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BackgroundIn November 2007 a study published in Nature Medicine proposed a simple test based on the abundance of 18 proteins in blood to predict the onset of clinical symptoms of Alzheimer's Disease (AD) two to six years before these symptoms manifest. Later, another study, published in PLoS ONE, showed that only five proteins (IL-1, IL-3, EGF, TNF- and G-CSF) have overall better prediction accuracy. These classifiers are based on the abundance of 120 proteins. Such values were standardised by a Z-score transformation, which means that their values are relative to the average of all others.MethodologyThe original datasets from the Nature Medicine paper are further studied using methods from combinatorial optimisation and Information Theory. We expand the original dataset by also including all pair-wise differences of z-score values of the original dataset (“metafeatures”). Using an exact algorithm to solve the resulting Feature Set problem, used to tackle the feature selection problem, we found signatures that contain either only features, metafeatures or both, and evaluated their predictive performance on the independent test set.ConclusionsIt was possible to show that a specific pattern of cell signalling imbalance in blood plasma has valuable information to distinguish between NDC and AD samples. The obtained signatures were able to predict AD in patients that already had a Mild Cognitive Impairment (MCI) with up to 84% of sensitivity, while maintaining also a strong prediction accuracy of 90% on a independent dataset with Non Demented Controls (NDC) and AD samples. The novel biomarkers uncovered with this method now confirms ANG-2, IL-11, PDGF-BB, CCL15/MIP-1; and supports the joint measurement of other signalling proteins not previously discussed: GM-CSF, NT-3, IGFBP-2 and VEGF-B.

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Consider the problem of scheduling a set of jobs to be processed exactly once, on any machine of a set of unrelated parallel machines, without preemption. Each job has a due date, weight, and, for each machine, an associated processing time and sequence-dependent setup time. The objective function considered is to minimize the total weighted tardiness of the jobs. This work proposes a non-delayed relax-and-cut algorithm, based on a Lagrangean relaxation of a time indexed formulation of the problem. A Lagrangean heuristic is also developed to obtain approximate solutions. Using the proposed methods, it is possible to obtain optimal solutions within reasonable time for some instances with up to 180 jobs and six machines. For the solutions for which it is not possible to prove optimality, interesting gaps are obtained.