Focused Proofreading: Efficiently Extracting Connectomes from Segmented EM Images

Identifying complex neural circuitry from electron microscopic (EM) images may help unlock the mysteries of the brain. However, identifying this circuitry requires time-consuming, manual tracing (proofreading) due to the size and intricacy of these image datasets, thus limiting state-of-the-art analysis to very small brain regions. Potential avenues to improve scalability include automatic image segmentation and crowd sourcing, but current efforts have had limited success. In this paper, we propose a new strategy, focused proofreading, that works with automatic segmentation and aims to limit proofreading to the regions of a dataset that are most impactful to the resulting circuit. We then introduce a novel workflow, which exploits biological information such as synapses, and apply it to a large dataset in the fly optic lobe. With our techniques, we achieve significant tracing speedups of 3-5x without sacrificing the quality of the resulting circuit. Furthermore, our methodology makes the task of proofreading much more accessible and hence potentially enhances the effectiveness of crowd sourcing

Equations of the moduli of pointed curves in the infinite Grassmannian

The main result of this paper is the explicit computation of the equations defining the moduli space of triples $(C,p,z)$ (where $C$ is an integral and complete algebraic curve, $p$ a smooth rational point and $z$ a formal trivialization around $p$) in the infinite Grassmannian of $k((t))$. This is achieved by introducing infinite Grassmannians, tau and Baker-Ahkiezer functions algebraically and by proving an Addition Formula for tau functions.Comment: Final version to appear in Journal of Differential Geometry. Some mistakes involving addition formulas for points of arbitrary connected components of \gr(V) have been removed. 35 pages. LaTe

Automorphism Group of k((t))k((t)): Applications to the Bosonic String

This paper is concerned with the formulation of a non-pertubative theory of the bosonic string. We introduce a formal group $G$ which we propose as the ``universal moduli space'' for such a formulation. This is motivated because $G$ establishes a natural link between representations of the Virasoro algebra and the moduli space of curves. Among other properties of $G$ it is shown that a ``local'' version of the Mumford formula holds on $G$.Comment: 29 page