We investigate the distribution of lengths obtained by intersecting a random geodesic with a geodesic lamination. We give an explicit formula for the distribution for the case of a maximal lamination and show that the distribution is independent of the surface and lamination. We also show how the moments of the distribution are related to the Riemann zeta function.

The ellipsoid body (EB) in the Drosophila brain is a central complex (CX) substructure that harbors circumferentially laminated ring (R) neuron axons and mediates multifaceted sensory integration and motor coordination functions. However, what regulates R axon lamination and how lamination affects R neuron function remain unknown. We show here that the EB is sequentially innervated by small-fie...

Coating and lamination are two functional processes which are used make a proper finishing to the textile material. The coating formulation with different textile grade polymer like PVC, PU, acrylic, PTFE are hugely used to make a textile product with multipurpose way likewaterproof protective clothing, tarpaulin, protective clothing, electrical insulation etc. on the other hand lamination proc...

0. Introduction. The notion of (Haken) normal form w.r.t. a triangulation of a 3-manifold traces back to Kneser's work in the 1930's on surfaces in 3-manifolds. Haken studied it extensively in the 1960's, and showed [8] how to use it to create nite algorithms for the determination of various properties of embedded surfaces. This has since culminated, in the work of Jaco and Oertel [10], in an a...

We survey explicit coordinate descriptions for two (A and X) versions of Teichmüller and lamination spaces for open 2D surfaces, and extend them to the more general setup of surfaces with distinguished collections of points on the boundary. Main features, such as mapping class group action, Poisson and symplectic structures and others, are described in these terms. The lamination spaces are int...

Cortical lamination is crucial for the assembly of cerebellar circuitry. In this process, granule neurons (GNs) migrate along Bergmann glia (BG), which are specialized astroglial cells, from the external granule layer to the internal granule layer. However, the molecular mechanisms underlying BG development are not well understood. Here, we show that GFAP::Cre;Erbb3 mice, which lack Erbb3 in bo...

Cortical lamination is crucial for the assembly of cerebellar circuitry. In this process, granule neurons (GNs) migrate along Bergmann glia (BG), which are specialized astroglial cells, from the external granule layer to the internal granule layer. However, the molecular mechanisms underlying BG development are not well understood. Here, we show that GFAP::Cre;Erbb3 mice, which lack Erbb3 in bo...

The fundamental germ is a generalization of π1, first defined for laminations which arise through group actions [4]. In this paper, the fundamental germ is extended to any lamination having a dense leaf admitting a smooth structure. In addition, an amplification of the fundamental germ called the mother germ is constructed, which is, unlike the fundamental germ, a topological invariant. The fun...

We define a laminar branched surface to be a branched surface satisfying the following conditions: (1) Its horizontal boundary is incompressible; (2) there is no monogon; (3) there is no Reeb component; (4) there is no sink disk (after eliminating trivial bubbles in the branched surface). The first three conditions are standard in the theory of branched surfaces, and a sink disk is a disk branc...