Orbit decomposition of Jordan matrix algebras of order three under the automorphism groups

The orbit decomposition is given under the automorphism group on the real split Jordan algebra of all hermitian matrices of order three corresponding to any real split composition algebra, or the automorphism group on the complexification, explicitly, in terms of the cross product of H. Freudenthal and the characteristic polynomial.Comment: v2, 32 pages, presentation improved, minor errors corrected, and the title changed as appeared in J. Math. Sci. Univ. Toky

Hamiltonian homogeneity on a complex contact manifold

The notion of c-manifolds is introduced as a generalization of complex contact manifolds as well as the degree of symplectifications. And the condition of infinitesimal Hamiltonian homogeneity on a c-manifold is established by means of a moment map defined on the symplectification.Comment: 26 pages; v4: major conceptual changes from v3 by deleting the section 3 because Theorem 3.2 (ii) is wrong

From Homma's theorem to Pick's theorem

From Homma’s PL Gauss-Bonnet theorem applied on a PL-complex in a plane, many generalizations of Pick’s theorem on a lattice PL-figure are obtained in a unified geometric way

The N⁶-methyladenosine methyltransferase METTL16 enables erythropoiesis through safeguarding genome integrity

RNA修飾による赤血球造血制御機構を解明 --RNAのメチル化がDNA修復に必要--. 京都大学プレスリリース. 2022-11-10.Mice show METTL in DNA blood repair: RNA methylation shows important role in erythropoiesis. 京都大学プレスリリース. 2022-11-25.During erythroid differentiation, the maintenance of genome integrity is key for the success of multiple rounds of cell division. However, molecular mechanisms coordinating the expression of DNA repair machinery in erythroid progenitors are poorly understood. Here, we discover that an RNA N⁶-methyladenosine (m⁶A) methyltransferase, METTL16, plays an essential role in proper erythropoiesis by safeguarding genome integrity via the control of DNA-repair-related genes. METTL16-deficient erythroblasts exhibit defective differentiation capacity, DNA damage and activation of the apoptotic program. Mechanistically, METTL16 controls m⁶A deposition at the structured motifs in DNA-repair-related transcripts including Brca2 and Fancm mRNAs, thereby upregulating their expression. Furthermore, a pairwise CRISPRi screen revealed that the MTR4-nuclear RNA exosome complex is involved in the regulation of METTL16 substrate mRNAs in erythroblasts. Collectively, our study uncovers that METTL16 and the MTR4-nuclear RNA exosome act as essential regulatory machinery to maintain genome integrity and erythropoiesis

Decorrelation Signal of Diabetic Hyperreflective Foci on Optical Coherence Tomography Angiography

Diabetic hyperreflective foci in the outer retinal layers are a clinically relevant finding on optical coherence tomography (OCT) images, although their characteristics remain to be elucidated. Here we investigated the decorrelation signal around hyperreflective foci on OCT angiography (OCTA) images in diabetic retinopathy (DR). We retrospectively reviewed sufficient quality OCTA images from 102 eyes of 66 patients that were obtained using split-spectrum amplitude-decorrelation angiography algorithm. Most confluent hyperreflective foci were randomly deposited or appeared in a radiating array on the en-face structural OCT images in the inner nuclear layer (INL) or Henle’s fiber layer (HFL), respectively. Within the INL, hyperreflective foci were not accompanied by decorrelation signals and attached to capillaries on OCTA images. Decorrelation signals were sometimes delineated in hyperreflective foci in the HFL and other times appeared to be pseudopod-like or wrapping around hyperreflective foci, referred to as reflectance-decorrelated foci. The decorrelation signal intensity of hyperreflective foci in the HFL was associated with logMAR VA (R = 0.553, P < 0.001) and central subfield thickness (R = 0.408, P < 0.001) but not with DR severity. These data suggest that reflectance-decorrelated foci on OCTA images are clinically relevant as well as shed lights on the properties in diabetic hyperreflective foci