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

Characterisation and genome sequence of the lytic Acinetobacter baumannii bacteriophage vB-AbaS-Loki

© 2017 Turner et al.This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Acinetobacter baumannii has emerged as an important nosocomial pathogen in healthcare and community settings. While over 100 of Acinetobacter phages have been described in the literature, relatively few have been sequenced. This work describes the characterisation and genome annotation of a new lytic Acinetobacter siphovirus, vB-AbaS-Loki, isolated from activated sewage sludge. Sequencing revealed that Loki encapsulates a 41,308 bp genome, encoding 51 predicted open reading frames. Loki is most closely related to Acinetobacter phage IME-AB3 and more distantly related to Burkholderia phage KL1, Paracoccus phage vB-PmaS-IMEP1 and Pseudomonas phages vB-Pae-Kakheti25, vB-PaeS-SCH-Ab26 and PA73. Loki is characterised by a narrow host range, among the 40 Acinetobacter isolates tested, productive infection was only observed for the propagating host, A. baumannii ATCC 17978. Plaque formation was found to be dependent upon the presence of Ca2+ ions and adsorption to host cells was abolished upon incubation with a mutant of ATCC 17978 encoding a premature stop codon in lpxA. The complete genome sequence of vB-AbaS-Loki was deposited in the European Nucleotide Archive (ENA) under the accession number LN890663. Copyright

Phage engineering: how advances in molecular biology and synthetic biology are being utilized to enhance the therapeutic potential of bacteriophages

Background The therapeutic potential of bacteriophages has been debated since their first isolation and characterisation in the early 20th century. However, a lack of consistency in application and observed efficacy during their early use meant that upon the discovery of antibiotic compounds research in the field of phage therapy quickly slowed. The rise of antibiotic resistance in bacteria and improvements in our abilities to modify and manipulate DNA, especially in the context of small viral genomes, has led to a recent resurgence of interest in utilising phage as antimicrobial therapeutics. Results In this article a number of results from the literature that have aimed to address key issues regarding the utility and efficacy of phage as antimicrobial therapeutics utilising molecular biology and synthetic biology approaches will be introduced and discussed, giving a general view of the recent progress in the field. Conclusions Advances in molecular biology and synthetic biology have enabled rapid progress in the field of phage engineering, with this article highlighting a number of promising strategies developed to optimise phages for the treatment of bacterial disease. Whilst many of the same issues that have historically limited the use of phages as therapeutics still exist, these modifications, or combinations thereof, may form a basis upon which future advances can be built. A focus on rigorous in vivo testing and investment in clinical trials for promising candidate phages may be required for the field to truly mature, but there is renewed hope that the potential benefits of phage therapy may finally be realised