8 research outputs found
On hyperbolicity of SU(2)-equivariant, punctured disc bundles over the complex affine quadric
Given a holomorphic line bundle over the complex affine quadric , we
investigate its Stein, SU(2)-equivariant disc bundles. Up to equivariant
biholomorphism, these are all contained in a maximal one, say .
By removing the zero section to one obtains the unique Stein,
SU(2)-equivariant, punctured disc bundle over which contains entire
curves. All other such punctured disc bundles are shown to be Kobayashi
hyperbolic.Comment: 15 pages, v2: minor changes, to appear in Transformation Group
Asymptotic theory of time-varying social networks with heterogeneous activity and tie allocation
The dynamic of social networks is driven by the interplay between diverse mechanisms that still challenge our theoretical and modelling efforts. Amongst them, two are known to play a central role in shaping the networks evolution, namely the heterogeneous propensity of individuals to i) be socially active and ii) establish a new social relationships with their alters. Here, we empirically characterise these two mechanisms in seven real networks describing temporal human interactions in three different settings: scientific collaborations, Twitter mentions, and mobile phone calls. We find that the individualsâ social activity and their strategy in choosing ties where to allocate their social interactions can be quantitatively described and encoded in a simple stochastic network modelling framework. The Master Equation of the model can be solved in the asymptotic limit. The analytical solutions provide an explicit description of both the system dynamic and the dynamical scaling laws characterising crucial aspects about the evolution of the networks. The analytical predictions match with accuracy the empirical observations, thus validating the theoretical approach. Our results provide a rigorous dynamical system framework that can be extended to include other processes shaping social dynamics and to generate data driven predictions for the asymptotic behaviour of social networks
Group Signatures from Lattices: Simpler, Tighter, Shorter, Ring-Based
Abstract. We introduce a lattice-based group signature scheme that provides several noticeable improvements over the contemporary ones: simpler construction, weaker hardness assumptions, and shorter sizes of keys and signatures. Moreover, our scheme can be transformed into the ring setting, resulting in a scheme based on ideal lattices, in which the public key and signature both have bit-size OÌ(n·logN), for security parameter n, and for group of N users. Towards our goal, we construct a new lattice-based cryptographic tool: a statistical zero-knowledge argument of knowledge of a valid message-signature pair for Boyenâs signature scheme (Boyen, PKCâ10), which potentially can be used as the building block to design various privacy-enhancing cryptographic constructions.
Approx-SVP in Ideal Lattices with Pre-processing
International audienc