Convexity in partial cubes: the hull number

We prove that the combinatorial optimization problem of determining the hull number of a partial cube is NP-complete. This makes partial cubes the minimal graph class for which NP-completeness of this problem is known and improves some earlier results in the literature. On the other hand we provide a polynomial-time algorithm to determine the hull number of planar partial cube quadrangulations. Instances of the hull number problem for partial cubes described include poset dimension and hitting sets for interiors of curves in the plane. To obtain the above results, we investigate convexity in partial cubes and characterize these graphs in terms of their lattice of convex subgraphs, improving a theorem of Handa. Furthermore we provide a topological representation theorem for planar partial cubes, generalizing a result of Fukuda and Handa about rank three oriented matroids.Comment: 19 pages, 4 figure

The Physics of the B Factories

This work is on the Physics of the B Factories. Part A of this book contains a brief description of the SLAC and KEK B Factories as well as their detectors, BaBar and Belle, and data taking related issues. Part B discusses tools and methods used by the experiments in order to obtain results. The results themselves can be found in Part C

Formulation, stabilisation and encapsulation of bacteriophage for phage therapy

Against a backdrop of global antibiotic resistance and increasing awareness of the importance of the human microbiota, there has been resurgent interest in the potential use of bacteriophages for therapeutic purposes, known as phage therapy. A number of phage therapy phase I and II clinical trials have concluded, and shown phages don’t present significant adverse safety concerns. These clinical trials used simple phage suspensions without any formulation and phage stability was of secondary concern. Phages have a limited stability in solution, and undergo a significant drop in phage titre during processing and storage which is unacceptable if phages are to become regulated pharmaceuticals, where stable dosage and well defined pharmacokinetics and pharmacodynamics are de rigueur. Animal studies have shown that the efficacy of phage therapy outcomes depend on the phage concentration (i.e. the dose) delivered at the site of infection, and their ability to target and kill bacteria, arresting bacterial growth and clearing the infection. In addition, in vitro and animal studies have shown the importance of using phage cocktails rather than single phage preparations to achieve better therapy outcomes. The in vivo reduction of phage concentration due to interactions with host antibodies or other clearance mechanisms may necessitate repeated dosing of phages, or sustained release approaches. Modelling of phage-bacterium population dynamics reinforces these points. Surprisingly little attention has been devoted to the effect of formulation on phage therapy outcomes, given the need for phage cocktails, where each phage within a cocktail may require significantly different formulation to retain a high enough infective dose. This review firstly looks at the clinical needs and challenges (informed through a review of key animal studies evaluating phage therapy) associated with treatment of acute and chronic infections and the drivers for phage encapsulation. An important driver for formulation and encapsulation is shelf life and storage of phage to ensure reproducible dosages. Other drivers include formulation of phage for encapsulation in micro- and nanoparticles for effective delivery, encapsulation in stimuli responsive systems for triggered controlled or sustained release at the targeted site of infection. Encapsulation of phage (e.g. in liposomes) may also be used to increase the circulation time of phage for treating systemic infections, for prophylactic treatment or to treat intracellular infections. We then proceed to document approaches used in the published literature on the formulation and stabilisation of phage for storage and encapsulation of bacteriophage in micro- and nanostructured materials using freeze drying (lyophilization), spray drying, in emulsions e.g. ointments, polymeric microparticles, nanoparticles and liposomes. As phage therapy moves forward towards Phase III clinical trials, the review concludes by looking at promising new approaches for micro- and nanoencapsulation of phages and how these may address gaps in the field