It has recently become clear that a whole range of problems of linear algebra can be formulated in a uniform way, and in this common formulation there arise general effective methods of investigating such problems. It is interesting that these methods turn out to be connected with such ideas as the Coxeter-Weyl group and the Dynkin diagrams.We explain these connections by means of a very simple problem. We assume no preliminary knowledge. We do not touch on the connections between these questions and the theory of group representations or the theory of infinite-dimensional Lie algebras. For this see [3]- [5].Let Γ be a finite connected graph; we denote the set of its vertices by Γ ο and the set of its edges by ΓΊ (we do not exclude the cases where two vertices are joined by several edges or there are loops joining a vertex to itself). We fix a certain orientation Λ of the graph Γ; this means that for each edge / e Γι we distinguish a starting-point a(/) e Γ ο and an end-point With each vertex a G Γ ο we associate a finite-dimensional linear space V a over a fixed field K. Furthermore, with each edge /€ Γι we associate a linear mapping / ; : V a(l) -> ν β0) (α(/) and β(1) are the starting-point and end-point of the edge /). We impose no relations on the linear mappings /,. We denote the collection of spaces V a and mappings f t by (V, f). DEFINITION 1. Let (Γ, Λ) be an oriented graph. We define a category Χ (Γ, Λ) in the following way. An object of ^(Γ, Λ) is any collection {V, f) of spaces V a (a e Γ ο ) and mappings /, (7 e Γ^. A morphism φ:

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BackgroundIn the context of sensory and cognitive-processing deficits in ADHD patients, there is considerable evidence of altered event related potentials (ERP). Most of the studies, however, were done on ADHD children. Using the independent component analysis (ICA) method, ERPs can be decomposed into functionally different components. Using the classification method of support vector machine, this study investigated whether features of independent ERP components can be used for discrimination of ADHD adults from healthy subjects.MethodsTwo groups of age- and sex-matched adults (74 ADHD, 74 controls) performed a visual two stimulus GO/NOGO task. ERP responses were decomposed into independent components by means of ICA. A feature selection algorithm defined a set of independent component features which was entered into a support vector machine.ResultsThe feature set consisted of five latency measures in specific time windows, which were collected from four different independent components. The independent components involved were a novelty component, a sensory related and two executive function related components. Using a 10-fold cross-validation approach, classification accuracy was 92%.ConclusionsThis study was a first attempt to classify ADHD adults by means of support vector machine which indicates that classification by means of non-linear methods is feasible in the context of clinical groups. Further, independent ERP components have been shown to provide features that can be used for characterizing clinical populations.