Let f be a computable function from finite sequences of 0ʼs and 1ʼs to real numbers. We prove that strong f-randomness implies strong f-randomness relative to a PA-degree. We also prove: if X is strongly f-random and Turing reducible to Y where Y is Martin-Löf random relative to Z, then X is strongly f-random relative to Z. In addition, we prove analogous propagation results for other notions of partial randomness, including non-K-triviality and autocomplexity. We prove that f-randomness relative to a (...) PA-degree implies strong f-randomness, hence f-randomness does not imply f-randomness relative to a PA-degree. (shrink)

We consider weak theories of concatenation, that is, theories for strings or texts. We prove that the theory of concatenation WTC-ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{WTC}^{-\varepsilon}}$$\end{document}, which is a weak subtheory of Grzegorczyk’s theory TC-ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{TC}^{-\varepsilon}}$$\end{document}, is a minimal essentially undecidable theory, that is, the theory WTC-ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{WTC}^{-\varepsilon}}$$\end{document} is essentially undecidable and if one omits an axiom scheme from WTC-ε\documentclass[12pt]{minimal} \usepackage{amsmath} (...) \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{WTC}^{-\varepsilon}}$$\end{document}, then the resulting theory is no longer essentially undecidable. Moreover, we give a positive answer to Grzegorczyk and Zdanowski’s conjecture that ‘The theory TC-ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{TC}^{-\varepsilon}}$$\end{document} is a minimal essentially undecidable theory’. For the alternative theories WTC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{WTC}}$$\end{document} and TC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{TC}}$$\end{document} which have the empty string, we also prove that the each theory without the neutrality of ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varepsilon}$$\end{document} is to be such a theory too. (shrink)

To compare two randomness notions with each other, we ask whether a given randomness notion can be defined via another randomness notion. Inspired by Yu's pioneering study, we formalize our question using the concept of relativization of randomness. We give some solutions to our formalized questions. Also, our results include the affirmative answer to the problem asked by Yu in a discussion with the second author, i.e., whether Schnorr randomness relative to the halting problem is equivalent to Martin‐Löf randomness relative (...) to all low 1‐generic reals. (shrink)

Kierstead showed that every computable marriage problem has a computable matching under the assumption of computable expanding Hall condition and computable local finiteness for boys and girls. The strength of the marriage theorem reaches or if computable expanding Hall condition or computable local finiteness for girls is weakened. In contrast, the provability of the marriage theorem is maintained in even if local finiteness for boys is completely removed. Using these conditions, we classify the strength of variants of marriage theorems in (...) the context of reverse mathematics. Furthermore, we introduce another condition that also makes the marriage theorem provable in, and investigate the sequential and Weihrauch strength of marriage theorems under that condition. (shrink)

In this paper, we perform theoretical analysis and experiments on the Simplex Crossover (SPX), which we have proposed. Real-coded GAs are expected to be a powerful function optimization technique for real-world applications where it is often hard to formulate the objective function. However, we believe there are two problems which will make such applications difficult; 1) performance of real-coded GAs depends on the coordinate system used to express the objective function, and 2) it costs much labor to adjust parameters so (...) that the GAs always find an optimum point efficiently. The result of our theoretical analysis and experiments shows that a performance of SPX is independent of linear coordinate transformation and that SPX always optimizes various test function efficiently when theoretical value for expansion rate, which is a parameter of SPX, is applied. We also show that BLX-α is equivalent to degenerate form of SPX. Experiments show that we have something misunderstood effect of epistasis on performance degradation of real-coded GAs. (shrink)

Building on Nietzsche’s view of power, Foucault developed an original analysis of power by making use of concepts like “disciplinary power,” “bio-power,” “governmentality,” etc.; however, existing studies have not sufficiently examined his reading of Nietzsche’s works on this topic. Therefore, in order to clarify the connection between the two, this article examines Foucault’s reading of Nietzsche in detail. Firstly, this article examines the notion of “force” which Foucault recognized is at the center of Nietzsche’s view of power, and will explicitly (...) shows its conceptual determinations. In doing so, this paper will also clarify related notions such as “event,” “body” and “history,” and thus bring to light the general principle of force. In addition, Foucault focused on the point at which Nietzsche—using these principles—radically reinterpreted a central concept of human intellectual activity, namely knowledge. Therefore, this article secondly examines how knowledge is formed under the principle of force, and explicitly shows the general mechanism of knowledge. Finally, the article explains that Nietzsche’s view of power is understood by Foucault as the duality between force and knowledge; in other words, as an ontology of force. (shrink)

The number of competing-brands changes by new product's entry. The new product introduction is endemic among consumer packaged goods firm and is an integral component of their marketing strategy. As a new product's entry affects markets, there is a pressing need to develop market response model that can adapt to such changes. In this paper, we develop a dynamic model that capture the underlying evolution of the buying behavior associated with the new product. This extends an application of a dynamic (...) linear model, which is used by a number of time series analyses, by allowing the observed dimension to change at some point in time. Our model copes with a problem that dynamic environments entail: changes in parameter over time and changes in the observed dimension. We formulate the model with framework of a state space model. We realize an estimation of the model using modified Kalman filter/fixed interval smoother. We find that new product's entry (1) decreases brand differentiation for existing brands, as indicated by decreasing difference between cross-price elasticities; (2) decreases commodity power for existing brands, as indicated by decreasing trend; and (3) decreases the effect of discount for existing brands, as indicated by a decrease in the magnitude of own-brand price elasticities. The proposed framework is directly applicable to other fields in which the observed dimension might be change, such as economic, bioinformatics, and so forth. (shrink)

Every computable function has to be continuous. To develop computability theory of discontinuous functions, we study low levels of the arithmetical hierarchy of nonuniformly computable functions on Baire space. First, we classify nonuniformly computable functions on Baire space from the viewpoint of learning theory and piecewise computability. For instance, we show that mind-change-bounded learnability is equivalent to finite View the MathML source2-piecewise computability 2 denotes the difference of two View the MathML sourceΠ10 sets), error-bounded learnability is equivalent to finite View (...) the MathML sourceΔ20-piecewise computability, and learnability is equivalent to countable View the MathML sourceΠ10-piecewise computability . Second, we introduce disjunction-like operations such as the coproduct based on BHK-like interpretations, and then, we see that these operations induce Galois connections between the Medvedev degree structure and associated Medvedev/ Muchnik-like degree structures. Finally, we interpret these results in the context of the Weihrauch degrees and Wadge-like games. (shrink)

私たちは、暴力的な存在なのか?人間にとって、暴力とは何か?その不可避性と、回避/克服の可能性をともに見すえつつ思考をつむぐ、「暴力の哲学/倫理学」の試み。.

It is known that infinitely many Medvedev degrees exist inside the Muchnik degree of any nontrivial Π10 subset of Cantor space. We shed light on the fine structures inside these Muchnik degrees related to learnability and piecewise computability. As for nonempty Π10 subsets of Cantor space, we show the existence of a finite-Δ20-piecewise degree containing infinitely many finite-2-piecewise degrees, and a finite-2-piecewise degree containing infinitely many finite-Δ20-piecewise degrees 2 denotes the difference of two Πn0 sets), whereas the greatest degrees in (...) these three “finite-Γ-piecewise” degree structures coincide. Moreover, as for nonempty Π10 subsets of Cantor space, we also show that every nonzero finite-2-piecewise degree includes infinitely many Medvedev degrees, every nonzero countable-Δ20-piecewise degree includes infinitely many finite-piecewise degrees, every nonzero finite-2-countable-Δ20-piecewise degree includes infinitely many countable-Δ20-piecewise degrees, and every nonzero Muchnik degree includes infinitely many finite-2-countable-Δ20-piecewise degrees. Indeed, we show that any nonzero Medvedev degree and nonzero countable-Δ20-piecewise degree of a nonempty Π10 subset of Cantor space have the strong anticupping properties. Finally, we obtain an elementary difference between the Medvedev degree structure and the finite-Γ-piecewise degree structure of all subsets of Baire space by showing that none of the finite-Γ-piecewise structures is Brouwerian, where Γ is any of the Wadge classes mentioned above. (shrink)

Probably very few people today would believe that, prior to Japan's modernization during the Meiji period, the Japanese were not able to run. It seems commonsensical that human beings should be able to perform the same body movements such as running—since, of course, we are human beings regardless of whether we live in modern countries. However, it appears, in fact, that people in the Edo Period did not run in the sense of how we run today. There was no need, (...) for example, for farmers to run in the midst of their daily agricultural activities.In addition, it has been also pointed out that, although some premodern Japanese, such as samurai or official messengers... (shrink)

ナショナリズムと親和的関係にある日本通史への欲望を拒否するために、山崎闇斎学派や武士道の語りにおけるナショナルな視線を相対化し、他者性を帯びた「江戸」の自国意識や対中国認識に注目することで、歴史の断面 を記述することの可能性を探る。.

いま、この危機と混迷の時代に、憲法学者・樋口陽一が、基本に立ち戻り、戦後日本を代表する英知・加藤周一と丸山眞男の「憲法論」と「思想」を再読し、その本質を語り尽くす。.

Preview: /Review: Satoshi Higuchi, Somaesthetics and the Philosophy of Culture: Projects in Japan (New York, NY; Oxford, England: Routledge, 2021), 138 pages./ Satoshi Higuchi’s Somaesthetics and the Philosophy of Culture is a succinct and innovative work in aesthetics and philosophy of education, despite what the title may otherwise imply. Indeed, the title may be the only shortcoming in this work, for it does not convey the scope of the concepts covered. It may be better titled Somaesthetics and the (...) Philosophy of Education, but even this does not express the important and fascinating discussions on the aesthetics of sports contained herein; and “education” is perhaps too narrow to encompass the range of application of the ideas (especially in the final part of the book). However, when the reader looks past the title, they will find a nicely organized work introducing readers to the topic of the aesthetics of sport, its application for improving pedagogy, and several avenues for further development in these areas. Higuchi’s previous work is a tireless series of granting legitimacy to the study of sports. Somaesthetics and the Philosophy of Culture is another important step in this project. Readers need not be familiar with Richard Shusterman’s multidisciplinary project of somaesthetics for, when it is necessary, Higuchi provides the relevant details. Readers who are familiar with somaesthetics will very quickly see how the ideas here complement it well. (shrink)

Kristiansen and Murwanashyaka recently proved that Robinson arithmetic, Q, is interpretable in an elementary theory of full binary trees, T. We prove that, conversely, T is interpretable in Q by producing a formal interpretation of T in an elementary concatenation theory QT+, thereby also establishing mutual interpretability of T with several well-known weak essentially undecidable theories of numbers, strings, and sets. We also introduce a “hybrid” elementary theory of strings and trees, WQT*, and establish its mutual interpretability with Robinson’s weak (...) arithmetic R, the weak theory of trees WT of Kristiansen and Murwanashyaka, and the weak concatenation theory WTCε of Higuchi and Horihata. (shrink)