The inversion formula and holomorphic extension of the minimal representation of the conformal group

The minimal representation $\pi$ of the indefinite orthogonal group $O(m+1,2)$ is realized on the Hilbert space of square integrable functions on $\mathbb R^m$ with respect to the measure $|x|^{-1} dx_1... dx_m$. This article gives an explicit integral formula for the holomorphic extension of $\pi$ to a holomorphic semigroup of $O(m+3, \mathbb C)$ by means of the Bessel function. Taking its `boundary value', we also find the integral kernel of the `inversion operator' corresponding to the inversion element on the Minkowski space $\mathbb R^{m,1}$

Special functions associated to a certain fourth order differential equation

We develop a theory of "special functions" associated to a certain fourth order differential operator $\mathcal{D}_{\mu,\nu}$ on $\mathbb{R}$ depending on two parameters $\mu,\nu$. For integers $\mu,\nu\geq-1$ with $\mu+\nu\in2\mathbb{N}_0$ this operator extends to a self-adjoint operator on $L^2(\mathbb{R}_+,x^{\mu+\nu+1}dx)$ with discrete spectrum. We find a closed formula for the generating functions of the eigenfunctions, from which we derive basic properties of the eigenfunctions such as orthogonality, completeness, $L^2$-norms, integral representations and various recurrence relations. This fourth order differential operator $\mathcal{D}_{\mu,\nu}$ arises as the radial part of the Casimir action in the Schr\"odinger model of the minimal representation of the group $O(p,q)$, and our "special functions" give $K$-finite vectors

Smaller total and subregional cerebellar volumes in posttraumatic stress disorder:a mega-analysis by the ENIGMA-PGC PTSD workgroup

Although the cerebellum contributes to higher-order cognitive and emotional functions relevant to posttraumatic stress disorder (PTSD), prior research on cerebellar volume in PTSD is scant, particularly when considering subregions that differentially map on to motor, cognitive, and affective functions. In a sample of 4215 adults (PTSD n = 1642; Control n = 2573) across 40 sites from the ENIGMA-PGC PTSD working group, we employed a new state-of-the-art deep-learning based approach for automatic cerebellar parcellation to obtain volumetric estimates for the total cerebellum and 28 subregions. Linear mixed effects models controlling for age, gender, intracranial volume, and site were used to compare cerebellum volumes in PTSD compared to healthy controls (88% trauma-exposed). PTSD was associated with significant grey and white matter reductions of the cerebellum. Compared to controls, people with PTSD demonstrated smaller total cerebellum volume, as well as reduced volume in subregions primarily within the posterior lobe (lobule VIIB, crus II), vermis (VI, VIII), flocculonodular lobe (lobule X), and corpus medullare (all p -FDR &lt; 0.05). Effects of PTSD on volume were consistent, and generally more robust, when examining symptom severity rather than diagnostic status. These findings implicate regionally specific cerebellar volumetric differences in the pathophysiology of PTSD. The cerebellum appears to play an important role in higher-order cognitive and emotional processes, far beyond its historical association with vestibulomotor function. Further examination of the cerebellum in trauma-related psychopathology will help to clarify how cerebellar structure and function may disrupt cognitive and affective processes at the center of translational models for PTSD.</p

Smaller total and subregional cerebellar volumes in posttraumatic stress disorder:a mega-analysis by the ENIGMA-PGC PTSD workgroup

Although the cerebellum contributes to higher-order cognitive and emotional functions relevant to posttraumatic stress disorder (PTSD), prior research on cerebellar volume in PTSD is scant, particularly when considering subregions that differentially map on to motor, cognitive, and affective functions. In a sample of 4215 adults (PTSD n = 1642; Control n = 2573) across 40 sites from the ENIGMA-PGC PTSD working group, we employed a new state-of-the-art deep-learning based approach for automatic cerebellar parcellation to obtain volumetric estimates for the total cerebellum and 28 subregions. Linear mixed effects models controlling for age, gender, intracranial volume, and site were used to compare cerebellum volumes in PTSD compared to healthy controls (88% trauma-exposed). PTSD was associated with significant grey and white matter reductions of the cerebellum. Compared to controls, people with PTSD demonstrated smaller total cerebellum volume, as well as reduced volume in subregions primarily within the posterior lobe (lobule VIIB, crus II), vermis (VI, VIII), flocculonodular lobe (lobule X), and corpus medullare (all p -FDR &lt; 0.05). Effects of PTSD on volume were consistent, and generally more robust, when examining symptom severity rather than diagnostic status. These findings implicate regionally specific cerebellar volumetric differences in the pathophysiology of PTSD. The cerebellum appears to play an important role in higher-order cognitive and emotional processes, far beyond its historical association with vestibulomotor function. Further examination of the cerebellum in trauma-related psychopathology will help to clarify how cerebellar structure and function may disrupt cognitive and affective processes at the center of translational models for PTSD.</p

Integrative Annotation of 21,037 Human Genes Validated by Full-Length cDNA Clones

The human genome sequence defines our inherent biological potential; the realization of the biology encoded therein requires knowledge of the function of each gene. Currently, our knowledge in this area is still limited. Several lines of investigation have been used to elucidate the structure and function of the genes in the human genome. Even so, gene prediction remains a difficult task, as the varieties of transcripts of a gene may vary to a great extent. We thus performed an exhaustive integrative characterization of 41,118 full-length cDNAs that capture the gene transcripts as complete functional cassettes, providing an unequivocal report of structural and functional diversity at the gene level. Our international collaboration has validated 21,037 human gene candidates by analysis of high-quality full-length cDNA clones through curation using unified criteria. This led to the identification of 5,155 new gene candidates. It also manifested the most reliable way to control the quality of the cDNA clones. We have developed a human gene database, called the H-Invitational Database (H-InvDB; http://www.h-invitational.jp/). It provides the following: integrative annotation of human genes, description of gene structures, details of novel alternative splicing isoforms, non-protein-coding RNAs, functional domains, subcellular localizations, metabolic pathways, predictions of protein three-dimensional structure, mapping of known single nucleotide polymorphisms (SNPs), identification of polymorphic microsatellite repeats within human genes, and comparative results with mouse full-length cDNAs. The H-InvDB analysis has shown that up to 4% of the human genome sequence (National Center for Biotechnology Information build 34 assembly) may contain misassembled or missing regions. We found that 6.5% of the human gene candidates (1,377 loci) did not have a good protein-coding open reading frame, of which 296 loci are strong candidates for non-protein-coding RNA genes. In addition, among 72,027 uniquely mapped SNPs and insertions/deletions localized within human genes, 13,215 nonsynonymous SNPs, 315 nonsense SNPs, and 452 indels occurred in coding regions. Together with 25 polymorphic microsatellite repeats present in coding regions, they may alter protein structure, causing phenotypic effects or resulting in disease. The H-InvDB platform represents a substantial contribution to resources needed for the exploration of human biology and pathology

Neuroimaging-based classification of PTSD using data-driven computational approaches: A multisite big data study from the ENIGMA-PGC PTSD consortium

Background: Recent advances in data-driven computational approaches have been helpful in devising tools to objectively diagnose psychiatric disorders. However, current machine learning studies limited to small homogeneous samples, different methodologies, and different imaging collection protocols, limit the ability to directly compare and generalize their results. Here we aimed to classify individuals with PTSD versus controls and assess the generalizability using a large heterogeneous brain datasets from the ENIGMA-PGC PTSD Working group. Methods: We analyzed brain MRI data from 3,477 structural-MRI; 2,495 resting state-fMRI; and 1,952 diffusion-MRI. First, we identified the brain features that best distinguish individuals with PTSD from controls using traditional machine learning methods. Second, we assessed the utility of the denoising variational autoencoder (DVAE) and evaluated its classification performance. Third, we assessed the generalizability and reproducibility of both models using leave-one-site-out cross-validation procedure for each modality. Results: We found lower performance in classifying PTSD vs. controls with data from over 20 sites (60 % test AUC for s-MRI, 59 % for rs-fMRI and 56 % for D-MRI), as compared to other studies run on single-site data. The performance increased when classifying PTSD from HC without trauma history in each modality (75 % AUC). The classification performance remained intact when applying the DVAE framework, which reduced the number of features. Finally, we found that the DVAE framework achieved better generalization to unseen datasets compared with the traditional machine learning frameworks, albeit performance was slightly above chance. Conclusion: These results have the potential to provide a baseline classification performance for PTSD when using large scale neuroimaging datasets. Our findings show that the control group used can heavily affect classification performance. The DVAE framework provided better generalizability for the multi-site data. This may be more significant in clinical practice since the neuroimaging-based diagnostic DVAE classification models are much less site-specific, rendering them more generalizable

トウシツスイジョウ ニ ダイ オ モツ カンスウ ノ ラドン ヘンカン

京都大学0048新制・課程博士博士(理学)甲第12794号理博第3104号新制||理||1462(附属図書館)UT51-2007-H67京都大学大学院理学研究科数学・数理解析専攻(主査)教授 小林 俊行, 教授 齋藤 恭司, 教授 柏原 正樹学位規則第4条第1項該当Doctor of ScienceKyoto UniversityDA