Journal Staff

Let $\{X_n\}_{n\geq1}$ be a sequence of i.i.d. standard Gaussian random variables, let $S_n=\sum_{i=1}^nX_i$ be the Gaussian random walk, and let $T_n=\sum_{i=1}^nS_i$ be the integrated (or iterated) Gaussian random walk. In this paper we derive the following upper and lower bounds for the conditional persistence:\begin{align*}\mathbb{P}\left\{\max_{1\leq k \leq n}T_{k} \leq 0\,\,\Big|\,\,T_n=0,S_n=0\right\}&\lesssim n^{-1/2},\\\mathbb{P}\left\{\max_{1\leq k \leq 2n}T_{k} \leq 0\,\,\Big|\,\,T_{2n}=0,S_{2n}=0\right\}&\gtrsim\frac{n^{-1/2}}{\log n},\end{align*}for $n\rightarrow\infty,$ which partially proves a conjecture by Caravenna and Deuschel (2008)

Comparison for upper tail probabilities of random series

Let $\{\xi_n\}$ be a sequence of independent and identically distributed random variables. In this paper we study the comparison for two upper tail probabilities $\mathbb{P}\{\sum_{n=1}^{\infty}a_n|\xi_n|^p\geq r\}$ and $\mathbb{P}\{\sum_{n=1}^{\infty}b_n|\xi_n|^p\geq r\}$ as $r\rightarrow\infty$ with two different real series $\{a_n\}$ and $\{b_n\}.$ The first result is for Gaussian random variables $\{\xi_n\},$ and in this case these two probabilities are equivalent after suitable scaling. The second result is for more general random variables, thus a weaker form of equivalence (namely, logarithmic level) is proved.Comment: 13 page

The Application of Magnetic Guidance Drilling Technology in Shengli Oilfield

The magnetic guidance drilling technology could use the magnetic guidance instrument to measure the distance between the signal source and the instrument, which is used to control the well trajectory. It is an essential supplement of the existing steering drilling technology. At present, the magnetic guidance drilling technology is mainly applied to dual horizontal wellslls for heavy oil reservoir, CBM horizontal connected wells, wells to mine underground soluble minerals, and relief wells. This paper mainly introduces the working process of magnetic guidance drilling technology and connected wells. In order to test the overall performance of this technology, an experimental study is conducted on it, and the field test was carried on Shengli oil field

Systematic Curation of miRBase Annotation Using Integrated Small RNA High-Throughput Sequencing Data for C. elegans and Drosophila

MicroRNAs (miRNAs) are a class of 20–23 nucleotide small RNAs that regulate gene expression post-transcriptionally in animals and plants. Annotation of miRNAs by the miRNA database (miRBase) has largely relied on computational approaches. As a result, many miRBase entries lack experimental validation, and discrepancies between miRBase annotation and actual miRNA sequences are often observed. In this study, we integrated the small RNA sequencing (smRNA-seq) datasets in Caenorhabditis elegans and Drosophila melanogaster and devised an analytical pipeline coupled with detailed manual inspection to curate miRNA annotation systematically in miRBase. Our analysis reveals 19 (17.0%) and 51 (31.3%) miRNAs entries with detectable smRNA-seq reads have mature sequence discrepancies in C. elegans and D. melanogaster, respectively. These discrepancies frequently occur either for conserved miRNA families whose mature sequences were predicted according to their homologous counterparts in other species or for miRNAs whose precursor miRNA (pre-miRNA) hairpins produce an abundance of multiple miRNA isoforms or variants. Our analysis shows that while Drosophila pre-miRNAs, on average, produce less than 60% accurate mature miRNA reads in addition to their 5′ and 3′ variant isoforms, the precision of miRNA processing in C. elegans is much higher, at over 90%. Based on the revised miRNA sequences, we analyzed expression patterns of the more conserved (MC) and less conserved (LC) miRNAs and found that, whereas MC miRNAs are often co-expressed at multiple developmental stages, LC miRNAs tend to be expressed specifically at fewer stages

Joint Power Splitting and Secure Beamforming Design in the Wireless-powered Untrusted Relay Networks

In this work, we maximize the secrecy rate of the wireless-powered untrusted relay network by jointly designing power splitting (PS) ratio and relay beamforming with the proposed global optimal algorithm (GOA) and local optimal algorithm (LOA). Different from the literature, artificial noise (AN) sent by the destination not only degrades the channel condition of the eavesdropper to improve the secrecy rate, but also becomes a new source of energy powering the untrusted relay based on PS. Hence, it is of high economic benefits and efficiency to take advantage of AN compared with the literature. Simulation results show that LOA can achieve satisfactory secrecy rate performance compared with that of GOA, but with less computation time.Comment: Submitted to GlobeCom201

Probabilities of hitting a convex hull

In this note, we consider the non-negative least square method with a random matrix. This problem has connections with the probability that the origin is not in the convex hull of many random points. As related problems, suitable estimates are obtained as well on the probability that a small ball does not hit the convex hull