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In this article we review essential natures of superconductivity in strongly correlated electron systems (SCES) from a universal point of view. First we summarize experimental results on SCES by focusing on typical materials such as cuprates, BEDT-TTF organic superconductors, and ruthenate Sr 2 RuO 4 . Experimental results on other important SCES, heavy-fermion systems, will be reviewed separately. The formalism to discuss superconducting properties of SCES is shown based on the Dyson-Gor'kov equations. Here two typical methods to evaluate the vertex function are introduced: One is the perturbation calculation up to the third-order terms with respect to electron correlation. Another is the fluctuationexchange (FLEX) method based on the Baym-Kadanoff conserving approximation. The results obtained by the FLEX method are in good agreement with those obtained by the perturbation calculation. In fact, a reasonable value of T c for spin-singlet d-wave superconductivity is successfully reproduced by using both methods for SCES such as cuprates and BEDT-TTF organic superconductors. As for Sr 2 RuO 4 exhibiting spin-triplet superconductivity, it is quite difficult to describe the superconducting transition by using the FLEX calculation. However, the superconductivity can be naturally explained by the perturbation calculation, since the third-order terms in the anomalous self-energy play the essential role to realize the triplet superconductivity. Another important purpose of this article is to review anomalous electronic properties of SCES near the Mott transition, since the nature of the normal state in SCES has been one of main issues to be discussed. Especially, we focus on pseudogap phenomena observed in under-doped cuprates and organic superconductors. A variety of scenarios to explain the pseudogap phenomena based on the superconducting and/or spin fluctuations are critically reviewed and examined in comparison with experimental results. According to the recent theory, superconducting fluctuations, inherent in the quasi-two-dimensional and strong-coupling superconductors, are the origin of the pseudogap formation. In these compounds, superconducting fluctuations induce a kind of resonance between the Fermi-liquid quasi-particle and the Cooper-pairing states. This resonance gives rise to a large damping effect of quasi-particles and reduces the spectral weight near the Fermi energy. We discuss the magnetic and transport properties as well as the single-particle spectra in the pseudogap state by the microscopic theory of the superconducting fluctuations. As for heavy-fermion superconductors, experimental results are reviewed and several theoretical analyses on the mechanism are provided based on the same viewpoint as explained above.

In order to discuss superconductivity in orbital degenerate systems, a microscopic Hamiltonian is introduced. Based on the degenerate model, a strong-coupling theory of superconductivity is developed within the fluctuation exchange (FLEX) approximation where spin and orbital fluctuations, spectra of electron, and superconducting gap function are self-consistently determined. Applying the FLEX approximation to the orbital degenerate model, it is shown that the d x 2 −y 2 -wave superconducting phase is induced by increasing the orbital splitting energy which leads to the development and suppression of the spin and orbital fluctuations, respectively. It is proposed that the orbital splitting energy is a controlling parameter changing from the paramagnetic to the antiferromagnetic phase with the d x 2 −y 2 -wave superconducting phase in between.

The ability to perceive and recognise a reflected mirror image as self (mirror self-recognition, MSR) is considered a hallmark of cognition across species. Although MSR has been reported in mammals and birds, it is not known to occur in any other major taxon. Potentially limiting our ability to test for MSR in other taxa is that the established assay, the mark test, requires that animals display contingency testing and self-directed behaviour. These behaviours may be difficult for humans to interpret in taxonomically divergent animals, especially those that lack the dexterity (or limbs) required to touch a mark. Here, we show that a fish, the cleaner wrasse Labroides dimidiatus, shows behaviour that may reasonably be interpreted as passing through all phases of the mark test: (i) social reactions towards the reflection, (ii) repeated idiosyncratic behaviours towards the mirror, and (iii) frequent observation of their reflection. When subsequently provided with a coloured tag in a modified mark test, fish attempt to remove the mark by scraping their body in the presence of a mirror but show no response towards transparent marks or to coloured marks in the absence of a mirror. This remarkable finding presents a challenge to our interpretation of the mark test—do we accept that these behavioural responses, which are taken as evidence of self-recognition in other species during the mark test, lead to the conclusion that fish are self-aware? Or do we rather decide that these behavioural patterns have a basis in a cognitive process other than self-recognition and that fish do not pass the mark test? If the former, what does this mean for our understanding of animal intelligence? If the latter, what does this mean for our application and interpretation of the mark test as a metric for animal cognitive abilities?Editor’s noteThis Short Report received both positive and negative reviews by experts. The Academic Editor has written an accompanying Primer that we are publishing alongside this article (https://doi.org/10.1371/journal.pbio.3000112). The linked Primer presents a complementary expert perspective; it discusses how the current study should be interpreted in the context of evidence for and against self-awareness in a wide range of animals.

The main properties of realistic models for manganites are studied using analytic mean-field approximations and computational numerical methods, focusing on the two-orbital model with electrons interacting through Jahn-Teller ͑JT͒ phonons and/or Coulombic repulsions. Analyzing the model including both interactions by the combination of the mean-field approximation and the exact diagonalization method, it is argued that the spin-charge-orbital structure in the insulating phase of the purely JT-phononic model with a large Hund coupling J H is not qualitatively changed by the inclusion of the Coulomb interactions. As an important application of the present mean-field approximation, the CE-type antiferromagnetic state, the charge-stacked structure along the z axis, and (3x 2 Ϫr 2 )/(3y 2 Ϫr 2 )-type orbital ordering are successfully reproduced based on the JT-phononic model with large J H for the half-doped manganite, in agreement with recent Monte Carlo simulation results. Topological arguments and the relevance of the Heisenberg exchange among localized t 2g spins explains why the inclusion of the nearest-neighbor Coulomb interaction does not destroy the charge stacking structure. It is also verified that the phase-separation tendency is observed both in purely JT-phononic ͑large J H ) and purely Coulombic models in the vicinity of the hole undoped region, as long as realistic hopping matrices are used. This highlights the qualitative similarities of both approaches and the relevance of mixedphase tendencies in the context of manganites. In addition, the rich and complex phase diagram of the two-orbital Coulombic model in one dimension is presented. Our results provide robust evidence that Coulombic and JT-phononic approaches to manganites are not qualitatively different ways to carry out theoretical calculations, but they share a variety of common features.