Classication in high-dimensional feature spaces where interpretation and dimension reduction are of great importance is common in biological and medical applications. For these applications standard methods as microarrays, 1D NMR, and spectroscopy have become everyday tools for measuring thousands of features in samples of interest. Furthermore, the samples are often costly and therefore many such problems have few observations in relation to the number of features. Traditionally such data are analyzed by rst performing a feature selection before classication. We propose a method which performs linear discriminant analysis with a sparseness criterion imposed such that the classication, feature selection and dimension reduction is merged into one analysis. The sparse discriminant analysis is faster than traditional feature selection methods based on computationally heavy criteria such as Wilk's lambda, and the results are better with regards to classication rates and sparseness. The method is extended to mixtures of Gaussians which is useful when e.g. biological clusters are present within each class. Finally, the methods proposed provide low-dimensional views of the discriminative directions.

Graph theoretical analyses applied to neuroimaging datasets have provided valuable insights into the large-scale anatomical organization of the human neocortex. Most of these studies were performed with different cortical scales leading to cortical networks with different levels of small-world organization. The present study investigates how resolution of thickness-based cortical scales impacts on topological properties of human anatomical cortical networks. To this end, we designed a novel approach aimed at determining the best trade-off between small-world attributes of anatomical cortical networks and the number of cortical regions included in the scale. Results revealed that schemes comprising 540-599 regions (surface areas spanning between 250 and 275 mm(2)) at sparsities below 10% showed a superior balance between small-world organization and the size of the cortical scale employed. Furthermore, we found that the cortical scale representing the best trade-off (599 regions) was more resilient to targeted attacks than atlas-based schemes (Desikan-Killiany atlas, 66 regions) and, most importantly, it did not differ that much from the finest cortical scale tested in the present study (1494 regions). In summary, our study confirms that topological organization of anatomical cortical networks varies with both sparsity and resolution of cortical scale, and it further provides a novel methodological framework aimed at identifying cortical schemes that maximize small-worldness with the lowest scale resolution possible.

Applications in biotechnology such as gene expression analysis and image processing have led to a tremendous development of statistical methods with emphasis on reliable solutions to severely underdetermined systems. Furthermore, interpretations of such solutions are of importance, meaning that the surplus of inputs has been reduced to a concise model. At the core of this development are methods which augment the standard linear models for regression, classification and decomposition such that sparse solutions are obtained. This toolbox aims at making public available carefully implemented and well-tested variants of the most popular of such methods for the MATLAB programming environment. These methods consist of easy-to-read yet efficient implementations of various coefficient-path following algorithms and implementations of sparse principal component analysis and sparse discriminant analysis which are not available in MATLAB. The toolbox builds on code made public in 2005 and which has since been used in several studies.

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A great number of factors can influence milk fermentation for yoghurt production such as fermentation conditions, starter cultures and milk characteristics. It is important for dairy companies to know the best combinations of these parameters for a controlled fermentation and for the desired qualities of yoghurt. This study investigates the use of a 1H-NMR metabolomics approach to monitor the changes in milk during fermentation from time 0 to 24 h, taking samples every hour in the first 8 h and then at the end-point at 24 h. Three different starter cultures (L. delbrueckii ssp. bulgaricus, S. thermophilus and their combination) were used and two different heat treatments (99 or 105 °C) were applied to milk. The results clearly show the breakdown of proteins and lactose as well as the concomitant increase in acetate, lactate and citrate during fermentation. Formate is found at different initial concentrations depending on the heat treatment of the milk and its different time trajectory depends on the starter cultures: Lactobacillus cannot produce formate, but needs it for growth, whilst Streptococcus is able to produce formate from pyruvate, therefore promoting the symbiotic relationship between the two strains. On the other hand, Lactobacillus can hydrolyze milk proteins into amino acids, enriching the quality of the final product. In this way, better insight into the protocooperation of lactic acid bacteria strains and information on the impact of a greater heat treatment in the initial matrix were obtained. The global chemical view on the fermentations provided using NMR is key information for yoghurt producers and companies producing starter cultures.