The Finite Spectrum of Fourth-Order Boundary Value Problems with Transmission Conditions

A class of fourth-order boundary value problems with transmission conditions are investigated. By constructing we prove that these class of fourth order problems consist of finite number of eigenvalues. Further, we show that the number of eigenvalues depend on the order of the equation, partition of the domain interval, and the boundary conditions (including the transmission conditions) given

Matrix representations of Sturm–Liouville problems with transmission conditions

AbstractWe identify a class of Sturm–Liouville equations with transmission conditions such that any Sturm–Liouville problem consisting of such an equation with transmission condition and an arbitrary separated or real coupled self-adjoint boundary condition has a representation as an equivalent finite dimensional matrix eigenvalue problem. Conversely, given any matrix eigenvalue problem of certain type and an arbitrary separated or real coupled self-adjoint boundary condition and transmission condition, we construct a class of Sturm–Liouville problems with this specified boundary condition and transmission condition, each of which is equivalent to the given matrix eigenvalue problem

Both Strands of siRNA Have Potential to Guide Posttranscriptional Gene Silencing in Mammalian Cells

Despite the widespread application of RNA interference (RNAi) as a research tool for diverse purposes, the key step of strand selection of siRNAs during the formation of RNA-induced silencing complex (RISC) remains poorly understood. Here, using siRNAs targeted to the complementary region of Survivin and the effector protease receptor 1 (EPR-1), we show that both strands of the siRNA duplex can find their target mRNA and are equally eligible for assembly into Argonaute 2 (Ago2) of RISC in HEK293 cells. Transfection of the synthetic siRNA duplexes with different thermodynamic profiles or short hairpin RNA (shRNA) vectors that generate double-stranded RNAs (dsRNAs), permitting processing specifically from either the 5′ or 3′ end of the incipient siRNA, results in the degradation of the respective target mRNAs of either strand of the siRNA duplex with comparable efficiencies. Thus, while most RNAi reactions may follow the thermodynamic asymmetry rule in strand selection, our study suggests an exceptional mode for certain siRNAs in which both strands of the duplex are competent in sponsoring RNAi, and implies additional factors that might dictate the RNAi targets

Quantum teleportation and entanglement distribution over 100-kilometre free-space channels

A long standing goal for quantum communication is to transfer a quantum state over arbitrary distances. Free-space quantum communication provides a promising solution towards this challenging goal. Here, through a 97-km free space channel, we demonstrate long distance quantum teleportation over a 35-53 dB loss one-link channel, and entanglement distribution over a 66-85 dB high-loss two-link channel. We achieve an average fidelity of {80.4(9)}% for teleporting six distinct initial states and observe the violation of the Clauser-Horne-Shimony-Holt inequality after distributing entanglement. Besides being of fundamental interest, our result represents a significant step towards a global quantum network. Moreover, the high-frequency and high-accuracy acquiring, pointing and tracking technique developed in our experiment provides an essential tool for future satellite-based quantum communication.Comment: 9 pages, 8 figure

A922 Sequential measurement of 1 hour creatinine clearance (1-CRCL) in critically ill patients at risk of acute kidney injury (AKI)

Meeting abstrac

Guidelines for the use and interpretation of assays for monitoring autophagy (4th edition)1.

In 2008, we published the first set of guidelines for standardizing research in autophagy. Since then, this topic has received increasing attention, and many scientists have entered the field. Our knowledge base and relevant new technologies have also been expanding. Thus, it is important to formulate on a regular basis updated guidelines for monitoring autophagy in different organisms. Despite numerous reviews, there continues to be confusion regarding acceptable methods to evaluate autophagy, especially in multicellular eukaryotes. Here, we present a set of guidelines for investigators to select and interpret methods to examine autophagy and related processes, and for reviewers to provide realistic and reasonable critiques of reports that are focused on these processes. These guidelines are not meant to be a dogmatic set of rules, because the appropriateness of any assay largely depends on the question being asked and the system being used. Moreover, no individual assay is perfect for every situation, calling for the use of multiple techniques to properly monitor autophagy in each experimental setting. Finally, several core components of the autophagy machinery have been implicated in distinct autophagic processes (canonical and noncanonical autophagy), implying that genetic approaches to block autophagy should rely on targeting two or more autophagy-related genes that ideally participate in distinct steps of the pathway. Along similar lines, because multiple proteins involved in autophagy also regulate other cellular pathways including apoptosis, not all of them can be used as a specific marker for bona fide autophagic responses. Here, we critically discuss current methods of assessing autophagy and the information they can, or cannot, provide. Our ultimate goal is to encourage intellectual and technical innovation in the field