On the slope conjecture of Barja and Stoppino for fibred surfaces

Let $f:\,S \to B$ be a locally non-trivial relatively minimal fibration of genus $g\geq 2$ with relative irregularity $q_f$. It was conjectured by Barja and Stoppino that the slope $\lambda_f\geq \frac{4(g-1)}{g-q_f}$. We prove the conjecture when $q_f$ is small with respect to $g$; we also construct counterexamples when $g$ is odd and $q_f=(g+1)/2$.Comment: any comment is welcom

On the slope of hyperelliptic fibrations with positive relative irregularity

Let $f:\, S \to B$ be a locally non-trivial relatively minimal fibration of hyperelliptic curves of genus $g\geq 2$ with relative irregularity $q_f$. We show a sharp lower bound on the slope $\lambda_f$ of $f$. As a consequence, we prove a conjecture of Barja and Stoppino on the lower bound of $\lambda_f$ as an increasing function of $q_f$ in this case, and we also prove a conjecture of Xiao on the ampleness of the direct image of the relative canonical sheaf if $\lambda_f<4$.Comment: final version, accepted by Trans. Amer. Math. So

On the Severi type inequalities for irregular surfaces

Let $X$ be a minimal surface of general type and maximal Albanese dimension with irregularity $q\geq 2$. We show that $K_X^2\geq 4\chi(\mathcal O_X)+4(q-2)$ if $K_X^2<\frac92\chi(\mathcal O_X)$, and also obtain the characterization of the equality. As a consequence, we prove a conjecture of Manetti on the geography of irregular surfaces if $K_X^2\geq 36(q-2)$ or $\chi(\mathcal O_X)\geq 8(q-2)$, and we also prove a conjecture that surfaces of general type and maximal Albanese dimension with $K_X^2=4\chi(\mathcal O_X)$ are exactly the resolution of double covers of abelian surfaces branched over ample divisors with at worst simple singularities.Comment: Any comment is welcom

A Trust-based Pollution Attack Prevention Scheme in Peer-to-Peer Streaming Networks

Nowadays, peer-to-peer (P2P) streaming systems have become a popular way to deliver multimedia content over the internet due to their low bandwidth requirement, high video streaming quality, and flexibility. However, P2P streaming systems are vulnerable to various attacks, especially pollution attacks, due to their distributed and dynamically changing infrastructure. In this paper, by exploring the features of various pollution attacks, we propose a trust management system tailored for P2P streaming systems. Both direct trust and indirect trust are taken into consideration when designing the trust management system. A new direct trust model is proposed. A dynamic confidence factor that can dynamically adjust the weight of direct and indirect trust in computing the trust is also proposed and studied. A novel double-threshold trust utilization scheme is given. It is shown that the proposed trust management system is effective in identifying polluters and preventing them from further sharing of polluted data chunks.Comment: to appear in Computer Network

On Shimura curves in the Torelli locus of curves

Oort has conjectured that there do not exist Shimura curves lying generically in the Torelli locus of curves of genus $g \geq 8$. We show that there do not exist one-dimensional Shimura families of semi-stable curves of genus $g\geq 5$ of Mumford type. We also show that there do not exist Shimura curves lying generically in the Torelli locus of hyperelliptic curves of genus $g\geq 8$. The first result proves a slightly weaker form of the conjecture for the case of Shimura curves of Mumford type. The second result proves the conjecture for the Torelli locus of hyperelliptic curves. We also present examples of Shimura curves contained generically in the Torelli locus of curves of genus $3$ and $4$.Comment: 42 pages. Some typos are corrected. comments are welcom

The Oort conjecture on Shimura curves in the Torelli locus of curves

Oort has conjectured that there do not exist Shimura curves contained generically in the Torelli locus of genus-$g$ curves when $g$ is large enough. In this paper we prove the Oort conjecture for Shimura curves of Mumford type and Shimura curves parameterizing principally polarized $g$-dimensional abelian varieties isogenous to $g$-fold self-products of elliptic curves for $g>11$. We also prove that there do not exist Shimura curves contained generically in the Torelli locus of hyperelliptic curves of genus $g>7$. As a consequence, we obtain a finiteness result regarding smooth genus-$g$ curves with completely decomposable Jacobians, which is related to a question of Ekedahl and Serre.Comment: 52 pages. Comments are welcome. Text subsumes arxiv.org/abs/1311.585

Incentive Mechanism Design for Heterogeneous Peer-to-Peer Networks: A Stackelberg Game Approach

With high scalability, high video streaming quality, and low bandwidth requirement, peer-to-peer (P2P) systems have become a popular way to exchange files and deliver multimedia content over the internet. However, current P2P systems are suffering from "free-riding" due to the peers' selfish nature. In this paper, we propose a credit-based incentive mechanism to encourage peers to cooperate with each other in a heterogeneous network consisting of wired and wireless peers. The proposed mechanism can provide differentiated service to peers with different credits through biased resource allocation. A Stackelberg game is formulated to obtain the optimal pricing and purchasing strategies, which can jointly maximize the revenue of the uploader and the utilities of the downloaders. In particular, peers' heterogeneity and selfish nature are taken into consideration when designing the utility functions for the Stackelberg game. It is shown that the proposed resource allocation scheme is effective in providing service differentiation for peers and stimulating them to make contribution to the P2P streaming system.Comment: to appear in IEEE Transactions on Mobile Computin

Localize energy in random media: A new phase state

This Letter reports a new wave phenomenon. We show that wave energy can be stored in random media. Associated with such energy storage is a global collective behavior. The features depicted are so general that they may be observed in many random systems.Comment: 3 pages revtex file, 1 eps figure

A note on Shimura subvarieties in the hyperelliptic Torelli locus

We prove the non-existence of Shimura subvarieties of positive dimension contained generically in the hyperelliptic Torelli locus for curves of genus at least 8, which is an analogue of Oort's conjecture in the hyperelliptic case

A note on the characteristic pp nonabelian Hodge theory in the geometric case

We provide a construction of associating a de Rham subbundle to a Higgs subbundle in characteristic $p$ in the geometric case. As applications, we obtain a Higgs semistability result and a $W_2$-unliftable result.Comment: 16 pages. The assumption (n\rank(E)-1)\leq p-2 in the Higgs semistability result has been removed in the current versio