11,285 research outputs found

    On the van der Waerden numbers w(2;3,t)

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    We present results and conjectures on the van der Waerden numbers w(2;3,t) and on the new palindromic van der Waerden numbers pdw(2;3,t). We have computed the new number w(2;3,19) = 349, and we provide lower bounds for 20 <= t <= 39, where for t <= 30 we conjecture these lower bounds to be exact. The lower bounds for 24 <= t <= 30 refute the conjecture that w(2;3,t) <= t^2, and we present an improved conjecture. We also investigate regularities in the good partitions (certificates) to better understand the lower bounds. Motivated by such reglarities, we introduce *palindromic van der Waerden numbers* pdw(k; t_0,...,t_{k-1}), defined as ordinary van der Waerden numbers w(k; t_0,...,t_{k-1}), however only allowing palindromic solutions (good partitions), defined as reading the same from both ends. Different from the situation for ordinary van der Waerden numbers, these "numbers" need actually to be pairs of numbers. We compute pdw(2;3,t) for 3 <= t <= 27, and we provide lower bounds, which we conjecture to be exact, for t <= 35. All computations are based on SAT solving, and we discuss the various relations between SAT solving and Ramsey theory. Especially we introduce a novel (open-source) SAT solver, the tawSolver, which performs best on the SAT instances studied here, and which is actually the original DLL-solver, but with an efficient implementation and a modern heuristic typical for look-ahead solvers (applying the theory developed in the SAT handbook article of the second author).Comment: Second version 25 pages, updates of numerical data, improved formulations, and extended discussions on SAT. Third version 42 pages, with SAT solver data (especially for new SAT solver) and improved representation. Fourth version 47 pages, with updates and added explanation

    A Holy Curiosity: Transformative Self-Directed Learning to Breakthrough New Knowledge in the Case of Einstein

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    The case of Einstein’s discovery of the relativity theory, explored with grounded theory methodology, illustrates a type of self-directed learning characterized by personal and non-personal, or technical, transformative learning, the result of which is iconic original, breakthrough learning. This dissertation explores three aspects of adult learning which are novel in adult education. First, this study of breakthrough process, for which there is only one apparent precedent in adult education, considers how an individual goes about a self-directed learning project that revolutionizes a field. In this regard, the concept of original learning, as opposed to transmitted learning, presents itself as a valid element of adult learning and adult education. Next, the results argue for an expanded view of transformative learning: that it is not limited to adulthood, or to personal or socio-cultural domains, or to absolute designations of either completed transformative or non-transformative learning. Finally, considering the patterns in Einstein’s breakthrough journey in light of other models of breakthrough yields a broadly common process of breakthrough via challenge formation, navigating new territory, persevering through a long ordeal, and finally an actualization process of validation and integration. This common pattern can be found in the other model of self-directed breakthrough learning (Cavaliere’s example of the Wright brothers’ invention of flight); in Mezirow’s model of personal or socio-cultural transformative learning; in Campbell’s archetype of the hero’s journey in literature, film, and other forms of myth and story (elaborating Aristotle’s three-part structure for plot dynamics), and also in a neurobiological model of exceptional creativity based on classic creativity theory and contemporary scientific research. This grounded theory of independent breakthrough learning integrates these concepts. The result is a model of a meaningful question (passionate curiosity in a personally meaningful context) meeting transformative attention (critical reflection and a multi-dimensional process of deep interaction with the question), resulting in a breakthrough learning posture that can yield results on a continuum from creatively discovered answers in the existing base of human knowledge, to incremental contributions to that knowledge base, to profoundly transformative changes in perspective and capability in a field of human endeavor

    Game Solving with Online Fine-Tuning

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    Game solving is a similar, yet more difficult task than mastering a game. Solving a game typically means to find the game-theoretic value (outcome given optimal play), and optionally a full strategy to follow in order to achieve that outcome. The AlphaZero algorithm has demonstrated super-human level play, and its powerful policy and value predictions have also served as heuristics in game solving. However, to solve a game and obtain a full strategy, a winning response must be found for all possible moves by the losing player. This includes very poor lines of play from the losing side, for which the AlphaZero self-play process will not encounter. AlphaZero-based heuristics can be highly inaccurate when evaluating these out-of-distribution positions, which occur throughout the entire search. To address this issue, this paper investigates applying online fine-tuning while searching and proposes two methods to learn tailor-designed heuristics for game solving. Our experiments show that using online fine-tuning can solve a series of challenging 7x7 Killall-Go problems, using only 23.54% of computation time compared to the baseline without online fine-tuning. Results suggest that the savings scale with problem size. Our method can further be extended to any tree search algorithm for problem solving. Our code is available at https://rlg.iis.sinica.edu.tw/papers/neurips2023-online-fine-tuning-solver.Comment: Accepted by the 37th Conference on Neural Information Processing Systems (NeurIPS 2023

    An evaluation of the total quality management implementation strategy for the advanced solid rocket motor project at NASA's Marshall Space Flight Center

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    An evaluation of the NASA's Marshall Space Flight Center (MSFC) strategy to implement Total Quality Management (TQM) in the Advanced Solid Rocket Motor (ASRM) Project is presented. The evaluation of the implementation strategy reflected the Civil Service personnel perspective at the project level. The external and internal environments at MSFC were analyzed for their effects on the ASRM TQM strategy. Organizational forms, cultures, management systems, problem solving techniques, and training were assessed for their influence on the implementation strategy. The influence of ASRM's effort was assessed relative to its impact on mature projects as well as future projects at MSFC

    Synchronous Online Philosophy Courses: An Experiment in Progress

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    There are two main ways to teach a course online: synchronously or asynchronously. In an asynchronous course, students can log on at their convenience and do the course work. In a synchronous course, there is a requirement that all students be online at specific times, to allow for a shared course environment. In this article, the author discusses the strengths and weaknesses of synchronous online learning for the teaching of undergraduate philosophy courses. The author discusses specific strategies and technologies he uses in the teaching of online philosophy courses. In particular, the author discusses how he uses videoconferencing to create a classroom-like environment in an online class

    Scalable Parallel DFPN Search

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    Abstract. We present Scalable Parallel Depth-First Proof Number Search, a new shared-memory parallel version of depth-first proof number search. Based on the serial DFPN 1+ε method of Pawlewicz and Lew, SPDFPN searches effectively even as the transposition table becomes almost full, and so can solve large prob-lems. To assign jobs to threads, SPDFPN uses proof and disproof numbers and two parameters. SPDFPN uses no domain-specific knowledge or heuristics, so it can be used in any domain. Our experiments show that SPDFPN scales well and performs well on hard problems. We tested SPDFPN on problems from the game of Hex. On a 24-core machine and a 4.2-hour single-thread task, parallel efficiency ranges from 0.8 on 4 threads to 0.74 on 16 threads. SPDFPN solved all previously intractable 9×9 Hex open-ing moves; the hardest opening took 111 days. Also, in 63 days, it solved one 10×10 Hex opening move. This is the first time a computer or human has solved a 10×10 Hex opening move.

    CHARACTERIZING ENABLING INNOVATIONS AND ENABLING THINKING

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    The pursuit of innovation is engrained throughout society whether in business via the introduction of offerings, non-profits in their mission-driven initiatives, universities and agencies in their drive for discoveries and inventions, or governments in their desire to improve the quality of life of their citizens. Yet, despite these pursuits, innovations with long-lasting, significant impact represent an infrequent outcome in most domains. The seemingly random nature of these results stems, in part, from the definitions of innovation and the models based on such definitions. Although there is debate on this topic, a comprehensive and pragmatic perspective developed in this work defines innovation as the introduction of a novel or different idea into practice that has a positive impact on society. To date, models of innovation have focused on, for example, new technological advances, new approaches to connectivity in systems, new conceptual frameworks, or even new dimensions of performance - all effectively building on the first half of the definition of innovation and encouraging its pursuit based on the novelty of ideas. However, as explored herein, achieving profound results by innovating on demand might require a perspective that focuses on the impact of an innovation. In this view, innovation does not only entail doing new things, but consciously driving them towards achieving impact through proactive design behaviors. Explicit consideration of the impact dimension in innovation models has been missing, even though it may arguably be the most important since it represents the outcome of innovation
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