Hierarchical Cache-Aided Networks for Linear Function Retrieval.

In a hierarchical caching system, a server is connected to multiple mirrors, each of which is connected to a different set of users, and both the mirrors and the users are equipped with caching memories. All the existing schemes focus on single file retrieval, i.e., each user requests one file. In this paper, we consider the linear function retrieval problem, i.e., each user requests a linear combination of files, which includes single file retrieval as a special case. We propose a new scheme that reduces the transmission load of the first hop by jointly utilizing the two layers' cache memories, and we show that our scheme achieves the optimal load for the second hop in some cases.

Matroidal Entropy Functions: A Quartet of Theories of Information, Matroid, Design, and Coding.

In this paper, we study the entropy functions on extreme rays of the polymatroidal region which contain a matroid, i.e., matroidal entropy functions. We introduce variable strength orthogonal arrays indexed by a connected matroid M and positive integer v which can be regarded as expanding the classic combinatorial structure orthogonal arrays. It is interesting that they are equivalent to the partition-representations of the matroid M with degree v and the (M,v) almost affine codes. Thus, a synergy among four fields, i.e., information theory, matroid theory, combinatorial design, and coding theory is developed, which may lead to potential applications in information problems such as network coding and secret-sharing. Leveraging the construction of variable strength orthogonal arrays, we characterize all matroidal entropy functions of order n≤5 with the exception of log10·U2,5 and logv·U3,5 for some v.

Finding motifs in DNA sequences using low-dispersion sequences.

Motif finding problems, abstracted as the planted (l, d)-motif finding problem, are a major task in molecular biology--finding functioning units and genes. In 2002, the random projection algorithm was introduced to solve the challenging (15, 4)-motif finding problem by using randomly chosen templates. Two years later, a so-called uniform projection algorithm was developed to improve the random projection algorithm by means of low-dispersion sequences generated by coverings. In this article, we introduce an improved projection algorithm called the low-dispersion projection algorithm, which uses low-dispersion sequences generated by developed almost difference families. Compared with the random projection algorithm, the low-dispersion projection algorithm can solve the (l, d)-motif finding problem with fewer templates without decreasing the success rate.