A new era for functional labeling of neurons: activity-dependent promoters have come of age

Genetic labeling of neurons with a specific response feature is an emerging technology for precise dissection of brain circuits that are functionally heterogeneous at the single-cell level. While immediate early gene mapping has been widely used for decades to identify brain regions which are activated by external stimuli, recent characterization of the promoter and enhancer elements responsible for neuronal activity-dependent transcription have opened new avenues for live imaging of active neurons. Indeed, these advancements provided the basis for a growing repertoire of novel experiments to address the role of active neuronal networks in cognitive behaviors. In this review, we summarize the current literature on the usage and development of activity-dependent promoters and discuss the future directions of this expanding new field

Closing Duality Gaps of SDPs through Perturbation

Let $({\bf P},{\bf D})$ be a primal-dual pair of SDPs with a nonzero finite duality gap. Under such circumstances, ${\bf P}$ and ${\bf D}$ are weakly feasible and if we perturb the problem data to recover strong feasibility, the (common) optimal value function $v$ as a function of the perturbation is not well-defined at zero (unperturbed data) since there are ``two different optimal values'' $v({\bf P})$ and $v({\bf D})$, where $v({\bf P})$ and $v({\bf D})$ are the optimal values of ${\bf P}$ and ${\bf D}$ respectively. Thus, continuity of $v$ is lost at zero though $v$ is continuous elsewhere. Nevertheless, we show that a limiting version ${v_a}$ of $v$ is a well-defined monotone decreasing continuous bijective function connecting $v({\bf P})$ and $v({\bf D})$ with domain $[0, \pi/2]$ under the assumption that both ${\bf P}$ and ${\bf D}$ have singularity degree one. The domain $[0,\pi/2]$ corresponds to directions of perturbation defined in a certain manner. Thus, ${v_a}$ ``completely fills'' the nonzero duality gap under a mild regularity condition. Our result is tight in that there exists an instance with singularity degree two for which ${v_a}$ is not continuous.Comment: 26 pages. Comments welcom