Consider a definably complete uniformly locally o-minimal expansion of the second kind of a densely linearly ordered abelian group. Let $f:X \rightarrow R^n$ be a definable map, where X is a definable set and R is the universe of the structure. We demonstrate the inequality $\dim ) \leq \dim $ in this paper. As a corollary, we get that the set of the points at which f is discontinuous is of dimension smaller than $\dim $. We also show that the (...) structure is definably Baire in the course of the proof of the inequality. (shrink)

We consider locally o-minimal structures possessing tame topological properties shared by models of DCTC and uniformly locally o-minimal expansions of the second kind of densely linearly ordered abelian groups. We derive basic properties of dimension of a set definable in the structures including the addition property, which is the dimension equality for definable maps whose fibers are equi-dimensional. A decomposition theorem into quasi-special submanifolds is also demonstrated.

We first show that the projection image of a discrete definable set is again discrete for an arbitrary definably complete locally o‐minimal structure. This fact together with the results in a previous paper implies a tame dimension theory and a decomposition theorem into good‐shaped definable subsets called quasi‐special submanifolds. Using this fact, we investigate definably complete locally o‐minimal expansions of ordered groups when the restriction of multiplication to an arbitrary bounded open box is definable. Similarly to o‐minimal expansions of ordered (...) fields, Łojasiewicz's inequality, Tietze's extension theorem and affiness of pseudo‐definable spaces hold true for such structures under the extra assumption that the domains of definition and the pseudo‐definable spaces are definably compact. Here, a pseudo‐definable space is a topological space having finite definable atlases. We also demonstrate Michael's selection theorem for definable set‐valued functions with definably compact domains of definition. (shrink)

The provability problem in intuitionistic propositional second-order logic with existential quantifier and implication (∃,→) is proved to be undecidable in presence of free type variables (constants). This contrasts with the result that inutitionistic propositional second-order logic with existential quantifier, conjunction and negation is decidable.

We define and investigate a uniformly locally o-minimal structure of the second kind in this paper. All uniformly locally o-minimal structures of the second kind have local monotonicity, which is a local version of monotonicity theorem of o-minimal structures. We also demonstrate a local definable cell decomposition theorem for definably complete uniformly locally o-minimal structures of the second kind. We define dimension of a definable set and investigate its basic properties when the given structure is a locally o-minimal structure which (...) admits local definable cell decomposition. (shrink)

Although dual-process or divided-mind models of self-control dominate the literature, they suffer from empirical and conceptual challenges. We propose an alternative approach, suggesting that self-control can be characterized by a fragmented part versus integrated whole dynamic. Whereas responses to events derived from fragmented parts of the mind undermine self-control, responses to events derived from integrated wholes enhance self-control. We review empirical evidence from psychology and related disciplines that support this model. We, moreover, discuss the implications of this work for psychology, (...) neuroscience, economics, and philosophy. In particular, we highlight how this model addresses many of the conceptual and empirical short-comings of divided-mind models. We suggest that understanding self-control as the interplay between fragmented parts versus integrated wholes, moreover, provides novel insights and testable new hypotheses. (shrink)

唐招提寺、薬師寺、法隆寺から、世界の名建築を経めぐり、そして桂離宮へ――。知られざる和辻倫理学のもうひとつの思想的源泉!

This paper discusses sufficient conditions for a definably complete expansion of a densely linearly ordered abelian group to have uniformly locally o‐minimal open cores of the first/second kind and strongly locally o‐minimal open core, respectively.

We define a discrete closure operator for definably complete locally o‐minimal structures. The pair of the underlying set of and the discrete closure operator forms a pregeometry. We define the rank of a definable set over a set of parameters using this fact and call it ‐dimension. A definable set X is of dimension equal to the ‐dimension of X. The structure is simultaneously a first‐order topological structure. The dimension rank of a set definable in the first‐order topological structure also (...) coincides with its dimension. (shrink)

BackgroundThe Act Regarding the Promotion of the Appropriate Supply of Hematopoietic Stem Cells for Transplant regulates only how public banks store and provide umbilical cord blood for research or transplantation. Japan had no laws to regulate how the private banks manage the procedures, harvesting, preparation, and storage of such blood. As a result, the status of UCB distribution remains unknown. We conducted a survey to investigate the current status of UCB storage and provision to private biobanks by Japanese institutions that (...) handle childbirth.MethodsQuestionnaire forms were mailed to 3,277 facilities handling childbirth that were registered in the Japan Council for Quality Health Care website.ResultsOf the 1,192 institutions handling childbirth that participated in the survey, 34.4% responded that they currently provide UCB to private biobanks, while 16.1% of facilities did so in the past. Moreover, some institutions currently provide or formerly provided UCB to medical treatment facilities, research institutions, companies, or overseas treatment facilities, research institutions, or companies. A certain number of institutions handling childbirth did not even provide explanations or obtain consent when the UCB was harvested from private bank users.ConclusionsThis is the first study to determine the status of UCB provision to private banks by Japanese institutions handling childbirth. Future studies will need to examine in detail how institutions handling childbirth provide explanations to private bank users and UCB providers as well as how these institutions obtain consent. (shrink)

There has been a long-standing controversy in the context of language evolution on whether the original function of human language was internal thought or external communication. However, given the fact that language clearly serves both functions, internalization and externalization must have been co-evolutionarily acted in the emergence of human language. This article proposes a theoretical hypothesis about this co-evolutionary relationship of internalization and externalization, which especially explains the emergence of the human lexicon. To discuss the evolution of language from a (...) comprehensive perspective, this article proposes a promising model that integrates two approaches with different standpoints: generative grammar and cognitive linguistics. This paper also examines the definition and nature of the lexicon and lexical items based on this integrated model. The hypothesis presented here demonstrates that the co-evolutionary work of internalization and externalization has been involved in two processes in the development of the lexicon: the establishment of syntactic objects (lexical items) and the improvement of creativity responsible for the expansion of lexicon size. The main conclusion is that these processes have formed a positive feedback loop and provided our lexicon with complex and unique properties. (shrink)

We study definably complete locally o‐minimal expansions of ordered groups. We propose a notion of special submanifolds with tubular neighborhoods and show that any definable set is decomposed into finitely many special submanifolds with tubular neighborhoods.

The following two assertions are equivalent for an o-minimal expansion of an ordered group $$\mathcal M=(M,<,+,0,\ldots )$$. There exists a definable bijection between a bounded interval and an unbounded interval. Any definable continuous function $$f:A \rightarrow M$$ defined on a definable closed subset of $$M^n$$ has a definable continuous extension $$F:M^n \rightarrow M$$.

If no property of a system of many particles discriminates among the particles, they are said to be indistinguishable. This indistinguishability is equivalent to the requirement that the many-particle distribution function and all of the dynamic functions for the system be symmetric. The indistinguishability defined in terms of the discrete symmetry of many-particle functions cannot change in the continuous classical statistical limit in which the number density n and the reciprocal temperature β become small. Thus, microscopic particles like electrons must (...) remain indistinguishable in the classical statistical limit although their behavior can be calculated as if they move following the classical laws of motion. In the classical mechanical limit in which quantum cells of volume (2πħ)3 are reduced to points in the phase space, the partition functionTr{exp(−βĤ) for N identical bosons (fermions) approaches (2πħ)−3N(N!) ∫ ... ∫ d3r1 d3p1 ... d3rN d3pN exp(−βH). The two factors, (2πħ)−3N and (N!)−1, which are often added in anad hoc manner in many books on statistical mechanics, are thus derived from the first principles. The criterion of the classical statistical approximation is that the thermal de Broglie wavelength be much shorter than the interparticle distance irrespective of any translation-invariant interparticle interaction. A new derivation of the Maxwell velocity distribution from Boltzmann's principle is given with the assumption of indistinguishable classical particles. (shrink)

Although chimpanzees have been reported to understand to some extent others' visual perception, previous studies using food requesting tasks are divided on whether or not chimpanzees understand the role of eye gaze. One plausible reason for this discrepancy may be the familiarity of the testing situation. Previous food requesting tasks with negative results used an unfamiliar situation that may be difficult for some chimpanzees to recognize as a requesting situation, whereas those with positive results used a familiar situation. The present (...) study tested chimpanzees' understanding of others' attentional states by comparing two requesting situations: an unfamiliar situation in which food was put on a table, and a familiar situation in which chimpanzees requested food held by an experimenter. Chimpanzees showed evidence of understanding the experimenter's attentional variations and the role of eye gaze only in the latter task. This suggests that an unfamiliar requesting situation may keep subjects from expressing their understanding of others' attentional states even though they are sensitive to them. Keywords: Understanding attention; Social cognition; Chimpanzees. (shrink)

Although chimpanzees have been reported to understand to some extent others’ visual perception, previous studies using food requesting tasks are divided on whether or not chimpanzees understand the role of eye gaze. One plausible reason for this discrepancy may be the familiarity of the testing situation. Previous food requesting tasks with negative results used an unfamiliar situation that may be difficult for some chimpanzees to recognize as a requesting situation, whereas those with positive results used a familiar situation. The present (...) study tested chimpanzees’ understanding of others’ attentional states by comparing two requesting situations: an unfamiliar situation in which food was put on a table, and a familiar situation in which chimpanzees requested food held by an experimenter. Chimpanzees showed evidence of understanding the experimenter’s attentional variations and the role of eye gaze only in the latter task. This suggests that an unfamiliar requesting situation may keep subjects from expressing their understanding of others’ attentional states even though they are sensitive to them. Keywords: Understanding attention; Social cognition; Chimpanzees. (shrink)