Cylindrical equilibrium shapes of fluid membranes

Within the framework of the well-known curvature models, a fluid lipid bilayer membrane is regarded as a surface embedded in the three-dimensional Euclidean space whose equilibrium shapes are described in terms of its mean and Gaussian curvatures by the so-called membrane shape equation. In the present paper, all solutions to this equation determining cylindrical membrane shapes are found and presented, together with the expressions for the corresponding position vectors, in explicit analytic form. The necessary and sufficient conditions for such a surface to be closed are derived and several sufficient conditions for its directrix to be simple or self-intersecting are given.Comment: 17 pages, 4 figures. Published in J. Phys. A: Math. Theore

Apoptosis and proliferation in the trigeminal placode

The neurogenic trigeminal placode develops from the crescent-shaped panplacodal primordium which delineates the neural plate anteriorly. We show that, in Tupaia belangeri, the trigeminal placode is represented by a field of focal ectodermal thickenings which over time changes positions from as far rostral as the level of the forebrain to as far caudal as opposite rhombomere 3. Delamination proceeds rostrocaudally from the ectoderm adjacent to the rostral midbrain, and contributes neurons to the trigeminal ganglion as well as to the ciliary ganglion/oculomotor complex. Proliferative events are centered on the field prior to the peak of delamination. They are preceded, paralleled and, finally, outnumbered by apoptotic events which proceed rostrocaudally from non-delaminating to delaminating parts of the field. Apoptosis persists upon regression of the placode, thereby exhibiting a massive “wedge” of apoptotic cells which includes the postulated position of the “ventrolateral postoptic placode” (Lee et al. in Dev Biol 263:176–190, 2003), merges with groups of lens-associated apoptotic cells, and disappears upon lens detachment. In conjunction with earlier work (Washausen et al. in Dev Biol 278:86–102, 2005) our findings suggest that apoptosis contributes repeatedly to the disintegration of the panplacodal primordium, to the elimination of subsets of premigratory placodal neuroblasts, and to the regression of placodes

Virtual Realities (Dagstuhl Seminar 13241, June 9-14, 2013)

This report documents the program and the outcomes of Dagstuhl Seminar 13241 "Virtual Realities". The main goal of the five day seminar was to bring together leading experts and promising young researchers to discuss current challenges and future directions in the field of virtual and augmented reality. The seminar was organized as series of individual presentations and seven working groups. Abstracts of the presentations and working group reports are collected in this report

The geometry of optimal degree reduction of Bezier curves

Optimal degree reductions, i.e. best approximations of n-th degree Bezier curves by Bezier curves of degree n - 1, with respect to different norms are studied. It is shown that for any L_p-norm the euclidean degree reduction where the norm is applied to the euclidean distance function of two curves is identical to componentwise degree reduction. The Bezier points of the degree reductions are found to lie on parallel lines through the Bezier points of any Taylor expansion of degree n - 1 of the original curve. This geometric situation is shown to hold also in the case of constrained degree reduction. The Bezier points of the degree reduction are explicitly given in the unconstrained case for p=1 and p=2 and in the constrained case for p=2. (orig.)Available from TIB Hannover: RN 7281(266) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman