Zeta functions of totally ramified p-covers of the projective line

In this paper we prove that there exists a Zariski dense open subset U defined over the rationals Q in the space of all one-variable rational functions with arbitrary k poles of prescribed orders, such that for every geometric point f in U(Qbar)$, the L-function of the exponential sum of f at a prime p has Newton polygon approaching the Hodge polygon as p approaches infinity. As an application to algebraic geometry, we prove that the p-adic Newton polygon of the zeta function of a p-cover of the projective line totally ramified at arbitrary k points of prescribed orders has an asymptotic generic lower bound.Comment: 17 page

Construction of some families of 2-dimensional crystalline representations

We construct explicitly some analytic families of etale (phi,Gamma)-modules, which give rise to analytic families of 2-dimensional crystalline representations. As an application of our constructions, we verify some conjectures of Breuil on the reduction modulo p of those representations, and extend some results (of Deligne, Edixhoven, Fontaine and Serre) on the representations arising from modular forms.Comment: 13 pages, english and french abstract

Measuring the Popularity of Job Skills in Recruitment Market: A Multi-Criteria Approach

To cope with the accelerating pace of technological changes, talents are urged to add and refresh their skills for staying in active and gainful employment. This raises a natural question: what are the right skills to learn? Indeed, it is a nontrivial task to measure the popularity of job skills due to the diversified criteria of jobs and the complicated connections within job skills. To that end, in this paper, we propose a data driven approach for modeling the popularity of job skills based on the analysis of large-scale recruitment data. Specifically, we first build a job skill network by exploring a large corpus of job postings. Then, we develop a novel Skill Popularity based Topic Model (SPTM) for modeling the generation of the skill network. In particular, SPTM can integrate different criteria of jobs (e.g., salary levels, company size) as well as the latent connections within skills, thus we can effectively rank the job skills based on their multi-faceted popularity. Extensive experiments on real-world recruitment data validate the effectiveness of SPTM for measuring the popularity of job skills, and also reveal some interesting rules, such as the popular job skills which lead to high-paid employment.Comment: 8 pages, 14 figures, AAAI 201

HFR Code: A Flexible Replication Scheme for Cloud Storage Systems

Fractional repetition (FR) codes are a family of repair-efficient storage codes that provide exact and uncoded node repair at the minimum bandwidth regenerating point. The advantageous repair properties are achieved by a tailor-made two-layer encoding scheme which concatenates an outer maximum-distance-separable (MDS) code and an inner repetition code. In this paper, we generalize the application of FR codes and propose heterogeneous fractional repetition (HFR) code, which is adaptable to the scenario where the repetition degrees of coded packets are different. We provide explicit code constructions by utilizing group divisible designs, which allow the design of HFR codes over a large range of parameters. The constructed codes achieve the system storage capacity under random access repair and have multiple repair alternatives for node failures. Further, we take advantage of the systematic feature of MDS codes and present a novel design framework of HFR codes, in which storage nodes can be wisely partitioned into clusters such that data reconstruction time can be reduced when contacting nodes in the same cluster.Comment: Accepted for publication in IET Communications, Jul. 201