Task design to foster the competence in social decision making on mathematics education

As society continues to progress, it is becoming increasingly more important to mathematically deal with issues, take risks and uncertainty into account, clarify the grounds for participating in judgements or decision making, and make critical deliberations. This competence is defined as "decision making”. We present the design of a task about saving more lives with automatic external defibrillators (AEDs) in order to foster this competency in mathematics lessons. In methodological terms, we use Lesson Study to carefully anticipate the process of students’ finding and solving problems. We review the design from different viewpoints, such as “What times and how should all the students in the class study?” or “When and what kind of materials should be presented?

Photochemical Characterization of a New Heliorhodopsin from the Gram-Negative Eubacterium Bellilinea caldifistulae (BcHeR) and Comparison with Heliorhodopsin-48C12

Many microorganisms express rhodopsins, pigmented membrane proteins capable of absorbing sunlight and harnessing that energy for important biological functions such as ATP synthesis and phototaxis. Microbial rhodopsins that have been discovered to date are categorized as type-1 rhodopsins. Interestingly, researchers have very recently unveiled a new microbial rhodopsin family named the heliorhodopsins, which are phylogenetically distant from type-1 rhodopsins. Among them, only heliorhodopsin-48C12 (HeR-48C12) from a Gram-positive eubacterium has been photochemically characterized [Pushkarev, A., et al. (2018) Nature 558, 595-599]. In this study, we photochemically characterize a purple-colored heliorhodopsin from Gram-negative eubacterium Bellilinea caldifistulae (BcHeR) as a second example and identify which properties are or are not conserved between BcHeR and HeR-48C12. A series of photochemical measurements revealed several conserved properties between them, including a visible absorption spectrum with a maximum at around 550 nm, the lack of ion-transport activity, and the existence of a second-order O-like intermediate during the photocycle that may activate an unidentified biological function. In contrast, as a property that is not conserved, although HeR-48C12 shows the light adaptation state of retinal, BcHeR showed the same retinal configuration under both dark- and light-adapted conditions. These comparisons of photochemical properties between BcHeR and HeR-48C12 are an important first step toward understanding the nature and functional role of heliorhodopsins

Dynamical generation of a nontrivial index on the fuzzy 2-sphere

In the previous paper hep-th/0312199 we studied the 't Hooft-Polyakov (TP) monopole configuration in the U(2) gauge theory on the fuzzy 2-sphere and showed that it has a nonzero topological charge in the formalism based on the Ginsparg-Wilson relation. In this paper, by showing that the TP monopole configuration is stabler than the U(2) gauge theory without any condensation in the Yang-Mills-Chern-Simons matrix model, we will present a mechanism for dynamical generation of a nontrivial index. We further analyze the instability and decay processes of the U(2) gauge theory and the TP monopole configuration.Comment: Latex2e, 30 pages, 4 figures, the topological charge for a monopole configuration is corrected, reference added, the final version to appear in Physical Review D (the typos mentioned in the erratum are corrected

Perturbative dynamics of fuzzy spheres at large N

We clarify some peculiar aspects of the perturbative expansion around a classical fuzzy-sphere solution in matrix models with a cubic term. While the effective action in the large-N limit is saturated at the one-loop level, we find that the ``one-loop dominance'' does not hold for generic observables due to one-particle reducible diagrams. However, we may exploit the one-loop dominance for the effective action and obtain various observables to all orders from one-loop calculation by simply shifting the center of expansion to the ``quantum solution'', which extremizes the effective action. We confirm the validity of this method by comparison with the direct two-loop calculation and with Monte Carlo results in the 3d Yang-Mills-Chern-Simons matrix model. From the all order result we find that the perturbative expansion has a finite radius of convergence.Comment: 21 pages, 9 figures, (v2) all order analyses added, (v3) some typos correcte

A blue-shifted anion channelrhodopsin from the Colpodellida alga Vitrella brassicaformis

Microbial rhodopsins, a family of photoreceptive membrane proteins containing the chromophore retinal, show a variety of light-dependent molecular functions. Channelrhodopsins work as light-gated ion channels and are widely utilized for optogenetics, which is a method for controlling neural activities by light. Since two cation channelrhodopsins were identified from the chlorophyte alga Chlamydomonas reinhardtii, recent advances in genomic research have revealed a wide variety of channelrhodopsins including anion channelrhodopsins (ACRs), describing their highly diversified molecular properties (e.g., spectral sensitivity, kinetics and ion selectivity). Here, we report two channelrhodopsin-like rhodopsins from the Colpodellida alga Vitrella brassicaformis, which are phylogenetically distinct from the known channelrhodopsins. Spectroscopic and electrophysiological analyses indicated that these rhodopsins are green- and blue-sensitive pigments (lambda(max) = similar to 550 and similar to 440 nm) that exhibit light-dependent ion channeling activities. Detailed electrophysiological analysis revealed that one of them works as a monovalent anion (Cl-, Br- and NO3-) channel and we named it V. brassicaformis anion channelrhodopsin-2, VbACR2. Importantly, the absorption maximum of VbACR2 (similar to 440 nm) is blue-shifted among the known ACRs. Thus, we identified the new blue-shifted ACR, which leads to the expansion of the molecular diversity of ACRs