Michael-Simon Sobolev inequalities in Euclidean space

Inspired by [1, 13], we prove Michael-Simon type inequalities for smooth symmetric uniformly positive define (0, 2)-tensor fields on compact submanifolds in Euclidean space by the Alexandrov-Bakelman-Pucci (ABP) method.Comment: 10 page

Concentrated Geo-Privacy

This paper proposes concentrated geo-privacy (CGP), a privacy notion that can be considered as the counterpart of concentrated differential privacy (CDP) for geometric data. Compared with the previous notion of geo-privacy [ABCP13, CABP13], which is the counterpart of standard differential privacy, CGP offers many benefits including simplicity of the mechanism, lower noise scale in high dimensions, and better composability known as advanced composition. The last one is the most important, as it allows us to design complex mechanisms using smaller building blocks while achieving better utilities. To complement this result, we show that the previous notion of geo-privacy inherently does not admit advanced composition even using its approximate version. Next, we study three problems on private geometric data: the identity query, k nearest neighbors, and convex hulls. While the first problem has been previously studied, we give the first mechanisms for the latter two under geo-privacy. For all three problems, composability is essential in obtaining good utility guarantees on the privatized query answer

Research on the carbon emission reduction effects of green finance in the context of environment regulations

The rise in carbon emissions has significantly aggravated issues related to climate change. In light of this background, there has been a strong focus on using financial methods to reduce carbon emissions. Based on panel data for China for the period 2003– 2019, we examine the effects of green finance on carbon emissions and the moderating effects of environmental regulations. The results indicate that green finance development alleviates carbon emissions. Meanwhile, our findings on the effects of green finance policies suggest that the implementation of such policies will strengthen the carbon-emission reduction effects of green finance. Additionally, the impacts of green finance on carbon emissions are moderated by administration and public-oriented environmental regulations rather than market-oriented environmental regulations. As the biggest emitter of carbon emissions in the world, China should prioritise the consistent and steady development of green finance and facilitate the green finance legislation. Furthermore, China should enhance the role of marketoriented environmental regulations while considering the synergy between environmental regulations and green finance

Can financial capability improve entrepreneurial performance? Evidence from rural China

The capability of individuals to manage their finances is essential to the outcomes of their entrepreneurial activities. Using panel data from the China Household Finance Survey (C.H.F.S.) in 2013, 2015 and 2017, this article examines how financial capability affects entrepreneurial performance in rural China. The results demonstrate that financial capability is positively correlated with the scale, profitability and sustainability of entrepreneurship, which is robust in consideration of endogeneity. The effects of financial capability are heterogeneous for different entrepreneurs. Furthermore, technology, labour and land act as the mediating variables through which financial capability improves entrepreneurial performance. Therefore, to facilitate entrepreneurial success, it is important to provide entrepreneurs with financial education. Meanwhile, improvements to the financial environment should also be considered. Additionally, financial institutions should combine financial services with factors, such as technology, land and labour, to improve entrepreneurial performance

Role of Tet1 in genomic imprinting erasure

Genomic imprinting is an allele-specific gene expression system important for mammalian development and function 1. The molecular basis of genomic imprinting is allele-specific DNA methylation 1,2. While it is well known that the de novo DNA methyltransferases Dnmt3a/b are responsible for the establishment of genomic imprinting 3, how the methylation mark is erased during primordial germ cell (PGC) reprogramming remains a mystery. Tet1 is one of the ten-eleven translocation family proteins, which have the capacity to oxidize 5-methylcytosine (5mC) 4-6, specifically expressed in reprogramming PGCs 7. Here we report that Tet1 plays a critical role in the erasure of genomic imprinting. We show that despite their identical genotype, progenies derived from mating between Tet1-KO males and wild-type females exhibit a number of variable phenotypes including placental, fetal and postnatal growth defects, and early embryonic lethality. These defects are, at least in part, caused by the dysregulation of imprinted genes, such as Peg10 and Peg3, which exhibit aberrant hypermethylation in the paternal allele of differential methylated regions (DMRs). RNA-seq reveals extensive dysregulation of imprinted genes in the next generation due to paternal loss function of Tet1. Genome-wide DNA methylation analysis of E13.5 PGCs and sperms of Tet1-KO mice revealed hypermethylation of DMRs of imprinted genes in sperm, which can be traced back to PGCs. Analysis of the DNA methylation dynamics in reprogramming PGCs suggests that Tet1 functions to wipe out remaining methylation, including imprinted genes, at the late reprogramming stage. We further provide evidence supporting Tet1's role in the erasure of paternal imprints in female germline. Thus, our study establishes a critical function of Tet1 in genomic imprinting erasure