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Approximation theory plays a central role in numerical analysis, undergoing continuous evolution through a spectrum of methodologies. Notably, Lebesgue, Weierstrass, Fourier, and Chebyshev approximations stand out among these methods. However, each technique possesses inherent limitations, underscoring the critical importance of selecting an appropriate approximation method tailored to specific problem domains. This article delves into the utilization of Chebyshev polynomials at Chebyshev nodes for approximation. For sufficiently smooth functions, the partial sum of Chebyshev series expansion offers optimal polynomial approximation, rendering it a preferred choice in various applications such as digital signal processing and graph filters due to its computational efficiency. In this article, we focus on functions of bounded variation, which find numerous applications across mathematical physics, hyperbolic conservations, and optimization. We present two optimal error estimations associated with Chebyshev polynomial approximations tailored for such functions. To validate our theoretical assertions, we conduct numerical experiments. Additionally, we delineate promising future avenues aligned with this research, particularly within the realms of machine learning and related fields.

Thermal spray coating is a critical process in many industries, involving the application of coatings to surfaces to enhance their functionality. This paper proposes a framework for modelling and predicting critical target variables in thermal spray coating processes, based on the application of statistical design of experiments (DoE) and the modelling of the data using generalized linear models (GLMs) with a particular emphasis on gamma regression. Experimental data obtained from thermal spray coating trials are used to validate the presented approach, demonstrating that it is able to accurately model and predict critical target variables. As such, the framework has significant potential for the optimization of thermal spray coating processes, and can contribute to the development of more efficient and effective coating technologies in various industries.

We consider a graph coloring algorithm that processes vertices in order taken uniformly at random and assigns colors to them using First-Fit strategy. We show that this algorithm uses, in expectation, at most $(\frac{1}{2} + o(1))\cdot \ln n \,/\, \ln\ln n$ different colors to color any forest with $n$ vertices. We also construct a family of forests that shows that this bound is best possible.

Test smells can pose difficulties during testing activities, such as poor maintainability, non-deterministic behavior, and incomplete verification. Existing research has extensively addressed test smells in automated software tests but little attention has been given to smells in natural language tests. While some research has identified and catalogued such smells, there is a lack of systematic approaches for their removal. Consequently, there is also a lack of tools to automatically identify and remove natural language test smells. This paper introduces a catalog of transformations designed to remove seven natural language test smells and a companion tool implemented using Natural Language Processing (NLP) techniques. Our work aims to enhance the quality and reliability of natural language tests during software development. The research employs a two-fold empirical strategy to evaluate its contributions. First, a survey involving 15 software testing professionals assesses the acceptance and usefulness of the catalog's transformations. Second, an empirical study evaluates our tool to remove natural language test smells by analyzing a sample of real-practice tests from the Ubuntu OS. The results indicate that software testing professionals find the transformations valuable. Additionally, the automated tool demonstrates a good level of precision, as evidenced by a F-Measure rate of 83.70%

Recently, fiber optic sensors such as fiber Bragg gratings (FBGs) have been widely investigated for shape reconstruction and force estimation of flexible surgical robots. However, most existing approaches need precise model parameters of FBGs inside the fiber and their alignments with the flexible robots for accurate sensing results. Another challenge lies in online acquiring external forces at arbitrary locations along the flexible robots, which is highly required when with large deflections in robotic surgery. In this paper, we propose a novel data-driven paradigm for simultaneous estimation of shape and force along highly deformable flexible robots by using sparse strain measurement from a single-core FBG fiber. A thin-walled soft sensing tube helically embedded with FBG sensors is designed for a robotic-assisted flexible ureteroscope with large deflection up to 270 degrees and a bend radius under 10 mm. We introduce and study three learning models by incorporating spatial strain encoders, and compare their performances in both free space and constrained environments with contact forces at different locations. The experimental results in terms of dynamic shape-force sensing accuracy demonstrate the effectiveness and superiority of the proposed methods.

Objective: Clinical trials are essential for advancing pharmaceutical interventions, but they face a bottleneck in selecting eligible participants. Although leveraging electronic health records (EHR) for recruitment has gained popularity, the complex nature of unstructured medical texts presents challenges in efficiently identifying participants. Natural Language Processing (NLP) techniques have emerged as a solution with a recent focus on transformer models. In this study, we aimed to evaluate the performance of a prompt-based large language model for the cohort selection task from unstructured medical notes collected in the EHR. Methods: To process the medical records, we selected the most related sentences of the records to the eligibility criteria needed for the trial. The SNOMED CT concepts related to each eligibility criterion were collected. Medical records were also annotated with MedCAT based on the SNOMED CT ontology. Annotated sentences including concepts matched with the criteria-relevant terms were extracted. A prompt-based large language model (Generative Pre-trained Transformer (GPT) in this study) was then used with the extracted sentences as the training set. To assess its effectiveness, we evaluated the model's performance using the dataset from the 2018 n2c2 challenge, which aimed to classify medical records of 311 patients based on 13 eligibility criteria through NLP techniques. Results: Our proposed model showed the overall micro and macro F measures of 0.9061 and 0.8060 which were among the highest scores achieved by the experiments performed with this dataset. Conclusion: The application of a prompt-based large language model in this study to classify patients based on eligibility criteria received promising scores. Besides, we proposed a method of extractive summarization with the aid of SNOMED CT ontology that can be also applied to other medical texts.

Reasoning, a crucial ability for complex problem-solving, plays a pivotal role in various real-world settings such as negotiation, medical diagnosis, and criminal investigation. It serves as a fundamental methodology in the field of Artificial General Intelligence (AGI). With the ongoing development of foundation models, e.g., Large Language Models (LLMs), there is a growing interest in exploring their abilities in reasoning tasks. In this paper, we introduce seminal foundation models proposed or adaptable for reasoning, highlighting the latest advancements in various reasoning tasks, methods, and benchmarks. We then delve into the potential future directions behind the emergence of reasoning abilities within foundation models. We also discuss the relevance of multimodal learning, autonomous agents, and super alignment in the context of reasoning. By discussing these future research directions, we hope to inspire researchers in their exploration of this field, stimulate further advancements in reasoning with foundation models, and contribute to the development of AGI.

Understanding causality helps to structure interventions to achieve specific goals and enables predictions under interventions. With the growing importance of learning causal relationships, causal discovery tasks have transitioned from using traditional methods to infer potential causal structures from observational data to the field of pattern recognition involved in deep learning. The rapid accumulation of massive data promotes the emergence of causal search methods with brilliant scalability. Existing summaries of causal discovery methods mainly focus on traditional methods based on constraints, scores and FCMs, there is a lack of perfect sorting and elaboration for deep learning-based methods, also lacking some considers and exploration of causal discovery methods from the perspective of variable paradigms. Therefore, we divide the possible causal discovery tasks into three types according to the variable paradigm and give the definitions of the three tasks respectively, define and instantiate the relevant datasets for each task and the final causal model constructed at the same time, then reviews the main existing causal discovery methods for different tasks. Finally, we propose some roadmaps from different perspectives for the current research gaps in the field of causal discovery and point out future research directions.

We consider the problem of explaining the predictions of graph neural networks (GNNs), which otherwise are considered as black boxes. Existing methods invariably focus on explaining the importance of graph nodes or edges but ignore the substructures of graphs, which are more intuitive and human-intelligible. In this work, we propose a novel method, known as SubgraphX, to explain GNNs by identifying important subgraphs. Given a trained GNN model and an input graph, our SubgraphX explains its predictions by efficiently exploring different subgraphs with Monte Carlo tree search. To make the tree search more effective, we propose to use Shapley values as a measure of subgraph importance, which can also capture the interactions among different subgraphs. To expedite computations, we propose efficient approximation schemes to compute Shapley values for graph data. Our work represents the first attempt to explain GNNs via identifying subgraphs explicitly and directly. Experimental results show that our SubgraphX achieves significantly improved explanations, while keeping computations at a reasonable level.

Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.