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Multivariate Time Series Classification (MTSC) enables the analysis if complex temporal data, and thus serves as a cornerstone in various real-world applications, ranging from healthcare to finance. Since the relationship among variables in MTS usually contain crucial cues, a large number of graph-based MTSC approaches have been proposed, as the graph topology and edges can explicitly represent relationships among variables (channels), where not only various MTS graph representation learning strategies but also different Graph Neural Networks (GNNs) have been explored. Despite such progresses, there is no comprehensive study that fairly benchmarks and investigates the performances of existing widely-used graph representation learning strategies/GNN classifiers in the application of different MTSC tasks. In this paper, we present the first benchmark which systematically investigates the effectiveness of the widely-used three node feature definition strategies, four edge feature learning strategies and five GNN architecture, resulting in 60 different variants for graph-based MTSC. These variants are developed and evaluated with a standardized data pipeline and training/validation/testing strategy on 26 widely-used suspensor MTSC datasets. Our experiments highlight that node features significantly influence MTSC performance, while the visualization of edge features illustrates why adaptive edge learning outperforms other edge feature learning methods. The code of the proposed benchmark is publicly available at \url{https://github.com/CVI-yangwn/Benchmark-GNN-for-Multivariate-Time-Series-Classification}.

Digital twin (DT) technology has a high potential to satisfy different requirements of the ever-expanding new applications. Nonetheless, the DT placement in wireless digital twin networks (WDTNs) poses a significant challenge due to the conflict between unpredictable workloads and the limited capacity of edge servers. In other words, each edge server has a risk of overload when handling an excessive number of tasks or services. Overload risks can have detrimental effects on a network's sustainability, yet this aspect is often overlooked in the literature. In this paper, we aim to study the sustainability-aware DT placement problem for WDTNs from a cost minimization perspective. To this end, we formulate the DT placement-driven cost optimization problem as a chance-constrained integer programming problem. For tractability, we transform the original non-deterministic problem into a deterministic integer linear programming (ILP) problem using the sample average approximation (SAA) approach. We prove that the transformed problem remains NP-hard and thus finding a global optimal solution is very difficult. To strike a balance between time efficiency and performance guarantee, we propose an improved local search algorithm for this ILP by identifying high-quality starting states from historical search data and enhancing the search process. Numerical results show a lower cost and higher efficiency of our proposed method compared with the previous schemes.

The rapid development of deep learning techniques has driven the emergence of a neural network-based variational Monte Carlo method (referred to as FermiNet), which has manifested high accuracy and strong predictive power in the electronic structure calculations of atoms, molecules as well as some periodic systems. Recently, the implementation of the effective core potential (ECP) scheme in it further facilitates more efffcient calculations in practice. But there still lack comprehensive assessments on the ECP's performance under the FermiNet. In this work, we set sail to ffll this gap by conducting extensive tests on the ffrst two row elements regarding their atomic spectral and molecular properties. Our major ffnding is that in general the qualities of ECPs have been correctly reffected under the FermiNet. Two recently built ECP tables, namely ccECP and eCEPP, seem to prevail on the overall performance. Speciffcally, ccECP performs slightly better on the spectral precision and covers more elements, while eCEPP is more systematically built from both shape and energy consistency, and better treats the core polarisation. On the other hand, the high accuracy of the all-electron calculations is hindered by the absence of relativistic effects as well as the numerical instabilities in some heavier elements. Finally, with further in-depth discussions, we generate possible directions for developing and improving the FermiNet in the near future.

In this paper, we apply the effective potentials in the localization landscape theory (Filoche et al., 2012, Arnold et al., 2016) to study the spectral properties of the incommensurate systems. We uniquely develop a plane wave method for the effective potentials of the incommensurate systems and utilize that, the localization of the electron density can be inferred from the effective potentials. Moreover, we show that the spectrum distribution can also be obtained from the effective potential version of Weyl's law. We perform some numerical experiments on some typical incommensurate systems, showing that the effective potential provides an alternative tool for investigating the localization and spectrum distribution of the systems., Comment: 14pages

This paper presents our Facial Action Units (AUs) detection submission to the fifth Affective Behavior Analysis in-the-wild Competition (ABAW). Our approach consists of three main modules: (i) a pre-trained facial representation encoder which produce a strong facial representation from each input face image in the input sequence; (ii) an AU-specific feature generator that specifically learns a set of AU features from each facial representation; and (iii) a spatio-temporal graph learning module that constructs a spatio-temporal graph representation. This graph representation describes AUs contained in all frames and predicts the occurrence of each AU based on both the modeled spatial information within the corresponding face and the learned temporal dynamics among frames. The experimental results show that our approach outperformed the baseline and the spatio-temporal graph representation learning allows our model to generate the best results among all ablated systems. Our model ranks at the 4th place in the AU recognition track at the 5th ABAW Competition. Our code is publicly available at https://github.com/wzh125/ABAW-5.

In this paper, we propose an extended plane wave framework to make the electronic structure calculations of the twisted bilayer 2D material systems practically feasible. Based on the foundation in [Y. Zhou, H. Chen, A. Zhou, J. Comput. Phys. 384, 99 (2019)], following extensions take place: (1) an tensor-producted basis set, which adopts PWs in the incommensurate dimensions, and localized basis in the interlayer dimension, (2) a practical application of a novel cutoff techniques we have recently developed, and (3) a quasi-band structure picture under the small twisted angles and weak interlayer coupling limits. With (1) and (2) now the dimensions of Hamiltonian matrix are reduced by about 2 orders of magnitude compared with the original framework. And (3) enables us to better organize the calculations and understand the results. For numerical examples, we study the electronic structures of the linear bilayer graphene lattice system with the magic twisted angle ($\sim 1.05^{\circ}$). The famous flat bands have been reproduced with their features in quantitative agreement with those from experiments and other theoretical calculations. Moreover, the extended framework has much less computational cost compared to the commensurate cell approximations, and is more extendable compared to the traditional model hamiltonians and tight binding models. Finally this framework can readily accommodate nonlinear models thus will laid the foundations for more effective yet accurate Density Functional Theory (DFT) calculations.

Incommensurate structures arise from stacking single layers of low-dimensional materials on top of one another with misalignment such as an in-plane twist in orientation. While these structures are of significant physical interest, they pose many theoretical challenges due to the loss of periodicity. In this paper, we characterize the density of states of Schr\"{o}dinger operators in the weak sense for the incommensurate system and develop novel numerical methods to approximate them. In particular, we (i) justify the thermodynamic limit of the density of states in the real space formulation; and (ii) propose efficient numerical schemes to evaluate the density of states based on planewave approximations and reciprocal space sampling. We present both rigorous analysis and numerical simulations to support the reliability and efficiency of our numerical algorithms., Comment: 29 pages

This work considers numerical methods for the time-dependent Schr\"{o}dinger equation of incommensurate systems. By using a plane wave method for spatial discretization, the incommensurate problem is lifted to a higher dimension that results in semidiscrete differential equations with extremely demanding computational cost. We propose several fully discrete time stepping schemes based on the idea of "layer-splitting", which decompose the semidiscrete problem into sub-problems that each corresponds to one of the periodic layers. Then these schemes handle only some periodic systems in the original lower dimension at each time step, which reduces the computational cost significantly and is natural to involve stochastic methods and parallel computing. Both theoretical analysis and numerical experiments are provided to support the reliability and efficiency of the algorithms.

Based on our recently proposed plane wave framework, we theoretically study the localized-extended transition in the one dimensional incommensurate systems with cosine type of potentials, which are in close connection to many recent experiments in the ultracold atom and photonic crystal. We formulate a propagator based scattering picture for the transition at the ground state and single particle mobility edge, in which the deeper connection between the incommensurate potentials, eigenstate compositions and transition mechanism is revealed. We further show that there exists a upper limit of localization length for all localized eigenstates, leading to an fundamental difference to the Anderson localization. Numerical calculations are presented alongside the analysis to justify our statements. The theoretical analysis and numerical methods can also be generalized to systems in higher dimensions, with different potentials or beyond the single particle regime, which would benefit the future studies in the related fields., Comment: 26 pages

We propose a novel numerical algorithm for computing the electronic structure related eigenvalue problem of incommensurate systems. Unlike the conventional practice that approximates the system by a large commensurate supercell, our algorithm directly discretizes the eigenvalue problem under the framework of a plane wave method. The emerging ergodicity and the interpretation from higher dimensions give rise to many unique features compared to what we have been familiar with in the periodic system. The numerical results of 1D and 2D quantum eigenvalue problems are presented to show the reliability and efficiency of our scheme. Furthermore, the extension of our algorithm to full Kohn-Sham density functional theory calculations are discussed., Comment: 21 pages

Kerker preconditioner, based on the dielectric function of homogeneous electron gas, is designed to accelerate the self-consistent field (SCF) iteration in the density functional theory (DFT) calculations. However, question still remains regarding its applicability to the inhomogeneous systems. In this paper, we develop a modified Kerker preconditioning scheme which captures the long-range screening behavior of inhomogeneous systems thus improve the SCF convergence. The effectiveness and efficiency is shown by the tests on long-z slabs of metals, insulators and metal-insulator contacts. For situations without a priori knowledge of the system, we design the a posteriori indicator to monitor if the preconditioner has suppressed charge sloshing during the iterations. Based on the a posteriori indicator, we demonstrate two schemes of the self-adaptive configuration for the SCF iteration.

The epitaxial growth of {111} oriented Au on MoS$_2$ is well documented despite the large lattice mismatch (~8% biaxial strain), and the fact that a Au {001} orientation results in much less elastic strain. An analysis based on density functional and linear elasticity theories reveals that the {111} orientation is stabilized by a combination of favorable surface and interfacial contributions to the energy, and the compliance of the first layer of the MoS$_2$.