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This paper proposes a mechanism to fine-tune convex approximations of probabilistic reachable sets (PRS) of uncertain dynamic systems. We consider the case of unbounded uncertainties, for which it may be impossible to find a bounded reachable set of the system. Instead, we turn to find a PRS that bounds system states with high confidence. Our data-driven approach builds on a kernel density estimator (KDE) accelerated by a fast Fourier transform (FFT), which is customized to model the uncertainties and obtain the PRS efficiently. However, the non-convex shape of the PRS can make it impractical for subsequent optimal designs. Motivated by this, we formulate a mixed integer nonlinear programming (MINLP) problem whose solution result is an optimal $n$ sided convex polygon that approximates the PRS. Leveraging this formulation, we propose a heuristic algorithm to find this convex set efficiently while ensuring accuracy. The algorithm is tested on comprehensive case studies that demonstrate its near-optimality, accuracy, efficiency, and robustness. The benefits of this work pave the way for promising applications to safety-critical, real-time motion planning of uncertain dynamic systems.

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This paper proposes an adaptive behavioral decision-making method for autonomous vehicles (AVs) focusing on complex merging scenarios. Leveraging principles from non-cooperative game theory, we develop a vehicle interaction behavior model that defines key traffic elements and integrates a multifactorial reward function. Maximum entropy inverse reinforcement learning (IRL) is employed for behavior model parameter optimization. Optimal matching parameters can be obtained using the interaction behavior feature vector and the behavior probabilities output by the vehicle interaction model. Further, a behavioral decision-making method adapted to dynamic environments is proposed. By establishing a mapping model between multiple environmental variables and model parameters, it enables parameters online learning and recognition, and achieves to output interactive behavior probabilities of AVs. Quantitative analysis employing naturalistic driving datasets (highD and exiD) and real-vehicle test data validates the model's high consistency with human decision-making. In 188 tested interaction scenarios, the average human-like similarity rate is 81.73%, with a notable 83.12% in the highD dataset. Furthermore, in 145 dynamic interactions, the method matches human decisions at 77.12%, with 6913 consistence instances. Moreover, in real-vehicle tests, a 72.73% similarity with 0% safety violations are obtained. Results demonstrate the effectiveness of our proposed method in enabling AVs to make informed adaptive behavior decisions in interactive environments.

This paper presents a comprehensive examination of the impact of tokenization strategies and vocabulary sizes on the performance of Arabic language models in downstream natural language processing tasks. Our investigation focused on the effectiveness of four tokenizers across various tasks, including News Classification, Hate Speech Detection, Sentiment Analysis, and Natural Language Inference. Leveraging a diverse set of vocabulary sizes, we scrutinize the intricate interplay between tokenization approaches and model performance. The results reveal that Byte Pair Encoding (BPE) with Farasa outperforms other strategies in multiple tasks, underscoring the significance of morphological analysis in capturing the nuances of the Arabic language. However, challenges arise in sentiment analysis, where dialect specific segmentation issues impact model efficiency. Computational efficiency analysis demonstrates the stability of BPE with Farasa, suggesting its practical viability. Our study uncovers limited impacts of vocabulary size on model performance while keeping the model size unchanged. This is challenging the established beliefs about the relationship between vocabulary, model size, and downstream tasks, emphasizing the need for the study of models' size and their corresponding vocabulary size to generalize across domains and mitigate biases, particularly in dialect based datasets. Paper's recommendations include refining tokenization strategies to address dialect challenges, enhancing model robustness across diverse linguistic contexts, and expanding datasets to encompass the rich dialect based Arabic. This work not only advances our understanding of Arabic language models but also lays the foundation for responsible and ethical developments in natural language processing technologies tailored to the intricacies of the Arabic language.

Optimal behaviours of a system to perform a specific task can be achieved by leveraging the coupling between trajectory optimization, stabilization, and design optimization. This approach is particularly advantageous for underactuated systems, which are systems that have fewer actuators than degrees of freedom and thus require for more elaborate control systems. This paper proposes a novel co-design algorithm, namely Robust Trajectory Control with Design optimization (RTC-D). An inner optimization layer (RTC) simultaneously performs direct transcription (DIRTRAN) to find a nominal trajectory while computing optimal hyperparameters for a stabilizing time-varying linear quadratic regulator (TVLQR). RTC-D augments RTC with a design optimization layer, maximizing the system's robustness through a time-varying Lyapunov-based region of attraction (ROA) analysis. This analysis provides a formal guarantee of stability for a set of off-nominal states. The proposed algorithm has been tested on two different underactuated systems: the torque-limited simple pendulum and the cart-pole. Extensive simulations of off-nominal initial conditions demonstrate improved robustness, while real-system experiments show increased insensitivity to torque disturbances.

This paper introduces a first-order method for solving optimal powered descent guidance (PDG) problems, that directly handles the nonconvex constraints associated with the maximum and minimum thrust bounds with varying mass and the pointing angle constraints on thrust vectors. This issue has been conventionally circumvented via lossless convexification (LCvx), which lifts a nonconvex feasible set to a higher-dimensional convex set, and via linear approximation of another nonconvex feasible set defined by exponential functions. However, this approach sometimes results in an infeasible solution when the solution obtained from the higher-dimensional space is projected back to the original space, especially when the problem involves a nonoptimal time of flight. Additionally, the Taylor series approximation introduces an approximation error that grows with both flight time and deviation from the reference trajectory. In this paper, we introduce a first-order approach that makes use of orthogonal projections onto nonconvex sets, allowing expansive projection (ExProj). We show that 1) this approach produces a feasible solution with better performance even for the nonoptimal time of flight cases for which conventional techniques fail to generate achievable trajectories and 2) the proposed method compensates for the linearization error that arises from Taylor series approximation, thus generating a superior guidance solution with less fuel consumption. We provide numerical examples featuring quantitative assessments to elucidate the effectiveness of the proposed methodology, particularly in terms of fuel consumption and flight time. Our analysis substantiates the assertion that the proposed approach affords enhanced flexibility in devising viable trajectories for a diverse array of planetary soft landing scenarios.

This paper proposes novel inferential procedures for discovering the network Granger causality in high-dimensional vector autoregressive models. In particular, we mainly offer two multiple testing procedures designed to control the false discovery rate (FDR). The first procedure is based on the limiting normal distribution of the $t$-statistics with the debiased lasso estimator. The second procedure is its bootstrap version. We also provide a robustification of the first procedure against any cross-sectional dependence using asymptotic e-variables. Their theoretical properties, including FDR control and power guarantee, are investigated. The finite sample evidence suggests that both procedures can successfully control the FDR while maintaining high power. Finally, the proposed methods are applied to discovering the network Granger causality in a large number of macroeconomic variables and regional house prices in the UK.

We present a comparative study between cross-encoder and LLMs rerankers in the context of re-ranking effective SPLADE retrievers. We conduct a large evaluation on TREC Deep Learning datasets and out-of-domain datasets such as BEIR and LoTTE. In the first set of experiments, we show how cross-encoder rerankers are hard to distinguish when it comes to re-rerank SPLADE on MS MARCO. Observations shift in the out-of-domain scenario, where both the type of model and the number of documents to re-rank have an impact on effectiveness. Then, we focus on listwise rerankers based on Large Language Models -- especially GPT-4. While GPT-4 demonstrates impressive (zero-shot) performance, we show that traditional cross-encoders remain very competitive. Overall, our findings aim to to provide a more nuanced perspective on the recent excitement surrounding LLM-based re-rankers -- by positioning them as another factor to consider in balancing effectiveness and efficiency in search systems.

We study dual number symmetric matrices, dual complex Hermitian matrices and dual quaternion Hermitian matrices in a unified frame of dual Hermitian matrices. Suppose we have a ring, which can be the real field, the complex field, or the quaternion ring. Then an $n \times n$ dual Hermitian matrix has $n$ dual number eigenvalues. We define supplement matrices for a dual Hermitian matrix. Supplement matrices are Hermitian matrices in the original ring. The standard parts of the eigenvalues of that dual Hermitian matrix are the eigenvalues of the standard part Hermitian matrix in the original ring, while the dual parts of the eigenvalues of that dual Hermitian matrix are the eigenvalues of those {supplement} matrices. Hence, by apply any practical method for computing eigenvalues of Hermitian matrices in the original ring, we have a practical method for computing eigenvalues of a dual Hermitian matrix. We call this method the supplement matrix method. Applications to low rank approximation and generalized inverses of dual matrices, dual least squares problem and formation control are discussed. Numerical experiments are reported.

Cybersecurity information is often technically complex and relayed through unstructured text, making automation of cyber threat intelligence highly challenging. For such text domains that involve high levels of expertise, pretraining on in-domain corpora has been a popular method for language models to obtain domain expertise. However, cybersecurity texts often contain non-linguistic elements (such as URLs and hash values) that could be unsuitable with the established pretraining methodologies. Previous work in other domains have removed or filtered such text as noise, but the effectiveness of these methods have not been investigated, especially in the cybersecurity domain. We propose different pretraining methodologies and evaluate their effectiveness through downstream tasks and probing tasks. Our proposed strategy (selective MLM and jointly training NLE token classification) outperforms the commonly taken approach of replacing non-linguistic elements (NLEs). We use our domain-customized methodology to train CyBERTuned, a cybersecurity domain language model that outperforms other cybersecurity PLMs on most tasks.

This study introduces a robust solution for the detection of Distributed Denial of Service (DDoS) attacks in Internet of Things (IoT) systems, leveraging the capabilities of Graph Convolutional Networks (GCN). By conceptualizing IoT devices as nodes within a graph structure, we present a detection mechanism capable of operating efficiently even in lossy network environments. We introduce various graph topologies for modeling IoT networks and evaluate them for detecting tunable futuristic DDoS attacks. By studying different levels of network connection loss and various attack situations, we demonstrate that the correlation-based hybrid graph structure is effective in spotting DDoS attacks, substantiating its good performance even in lossy network scenarios. The results indicate a remarkable performance of the GCN-based DDoS detection model with an F1 score of up to 91%. Furthermore, we observe at most a 2% drop in F1-score in environments with up to 50% connection loss. The findings from this study highlight the advantages of utilizing GCN for the security of IoT systems which benefit from high detection accuracy while being resilient to connection disruption.

This paper explores meta-learning in sequential recommendation to alleviate the item cold-start problem. Sequential recommendation aims to capture user's dynamic preferences based on historical behavior sequences and acts as a key component of most online recommendation scenarios. However, most previous methods have trouble recommending cold-start items, which are prevalent in those scenarios. As there is generally no side information in the setting of sequential recommendation task, previous cold-start methods could not be applied when only user-item interactions are available. Thus, we propose a Meta-learning-based Cold-Start Sequential Recommendation Framework, namely Mecos, to mitigate the item cold-start problem in sequential recommendation. This task is non-trivial as it targets at an important problem in a novel and challenging context. Mecos effectively extracts user preference from limited interactions and learns to match the target cold-start item with the potential user. Besides, our framework can be painlessly integrated with neural network-based models. Extensive experiments conducted on three real-world datasets verify the superiority of Mecos, with the average improvement up to 99%, 91%, and 70% in HR@10 over state-of-the-art baseline methods.

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