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Formalization of mathematics is the process of digitizing mathematical knowledge, which allows for formal proof verification as well as efficient semantic searches. Given the large and ever-increasing gap between the set of formalized and unformalized mathematical knowledge, there is a clear need to encourage more computer scientists and mathematicians to solve and formalize mathematical problems together. With blockchain technology, we are able to decentralize this process, provide time-stamped verification of authorship and encourage collaboration through implementation of incentive mechanisms via smart contracts. Currently, the formalization of mathematics is done through the use of proof assistants, which can be used to verify programs and protocols as well. Furthermore, with the advancement in artificial intelligence (AI), particularly machine learning, we can apply automated AI reasoning tools in these proof assistants and (at least partially) automate the process of synthesizing proofs. In our paper, we demonstrate a blockchain-based system for collaborative formalization of mathematics and programs incorporating both human labour as well as automated AI tools. We explain how Token-Curated Registries (TCR) and smart contracts are used to ensure appropriate documents are recorded and encourage collaboration through implementation of incentive mechanisms respectively. Using an illustrative example, we show how formalized proofs of different sorting algorithms can be produced collaboratively in our proposed blockchain system.

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Automator是蘋果公司為他們的Mac OS X系統開發的一款軟件。 只要通過點擊拖拽鼠標等操作就可以將一系列動作組合成一個工作流,從而幫助你自動的(可重復的)完成一些復雜的工作。Automator還能橫跨很多不同種類的程序,包括:查找器、Safari網絡瀏覽器、iCal、地址簿或者其他的一些程序。它還能和一些第三方的程序一起工作,如微軟的Office、Adobe公司的Photoshop或者Pixelmator等。

This paper relates findings of own research in the domain of co-design tools in terms of ethical aspects and their opportunities for inspiration and in HCI education. We overview a number of selected general-purpose HCI/design tools as well as domain specific tools for the Internet of Things. These tools are often card-based, not only suitable for workshops with co-designers but also for internal workshops with students to include these aspects in the built-up of their expertise, sometimes even in a playful way.

Inductive Logic Programming (ILP) is a form of machine learning (ML) which in contrast to many other state of the art ML methods typically produces highly interpretable and reusable models. However, many ILP systems lack the ability to naturally learn from any noisy or partially misclassified training data. We introduce the relaxed learning from failures approach to ILP, a noise handling modification of the previously introduced learning from failures (LFF) approach which is incapable of handling noise. We additionally introduce the novel Noisy Popper ILP system which implements this relaxed approach and is a modification of the existing Popper system. Like Popper, Noisy Popper takes a generate-test-constrain loop to search its hypothesis space wherein failed hypotheses are used to construct hypothesis constraints. These constraints are used to prune the hypothesis space, making the hypothesis search more efficient. However, in the relaxed setting, constraints are generated in a more lax fashion as to avoid allowing noisy training data to lead to hypothesis constraints which prune optimal hypotheses. Constraints unique to the relaxed setting are generated via hypothesis comparison. Additional constraints are generated by weighing the accuracy of hypotheses against their sizes to avoid overfitting through an application of the minimum description length. We support this new setting through theoretical proofs as well as experimental results which suggest that Noisy Popper improves the noise handling capabilities of Popper but at the cost of overall runtime efficiency.

By seamlessly integrating everyday objects and by changing the way we interact with our surroundings, Internet of Things (IoT) is drastically improving the life quality of households and enhancing the productivity of businesses. Given the unique IoT characteristics, IoT applications have emerged distinctively from the mainstream application types. Inspired by the outlook of a programmable world, we further foresee an IoT-native trend in designing, developing, deploying, and maintaining software systems. However, although the challenges of IoT software projects are frequently discussed, addressing those challenges are still in the "crossing the chasm" period. By participating in a few various IoT projects, we gradually distilled three fundamental principles for engineering IoT-native software systems, such as just enough, just in time, and just for "me". These principles target the challenges that are associated with the most typical features of IoT environments, ranging from resource limits to technology heterogeneity of IoT devices. We expect this research to trigger dedicated efforts, techniques and theories for the topic IoT-native software engineering.

This paper presents a probabilistic extension of the well-known cellular automaton, Game of Life. In Game of Life, cells are placed in a grid and then watched as they evolve throughout subsequent generations, as dictated by the rules of the game. In our extension, called ProbLife, these rules now have probabilities associated with them. Instead of cells being either dead or alive, they are denoted by their chance to live. After presenting the rules of ProbLife and its underlying characteristics, we show a concrete implementation in ProbLog, a probabilistic logic programming system. We use this to generate different images, as a form of rule-based generative art.

We introduce Stochastic Asymptotical Regularization (SAR) methods for the uncertainty quantification of the stable approximate solution of ill-posed linear-operator equations, which are deterministic models for numerous inverse problems in science and engineering. We prove the regularizing properties of SAR with regard to mean-square convergence. We also show that SAR is an optimal-order regularization method for linear ill-posed problems provided that the terminating time of SAR is chosen according to the smoothness of the solution. This result is proven for both a priori and a posteriori stopping rules under general range-type source conditions. Furthermore, some converse results of SAR are verified. Two iterative schemes are developed for the numerical realization of SAR, and the convergence analyses of these two numerical schemes are also provided. A toy example and a real-world problem of biosensor tomography are studied to show the accuracy and the advantages of SAR: compared with the conventional deterministic regularization approaches for deterministic inverse problems, SAR can provide the uncertainty quantification of the quantity of interest, which can in turn be used to reveal and explicate the hidden information about real-world problems, usually obscured by the incomplete mathematical modeling and the ascendence of complex-structured noise.

The ability to use symbols is the pinnacle of human intelligence, but has yet to be fully replicated in machines. Here we argue that the path towards symbolically fluent artificial intelligence (AI) begins with a reinterpretation of what symbols are, how they come to exist, and how a system behaves when it uses them. We begin by offering an interpretation of symbols as entities whose meaning is established by convention. But crucially, something is a symbol only for those who demonstrably and actively participate in this convention. We then outline how this interpretation thematically unifies the behavioural traits humans exhibit when they use symbols. This motivates our proposal that the field place a greater emphasis on symbolic behaviour rather than particular computational mechanisms inspired by more restrictive interpretations of symbols. Finally, we suggest that AI research explore social and cultural engagement as a tool to develop the cognitive machinery necessary for symbolic behaviour to emerge. This approach will allow for AI to interpret something as symbolic on its own rather than simply manipulate things that are only symbols to human onlookers, and thus will ultimately lead to AI with more human-like symbolic fluency.

Constrained tensor and matrix factorization models allow to extract interpretable patterns from multiway data. Therefore identifiability properties and efficient algorithms for constrained low-rank approximations are nowadays important research topics. This work deals with columns of factor matrices of a low-rank approximation being sparse in a known and possibly overcomplete basis, a model coined as Dictionary-based Low-Rank Approximation (DLRA). While earlier contributions focused on finding factor columns inside a dictionary of candidate columns, i.e. one-sparse approximations, this work is the first to tackle DLRA with sparsity larger than one. I propose to focus on the sparse-coding subproblem coined Mixed Sparse-Coding (MSC) that emerges when solving DLRA with an alternating optimization strategy. Several algorithms based on sparse-coding heuristics (greedy methods, convex relaxations) are provided to solve MSC. The performance of these heuristics is evaluated on simulated data. Then, I show how to adapt an efficient MSC solver based on the LASSO to compute Dictionary-based Matrix Factorization and Canonical Polyadic Decomposition in the context of hyperspectral image processing and chemometrics. These experiments suggest that DLRA extends the modeling capabilities of low-rank approximations, helps reducing estimation variance and enhances the identifiability and interpretability of estimated factors.

A method of Sequential Log-Convex Programming (SLCP) is constructed that exploits the log-convex structure present in many engineering design problems. The mathematical structure of Geometric Programming (GP) is combined with the ability of Sequential Quadratic Program (SQP) to accommodate a wide range of objective and constraint functions, resulting in a practical algorithm that can be adopted with little to no modification of existing design practices. Three test problems are considered to demonstrate the SLCP algorithm, comparing it with SQP and the modified Logspace Sequential Quadratic Programming (LSQP). In these cases, SLCP shows up to a 77% reduction in number of iterations compared to SQP, and an 11% reduction compared to LSQP. The airfoil analysis code XFOIL is integrated into one of the case studies to show how SLCP can be used to evolve the fidelity of design problems that have initially been modeled as GP compatible. Finally, a methodology for design based on GP and SLCP is briefly discussed.

We describe the new field of mathematical analysis of deep learning. This field emerged around a list of research questions that were not answered within the classical framework of learning theory. These questions concern: the outstanding generalization power of overparametrized neural networks, the role of depth in deep architectures, the apparent absence of the curse of dimensionality, the surprisingly successful optimization performance despite the non-convexity of the problem, understanding what features are learned, why deep architectures perform exceptionally well in physical problems, and which fine aspects of an architecture affect the behavior of a learning task in which way. We present an overview of modern approaches that yield partial answers to these questions. For selected approaches, we describe the main ideas in more detail.

Interest in the field of Explainable Artificial Intelligence has been growing for decades and has accelerated recently. As Artificial Intelligence models have become more complex, and often more opaque, with the incorporation of complex machine learning techniques, explainability has become more critical. Recently, researchers have been investigating and tackling explainability with a user-centric focus, looking for explanations to consider trustworthiness, comprehensibility, explicit provenance, and context-awareness. In this chapter, we leverage our survey of explanation literature in Artificial Intelligence and closely related fields and use these past efforts to generate a set of explanation types that we feel reflect the expanded needs of explanation for today's artificial intelligence applications. We define each type and provide an example question that would motivate the need for this style of explanation. We believe this set of explanation types will help future system designers in their generation and prioritization of requirements and further help generate explanations that are better aligned to users' and situational needs.

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