Timelike surfaces of constant mean curvature 1 in anti-de Sitter 3-space

It is shown that timelike surfaces of constant mean curvature 1 in anti-de Sitter 3-space can be constructed from a pair of Lorentz holomorphic and Lorentz antiholomorphic null curves in PSL(2,R) via Bryant type representation formulae. These formulae are used to investigate an explicit one-to-one correspondence, the so-called Lawson correspondence, between timelike surfaces of constant mean curvature 1 in anti-de Sitter 3-space and timelike minimal surfaces in Minkowski 3-space. The hyperbolic Gauss map of timelike surfaces in anti-de Sitter 3-space, which is a close analogue of the classical Gauss map is considered. It is discussed that the hyperbolic Gauss map plays an important role in the study of timelike surfaces of constant mean curvature 1 in anti-de Sitter 3-space. In particular, the relationship between the Lorentz holomorphicity of the hyperbolic Gauss map and timelike surfaces of constant mean curvature 1 in anti-de Sitter 3-space is studied.Comment: 47 pages, 24 figures, references revised, Annals of Global Analysis and Geometr

The Universal Phase Space of AdS3 Gravity

We describe what can be called the "universal" phase space of AdS3 gravity, in which the moduli spaces of globally hyperbolic AdS spacetimes with compact spatial sections, as well as the moduli spaces of multi-black-hole spacetimes are realized as submanifolds. The universal phase space is parametrized by two copies of the Universal Teichm\"uller space T(1) and is obtained from the correspondence between maximal surfaces in AdS3 and quasisymmetric homeomorphisms of the unit circle. We also relate our parametrization to the Chern-Simons formulation of 2+1 gravity and, infinitesimally, to the holographic (Fefferman-Graham) description. In particular, we obtain a relation between the generators of quasiconformal deformations in each T(1) sector and the chiral Brown-Henneaux vector fields. We also relate the charges arising in the holographic description (such as the mass and angular momentum of an AdS3 spacetime) to the periods of the quadratic differentials arising via the Bers embedding of T(1)xT(1). Our construction also yields a symplectic map from T*T(1) to T(1)xT(1) generalizing the well-known Mess map in the compact spatial surface setting.Comment: 41 pages, 2 figures, revised version accepted for publication in Commun.Math.Phy

Cooperative object transport with a swarm of e-puck robots: robustness and scalability of evolved collective strategies

Cooperative object transport in distributed multi-robot systems requires the coordination and synchronisation of pushing/pulling forces by a group of autonomous robots in order to transport items that cannot be transported by a single agent. The results of this study show that fairly robust and scalable collective transport strategies can be generated by robots equipped with a relatively simple sensory apparatus (i.e. no force sensors and no devices for direct communication). In the experiments described in this paper, homogeneous groups of physical e-puck robots are required to coordinate and synchronise their actions in order to transport a heavy rectangular cuboid object as far as possible from its starting position to an arbitrary direction. The robots are controlled by dynamic neural networks synthesised using evolutionary computation techniques. The best evolved controller demonstrates an effective group transport strategy that is robust to variability in the physical characteristics of the object (i.e. object mass and size of the longest object’s side) and scalable to different group sizes. To run these experiments, we designed, built, and mounted on the robots a new sensor that returns the agents’ displacement on a 2D plane. The study shows that the feedback generated by the robots’ sensors relative to the object’s movement is sufficient to allow the robots to coordinate their efforts and to sustain the transports for an extended period of time. By extensively analysing successful behavioural strategies, we illustrate the nature of the operational mechanisms underpinning the coordination and synchronisation of actions during group transport

Cyclical and Patch-Like GDNF Distribution along the Basal Surface of Sertoli Cells in Mouse and Hamster Testes

BACKGROUND AND AIMS: In mammalian spermatogenesis, glial cell line-derived neurotrophic factor (GDNF) is one of the major Sertoli cell-derived factors which regulates the maintenance of undifferentiated spermatogonia including spermatogonial stem cells (SSCs) through GDNF family receptor α1 (GFRα1). It remains unclear as to when, where and how GDNF molecules are produced and exposed to the GFRα1-positive spermatogonia in vivo. METHODOLOGY AND PRINCIPAL FINDINGS: Here we show the cyclical and patch-like distribution of immunoreactive GDNF-positive signals and their close co-localization with a subpopulation of GFRα1-positive spermatogonia along the basal surface of Sertoli cells in mice and hamsters. Anti-GDNF section immunostaining revealed that GDNF-positive signals are mainly cytoplasmic and observed specifically in the Sertoli cells in a species-specific as well as a seminiferous cycle- and spermatogenic activity-dependent manner. In contrast to the ubiquitous GDNF signals in mouse testes, high levels of its signals were cyclically observed in hamster testes prior to spermiation. Whole-mount anti-GDNF staining of the seminiferous tubules successfully visualized the cyclical and patch-like extracellular distribution of GDNF-positive granular deposits along the basal surface of Sertoli cells in both species. Double-staining of GDNF and GFRα1 demonstrated the close co-localization of GDNF deposits and a subpopulation of GFRα1-positive spermatogonia. In both species, GFRα1-positive cells showed a slender bipolar shape as well as a tendency for increased cell numbers in the GDNF-enriched area, as compared with those in the GDNF-low/negative area of the seminiferous tubules. CONCLUSION/SIGNIFICANCE: Our data provide direct evidence of regionally defined patch-like GDNF-positive signal site in which GFRα1-positive spermatogonia possibly interact with GDNF in the basal compartment of the seminiferous tubules