We present new algorithm for growth of non-clustered planar graphs by aggregation of cells with given distribution of size and constraint of connectivity k = 3 per node. The emergent graph structures are controlled by two parameters—chemical potential of the cell aggregation and the width of the cell size distribution. We compute several statistical properties of these graphs—fractal dimension ...

We introduce a novel algorithm for hierarchical clustering on planar graphs we call “Hierarchical Greedy Planar Correlation Clustering” (HGPCC). We formulate hierarchical image segmentation as an ultrametric rounding problem on a superpixel graph where there are edges between superpixels that are adjacent in the image. We apply coordinate descent optimization where updates are based on planar c...

The generation of planar cell polarity (PCP) and tissue shape during morphogenesis is tightly linked, but it is not clear how. Aigouy et al. (2010) now show in the developing Drosophila wing that PCP initially has a radial orientation that becomes realigned to the proximal-distal axis of organ shape by mechanical forces and cell rearrangements mediated by Dachsous.

The Fat pathway controls both planar cell polarity (PCP) and organ growth. Fat signaling is regulated by the graded expression of the Fat ligand Dachsous (Ds) and the cadherin-domain kinase Four-jointed (Fj). The vectors of these gradients influence PCP, whereas their slope can influence growth. The Fj and Ds gradients direct the polarized membrane localization of the myosin Dachs, which is a c...

Planar cell polarity (PCP) occurs in the epithelia of many animals and can lead to the alignment of hairs, bristles, and feathers. Here, we present two approaches to modelling this phenomenon. The aim is to discover the basic mechanisms that drive PCP, while keeping the models mathematically tractable. We present a feedback and diffusion model, in which adjacent cell sides of neighbouring cells...

A growing list of medically important developmental defects and disease mechanisms can be traced to disruption of the planar cell polarity (PCP) pathway. The PCP system polarizes cells in epithelial sheets along an axis orthogonal to their apical-basal axis. Studies in the fruitfly, Drosophila, have suggested that components of the PCP signaling system function in distinct modules, and that the...

Here we present a planar patch clamp chip based on biomimetic cell membrane fusion. This architecture uses nanometer length-scale surface patterning to replicate the structure and function of membrane proteins, creating a gigaohm seal between the cell and a planar electrode array. The seal is generated passively during cell spreading, without the application of a vacuum to the cell surface. Thi...

the crossing number of a graph  is the minimum number of edge crossings over all possible drawings of  in a plane. the crossing number is an important measure of the non-planarity of a graph, with applications in discrete and computational geometry and vlsi circuit design. in this paper we introduce vertex centered crossing number and study the same for maximal planar graph.

in this paper a performance analysis is presented for a cable-suspended parallel manipulator. experimental results from some first tests are presented and discussed to validate the theoretical calculation of load carrying capacity. the load-carrying capacity during a given trajectory is obtained. this computational technique is tested on a typical planar cable suspended manipulator. the experim...

introduction echo-planar imaging (epi) is a group of fast data acquisition methods commonly used in fmri studies. it acquires multiple image lines in k-space after a single excitation, which leads to a very short scan time. a well-known problem with epi is that it is more sensitive to distortions due to the used encoding scheme. source of distortion is inhomogeneity in the static b0 field that ...