The number of ramified covering of a Riemann surface by Riemann surface

Interpreting the number of ramified covering of a Riemann surface by Riemann surfaces as the relative Gromov-Witten invariants and applying a gluing formula, we derive a recursive formula for the number of ramified covering of a Riemann surface by Riemann surface with elementary branch points and prescribed ramification type over a special point.Comment: LaTex, 14 page

Isoparametric surfaces in 3-dimensional de Sitter space and anti-de Sitter space

A spacelike surface $M$ in 3-dimensional de Sitter space $\mathbb{S}^3_1$ or 3-dimensional anti-de Sitter space $\mathbb{H}^3_1$ is called isoparametric, if $M$ has constant principle curvatures. A timelike surface is called isoparametric, if its minimal polynomial of the shape operator is constant. In this paper, we determine the spacelike isoparametric surfaces and the timelike isoparametric surfacesx in $\mathbb{S}^3_1$ and $\mathbb{H}^3_1$

Enhancement of Learning and Memory by Elevating Brain Magnesium

Learning and memory are fundamental brain functions affected by dietary and environmental factors. Here, we show that increasing brain magnesium using a newly developed magnesium compound (magnesium-L-threonate, MgT) leads to the enhancement of learning abilities, working memory, and short- and long-term memory in rats. The pattern completion ability was also improved in aged rats. MgT-treated rats had higher density of synaptophysin-/synaptobrevin-positive puncta in DG and CA1 subregions of hippocampus that were correlated with memory improvement. Functionally, magnesium increased the number of functional presynaptic release sites, while it reduced their release probability. The resultant synaptic reconfiguration enabled selective enhancement of synaptic transmission for burst inputs. Coupled with concurrent upregulation of NR2B-containing NMDA receptors and its downstream signaling, synaptic plasticity induced by correlated inputs was enhanced. Our findings suggest that an increase in brain magnesium enhances both short-term synaptic facilitation and long-term potentiation and improves learning and memory functions.National Institutes of Health (U.S.) (NS37342)National Basic Research Program of China (2006CB3031)National Basic Research Program of China (2009CB941303)National Natural Science Foundation (China) (30630026)National High Technology Research and Development Program of China (2007AA02Z443)Tsinghua-Yue-Yuen Medical Sciences Fun

Through-skull fluorescence imaging of the brain in a new near-infrared window

To date, brain imaging has largely relied on X-ray computed tomography and magnetic resonance angiography with limited spatial resolution and long scanning times. Fluorescence-based brain imaging in the visible and traditional near-infrared regions (400–900 nm) is an alternative but currently requires craniotomy, cranial windows and skull thinning techniques, and the penetration depth is limited to 1–2 mm due to light scattering. Here, we report through-scalp and through-skull fluorescence imaging of mouse cerebral vasculature without craniotomy utilizing the intrinsic photoluminescence of single-walled carbon nanotubes in the 1.3–1.4 micrometre near-infrared window. Reduced photon scattering in this spectral region allows fluorescence imaging reaching a depth of >2 mm in mouse brain with sub-10 micrometre resolution. An imaging rate of ~5.3 frames/s allows for dynamic recording of blood perfusion in the cerebral vessels with sufficient temporal resolution, providing real-time assessment of blood flow anomaly in a mouse middle cerebral artery occlusion stroke model

Small RNAs Targeting Transcription Start Site Induce Heparanase Silencing through Interference with Transcription Initiation in Human Cancer Cells

Heparanase (HPA), an endo-h-D-glucuronidase that cleaves the heparan sulfate chain of heparan sulfate proteoglycans, is overexpressed in majority of human cancers. Recent evidence suggests that small interfering RNA (siRNA) induces transcriptional gene silencing (TGS) in human cells. In this study, transfection of siRNA against −9/+10 bp (siH3), but not −174/−155 bp (siH1) or −134/−115 bp (siH2) region relative to transcription start site (TSS) locating at 101 bp upstream of the translation start site, resulted in TGS of heparanase in human prostate cancer, bladder cancer, and gastric cancer cells in a sequence-specific manner. Methylation-specific PCR and bisulfite sequencing revealed no DNA methylation of CpG islands within heparanase promoter in siH3-transfected cells. The TGS of heparanase did not involve changes of epigenetic markers histone H3 lysine 9 dimethylation (H3K9me2), histone H3 lysine 27 trimethylation (H3K27me3) or active chromatin marker acetylated histone H3 (AcH3). The regulation of alternative splicing was not involved in siH3-mediated TGS. Instead, siH3 interfered with transcription initiation via decreasing the binding of both RNA polymerase II and transcription factor II B (TFIIB), but not the binding of transcription factors Sp1 or early growth response 1, on the heparanase promoter. Moreover, Argonaute 1 and Argonaute 2 facilitated the decreased binding of RNA polymerase II and TFIIB on heparanase promoter, and were necessary in siH3-induced TGS of heparanase. Stable transfection of the short hairpin RNA construct targeting heparanase TSS (−9/+10 bp) into cancer cells, resulted in decreased proliferation, invasion, metastasis and angiogenesis of cancer cells in vitro and in athymic mice models. These results suggest that small RNAs targeting TSS can induce TGS of heparanase via interference with transcription initiation, and significantly suppress the tumor growth, invasion, metastasis and angiogenesis of cancer cells