On Caching with More Users than Files

Caching appears to be an efficient way to reduce peak hour network traffic congestion by storing some content at the user's cache without knowledge of later demands. Recently, Maddah-Ali and Niesen proposed a two-phase, placement and delivery phase, coded caching strategy for centralized systems (where coordination among users is possible in the placement phase), and for decentralized systems. This paper investigates the same setup under the further assumption that the number of users is larger than the number of files. By using the same uncoded placement strategy of Maddah-Ali and Niesen, a novel coded delivery strategy is proposed to profit from the multicasting opportunities that arise because a file may be demanded by multiple users. The proposed delivery method is proved to be optimal under the constraint of uncoded placement for centralized systems with two files, moreover it is shown to outperform known caching strategies for both centralized and decentralized systems.Comment: 6 pages, 3 figures, submitted to ISIT 201

NBLDA: Negative Binomial Linear Discriminant Analysis for RNA-Seq Data

RNA-sequencing (RNA-Seq) has become a powerful technology to characterize gene expression profiles because it is more accurate and comprehensive than microarrays. Although statistical methods that have been developed for microarray data can be applied to RNA-Seq data, they are not ideal due to the discrete nature of RNA-Seq data. The Poisson distribution and negative binomial distribution are commonly used to model count data. Recently, Witten (2011) proposed a Poisson linear discriminant analysis for RNA-Seq data. The Poisson assumption may not be as appropriate as negative binomial distribution when biological replicates are available and in the presence of overdispersion (i.e., when the variance is larger than the mean). However, it is more complicated to model negative binomial variables because they involve a dispersion parameter that needs to be estimated. In this paper, we propose a negative binomial linear discriminant analysis for RNA-Seq data. By Bayes' rule, we construct the classifier by fitting a negative binomial model, and propose some plug-in rules to estimate the unknown parameters in the classifier. The relationship between the negative binomial classifier and the Poisson classifier is explored, with a numerical investigation of the impact of dispersion on the discriminant score. Simulation results show the superiority of our proposed method. We also analyze four real RNA-Seq data sets to demonstrate the advantage of our method in real-world applications

Caching in Combination Networks: Novel Multicast Message Generation and Delivery by Leveraging the Network Topology

Maddah-Ali and Niesen's original coded caching scheme for shared-link broadcast networks is now known to be optimal to within a factor two, and has been applied to other types of networks. For practical reasons, this paper considers that a server communicates to cache-aided users through $H$ intermediate relays. In particular, it focuses on combination networks where each of the $K = \binom{H}{r}$ users is connected to a distinct $r$-subsets of relays. By leveraging the symmetric topology of the network, this paper proposes a novel method to general multicast messages and to deliver them to the users. By numerical evaluations, the proposed scheme is shown to reduce the download time compared to the schemes available in the literature. The idea is then extended to decentralized combination networks, more general relay networks, and combination networks with cache-aided relays and users. Also in these cases the proposed scheme outperforms known ones.Comment: 6 pages, 3 figures, accepted in ICC 2018, correct the typo in (6) of the previous versio