A Forward-Reverse Brascamp-Lieb Inequality: Entropic Duality and Gaussian Optimality.

Inspired by the forward and the reverse channels from the image-size characterization problem in network information theory, we introduce a functional inequality that unifies both the Brascamp-Lieb inequality and Barthe's inequality, which is a reverse form of the Brascamp-Lieb inequality. For Polish spaces, we prove its equivalent entropic formulation using the Legendre-Fenchel duality theory. Capitalizing on the entropic formulation, we elaborate on a "doubling trick" used by Lieb and Geng-Nair to prove the Gaussian optimality in this inequality for the case of Gaussian reference measures.

Publisher Correction: Optimal compressed representation of high throughput sequence data via light assembly.

The original version of this Article contained errors in the affiliations of the authors Ibrahim Numanagić and Thomas A. Courtade, which were incorrectly given as 'Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA 94720, USA' and 'Computer Science & Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA', respectively. Also, the hyperlink for the source code in the Data Availability section was incorrectly given as https://github.

Optimal compressed representation of high throughput sequence data via light assembly.

The most effective genomic data compression methods either assemble reads into contigs, or replace them with their alignment positions on a reference genome. Such methods require significant computational resources, but faster alternatives that avoid using explicit or de novo-constructed references fail to match their performance. Here, we introduce a new reference-free compressed representation for genomic data based on light de novo assembly of reads, where each read is represented as a node in a (compact) trie.

HINGE: long-read assembly achieves optimal repeat resolution.

Long-read sequencing technologies have the potential to produce gold-standard de novo genome assemblies, but fully exploiting error-prone reads to resolve repeats remains a challenge. Aggressive approaches to repeat resolution often produce misassemblies, and conservative approaches lead to unnecessary fragmentation. We present HINGE, an assembler that seeks to achieve optimal repeat resolution by distinguishing repeats that can be resolved given the data from those that cannot.

Novel probabilistic models of spatial genetic ancestry with applications to stratification correction in genome-wide association studies.

Motivation: Genetic variation in human populations is influenced by geographic ancestry due to spatial locality in historical mating and migration patterns. Spatial population structure in genetic datasets has been traditionally analyzed using either model-free algorithms, such as principal components analysis (PCA) and multidimensional scaling, or using explicit spatial probabilistic models of allele frequency evolution. We develop a general probabilistic model and an associated inference algorithm that unify the model-based and data-driven approaches to visualizing and inferring population structure.

Information-optimal genome assembly via sparse read-overlap graphs.

Motivation: In the context of third-generation long-read sequencing technologies, read-overlap-based approaches are expected to play a central role in the assembly step. A fundamental challenge in assembling from a read-overlap graph is that the true sequence corresponds to a Hamiltonian path on the graph, and, under most formulations, the assembly problem becomes NP-hard, restricting practical approaches to heuristics. In this work, we avoid this seemingly fundamental barrier by first setting the computational complexity issue aside, and seeking an algorithm that targets information limits In particular, we consider a basic feasibility question: when does the set of reads contain enough information to allow unambiguous reconstruction of the true sequence?

Results: Based on insights from this information feasibility question, we present an algorithm-the Not-So-Greedy algorithm-to construct a sparse read-overlap graph.