Maximum weight cycle packing in directed graphs, with application to kidney exchange programs

Centralized matching programs have been established in several countries to organize kidney exchanges between incompatible patient-donor pairs. At the heart of these programs are algorithms to solve kidney exchange problems, which can be modelled as cycle packing problems in a directed graph, involving cycles of length 2, 3, or even longer. Usually, the goal is to maximize the number of transplants, but sometimes the total benefit is maximized by considering the differences between suitable kidneys. These problems correspond to computing cycle packings of maximum size or maximum weight in directed graphs. Here we prove the APX-completeness of the problem of finding a maximum size exchange involving only 2-cycles and 3-cycles. We also present an approximation algorithm and an exact algorithm for the problem of finding a maximum weight exchange involving cycles of bounded length. The exact algorithm has been used to provide optimal solutions to real kidney exchange problems arising from the National Matching Scheme for Paired Donation run by NHS Blood and Transplant, and we describe practical experience based on this collaboration

Non-stationary electrochemical response of polycrystalline cadmium in sodium hydroxide solutions

The anodization of cadmium in NaOH solutions produces a hydrous cadmium hydroxide-cadmium oxide layer and soluble cadmium species in solution. These processes are investigated through conventional voltammetry, potentiostatic, rotating ring disc electrode and complex voltammetric techniques by using NaOH solutions in the 0.01-1 M range at 25°C. The threshold potential of the anodic reaction is very close to the reversible potential of the Cd/Cd(OH)2 electrode. The overall anodic and cathodic reactions can be interpreted through a complex reaction model comprising a number of parallel reactions following the initial formation of CdOHad species at the electrode surface level. The relative contribution of each parallel reaction is determined by the concentration of OH− ion at the interface. The reaction model implies a composite structure of layers starting from CdOHad at the electrode surface, and subsequent layers with an increase in the water content on approaching the outmost oxide layer. The water content of anodic layer should increase according to the pH and layer thickness and decrease on increasing the applied potential. Under certain conditions the electrochemical reactions become ohmic resistance controlled. This fact presumably involves the formation of aged species and the onset of passivity.Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicada

Kinetics and mechanism of the electroreduction of anodic layers produced on cadmium in alkaline solution containing sodium sulphide

The kinetics of the potentiostatic electroreduction of different anodic layers produced on cadmium in Na₂S containing alkaline solutions has been studied at 25°C. Two types of anodic layer were used: (i) layers produced in the potential range of CdS and Cd(OH)₂ stability, and (ii) layers predominantly composed of CdS. The electroreduction kinetics for both layers can be explained reasonably well throughout the nucleation and growth processes under diffusion control.Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicada

Ellipsometric changes produced by oxidation—reduction potential cycles applied to cadmium in sodium hydroxide solutions

Ellipsometry data obtained for the Cd-NaOH solution interface under the influence of potential cycles in the potential window where the Cd(OH)2-CdO layer can be electroformed and electroreduced, are particularly sensitive to both the layer thickness and the upper electroformation potential limit. The best fitting of the experimental results is obtained for two limiting situations. For thin anodic layers (d ⩽ 6 nm) the ellipsometric data fit the equation ñ=1.55−i 0.005, whereas for relatively thicker anodic layers (d > 7 nm) data can be adjusted through the equation ñ=2.6−i 0.10. These equations are consistent with the electroformation of a hydrous cadmium oxide layer at low potentials, and a cadmium oxide layer with a lower water content which grows beneath the former one at high potentials. Otherwise, the electroreduction of the anodic oxide layer yields a cadmium overlayer which exhibits a shift of the corresponding ellipsometric data as compared to the starting cadmium surface. This shift is presumably related to the development of different metal surface textures resulting from the different electroreduction conditions.Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicada

Ellipsometric data of cadmium oxide layers formed anodically in sodium hydroxide solutions

The voltammetric formation of cadmium oxide layers in alkaline solutions is related to the appearance of two peaks which were assigned to successive reactions occurring within well defined potential ranges. It is interesting to attempt to follow the electroformation and electroreduction of the cadmium oxide layers by means of ellipsometry and to combine the latter to voltammetry in order to provide throughout the correlation of data a way to achieve a better knowledge of the ellipsometric parameters of Cd(OH), and Cd0 layers in contact with the alkaline solution. [Extraído a modo de resumen]Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicada