Optimal three-ball inequalities and quantitative uniqueness for the Lam\'e system with Lipschitz coefficients

In this paper we study the local behavior of a solution to the Lam\'e system with \emph{Lipschitz} coefficients in dimension $n\ge 2$. Our main result is the bound on the vanishing order of a nontrivial solution, which immediately implies the strong unique continuation property. This paper solves the open problem of the strong uniqueness continuation property for the Lam\'e system with Lipschitz coefficients in any dimension

A three-phase parallel algorithm for solving linear recurrences

AbstractWe present in this paper a three-phase parallel algorithm on the unshuffle network for solving linear recurrences. Through a detailed analysis on the special matrix multiplications involved in the computation we show that the first n terms of an mth order linear recurrence can be computed in O(m3 log nm) time using Θ(nm log nm) processors. For the usual case when m is a small constant. the algorithm achieves cost optimality

Sequence features involved in the mechanism of 3' splice junction wobbling

Background Alternative splicing is an important mechanism mediating the diversified functions of genes in multicellular organisms, and such event occurs in around 40-60% of human genes. Recently, a new splice-junction wobbling mechanism was proposed that subtle modifications exist in mRNA maturation by alternatively choosing at 5'- GTNGT and 3'- NAGNAG, which created single amino acid insertion and deletion isoforms. Results By browsing the Alternative Splicing Database information, we observed that most 3' alternative splice site choices occur within six nucleotides of the dominant splice site and the incidence significantly decreases further away from the dominant acceptor site. Although a lower frequency of alternative splicing occurs within the intronic region (alternative splicing at the proximal AG) than in the exonic region (alternative splicing at the distal AG), alternative AG sites located within the intronic region show stronger potential as the acceptor. These observations revealed that the choice of 3' splice sites during 3' splicing junction wobbling could depend on the distance between the duplicated AG and the branch point site (BPS). Further mutagenesis experiments demonstrated that the distance of AG-to-AG and BPS-to-AG can greatly influence 3' splice site selection. Knocking down a known alternative splicing regulator, hSlu7, failed to affect wobble splicing choices. Conclusion Our results implied that nucleotide distance between proximal and distal AG sites has an important regulatory function. In this study, we showed that occurrence of 3' wobble splicing occurs in a distance-dependent manner and that most of this wobble splicing is probably caused by steric hindrance from a factor bound at the neighboring tandem motif sequence

A rare, highly aggressive primitive neuroectodermal tumor of the kidney: Case report and literature review

AbstractWe report a case of a 14-year-old boy who initially suffered from a sudden onset of abdominal pain for 2 weeks with a protrusive soft mass over the left upper abdomen. No obvious symptomatic symptoms or body weight loss were observed. However, early lung metastasis was detected after an initial computed tomographic examination. Even after we performed salvage en bloc resection of the huge retroperitoneal tumor after primary neoadjuvant chemotherapy, the final outcome was still poor. A diagnosis according to radiologic findings was uncharacteristic. Finally, a pathologic diagnosis based on histologic and immunohistochemical results revealed a rare renal peripheral primitive neuroectodermal tumor