Optimization bounds from the branching dual

We present a general method for obtaining strong bounds for discrete optimization problems that is based on a concept of branching duality. It can be applied when no useful integer programming model is available, and we illustrate this with the minimum bandwidth problem. The method strengthens a known bound for a given problem by formulating a dual problem whose feasible solutions are partial branching trees. It solves the dual problem with a “worst-bound” local search heuristic that explores neighboring partial trees. After proving some optimality properties of the heuristic, we show that it substantially improves known combinatorial bounds for the minimum bandwidth problem with a modest amount of computation. It also obtains significantly tighter bounds than depth-first and breadth-first branching, demonstrating that the dual perspective can lead to better branching strategies when the object is to find valid bounds.Accepted manuscrip

Detecting embedded horn structure in propositional logic

We show that the problem of finding a maximum renamable Horn problem within a propositional satisfiability problem is NP-hard but can be formulated as a set packing and therefore a maximum clique problem, for which numerous algorithms and heuristics have been developed

Combined visible and near-infrared OPA for wavelength scaling experiments in strong-field physics

We report the operation of an optical parametric amplifier (OPA) capable of producing gigawatt peak-power laser pulses with tunable wavelength in either the visible or near-infrared spectrum. The OPA has two distinct operation modes (i) generation of >350 uJ, sub 100 fs pulses, tunable between 1250 - 1550 nm; (ii) generation of >190 uJ, sub 150 fs pulses tunable between 490 - 530 nm. We have recorded high-order harmonic spectra over a wide range of driving wavelengths. This flexible source of femtosecond pulses presents a useful tool for exploring the wavelength-dependence of strong-field phenomena, in both the multi-photon and tunnel ionization regimes.Comment: 14 pages, 9 figures, This paper was published in Proceedings of SPIE 10088, Nonlinear Frequency Generation and Conversion: Materials and Devices XVI, doi 10.1117/12.225077

Discrete-choice modelling of patient preferences for modes of drug administration.

The administration of (biologically-derived) drugs for various disease conditions involves consumption of resources that constitutes a direct monetary cost to healthcare payers and providers. An often ignored cost relates to a mismatch between patients' preferences and the mode of drug administration. The "intangible" benefits of giving patients what they want in terms of the mode of drug delivery is seldom considered. This study aims to evaluate, in monetary terms, end-user preferences for the non-monetary attributes of different modes of drug administration using a discrete-choice experiment. It provides empirical support to the notion that there are significant benefits from developing patient-friendly approaches to drug delivery. The gross benefits per patient per unit administration is in the same order of magnitude as the savings in resource costs of administering drugs. The study argues that, as long as the underlying manufacturing science is capable, a patient-centred approach to producing drug delivery systems should be encouraged and pursued