On the CR transversality of holomorphic maps into hyperquadrics

Let $M_\ell$ be a smooth Levi-nondegenerate hypersurface of signature $\ell$ in $\mathbf C^n$ with $n\ge 3$, and write $H_\ell^N$ for the standard hyperquadric of the same signature in $\mathbf C^N$ with $N-n< \frac{n-1}{2}$. Let $F$ be a holomorphic map sending $M_\ell$ into $H_\ell^N$. Assume $F$ does not send a neighborhood of $M_\ell$ in $\mathbf C^n$ into $H_\ell^N$. We show that $F$ is necessarily CR transversal to $M_\ell$ at any point. Equivalently, we show that $F$ is a local CR embedding from $M_\ell$ into $H_\ell^N$.Comment: To appear in Abel Symposia, dedicated to Professor Yum-Tong Siu on the occasion of his 70th birthda

Superconductivity and Phase Diagram in (Li0.8_{0.8}Fe0.2_{0.2})OHFeSe1−x_{1-x}Sx_x

A series of (Li$_{0.8}$Fe$_{0.2}$)OHFeSe$_{1-x}$S$_x$ (0 $\leq$ x $\leq$ 1) samples were successfully synthesized via hydrothermal reaction method and the phase diagram is established. Magnetic susceptibility suggests that an antiferromagnetism arising from (Li$_{0.8}$Fe$_{0.2}$)OH layers coexists with superconductivity, and the antiferromagnetic transition temperature nearly remains constant for various S doping levels. In addition, the lattice parameters of the both a and c axes decrease and the superconducting transition temperature T$_c$ is gradually suppressed with the substitution of S for Se, and eventually superconductivity vanishes at $x$ = 0.90. The decrease of T$_c$ could be attributed to the effect of chemical pressure induced by the smaller ionic size of S relative to that of Se, being consistent with the effect of hydrostatic pressure on (Li$_{0.8}$Fe$_{0.2}$)OHFeSe. But the detailed investigation on the relationships between $T_{\rm c}$ and the crystallographic facts suggests a very different dependence of $T_{\rm c}$ on anion height from the Fe2 layer or $Ch$-Fe2-$Ch$ angle from those in FeAs-based superconductors.Comment: 6 pages, 6 figure

On the IMF in a Triggered Star Formation Context

The origin of the stellar initial mass function (IMF) is a fundamental issue in the theory of star formation. It is generally fit with a composite power law. Some clues on the progenitors can be found in dense starless cores that have a core mass function (CMF) with a similar shape. In the low-mass end, these mass functions increase with mass, albeit the sample may be somewhat incomplete; in the high-mass end, the mass functions decrease with mass. There is an offset in the turn-over mass between the two mass distributions. The stellar mass for the IMF peak is lower than the corresponding core mass for the CMF peak in the Pipe Nebula by about a factor of three. Smaller offsets are found between the IMF and the CMFs in other nebulae. We suggest that the offset is likely induced during a starburst episode of global star formation which is triggered by the formation of a few O/B stars in the multi-phase media, which naturally emerged through the onset of thermal instability in the cloud-core formation process. We consider the scenario that the ignition of a few massive stars photoionizes the warm medium between the cores, increases the external pressure, reduces their Bonnor?Ebert mass, and triggers the collapse of some previously stable cores. We quantitatively reproduce the IMF in the low-mass end with the assumption of additional rotational fragmentation.Comment: 3 figure

Comprehensive Characterization of the Transmitted/Founder env Genes From a Single MSM Cohort in China

Background: The men having sex with men (MSM) population has become one of the major risk groups for HIV-1 infection in China. However, the epidemiological patterns, function of the env genes, and autologous and heterologous neutralization activity in the same MSM population have not been systematically characterized. Methods: The env gene sequences were obtained by the single genome amplification. The time to the most recent common ancestor was estimated for each genotype using the Bayesian Markov Chain Monte Carlo approach. Coreceptor usage was determined in NP-2 cells. Neutralization was analyzed using Env pseudoviruses in TZM-bl cells. Results: We have obtained 547 full-length env gene sequences by single genome amplification from 30 acute/early HIV-1–infected individuals in the Beijing MSM cohort. Three genotypes (subtype B, CRF01_AE, and CRF07_BC) were identified and 20% of the individuals were infected with multiple transmitted/founder (T/F) viruses. The tight clusters of the MSM sequences regardless of geographic origins indicated nearly exclusive transmission within the MSM population and limited number of introductions. The time to the most recent common ancestor for each genotype was 10–15 years after each was first introduced in China. Disparate preferences for coreceptor usages among 3 genotypes might lead to the changes in percentage of different genotypes in the MSM population over time. The genotype-matched and genotype-mismatched neutralization activity varied among the 3 genotypes. Conclusions: The identification of unique characteristics for transmission, coreceptor usage, neutralization profile, and epidemic patterns of HIV-1 is critical for the better understanding of transmission mechanisms, development of preventive strategies, and evaluation of vaccine efficacy in the MSM population in China

Scatteract: Automated extraction of data from scatter plots

Charts are an excellent way to convey patterns and trends in data, but they do not facilitate further modeling of the data or close inspection of individual data points. We present a fully automated system for extracting the numerical values of data points from images of scatter plots. We use deep learning techniques to identify the key components of the chart, and optical character recognition together with robust regression to map from pixels to the coordinate system of the chart. We focus on scatter plots with linear scales, which already have several interesting challenges. Previous work has done fully automatic extraction for other types of charts, but to our knowledge this is the first approach that is fully automatic for scatter plots. Our method performs well, achieving successful data extraction on 89% of the plots in our test set.Comment: Submitted to ECML PKDD 2017 proceedings, 16 page

Formal and finite order equivalences

We show that two families of germs of real-analytic subsets in $C^{n}$ are formally equivalent if and only if they are equivalent of any finite order. We further apply the same technique to obtain analogous statements for equivalences of real-analytic self-maps and vector fields under conjugations. On the other hand, we provide an example of two sets of germs of smooth curves that are equivalent of any finite order but not formally equivalent