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

The B Lymphocyte Adaptor Molecule of 32 kD (Bam32) Regulates B Cell Antigen Receptor Signaling and Cell Survival

The B lymphocyte–associated adaptor protein 32 kD in size (Bam32) is expressed at high levels in germinal center (GC) B cells. It has an NH2-terminal src homology 2 (SH2) domain which binds phospholipase C (PLC)γ2, and a COOH-terminal pleckstrin homology (PH) domain. Thus, Bam32 may function to integrate protein tyrosine kinase (PTK) and phosphatidylinositol 3-kinase (PI3K) signaling pathways in B cells. To further define the role Bam32 plays in B cells, we generated Bam32-deficient DT40 cells. These Bam32−/− cells exhibited lower levels of B cell antigen receptor (BCR)-induced calcium mobilization with modest decreases in tyrosine phosphorylation of phospholipase C (PLC)γ2. Moreover, BCR-induced activation of extracellular signal-regulated kinase (ERK), c-jun NH2-terminal kinase (JNK), and p38 mitogen-activated protein kinase (MAPK) pathways was impaired in Bam32−/− cells but not the activation of Akt-related pathways. Activation of downstream transcription factors such as nuclear factor of activated T cells (NF-AT) and nuclear factor of κ binding (NF-κB) was also impaired in Bam32−/− cells. Furthermore, Bam32−/− cells were more susceptible to BCR-induced death. Taken together, these findings suggest that Bam32 functions to regulate BCR-induced signaling and cell survival most likely in germinal centers