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.

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.

Solid contact PVC membrane electrodes based on neutral or charged carriers for the selective reading of anionic sulfamethoxazole and their application to the analysis of aquaculture water

Sulfamethoxazole (SMX) is among the antibiotics employed in aquaculture for prophylactic and therapeutic reasons. Environmental and food spread may be prevented by controlling its levels in several stages of fish farming. The present work proposes for this purpose new SMX selective electrodes for the potentiometric determination of this sulphonamide in water. The selective membranes were made of polyvinyl chloride (PVC) with tetraphenylporphyrin manganese (III) chloride or cyclodextrin-based acting as ionophores. 2-nitrophenyl octyl ether was employed as plasticizer and tetraoctylammonium, dimethyldioctadecylammonium bromide or potassium tetrakis (4-chlorophenyl) borate was used as anionic or cationic additive. The best analytical performance was reported for ISEs of tetraphenylporphyrin manganese (III) chloride with 50% mol of potassium tetrakis (4-chlorophenyl) borate compared to ionophore. Nersntian behaviour was observed from 4.0 × 10−5 to 1.0 × 10−2 mol/L (10.0 to 2500 µg/mL), and the limit of detection was 1.2 × 10−5 mol/L (3.0 µg/mL). In general, the electrodes displayed steady potentials in the pH range of 6 to 9. Emf equilibrium was reached before 15 s in all concentration levels. The electrodes revealed good discriminating ability in environmental samples. The analytical application to contaminated waters showed recoveries from 96 to 106%.