A note on a theorem of Xiao Gang

In 1985 Xiao Gang proved that the bicanonical system of a complex surface $S$ of general type with $p_2(S)>2$ is not composed of a pencil [Bull. Soc. Math. France, 113 (1985), 23--51]. When in the end of the 80's it was finally proven that $| 2K_S|$ is base point free, whenever $p_g\geq 1$, the part of this theorem concerning surfaces with $p_g\geq 1$ became trivial. In this note a new proof of this theorem for surfaces with $p_g=0$ is presented.Comment: Latex, 4 page

Hurwitz ball quotients

We consider the analogue of Hurwitz curves, smooth projective curves $C$ of genus $g \ge 2$ that realize equality in the Hurwitz bound $|\mathrm{Aut}(C)| \le 84 (g - 1)$, to smooth compact quotients $S$ of the unit ball in $\mathbb{C}^2$. When $S$ is arithmetic, we show that $|\mathrm{Aut}(S)| \le 288 e(S)$, where $e(S)$ is the (topological) Euler characteristic, and in the case of equality show that $S$ is a regular cover of a particular Deligne--Mostow orbifold. We conjecture that this inequality holds independent of arithmeticity, and note that work of Xiao makes progress on this conjecture and implies the best-known lower bound for the volume of a complex hyperbolic $2$-orbifold.Comment: Several improvements incorporating referee's comments. To appear in Math.

Security of a key agreement protocol based on chaotic maps

Kacorev et al. proposed new public key encryption scheme using chaotic maps. Subsequently, Bergamo et al. has broken Kacorev and Tasev?s encryption scheme and then applied the attack on a key agreement protocol based on Kacorev et al.?s system. In order to address Bergamo et al.? attack, Xiao et al. proposed a novel key agreement protocol. In this paper, we will present two attacks on Xiao et al.?s key agreement protocol using chaotic maps. Our new attack method is different from the one that Bergamo et al. developed. The proposed attacks work in a way that an adversary can prevent the user and the server from establishing a shared session key even though the adversary cannot get any private information from the user and the server?s communications

Touching artefacts in an ancient world on a browser-based platform

Title: Touching artefacts in an ancient world on a browser-based platform Article & version: Published version Original citation & hyperlink: Arnab, S., Petridis, P., Dunwell, I. and de Freitas, S. (2010). Touching artefacts in an ancient world on a browser-based platform. In Y. Xiao, T. Amon & R. Muffolett