Organometal halide perovskites have attracted widespread attention as the most favorable prospective material for photovoltaic technology because of their high photoinduced charge separation and carrier transport performance. However, the microstructural aspects within the organometal halide perovskite are still unknown, even though it belongs to a crystal system. Here direct observation of the microstructure of the thin film organometal halide perovskite using transmission electron microscopy is reported. Unlike previous reports claiming each phase of the organometal halide perovskite solely exists at a given temperature range, it is identified that the tetragonal and cubic phases coexist at room temperature, and it is confirmed that superlattices composed of a mixture of tetragonal and cubic phases are self-organized without a compositional change. The organometal halide perovskite self-adjusts the configuration of phases and automatically organizes a buffer layer at boundaries by introducing a superlattice. This report shows the fundamental crystallographic information for the organometal halide perovskite and demonstrates new possibilities as promising materials for various applications.

Abstract. Let G be a finite simple graph on [n] and

Cognitive impairments are a core feature in schizophrenia patients (SCZ) and are also observed in first-degree relatives (FR) of SCZ. However, substantial variability in the impairments exists within and among SCZ, FR and healthy controls (HC). A cluster-analytic approach can group individuals based on profiles of traits and create more homogeneous groupings than predefined categories. Here, we investigated differences in the Brief Assessment of Cognition in Schizophrenia (BACS) neuropsychological battery (six subscales) among SCZ, unaffected FR and HC. To identify three homogeneous and meaningful cognitive groups regardless of categorical diagnoses (SCZ, FR and HC), cognitive clustering was performed, and differences in the BACS subscales among the cognitive cluster groups were investigated. Finally, the effects of diagnosis and cognition on brain volumes were examined. As expected, there were significant differences in the five BACS subscales among the diagnostic groups. The cluster-analytic approach generated three meaningful subgroups: (i) neuropsychologically normal, (ii) intermediate impaired and (iii) widespread impaired. The cognitive subgroups were mainly affected by the clinical diagnosis, and significant differences in all BACS subscales among clusters were found. The effects of the diagnosis and cognitive clusters on brain volumes overlapped in the frontal, temporal and limbic regions. Frontal and temporal volumes were mainly affected by the diagnosis, whereas the anterior cingulate cortex (ACC) volumes were affected by the additive effects of diagnosis and cognition. Our findings demonstrate a cognitive continuum among SCZ, FR and HC and support the concept of cognitive impairment and the related ACC volumes as intermediate phenotypes in SCZ.

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In this paper, we prove that the arithmetical rank of a squarefree monomial ideal I is equal to the projective dimension of R/I in the following cases: (a) I is an almost complete intersection; (b) arithdeg I = reg I ; (c) arithdeg I = indeg I + 1.We also classify all almost complete intersection squarefree monomial ideals in terms of hypergraphs, and use this classification in the proof in case (c).