Resistant orthogonal procrustes analysis

In this paper two alternative loss criteria for the least squares Procrustes problem are studied. These alternative criteria are based on the Huber function and on the more radical biweight function, which are designed to be resistant to outliers. Using iterative majorization it is shown how a convergent reweighted least squares algorithm can be developed. In asimulation study it turns out that the proposed methods perform well over a specific range of contamination. When a uniform dilation factor is included, mixed results are obtained. The methods also yield a set of weights that can be used for diagnostic purposes.     

Global Optimization in Any Minkowski Metric: A Permutation-Translation Simulated Annealing Algorithm for Multidimensional Scaling

It is well known that considering a non-Euclidean Minkowski metric in Multidimensional Scaling, either for the distance model or for the loss function, increases the computational problem of local minima considerably. In this paper, we propose an algorithm in which both the loss function and the composition rule can be considered in any Minkowski metric, using a multivariate randomly alternating Simulated Annealing procedure with permutation and translation phases. The algorithm has been implemented in Fortran and tested over classical and simulated data matrices with sizes up to 200 objects. A study has been carried out with some of the common loss functions to determine the most suitable values for the main parameters. The experimental results confirm the theoretical expectation that Simulated Annealing is a suitable strategy to deal by itself with the optimization problems in Multidimensional Scaling, in particular for City-Block, Euclidean and Infinity metrics.     

Integrin cytoplasmic tyrosine motif is required for outside-in alphaIIbbeta3 signalling and platelet function.

Integrins not only bind adhesive ligands, they also act as signalling receptors. Both functions allow the integrin alphaIIbbeta3 to mediate platelet aggregation. Platelet agonists activate alphaIIbbeta3 (inside-out signalling) to allow the binding of soluble fibrinogen. Subsequent platelet aggregation leads to outside-in alphaIIbbeta3 signalling, which results in calcium mobilization, tyrosine phosphorylation of numerous proteins including beta3 itself, increased cytoskeletal reorganisation and further activation of alphaIIbbeta3. Thus, outside-in signals enhance aggregation, although the mechanisms and functional consequences of specific signalling events remain unclear. Here we describe a mouse that expresses an alphaIIbbeta3 in which the tyrosines in the integrin cytoplasmic tyrosine motif have been mutated to phenylalanines. These mice are selectively impaired in outside-in alphaIIbbeta3 signalling, with defective aggregation and clot-retraction responses in vitro, and an in vivo bleeding defect which is characterized by a pronounced tendency to rebleed. These data provide evidence for an important role of outside-in signalling in platelet physiology. Furthermore, they identify the integrin cytoplasmic tyrosine motif as a key mediator of beta-integrin signals and a potential target for new therapeutic agents.     

Hierarchical trees can be perfectly scaled in one dimension

Holman (1972) proved theorems which led him to suggest that there was a fundamental opposition between hierarchical clustering and non-metric Euclidean multidimensional scaling. Empirical experience has shown this to be untrue. Explanations of this apparent contradiction have been offered previously by Kruskal (1977) and Critchley (1986). In this paper we point out the feasibility of perfectly scaling a hierarchical tree in one dimension when the primary approach to ties (Kruskal 1964) is taken. Indeed, there is a whole polyhedral convex cone of solutions for which we obtain an explicit expression.