Riesz transform on manifolds with ends of different volume growth for 1<p<21<p<2

Let $M_1$, $\cdots$, $M_\ell$ be complete, connected and non-collapsed manifolds of the same dimension, where $2\le \ell\in\mathbb{N}$, and suppose that each $M_i$ satisfies a doubling condition and a Gaussian upper bound for the heat kernel. If each manifold $M_i$ has volume growth either bigger than two or equal to two, then we show that the Riesz transform \nabla \L^{-1/2} is bounded on $L^p(M)$ for each $1<p<2$ on the gluing manifold $M=M_1\#M_2\#\cdots \# M_\ell$.Comment: 38p

Financial Volatility Forecasting with Range-based Autoregressive Volatility Model

The classical volatility models, such as GARCH, are return-based models, which are constructed with the data of closing prices. It might neglect the important intraday information of the price movement, and will lead to loss of information and efficiency. This study introduces and extends the range-based autoregressive volatility model to make up for these weaknesses. The empirical results consistently show that the new model successfully captures the dynamics of the volatility and gains good performance relative to GARCH model.This paper is forthcoming in Finance Research Letters

Transcription of AAT•ATT Triplet Repeats in Escherichia coli Is Silenced by H-NS and IS1E Transposition

The trinucleotide repeats AAT•ATT are simple DNA sequences that potentially form different types of non-B DNA secondary structures and cause genomic instabilities in vivo.The molecular mechanism underlying the maintenance of a 24-triplet AAT•ATT repeat was examined in E. coli by cloning the repeats into the EcoRI site in plasmid pUC18 and into the attB site on the E. coli genome. Either the AAT or the ATT strand acted as lagging strand template in a replication fork. Propagations of the repeats in either orientation on plasmids did not affect colony morphology when triplet repeat transcription using the lacZ promoter was repressed either by supplementing LacI(Q)in trans or by adding glucose into the medium. In contrast, transparent colonies were formed by inducing transcription of the repeats, suggesting that transcription of AAT•ATT repeats was toxic to cell growth. Meanwhile, significant IS1E transposition events were observed both into the triplet repeats region proximal to the promoter side, the promoter region of the lacZ gene, and into the AAT•ATT region itself. Transposition reversed the transparent colony phenotype back into healthy, convex colonies. In contrast, transcription of an 8-triplet AAT•ATT repeat in either orientation on plasmids did not produce significant changes in cell morphology and did not promote IS1E transposition events. We further found that a role of IS1E transposition into plasmids was to inhibit transcription through the repeats, which was influenced by the presence of the H-NS protein, but not of its paralogue StpA.Our findings thus suggest that the longer AAT•ATT triplet repeats in E. coli become vulnerable after transcription. H-NS and its facilitated IS1E transposition can silence long triplet repeats transcription and preserve cell growth and survival