The Jordan algebra of complex symmetric operators

For a conjugation $C$ on a separable, infinite dimensional, complex Hilbert space $\mathcal H$, the set $\mathcal{S}_C$ of $C$-symmetric operators on $\mathcal H$ forms a weakly closed, selfadjoint, Jordan operator algebra, which has been studied under the name of Cartan factor of type II. We study $\mathcal{S}_C$ in comparison with the algebra $\mathcal{B(H)}$ of all bounded linear operators on $\mathcal H$, and develop some algebraic properties of $\mathcal{S}_C$ as well as some properties of individual elements. We determine the Jordan ideals of $\mathcal{S}_C$ and their dual spaces. Jordan automorphisms of $\mathcal{S}_C$ are classified. We describe $C^*$-algebras contained in $\mathcal{S}_C$ and determine the $C^*$-algebra generated by $\mathcal{S}_C$. It is proved that invertible operators in $\mathcal{S}_C$ constitute a dense, path connected subset of $\mathcal{S}_C$. We establish the Weyl-von Neumann-Berg Theorem in $\mathcal{S}_C$, that is, every normal operator in $\mathcal{S}_C$ is the sum of a diagonal and a small compact operator in $\mathcal{S}_C$. As an application, it is proved that each operator in $\mathcal{S}_C$ is a small compact perturbation of irreducible ones in $\mathcal{S}_C$. We discuss a Brown-Douglas-Fillmore type theorem for $\mathcal{S}_C$. We determine the spectra of Jordan multiplication operators on $\mathcal{S}_C$.Comment: 32 page

Simultaneous profiling of transcriptome and DNA methylome from a single cell.

BackgroundSingle-cell transcriptome and single-cell methylome technologies have become powerful tools to study RNA and DNA methylation profiles of single cells at a genome-wide scale. A major challenge has been to understand the direct correlation of DNA methylation and gene expression within single-cells. Due to large cell-to-cell variability and the lack of direct measurements of transcriptome and methylome of the same cell, the association is still unclear.ResultsHere, we describe a novel method (scMT-seq) that simultaneously profiles both DNA methylome and transcriptome from the same cell. In sensory neurons, we consistently identify transcriptome and methylome heterogeneity among single cells but the majority of the expression variance is not explained by proximal promoter methylation, with the exception of genes that do not contain CpG islands. By contrast, gene body methylation is positively associated with gene expression for only those genes that contain a CpG island promoter. Furthermore, using single nucleotide polymorphism patterns from our hybrid mouse model, we also find positive correlation of allelic gene body methylation with allelic expression.ConclusionsOur method can be used to detect transcriptome, methylome, and single nucleotide polymorphism information within single cells to dissect the mechanisms of epigenetic gene regulation

Influence of acupuncture on cognitive function and markers of oxidative DNA damage in patients with vascular dementia

AbstractObjectiveTo test the influence of acupuncture on cognitive function and a marker of oxidative DNA damage in patients with vascular dementia (VD).MethodsSixteen VD patients were evaluated before and after acupuncture, using the Folstein Mini-Mental State Examination-Revised (MMSE-R) to assess cognitive function, and the ADL-R scale to assess independence in activities of daily living (ADL). Life quality was evaluated using the DEMQOL (Dementia quality of life questionnaire) questionnaire, and syndromes and expression of vascular dementia were evaluated with the Scale for the Differentiation of Syndromes of Vascular Dementia (SDSVD). In addition, the urine concentration of 8-hydroxy-2′-deoxyguanosine (8-OHdG) —a marker of oxidative damage—was quantified with enzyme-linked immunosorbent assay.ResultsThe MMSE-R and DEMQOL scores were higher after acupuncture than before (P<0.05), while there were no obvious differences in the ADL-R or SDSVD scores (P>0.05). The 8-OHdG content in urine significantly decreased after acupuncture (P<0.05).ConclusionAcupuncture reduces the levels of 8-OHdG and improves cognitive function and quality of life in VD patients, suggesting that acupuncture is beneficial at least in part by preventing oxidative damage