In this issue of the Biochemical Journal, Xu et al. describe how they use a spot peptide array to identify a unique sequence within beta-arrestin-2 that is required for both multimerization and ERK1/2 (extracellular-signal-related kinase 1/2) scaffolding. They provide evidence that dimers may serve as more than just 'storage forms' of beta-arrestins, incapable of interacting with receptors but,...

There are two objects naturally associated with a braid $\beta\in B_n$ of pseudo-Anosov type: (relative) homeomorphism $\varphi_\beta\colon S^2\to S^2$; and the finite volume complete hyperbolic structure on 3-manifold $M_\beta$ obtained by excising closure $\beta$, together its axis, from $S^3$. We show disconnect between these objects, exhibiting family braids $\{\beta_q:q\in{\mathbb{Q}}\cap(...

We study the existence of sign-changing solutions for following supercritical problem with variable exponent and logarithmic nonlinearity$ \begin{equation*} \left\{ \begin{aligned} - \Delta u& = |u|^{2^{*}-2} u\big( \ln( \tau +|u|) \big)^{ |x|^{\beta} } & \ \mbox{in} B_{1}, \\ 0 \mbox{on} \partial \end{aligned} \right. \end{equation*} $where $ B_{1} is unit ball in \mathbb{R}^{N} $, N\g...

We establish uniform error bounds of an exponential wave integrator Fourier pseudospectral (EWI-FP) method for the long-time dynamics nonlinear Klein--Gordon equation (NKGE) with a cubic nonlinearity whose strength is characterized by $\varepsilon^2$ $\varepsilon \in (0, 1]$ dimensionless parameter. When $0 < \varepsilon \ll 1$, problem equivalent to NKGE small initial data (and $O(1)$ nonlinea...