Deep Ridgelet Transform: Voice with Koopman Operator Proves Universality of Formal Deep Networks

We identify hidden layers inside a deep neural network (DNN) with group actions on the data domain, and formulate a formal deep network as a dual voice transform with respect to the Koopman operator, a linear representation of the group action. Based on the group theoretic arguments, particularly by using Schur's lemma, we show a simple proof of the universality of DNNs.Comment: NeurReps 202

Koopman spectral analysis of skew-product dynamics on Hilbert C∗C^*-modules

We introduce a linear operator on a Hilbert $C^*$-module for analyzing skew-product dynamical systems. The operator is defined by composition and multiplication. We show that it admits a decomposition in the Hilbert $C^*$-module, called eigenoperator decomposition, that generalizes the concept of the eigenvalue decomposition. This decomposition reconstructs the Koopman operator of the system in a manner that represents the continuous spectrum through eigenoperators. In addition, it is related to the notions of cocycle and Oseledets subspaces and it is useful for characterizing coherent structures under skew-product dynamics. We present numerical applications to simple systems on two-dimensional domains

Molecular Pathology of Murine Ureteritis Causing Obstructive Uropathy with Hydronephrosis

Primary causes of urinary tract obstruction that induces urine retention and results in hydronephrosis include uroliths, inflammation, and tumors. In this study, we analyzed the molecular pathology of ureteritis causing hydronephrosis in laboratory rodents

Methylation Analysis in Treatment-Resistant Schizophrenia

Schizophrenia is a mental illness that involves both genetic and environmental factors. Clozapine, an atypical antipsychotic, is a well-established therapy for treatment-resistant schizophrenia. In this study, we focused on a set of monozygotic twins with treatment-resistant schizophrenia in which one twin effectively responded to clozapine treatment and the other did not. Our previous study generated neurons from induced pluripotent stem (iPS) cells derived from these patients and compared the transcriptome profiles between mock- and clozapine-treated neurons. In this study, we performed genome-wide DNA methylation profiling to investigate the mechanisms underlying gene expression changes. First, we extracted the differentially methylated sites from each twin based on statistical analysis. Then, we combined the DNA methylation profiling with transcriptome profiling from our previous RNA-seq data. Among the genes with altered methylation and expression, we found the different proportions of the genes related to neuronal and synaptic functions between the clozapine responder and non-responder (35.7 and 6.7%, respectively). This trend was observed even when the basal differences between the responder and non-responder was excluded. These results suggest that effective clozapine action may correct the abnormalities of neuronal and synapse functions in schizophrenia via changes in methylation

A semi-automated non-radiactive system for measuring recovery of RNA synthesis and unscheduled DNA synthesis using ethynyluracil derivatives

Nucleotide excision repair (NER) removes the major UV-photolesions from cellular DNA. In humans, compromised NER activity is the cause of several photosensitive diseases, one of which is the skin-cancer predisposition disorder, xeroderma pigmentosum (XP). Two assays commonly used in measurement of NER activity are ‘unscheduled DNA synthesis (UDS)’, and ‘recovery of RNA synthesis (RRS)’, the latter being a specific measure of the transcription-coupled repair sub-pathway of NER. Both assays are key techniques for research in NER as well as in diagnoses of NER-related disorders. Until very recently, reliable methods for these assays involved measurements of incorporation of radio-labeled nucleosides. We have established non-radioactive procedures for determining UDS and RRS levels by incorporation of recently developed alkyne-conjugated nucleoside analogues, 5-ethynyl-2′-deoxyuridine (EdU) and 5-ethynyuridine (EU). EdU and EU are respectively used as alternatives for 3H-thymidine in UDS and for 3H-uridine in RRS. Based on these alkyne-nucleosides and an integrated image analyser, we have developed a semi-automated assay system for NER-activity. We demonstrate the utility of this system for NER-activity assessments of lymphoblastoid samples as well as primary fibroblasts. Potential use of the system for large-scale siRNA-screening for novel NER defects as well as for routine XP diagnosis are also considered