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In this paper, two new families of fourth-order explicit exponential Runge-Kutta methods with four stages are studied for solving stiff or highly oscillatory systems $y'(t)+My(t)=f(y(t))$. By comparing the Taylor expansions of numerical and exact solutions, we derive the order conditions of these new explicit exponential methods, which are exactly identical to the order conditions of the classical explicit Runge-Kutta methods, and these exponential methods reduce to the classical Runge-Kutta methods once $M\rightarrow \mathbf{0}$. Furthermore, we analyze the linear stability properties and the convergence of these new exponential methods in detail. Finally, several numerical examples are carried out to illustrate the accuracy and efficiency of these new exponential methods when applied to the stiff systems or highly oscillatory problems than standard exponential integrators.

In this paper, we derive diffusion equation models in the spectral domain for the evolution of training errors of two-layer multi-scale deep neural networks (MscaleDNN) \cite{caixu2019,liu2020multi}, designed to reduce the spectral bias of fully connected deep neural networks in approximating oscillatory functions. The diffusion models are obtained from the spectral form of the error equation of the MscaleDNN, derived with a neural tangent kernel approach and gradient descent training and a sine activation function, assuming a vanishing learning rate and infinite network width and domain size. The involved diffusion coefficients are shown to have larger supports if more scales are used in the MscaleDNN, and thus, the proposed diffusion equation models in the frequency domain explain the MscaleDNN's spectral bias reduction capability. Numerical results of the diffusion models for a two-layer MscaleDNN training match with the error evolution of actual gradient descent training with a reasonably large network width, thus validating the effectiveness of the diffusion models. Meanwhile, the numerical results for MscaleDNN show error decay over a wide frequency range and confirm the advantage of using the MscaleDNN in approximating functions with a wide range of frequencies.

In the current landscape of explanation methodologies, most predominant approaches, such as SHAP and LIME, employ removal-based techniques to evaluate the impact of individual features by simulating various scenarios with specific features omitted. Nonetheless, these methods primarily emphasize efficiency in the original context, often resulting in general inconsistencies. In this paper, we demonstrate that such inconsistency is an inherent aspect of these approaches by establishing the Impossible Trinity Theorem, which posits that interpretability, efficiency, and consistency cannot hold simultaneously. Recognizing that the attainment of an ideal explanation remains elusive, we propose the utilization of interpretation error as a metric to gauge inefficiencies and inconsistencies. To this end, we present two novel algorithms founded on the standard polynomial basis, aimed at minimizing interpretation error. Our empirical findings indicate that the proposed methods achieve a substantial reduction in interpretation error, up to 31.8 times lower when compared to alternative techniques. Code is available at //github.com/trusty-ai/efficient-consistent-explanations.

In this work, we tackle the scenario of understanding characters in scripts, which aims to learn the characters' personalities and identities from their utterances. We begin by analyzing several challenges in this scenario, and then propose a multi-level contrastive learning framework to capture characters' global information in a fine-grained manner. To validate the proposed framework, we conduct extensive experiments on three character understanding sub-tasks by comparing with strong pre-trained language models, including SpanBERT, Longformer, BigBird and ChatGPT-3.5. Experimental results demonstrate that our method improves the performances by a considerable margin. Through further in-depth analysis, we show the effectiveness of our method in addressing the challenges and provide more hints on the scenario of character understanding. We will open-source our work on github at //github.com/David-Li0406/Script-based-Character-Understanding.

The idea of next-generation ports has become more apparent in the last ten years in response to the challenge posed by the rising demand for efficiency and the ever-increasing volume of goods. In this new era of intelligent infrastructure and facilities, it is evident that cyber-security has recently received the most significant attention from the seaport and maritime authorities, and it is a primary concern on the agenda of most ports. Traditional security solutions can be applied to safeguard IoT and Cyber-Physical Systems (CPS) from harmful entities. Nevertheless, security researchers can only watch, examine, and learn about the behaviors of attackers if these solutions operate more transparently. Herein, honeypots are potential solutions since they offer valuable information about the attackers. It can be virtual or physical. Virtual honeypots must be more realistic to entice attackers, necessitating better high-fidelity. To this end, Digital Twin (DT) technology can be employed to increase the complexity and simulation fidelity of the honeypots. Seaports can be attacked from both their existing devices and external devices at the same time. Existing mechanisms are insufficient to detect external attacks; therefore, the current systems cannot handle attacks at the desired level. DT and honeypot technologies can be used together to tackle them. Consequently, we suggest a DT-assisted honeypot, called TwinPot, for external attacks in smart seaports. Moreover, we propose an intelligent attack detection mechanism to handle different attack types using DT for internal attacks. Finally, we build an extensive smart seaport dataset for internal and external attacks using the MANSIM tool and two existing datasets to test the performance of our system. We show that under simultaneous internal and external attacks on the system, our solution successfully detects internal and external attacks.

This paper studies the utility of techniques within uncertainty quantification, namely spectral projection and polynomial chaos expansion, in reducing sampling needs for characterizing acoustic metamaterial dispersion band responses given stochastic material properties and geometric defects. A novel method of encoding geometric defects in an interpretable, resolution independent is showcased in the formation of input space probability distributions. Orders of magnitude sampling reductions down to $\sim10^0$ and $\sim10^1$ are achieved in the 1D and 7D input space scenarios respectively while maintaining accurate output space probability distributions through combining Monte Carlo, quadrature rule, and sparse grid sampling with surrogate model fitting.

In this paper we revisit some common recommendations regarding the analysis of matched-pair and stratified experimental designs in the presence of attrition. Our main objective is to clarify a number of well-known claims about the practice of dropping pairs with an attrited unit when analyzing matched-pair designs. Contradictory advice appears in the literature about whether or not dropping pairs is beneficial or harmful, and stratifying into larger groups has been recommended as a resolution to the issue. To address these claims, we derive the estimands obtained from the difference-in-means estimator in a matched-pair design both when the observations from pairs with an attrited unit are retained and when they are dropped. We find limited evidence to support the claims that dropping pairs helps recover the average treatment effect, but we find that it may potentially help in recovering a convex weighted average of conditional average treatment effects. We report similar findings for stratified designs when studying the estimands obtained from a regression of outcomes on treatment with and without strata fixed effects.

In this thought-provoking article, we discuss certain myths and legends that are folklore among members of the high-performance computing community. We gathered these myths from conversations at conferences and meetings, product advertisements, papers, and other communications such as tweets, blogs, and news articles within and beyond our community. We believe they represent the zeitgeist of the current era of massive change, driven by the end of many scaling laws such as Dennard scaling and Moore's law. While some laws end, new directions are emerging, such as algorithmic scaling or novel architecture research. Nevertheless, these myths are rarely based on scientific facts, but rather on some evidence or argumentation. In fact, we believe that this is the very reason for the existence of many myths and why they cannot be answered clearly. While it feels like there should be clear answers for each, some may remain endless philosophical debates, such as whether Beethoven was better than Mozart. We would like to see our collection of myths as a discussion of possible new directions for research and industry investment.

Promoting behavioural diversity is critical for solving games with non-transitive dynamics where strategic cycles exist, and there is no consistent winner (e.g., Rock-Paper-Scissors). Yet, there is a lack of rigorous treatment for defining diversity and constructing diversity-aware learning dynamics. In this work, we offer a geometric interpretation of behavioural diversity in games and introduce a novel diversity metric based on \emph{determinantal point processes} (DPP). By incorporating the diversity metric into best-response dynamics, we develop \emph{diverse fictitious play} and \emph{diverse policy-space response oracle} for solving normal-form games and open-ended games. We prove the uniqueness of the diverse best response and the convergence of our algorithms on two-player games. Importantly, we show that maximising the DPP-based diversity metric guarantees to enlarge the \emph{gamescape} -- convex polytopes spanned by agents' mixtures of strategies. To validate our diversity-aware solvers, we test on tens of games that show strong non-transitivity. Results suggest that our methods achieve much lower exploitability than state-of-the-art solvers by finding effective and diverse strategies.

In this paper, we focus on the self-supervised learning of visual correspondence using unlabeled videos in the wild. Our method simultaneously considers intra- and inter-video representation associations for reliable correspondence estimation. The intra-video learning transforms the image contents across frames within a single video via the frame pair-wise affinity. To obtain the discriminative representation for instance-level separation, we go beyond the intra-video analysis and construct the inter-video affinity to facilitate the contrastive transformation across different videos. By forcing the transformation consistency between intra- and inter-video levels, the fine-grained correspondence associations are well preserved and the instance-level feature discrimination is effectively reinforced. Our simple framework outperforms the recent self-supervised correspondence methods on a range of visual tasks including video object tracking (VOT), video object segmentation (VOS), pose keypoint tracking, etc. It is worth mentioning that our method also surpasses the fully-supervised affinity representation (e.g., ResNet) and performs competitively against the recent fully-supervised algorithms designed for the specific tasks (e.g., VOT and VOS).