Cellular Interference Alignment

Interference alignment promises that, in Gaussian interference channels, each link can support half of a degree of freedom (DoF) per pair of transmit-receive antennas. However, in general, this result requires to precode the data bearing signals over a signal space of asymptotically large diversity, e.g., over an infinite number of dimensions for time-frequency varying fading channels, or over an infinite number of rationally independent signal levels, in the case of time-frequency invariant channels. In this work we consider a wireless cellular system scenario where the promised optimal DoFs are achieved with linear precoding in one-shot (i.e., over a single time-frequency slot). We focus on the uplink of a symmetric cellular system, where each cell is split into three sectors with orthogonal intra-sector multiple access. In our model, interference is "local", i.e., it is due to transmitters in neighboring cells only. We consider a message-passing backhaul network architecture, in which nearby sectors can exchange already decoded messages and propose an alignment solution that can achieve the optimal DoFs. To avoid signaling schemes relying on the strength of interference, we further introduce the notion of \emph{topologically robust} schemes, which are able to guarantee a minimum rate (or DoFs) irrespectively of the strength of the interfering links. Towards this end, we design an alignment scheme which is topologically robust and still achieves the same optimum DoFs

Barcode, UMI, Set format and BUStools

We introduce the Barcode-UMI-Set format (BUS) for representing pseudoalignments of reads from single-cell RNA-seq experiments. The format can be used with all single-cell RNA-seq technologies, and we show that BUS files can be efficiently generated. BUStools is a suite of tools for working with BUS files and facilitates rapid quantification and analysis of single-cell RNA-seq data. The BUS format therefore makes possible the development of modular, technology-specific and robust workflows for single-cell RNA-seq analysis

Understanding interdependency through complex information sharing

The interactions between three or more random variables are often nontrivial, poorly understood, and yet, are paramount for future advances in fields such as network information theory, neuroscience, genetics and many others. In this work, we propose to analyze these interactions as different modes of information sharing. Towards this end, we introduce a novel axiomatic framework for decomposing the joint entropy, which characterizes the various ways in which random variables can share information. The key contribution of our framework is to distinguish between interdependencies where the information is shared redundantly, and synergistic interdependencies where the sharing structure exists in the whole but not between the parts. We show that our axioms determine unique formulas for all the terms of the proposed decomposition for a number of cases of interest. Moreover, we show how these results can be applied to several network information theory problems, providing a more intuitive understanding of their fundamental limits.Comment: 39 pages, 4 figure

Determining sequencing depth in a single-cell RNA-seq experiment

An underlying question for virtually all single-cell RNA sequencing experiments is how to allocate the limited sequencing budget: deep sequencing of a few cells or shallow sequencing of many cells? Here we present a mathematical framework which reveals that, for estimating many important gene properties, the optimal allocation is to sequence at a depth of around one read per cell per gene. Interestingly, the corresponding optimal estimator is not the widely-used plug-in estimator, but one developed via empirical Bayes

A discriminative learning approach to differential expression analysis for single-cell RNA-seq

Single-cell RNA-seq makes it possible to characterize the transcriptomes of cell types across different conditions and to identify their transcriptional signatures via differential analysis. Our method detects changes in transcript dynamics and in overall gene abundance in large numbers of cells to determine differential expression. When applied to transcript compatibility counts obtained via pseudoalignment, our approach provides a quantification-free analysis of 3′ single-cell RNA-seq that can identify previously undetectable marker genes

Barcode, UMI, Set format and BUStools

We introduce the Barcode-UMI-Set format (BUS) for representing pseudoalignments of reads from single-cell RNA-seq experiments. The format can be used with all single-cell RNA-seq technologies, and we show that BUS files can be efficiently generated. BUStools is a suite of tools for working with BUS files and facilitates rapid quantification and analysis of single-cell RNA-seq data. The BUS format therefore makes possible the development of modular, technology-specific and robust workflows for single-cell RNA-seq analysis