Examples of non-quasiconvex functions that are rank-one convex are rare. In this paper we construct a family of such functions by means of the algebraic methods of the theory of exact relations for polycrystalline composite materials, developed to identify G-closed sets of positive codimensions. The algebraic methods are used to construct a set of materials of positive codimension that is close...

All plastics can be divided into two groups called thermoplastics and thermosets, and each group exhibits very different behaviors. Unlike thermosets, thermoplastics are empirically known by the viscoelastic behavior of the thermoplastic layers; the stress generated by building subsequent layers can be significantly relieved in a multilayer structure. In this study, we quantitatively investigat...

A common feature of the brain is the arrangement of synapses in layers. To examine the significance of this organizational feature, we studied the functional development of direction-selective (DS) circuits in the tectum of astray mutant zebrafish in which lamination of retinal ganglion cell (RGC) axons is lost. We show that although never laminar, the tuning of DS-RGC axons targeting the mutan...

In the vertebrate retina, neurites from distinct neuronal cell types are constrained within the plexiform layers, allowing for establishment of retinal lamination. However, the mechanisms by which retinal neurites are segregated within the inner or outer plexiform layers are not known. We find that the transmembrane semaphorins Sema5A and Sema5B constrain neurites from multiple retinal neuron s...

We investigate topological and combinatorial structures of Lyubich and Minsky’s affine and hyperbolic 3-laminations associated with the hyperbolic and parabolic quadratic maps. We begin by showing that hyperbolic rational maps in the same hyperbolic component have quasi-isometrically the same 3-laminations. Then we describe the topological and combinatorial changes of laminations associated wit...

In the inner plexiform layer (IPL) of the mouse retina, ~70 neuronal subtypes organize their neurites into an intricate laminar structure that underlies visual processing. To find recognition proteins involved in lamination, we utilized microarray data from 13 subtypes to identify differentially-expressed extracellular proteins and performed a high-throughput biochemical screen. We identified ~...

The arrangement of neurons into distinct layers is critical for neuronal connectivity and function. During development, most neurons move from their birthplace to the appropriate layer, where they polarize. However, kinetics and modes of many neuronal translocation events still await exploration. In this study, we investigate retinal ganglion cell (RGC) translocation across the embryonic zebraf...

The doublecortin (Dcx) and doublecortin-like kinase 1 (Dclk) genes are developmentally expressed neuronal microtubule-associated proteins. Humans with DCX mutations show a severe defect in hippocampal development, but targeted deletion in mouse shows only a defect in pyramidal neuron lamination. There is significant sequence overlap between Dcx and Dclk, suggesting functional redundancy. Here w...