit root model and the explosive AR(1).Comment: Published in at http://dx.doi.org/10.3150/10-BEJ306 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

On the uniqueness of the planar 5-body central configuration with a trapezoidal convex hull

In order to apply Morse's critical point theory, we use mutual distances as coordinates to discuss a kind of central configuration of the planar Newtonian 5-body problem with a trapezoidal convex hull which is convex but not strictly convex, i.e., four of the five bodies are located at the vertices of a trapezoid, and the fifth one is located on one of the parallel sides. We show that there is at most one central configuration of this geometrical shape for a given cyclic order of the five bodies along the convex hull. In addition, if the parallel side containing the three collinear bodies is strictly shorter than the other parallel side, the configuration must be symmetric, i.e., the trapezoid is isosceles, and the last body is at the midpoint of the shorter parallel side.Comment: 26pages, 7 figure

A Survey on Surrogate-assisted Efficient Neural Architecture Search

Neural architecture search (NAS) has become increasingly popular in the deep learning community recently, mainly because it can provide an opportunity to allow interested users without rich expertise to benefit from the success of deep neural networks (DNNs). However, NAS is still laborious and time-consuming because a large number of performance estimations are required during the search process of NAS, and training DNNs is computationally intensive. To solve the major limitation of NAS, improving the efficiency of NAS is essential in the design of NAS. This paper begins with a brief introduction to the general framework of NAS. Then, the methods for evaluating network candidates under the proxy metrics are systematically discussed. This is followed by a description of surrogate-assisted NAS, which is divided into three different categories, namely Bayesian optimization for NAS, surrogate-assisted evolutionary algorithms for NAS, and MOP for NAS. Finally, remaining challenges and open research questions are discussed, and promising research topics are suggested in this emerging field.Comment: 18 pages, 7 figure

Study on Negative Poisson Ratio and Energy Absorption Characteristics of Embedded Arrow Honeycomb Structure

 Impact collision exists widely in people's daily life and threatens people's life safety. Negative Poisson's ratio structure has good mechanical properties. Therefore, it is of great significance to design and study the energy absorption structure with negative Poisson's ratio effect. Based on the traditional symmetrical concave honeycomb structure (SCHS) with negative Poisson's ratio, two modified negative Poisson's ratio honeycomb structures are proposed by adding embedded straight rib arrow structure and embedded curved rib arrow structure, which are respectively called embedded straight rib arrow honeycomb structure (SRAH) and embedded curved rib arrow honeycomb structure (CRAH). Through finite element simulation experiment, the negative Poisson's ratio characteristics of two cellular cells were studied and the influence of structural parameters of the cells on the Poisson's ratio was discussed. ANSYS/LS-DYNA was used to analyze the energy absorption of the proposed three cellular structures at different impact velocities. Numerical simulation results show that the SRHS and CRAH have greater stress platform value, specific energy absorption and impact force efficiency than SCHS, indicating that the SRAH and CRAH exhibited better energy absorption efficiency and impact resistance performance

End-to-End Pareto Set Prediction with Graph Neural Networks for Multi-objective Facility Location

The facility location problems (FLPs) are a typical class of NP-hard combinatorial optimization problems, which are widely seen in the supply chain and logistics. Many mathematical and heuristic algorithms have been developed for optimizing the FLP. In addition to the transportation cost, there are usually multiple conflicting objectives in realistic applications. It is therefore desirable to design algorithms that find a set of Pareto solutions efficiently without enormous search cost. In this paper, we consider the multi-objective facility location problem (MO-FLP) that simultaneously minimizes the overall cost and maximizes the system reliability. We develop a learning-based approach to predicting the distribution probability of the entire Pareto set for a given problem. To this end, the MO-FLP is modeled as a bipartite graph optimization problem and two graph neural networks are constructed to learn the implicit graph representation on nodes and edges. The network outputs are then converted into the probability distribution of the Pareto set, from which a set of non-dominated solutions can be sampled non-autoregressively. Experimental results on MO-FLP instances of different scales show that the proposed approach achieves a comparable performance to a widely used multi-objective evolutionary algorithm in terms of the solution quality while significantly reducing the computational cost for search.Comment: 14 pages, 3 figure

Epitaxial ferroelectric hafnia stabilized by symmetry constraints

Ferroelectric memories experienced a revival in the last decade due to the discovery of ferroelectricity in HfO$_2$-based nanometer-thick thin films. These films exhibit exceptional silicon compatibility, overcoming the scaling and integration obstacles that impeded perovskite ferroelectrics' use in high-density integrated circuits. The exact phase responsible for ferroelectricity in hafnia films remains debated with no single factor identified that could stabilize the ferroelectric phase thermodynamically. Here, supported by density functional theory (DFT) high-throughput (HT) calculations that screen a broad range of epitaxial conditions, we demonstrate conclusively that specific epitaxial conditions achievable with common substrates such as yttria-stabilized zirconia (YSZ) and SrTiO$_3$ can favor the polar Pca2$_1$ phase thermodynamically over other polar phases such as R3m and Pmn2$_1$ and nonpolar P2$_1$/c phase. The substrate's symmetry constraint-induced shear strain is crucial for the preference of Pca2$_1$. The strain-stability phase diagrams resolve experiment-theory discrepancies and can guide the improvement of ferroelectric properties of epitaxial hafnia thin films

An Edge-Aware Graph Autoencoder Trained on Scale-Imbalanced Data for Travelling Salesman Problems

Recent years have witnessed a surge in research on machine learning for combinatorial optimization since learning-based approaches can outperform traditional heuristics and approximate exact solvers at a lower computation cost. However, most existing work on supervised neural combinatorial optimization focuses on TSP instances with a fixed number of cities and requires large amounts of training samples to achieve a good performance, making them less practical to be applied to realistic optimization scenarios. This work aims to develop a data-driven graph representation learning method for solving travelling salesman problems (TSPs) with various numbers of cities. To this end, we propose an edge-aware graph autoencoder (EdgeGAE) model that can learn to solve TSPs after being trained on solution data of various sizes with an imbalanced distribution. We formulate the TSP as a link prediction task on sparse connected graphs. A residual gated encoder is trained to learn latent edge embeddings, followed by an edge-centered decoder to output link predictions in an end-to-end manner. To improve the model's generalization capability of solving large-scale problems, we introduce an active sampling strategy into the training process. In addition, we generate a benchmark dataset containing 50,000 TSP instances with a size from 50 to 500 cities, following an extremely scale-imbalanced distribution, making it ideal for investigating the model's performance for practical applications. We conduct experiments using different amounts of training data with various scales, and the experimental results demonstrate that the proposed data-driven approach achieves a highly competitive performance among state-of-the-art learning-based methods for solving TSPs.Comment: 35 pages, 7 figure

Visual SLAM based on dynamic object removal

Visual simultaneous localization and mapping (SLAM) is the core of intelligent robot navigation system. Many traditional SLAM algorithms assume that the scene is static. When a dynamic object appears in the environment, the accuracy of visual SLAM can degrade due to the interference of dynamic features of moving objects. This strong hypothesis limits the SLAM applications for service robot or driverless car in the real dynamic environment. In this paper, a dynamic object removal algorithm that combines object recognition and optical flow techniques is proposed in the visual SLAM framework for dynamic scenes. The experimental results show that our new method can detect moving object effectively and improve the SLAM performance compared to the state of the art methods