Envelopes and osculates of Willmore surfaces

We view conformal surfaces in the 4--sphere as quaternionic holomorphic curves in quaternionic projective space. By constructing enveloping and osculating curves, we obtain new holomorphic curves in quaternionic projective space and thus new conformal surfaces. Applying these constructions to Willmore surfaces, we show that the osculating and enveloping curves of Willmore spheres remain Willmore.Comment: 12 pages, 2 figures; v2: improved definition of Frenet curves, minor changes in presentatio

On a new conformal functional for simplicial surfaces

We introduce a smooth quadratic conformal functional and its weighted version $$W_2=\sum_e \beta^2(e)\quad W_{2,w}=\sum_e (n_i+n_j)\beta^2(e),$$ where $\beta(e)$ is the extrinsic intersection angle of the circumcircles of the triangles of the mesh sharing the edge $e=(ij)$ and $n_i$ is the valence of vertex $i$. Besides minimizing the squared local conformal discrete Willmore energy $W$ this functional also minimizes local differences of the angles $\beta$. We investigate the minimizers of this functionals for simplicial spheres and simplicial surfaces of nontrivial topology. Several remarkable facts are observed. In particular for most of randomly generated simplicial polyhedra the minimizers of $W_2$ and $W_{2,w}$ are inscribed polyhedra. We demonstrate also some applications in geometry processing, for example, a conformal deformation of surfaces to the round sphere. A partial theoretical explanation through quadratic optimization theory of some observed phenomena is presented.Comment: 14 pages, 8 figures, to appear in the proceedings of "Curves and Surfaces, 8th International Conference", June 201

On Density of State of Quantized Willmore Surface-A Way to Quantized Extrinsic String in R^3

Recently I quantized an elastica with Bernoulli-Euler functional in two-dimensional space using the modified KdV hierarchy. In this article, I will quantize a Willmore surface, or equivalently a surface with the Polyakov extrinsic curvature action, using the modified Novikov-Veselov (MNV) equation. In other words, I show that the density of state of the partition function for the quantized Willmore surface is expressed by volume of a subspace of the moduli of the MNV equation.Comment: AMS-Tex Us

Bogomol'nyi Decomposition for Vesicles of Arbitrary Genus

We apply the Bogomol'nyi technique, which is usually invoked in the study of solitons or models with topological invariants, to the case of elastic energy of vesicles. We show that spontaneous bending contribution caused by any deformation from metastable bending shapes falls in two distinct topological sets: shapes of spherical topology and shapes of non-spherical topology experience respectively a deviatoric bending contribution a la Fischer and a mean curvature bending contribution a la Helfrich. In other words, topology may be considered to describe bending phenomena. Besides, we calculate the bending energy per genus and the bending closure energy regardless of the shape of the vesicle. As an illustration we briefly consider geometrical frustration phenomena experienced by magnetically coated vesicles.Comment: 8 pages, 1 figure; LaTeX2e + IOPar

Oxidative stress and partial migration in brown trout (Salmo trutta)

During migration, animals are typically limited by their endogenous energetic resources that must be allocated to the physiological costs associated with locomotion, as well as avoiding and (or) compensating for oxidative stress. To date, there have been few attempts to understand the role of oxidative status in migration biology, particularly in fish. Semi-anadromous brown trout (Salmo trutta L., 1758) exhibit partial migration, where some individuals smoltify and migrate to sea, and others become stream residents, providing us with an excellent model to investigate the link between oxidative stress and migration. Using the brown trout, we obtained blood samples from juveniles from a coastal stream in Denmark in the fall prior to peak seaward migration that occurs in the spring, and assayed for antioxidant capacity (oxygen radical absorbance capacity) and oxidative stress levels (ratio of oxidized to reduced glutathione). We found that individuals that migrated had higher antioxidant capacity than residents and that future migration date was negatively correlated with both antioxidant capacity and body length in the fall. This study provides the first evidence that oxidative status is associated with migration strategy and timing, months in advance of the actual migration, and provides insight into the role of oxidative status in animal migration. </jats:p

X-ray time variability across the atoll source states of 4U 1636--53

We have studied the rapid X-ray time variability in 149 pointed observations with the \textit{Rossi X-ray Timing Explorer} (RXTE)'s Proportional Counter Array of the atoll source 4U~1636--53 in the banana state and, for the first time with RXTE, in the island state. We compare the frequencies of the variability components of 4U~1636--53 with those in other atoll and Z-sources and find that 4U~1636--53 follows the universal scheme of correlations previously found for other atoll sources at (sometimes much) lower luminosities. Our results on the hectohertz QPO suggest that the mechanism that sets its frequency differs from that for the other components, while the amplitude setting mechanism is common. A previously proposed interpretation of the narrow low-frequency QPO frequencies in different sources in terms of harmonic mode switching is not supported by our data, nor by some previous data on other sources and the frequency range that this QPO covers is found not to be related to spin, angular momentum or luminosity.Comment: 16 pages, 13 figures, accepted for publication in Ap

DULIP: A dual luminescence-based co-immunoprecipitation assay for interactome mapping in mammalian cells

Mapping of protein-protein interactions (PPIs) is critical for understanding protein function and complex biological processes. Here, we present DULIP, a dual luminescence-based co-immunoprecipitation assay, for systematic PPI mapping in mammalian cells. DULIP is a second-generation luminescence-based PPI screening method for the systematic and quantitative analysis of co-immunoprecipitations using two different luciferase tags. Benchmarking studies with positive and negative PPI reference sets revealed that DULIP allows the detection of interactions with high sensitivity and specificity. Furthermore, the analysis of a PPI reference set with known binding affinities demonstrated that both low- and high-affinity interactions can be detected with DULIP assays. Finally, using the well-characterized interaction between Syntaxin-1 and Munc18, we found that DULIP is capable of detecting the effects of point mutations on interaction strength. Taken together, our studies demonstrate that DULIP is a sensitive and reliable method of great utility for systematic interactome research. It can be applied for interaction screening as well as for the validation of PPIs in mammalian cells. Moreover, DULIP permits the specific analysis of mutation-dependent binding patterns

Non-spherical shapes of capsules within a fourth-order curvature model

We minimize a discrete version of the fourth-order curvature based Landau free energy by extending Brakke's Surface Evolver. This model predicts spherical as well as non-spherical shapes with dimples, bumps and ridges to be the energy minimizers. Our results suggest that the buckling and faceting transitions, usually associated with crystalline matter, can also be an intrinsic property of non-crystalline membranes.Comment: 6 pages, 4 figures (LaTeX macros EPJ), accepted for publication in EPJ

On CP1 and CP2 maps and Weierstrass representations for surfaces immersed into multi-dimensional Euclidean spaces

An extension of the classic Enneper-Weierstrass representation for conformally parametrised surfaces in multi-dimensional spaces is presented. This is based on low dimensional CP^1 and CP^2 sigma models which allow the study of the constant mean curvature (CMC) surfaces immersed into Euclidean 3- and 8-dimensional spaces, respectively. Relations of Weierstrass type systems to the equations of these sigma models are established. In particular, it is demonstrated that the generalised Weierstrass representation can admit different CMC-surfaces in R^3 which have globally the same Gauss map. A new procedure for constructing CMC-surfaces in R^n is presented and illustrated in some explicit examples.Comment: arxiv version is already officia

Double deletion of Panx1 and Panx3 affects skin and bone but not hearing

Pannexins (Panxs), large-pore channel forming glycoproteins, are expressed in a wide variety of tissues including the skin, bone, and cochlea. To date, the use of single knock-out mouse models of both Panx1 and Panx3 have demonstrated their roles in skin development, bone formation, and auditory phenotypes. Due to sequence homology between Panx1 and Panx3, when one Panx is ablated from germline, the other may be upregulated in a compensatory mechanism to maintain tissue homeostasis and function. To evaluate the roles of Panx1 and Panx3 in the skin, bone, and cochlea, we created the first Panx1/Panx3 double knock-out mouse model (dKO). These mice had smaller litters and reduced body weight compared to wildtype controls. The dKO dorsal skin had decreased epidermal and dermal area as well as decreased hypodermal area in neonatal but not in older mice. In addition, mouse skull shape and size were altered, and long bone length was decreased in neonatal dKO mice. Finally, auditory tests revealed that dKO mice did not exhibit hearing loss and were even slightly protected against noise-induced hearing damage at mid-frequency regions. Taken together, our findings suggest that Panx1 and Panx3 are important at early stages of development in the skin and bone but may be redundant in the auditory system. Key messages Panx double KO mice had smaller litters and reduced body weight. dKO skin had decreased epidermal and dermal area in neonatal mice. Skull shape and size changed plus long bone length decreased in neonatal dKO mice. dKO had no hearing loss and were slightly protected against noise-induced damage