New insights on integer-programming models for the kidney exchange problem

In recent years several countries have set up policies that allow exchange of kidneys between two or more incompatible patient–donor pairs. These policies lead to what is commonly known as kidney exchange programs. The underlying optimization problems can be formulated as integer programming models. Previously proposed models for kidney exchange programs have exponential numbers of constraints or variables, which makes them fairly difficult to solve when the problem size is large. In this work we propose two compact formulations for the problem, explain how these formulations can be adapted to address some problem variants, and provide results on the dominance of some models over others. Finally we present a systematic comparison between our models and two previously proposed ones via thorough computational analysis. Results show that compact formulations have advantages over non-compact ones when the problem size is large.

The capacity exchange protocol

This paper proposes a new strategy to integrate shared resources and precedence constraints among real-time tasks, assuming no precise information on critical sections and computation times is available. The concept of bandwidth inheritance is combined with a capacity sharing and stealing mechanism to efficiently exchange bandwidth among tasks to minimise the degree of deviation from the ideal system’s behaviour caused by inter-application blocking. The proposed Capacity Exchange Protocol (CXP) is simpler than other proposed solutions for sharing resources in open real-time systems since it does not attempt to return the inherited capacity in the same exact amount to blocked servers. This loss of optimality is worth the reduced complexity as the protocol’s behaviour nevertheless tends to be fair and outperforms the previous solutions in highly dynamic scenarios as demonstrated by extensive simulations. A formal analysis of CXP is presented and the conditions under which it is possible to guarantee hard real-time tasks are discussed.

Enantiomeric fraction evaluation of pharmaceuticals in environmentalmatrices by liquid chromatography-tandem mass spectrometry

The interest for environmental fate assessment of chiral pharmaceuticals is increasing and enantioselective analytical methods are mandatory. This study presents an enantioselective analytical method for the quantification of seven pairs of enantiomers of pharmaceuticals and a pair of a metabolite. The selected chiral pharmaceuticals belong to three different therapeutic classes, namely selective serotonin reuptake inhibitors (venlafaxine, fluoxetine and its metabolite norfluoxetine), beta-blockers (alprenolol, bisoprolol, metoprolol, propranolol) and a beta2-adrenergic agonist (salbutamol). The analytical method was based on solid phase extraction followed by liquid chromatography tandem mass spectrometry with a triple quadrupole analyser. Briefly, Oasis® MCX cartridges were used to preconcentrate 250 mL of water samples and the reconstituted extracts were analysed with a Chirobiotic™ V under reversed mode. The effluent of a laboratory-scale aerobic granular sludge sequencing batch reactor (AGS-SBR) was used to validate the method. Linearity (r2 > 0.99), selectivity and sensitivity were achieved in the range of 20–400 ng L−1 for all enantiomers, except for norfluoxetine enantiomers which range covered 30–400 ng L−1. The method detection limits were between 0.65 and 11.5 ng L−1 and the method quantification limits were between 1.98 and 19.7 ng L−1. The identity of all enantiomers was confirmed using two MS/MS transitions and its ion ratios, according to European Commission Decision 2002/657/EC. This method was successfully applied to evaluate effluents of wastewater treatment plants (WWTP) in Portugal. Venlafaxine and fluoxetine were quantified as non-racemic mixtures (enantiomeric fraction ≠ 0.5). The enantioselective validated method was able to monitor chiral pharmaceuticals in WWTP effluents and has potential to assess the enantioselective biodegradation in bioreactors. Further application in environmental matrices as surface and estuarine waters can be exploited.

Cantor exchange systems and renormalization

We prove a one-to-one correspondence between (i) C1+ conjugacy classes of C1+H Cantor exchange systems that are C1+H fixed points of renormalization and (ii) C1+ conjugacy classes of C1+H diffeomorphisms f with a codimension 1 hyperbolic attractor Lambda that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Lambda. However, we prove that there is no C1+alpha Cantor exchange system, with bounded geometry, that is a C1+alpha fixed point of renormalization with regularity alpha greater than the Hausdorff dimension of its invariant Cantor set.

Arc exchange systems and renormalization

We exhibit the construction of stable arc exchange systems from the stable laminations of hyperbolic diffeomorphisms. We prove a one-to-one correspondence between (i) Lipshitz conjugacy classes of C(1+H) stable arc exchange systems that are C(1+H) fixed points of renormalization and (ii) Lipshitz conjugacy classes of C(1+H) diffeomorphisms f with hyperbolic basic sets Lambda that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Lambda. Let HD(s)(Lambda) and HD(u)(Lambda) be, respectively, the Hausdorff dimension of the stable and unstable leaves intersected with the hyperbolic basic set L. If HD(u)(Lambda) = 1, then the Lipschitz conjugacy is, in fact, a C(1+H) conjugacy in (i) and (ii). We prove that if the stable arc exchange system is a C(1+HDs+alpha) fixed point of renormalization with bounded geometry, then the stable arc exchange system is smooth conjugate to an affine stable arc exchange system.