Scattering and inverse scattering for nonlinear quantum walks

We study large time behavior of quantum walks (QWs) with self-dependent (nonlinear) coin. In particular, we show scattering and derive the reproducing formula for inverse scattering in the weak nonlinear regime. The proof is based on space-time estimate of (linear) QWs such as dispersive estimates and Strichartz estimate. Such argument is standard in the study of nonlinear Schr\"odinger equations and discrete nonlinear Schr\"odinger equations but it seems to be the first time to be applied to QW.Comment: 18 pages, text overlap with arXiv:1711.0062

A Language Support for Exhaustive Fault-Injection in Message-Passing System Models

This paper presents an approach towards specifying and verifying adaptive distributed systems. We here take fault-handling as an example of adaptive behavior and propose a modeling language Sandal for describing fault-prone message-passing systems. One of the unique mechanisms of the language is a linguistic support for abstracting typical faults such as unexpected termination of processes and random loss of messages. The Sandal compiler translates a model into a set of NuSMV modules. During the compilation process, faults specified in the model will be woven into the output. One can thus enjoy full-automatic exhaustive fault-injection without writing faulty behaviors explicitly. We demonstrate the advantage of the language by verifying a model of the two-phase commit protocol under faulty environment.Comment: In Proceedings MOD* 2014, arXiv:1411.345

pXBP1(U) encoded in XBP1 pre-mRNA negatively regulates unfolded protein response activator pXBP1(S) in mammalian ER stress response

Upon the accumulation of unfolded proteins in the mammalian endoplasmic reticulum (ER), X-box binding protein 1 (XBP1) premessenger RNA (premRNA) is converted to mature mRNA by unconventional splicing that is mediated by the endonuclease inositol-requiring enzyme 1. The transcription factor protein (p) XBP1 spliced (S), which is translated from mature XBP1 mRNA, contains the nuclear localization signal and the transcriptional activation domain and activates the transcription of target genes, including those encoding ER chaperones in the nucleus. We show that pXBP1 unspliced (U) encoded in XBP1 pre-mRNA was constitutively expressed and markedly accumulated at the recovery phase of ER stress. pXBP1(U) contained the nuclear exclusion signal instead of the transcriptional activation domain and shuttled between the nucleus and the cytoplasm. Interestingly, pXBP1(U) formed a complex with pXBP1(S), and the pXBP1(U)–pXBP1(S) complex was sequestered from the nucleus. Moreover, the complex was rapidly degraded by proteasomes because of the degradation motif contained in pXBP1(U). Thus, pXBP1(U) is a negative feedback regulator of pXBP1(S), which shuts off the transcription of target genes during the recovery phase of ER stress