Towards key-frame extraction methods for 3D video: a review

The increasing rate of creation and use of 3D video content leads to a pressing need for methods capable of lowering the cost of 3D video searching, browsing and indexing operations, with improved content selection performance. Video summarisation methods specifically tailored for 3D video content fulfil these requirements. This paper presents a review of the state-of-the-art of a crucial component of 3D video summarisation algorithms: the key-frame extraction methods. The methods reviewed cover 3D video key-frame extraction as well as shot boundary detection methods specific for use in 3D video. The performance metrics used to evaluate the key-frame extraction methods and the summaries derived from those key-frames are presented and discussed. The applications of these methods are also presented and discussed, followed by an exposition about current research challenges on 3D video summarisation methods

Geometric methods on low-rank matrix and tensor manifolds

In this chapter we present numerical methods for low-rank matrix and tensor problems that explicitly make use of the geometry of rank constrained matrix and tensor spaces. We focus on two types of problems: The first are optimization problems, like matrix and tensor completion, solving linear systems and eigenvalue problems. Such problems can be solved by numerical optimization for manifolds, called Riemannian optimization methods. We will explain the basic elements of differential geometry in order to apply such methods efficiently to rank constrained matrix and tensor spaces. The second type of problem is ordinary differential equations, defined on matrix and tensor spaces. We show how their solution can be approximated by the dynamical low-rank principle, and discuss several numerical integrators that rely in an essential way on geometric properties that are characteristic to sets of low rank matrices and tensors

Author Correction: Comprehensive analysis of chromothripsis in 2,658 human cancers using whole-genome sequencing (Nature Genetics, (2020), 52, 3, (331-341), 10.1038/s41588-019-0576-7)

Correction to: Nature Genetics, published online 05 February 2020. In the published version of this paper, the members of the Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium were listed in the Supplementary Information; however, these members should have been included in the main paper. The original Article has been corrected to include the members and affiliations of the PCAWG Consortium in the main paper; the corrections have been made to the HTML version of the Article but not the PDF version. Additional corrections to affiliations have been made to the PDF and HTML versions of the original Article for consistency of information between the PCAWG list and the main paper

Author Correction: Disruption of chromatin folding domains by somatic genomic rearrangements in human cancer

Correction to: Nature Genetics https://doi.org/10.1038/s41588-019-0564-y, published online 05 February 2020

Pan-cancer analysis of whole genomes

Cancer is driven by genetic change, and the advent of massively parallel sequencing has enabled systematic documentation of this variation at the whole-genome scale(1-3). Here we report the integrative analysis of 2,658 whole-cancer genomes and their matching normal tissues across 38 tumour types from the Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium of the International Cancer Genome Consortium (ICGC) and The Cancer Genome Atlas (TCGA). We describe the generation of the PCAWG resource, facilitated by international data sharing using compute clouds. On average, cancer genomes contained 4-5 driver mutations when combining coding and non-coding genomic elements; however, in around 5% of cases no drivers were identified, suggesting that cancer driver discovery is not yet complete. Chromothripsis, in which many clustered structural variants arise in a single catastrophic event, is frequently an early event in tumour evolution; in acral melanoma, for example, these events precede most somatic point mutations and affect several cancer-associated genes simultaneously. Cancers with abnormal telomere maintenance often originate from tissues with low replicative activity and show several mechanisms of preventing telomere attrition to critical levels. Common and rare germline variants affect patterns of somatic mutation, including point mutations, structural variants and somatic retrotransposition. A collection of papers from the PCAWG Consortium describes non-coding mutations that drive cancer beyond those in the TERT promoter(4); identifies new signatures of mutational processes that cause base substitutions, small insertions and deletions and structural variation(5,6); analyses timings and patterns of tumour evolution(7); describes the diverse transcriptional consequences of somatic mutation on splicing, expression levels, fusion genes and promoter activity(8,9); and evaluates a range of more-specialized features of cancer genomes(8,10-18).Peer reviewe

Almost-sure identifiability of multidimensional harmonic retrieval

Two-dimensional (2-D) and, more generally, multidimensional harmonic retrieval is of interest in a variety of applications, including transmitter localization and joint time and frequency offset estimation in wireless communications. The associated identifiability problem is key in understanding the fundamental limitations of parametric methods in terms of the number of harmonies that can be resolved for a given sample size. Consider a mixture of 2-D exponentials, each parameterized by amplitude, phase, and decay rate plus frequency in each dimension. Suppose that I equispaced samples are taken along one dimension and, likewise, J along the other dimension. We prove that if the number of exponentials is less than or equal to roughly IJ/4, then, assuming sampling at the Nyquist rate or above, the parameterization is almost surely identifiable. This is significant because the best previously known achievable bound was roughly (I + J) / 2. For example, consider I = J = 32; our result yields 256 versus 32 identifiable exponentials. We also generalize the result to N dimensions, proving that the number of exponentials that can be resolved is proportional to total sample size