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We propose an axiomatic foundation of mathematics based on the finite sequence as the foundational concept, rather than based on logic and set, as in set theory, or based on type as in dependent type theories. Finite sequences lead to a concept of pure data, which is used to represent all mathematical objects. As an axiomatic system, the foundation has only one axiom which defines what constitutes a valid definition. Using the axiom, an internal true/false/undecided valued logic and an internal language are defined, making logic and language-related axioms un- necessary. Valid proof and valid computation are defined in terms of equality of pure data. An algebra of pure data leads to a rich theory of spaces and morphisms which play a role similar to the role of Category Theory in modern Mathematics. As applications, we explore Mathematical Machine Learning, the consistency of Mathematics and address paradoxes due to Godel, Berry, Curry and Yablo.

eXplainable artificial intelligence (XAI) methods have emerged to convert the black box of machine learning models into a more digestible form. These methods help to communicate how the model works with the aim of making machine learning models more transparent and increasing the trust of end-users into their output. SHapley Additive exPlanations (SHAP) and Local Interpretable Model Agnostic Explanation (LIME) are two widely used XAI methods particularly with tabular data. In this commentary piece, we discuss the way the explainability metrics of these two methods are generated and propose a framework for interpretation of their outputs, highlighting their weaknesses and strengths.

Deep learning becomes an elevated context regarding disposing of many machine learning tasks and has shown a breakthrough upliftment to extract features from unstructured data. Though this flourishing context is developing in the medical image processing sector, scarcity of problem-dependent training data has become a larger issue in the way of easy application of deep learning in the medical sector. To unravel the confined data source, researchers have developed a model that can solve machine learning problems with fewer data called ``Few shot learning". Few hot learning algorithms determine to solve the data limitation problems by extracting the characteristics from a small dataset through classification and segmentation methods. In the medical sector, there is frequently a shortage of available datasets in respect of some confidential diseases. Therefore, Few shot learning gets the limelight in this data scarcity sector. In this chapter, the background and basic overview of a few shots of learning is represented. Henceforth, the classification of few-shot learning is described also. Even the paper shows a comparison of methodological approaches that are applied in medical image analysis over time. The current advancement in the implementation of few-shot learning concerning medical imaging is illustrated. The future scope of this domain in the medical imaging sector is further described.

Gun violence is a major problem in contemporary American society, with tens of thousands injured each year. However, relatively little is known about the effects on family members and how effects vary across subpopulations. To study these questions and, more generally, to address a gap in the causal inference literature, we present a framework for the study of effect modification or heterogeneous treatment effects in difference-in-differences designs. We implement a new matching technique, which combines profile matching and risk set matching, to (i) preserve the time alignment of covariates, exposure, and outcomes, avoiding pitfalls of other common approaches for difference-in-differences, and (ii) explicitly control biases due to imbalances in observed covariates in subgroups discovered from the data. Our case study shows significant and persistent effects of nonfatal firearm injuries on several health outcomes for those injured and on the mental health of their family members. Sensitivity analyses reveal that these results are moderately robust to unmeasured confounding bias. Finally, while the effects for those injured are modified largely by the severity of the injury and its documented intent, for families, effects are strongest for those whose relative's injury is documented as resulting from an assault, self-harm, or law enforcement intervention.

Over the past half century, there have been several false dawns during which the "arrival" of world-changing artificial intelligence (AI) has been heralded. Tempting fate, the authors believe the age of AI has, indeed, finally arrived. Powerful image generators, such as DALL-E2 and Midjourney have suddenly allowed anyone with access the ability easily to create rich and complex art. In a similar vein, text generators, such as GPT3.5 (including ChatGPT) and BLOOM, allow users to compose detailed written descriptions of many topics of interest. And, it is even possible now for a person without extensive expertise in writing software to use AI to generate code capable of myriad applications. While AI will continue to evolve and improve, probably at a rapid rate, the current state of AI is already ushering in profound changes to many different sectors of society. Every new technology challenges the ability of humanity to govern it wisely. However, governance is usually viewed as both possible and necessary due to the disruption new technology often poses to social structures, industries, the environment, and other important human concerns. In this article, we offer an analysis of a range of interactions between AI and governance, with the hope that wise decisions may be made that maximize benefits and minimize costs. The article addresses two main aspects of this relationship: the governance of AI by humanity, and the governance of humanity by AI. The approach we have taken is itself informed by AI, as this article was written collaboratively by the authors and ChatGPT.

Blockchain is an emerging decentralized data collection, sharing and storage technology, which have provided abundant transparent, secure, tamper-proof, secure and robust ledger services for various real-world use cases. Recent years have witnessed notable developments of blockchain technology itself as well as blockchain-adopting applications. Most existing surveys limit the scopes on several particular issues of blockchain or applications, which are hard to depict the general picture of current giant blockchain ecosystem. In this paper, we investigate recent advances of both blockchain technology and its most active research topics in real-world applications. We first review the recent developments of consensus mechanisms and storage mechanisms in general blockchain systems. Then extensive literature is conducted on blockchain enabled IoT, edge computing, federated learning and several emerging applications including healthcare, COVID-19 pandemic, social network and supply chain, where detailed specific research topics are discussed in each. Finally, we discuss the future directions, challenges and opportunities in both academia and industry.

A proper fusion of complex data is of interest to many researchers in diverse fields, including computational statistics, computational geometry, bioinformatics, machine learning, pattern recognition, quality management, engineering, statistics, finance, economics, etc. It plays a crucial role in: synthetic description of data processes or whole domains, creation of rule bases for approximate reasoning tasks, reaching consensus and selection of the optimal strategy in decision support systems, imputation of missing values, data deduplication and consolidation, record linkage across heterogeneous databases, and clustering. This open-access research monograph integrates the spread-out results from different domains using the methodology of the well-established classical aggregation framework, introduces researchers and practitioners to Aggregation 2.0, as well as points out the challenges and interesting directions for further research.

Automated Driving Systems (ADS) have made great achievements in recent years thanks to the efforts from both academia and industry. A typical ADS is composed of multiple modules, including sensing, perception, planning and control, which brings together the latest advances in multiple domains. Despite these achievements, safety assurance of the systems is still of great significance, since the unsafe behavior of ADS can bring catastrophic consequences and unacceptable economic and social losses. Testing is an important approach to system validation for the deployment in practice; in the context of ADS, it is extremely challenging, due to the system complexity and multidisciplinarity. There has been a great deal of literature that focuses on the testing of ADS, and a number of surveys have also emerged to summarize the technical advances. However, most of these surveys focus on the system-level testing that is performed within software simulators, and thereby ignore the distinct features of individual modules. In this paper, we provide a comprehensive survey on the existing ADS testing literature, which takes into account both module-level and system-level testing. Specifically, we make the following contributions: (1) we build a threat model that reveals the potential safety threats for each module of an ADS; (2) we survey the module-level testing techniques for ADS and highlight the technical differences affected by the properties of the modules; (3) we also survey the system-level testing techniques, but we focus on empirical studies that take a bird's-eye view on the system, the problems due to the collaborations between modules, and the gaps between ADS testing in simulators and real world; (4) we identify the challenges and opportunities in ADS testing, which facilitates the future research in this field.

The notion of uncertainty is of major importance in machine learning and constitutes a key element of machine learning methodology. In line with the statistical tradition, uncertainty has long been perceived as almost synonymous with standard probability and probabilistic predictions. Yet, due to the steadily increasing relevance of machine learning for practical applications and related issues such as safety requirements, new problems and challenges have recently been identified by machine learning scholars, and these problems may call for new methodological developments. In particular, this includes the importance of distinguishing between (at least) two different types of uncertainty, often refereed to as aleatoric and epistemic. In this paper, we provide an introduction to the topic of uncertainty in machine learning as well as an overview of hitherto attempts at handling uncertainty in general and formalizing this distinction in particular.

The era of big data provides researchers with convenient access to copious data. However, people often have little knowledge about it. The increasing prevalence of big data is challenging the traditional methods of learning causality because they are developed for the cases with limited amount of data and solid prior causal knowledge. This survey aims to close the gap between big data and learning causality with a comprehensive and structured review of traditional and frontier methods and a discussion about some open problems of learning causality. We begin with preliminaries of learning causality. Then we categorize and revisit methods of learning causality for the typical problems and data types. After that, we discuss the connections between learning causality and machine learning. At the end, some open problems are presented to show the great potential of learning causality with data.