Development of a Comprehensive Network for Scientific and Technical Information in Japan

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Stereographical visualization of a polarization state using weak measurements with an optical-vortex beam

We propose a stereographical-visualization scheme for a polarization state by two-dimensional imaging of a weak value with a single setup. The key idea is to employ Laguerre-Gaussian modes or an optical vortex beam for a probe state in weak measurement. Our scheme has the advantage that we can extract information on the polarization state from the single image in which the zero-intensity point of the optical vortex beam corresponds to a stereographic projection point of the Poincare sphere. We experimentally perform single-setup weak measurement to validate the stereographical relationship between the polarization state on the Poincare sphere and the location of the zero-intensity point.Comment: 6 pages, 4 figure

Exploring new technologies for the future generation: exploration–exploitation trade-off in an intergenerational framework

Decision making on exploring or exploiting technology was studied by means of a laboratory experiment with a two-generation framework. In this framework, the design of a virtual tool is transmitted from the first to second generation, and hence, the former can help the latter by frequently exploring better tool designs but at the cost of reduced opportunities to exploit the existing tool to increase its own benefits. We set two experimental conditions (‘repaid’ and ‘unrepaid’) as well as a control condition (asocial), in which the second generation is absent. In the ‘repaid’ experimental condition, participants received an extra payment proportional to the score gained by the second generation, such that they were monetarily incentivized to help the second generation. Such an incentive was not given in the ‘unrepaid’ condition. An analysis of a formal model and computer simulations predicted that rational participants should increase investment in exploration only in the repaid condition when compared with the asocial control. The prediction was confirmed by the results of the experiment. These findings together suggest that humans may not have a propensity to invest in costly exploration of new technologies solely to help future generations

Exploring new technologies for the future generation: exploration–exploitation trade-off in an intergenerational framework

Decision making on exploring or exploiting technology was studied by means of a laboratory experiment with a two-generation framework. In this framework, the design of a virtual tool is transmitted from the first to second generation, and hence, the former can help the latter by frequently exploring better tool designs but at the cost of reduced opportunities to exploit the existing tool to increase its own benefits. We set two experimental conditions (‘repaid’ and ‘unrepaid’) as well as a control condition (asocial), in which the second generation is absent. In the ‘repaid’ experimental condition, participants received an extra payment proportional to the score gained by the second generation, such that they were monetarily incentivized to help the second generation. Such an incentive was not given in the ‘unrepaid’ condition. An analysis of a formal model and computer simulations predicted that rational participants should increase investment in exploration only in the repaid condition when compared with the asocial control. The prediction was confirmed by the results of the experiment. These findings together suggest that humans may not have a propensity to invest in costly exploration of new technologies solely to help future generations

Exploring new technologies for the future generation: exploration–exploitation trade-off in an intergenerational framework

Decision making on exploring or exploiting technology was studied by means of a laboratory experiment with a two-generation framework. In this framework, the design of a virtual tool is transmitted from the first to second generation, and hence, the former can help the latter by frequently exploring better tool designs but at the cost of reduced opportunities to exploit the existing tool to increase its own benefits. We set two experimental conditions (‘repaid’ and ‘unrepaid’) as well as a control condition (asocial), in which the second generation is absent. In the ‘repaid’ experimental condition, participants received an extra payment proportional to the score gained by the second generation, such that they were monetarily incentivized to help the second generation. Such an incentive was not given in the ‘unrepaid’ condition. An analysis of a formal model and computer simulations predicted that rational participants should increase investment in exploration only in the repaid condition when compared with the asocial control. The prediction was confirmed by the results of the experiment. These findings together suggest that humans may not have a propensity to invest in costly exploration of new technologies solely to help future generations

Stable extendibility of vector bundles over RPn and the stable splitting problem

AbstractLet F be the real number field R or the complex number field C, and let RPn denote the real projective n-space. In this paper, we study the conditions for a given F-vector bundle over RPn to be stably extendible to RPm for every m>n, and establish the formulas on the power ζr=ζ⊗⋯⊗ζ (r-fold) of an F-vector bundle ζ over RPn. Our results are improvements of the previous papers [T. Kobayashi, H. Yamasaki, T. Yoshida, The power of the tangent bundle of the real projective space, its complexification and extendibility, Proc. Amer. Math. Soc. 134 (2005) 303–310] and [Y. Hemmi, T. Kobayashi, Min Lwin Oo, The power of the normal bundle associated to an immersion of RPn, its complexification and extendibility, Hiroshima Math. J. 37 (2007) 101–109]. Furthermore, we answer the stable splitting problem for F-vector bundles over RPn by means of arithmetic conditions