Dissecting Euclidean d-space with the power diagram of n weighted point sites partitions a given m-point set into clusters, one cluster for each region of the diagram. In this manner, an assignment of points to sites is induced. We show the equivalence of such assignments to constrained Euclidean least-squares assignments. As a corollary, there always exists a power diagram whose regions partition a given d-dimensional m-point set into clusters of prescribed sizes, no matter where the sites are placed. Another consequence is that constrained least-squares assignments can be computed by finding suitable weights for the sites. In the plane, this takes roughly O(n 2 m) time and optimal space O(m), which improves on previous methods. We further show that a constrained least-squares assignment can be computed by solving a specially structured linear program in n + 1 dimensions. This leads to an algorithm for iteratively improving the weights, based on the gradient-descent method. Besides having the obvious optimization property, least-squares assignments are shown to be useful in solving a certain transportation problem, and in finding a least-squares fitting of two point sets where translation and scaling are allowed. Finally, we extend the concept of a constrained least-squares assignment to continuous distributions of points, thereby obtaining existence results for power diagrams with prescribed region volumes. These results are related to Minkowski's theorem for convex polytopes. The aforementioned iterative method for approximating the desired power diagram applies to continuous distributions as well.

Autosomal dominant hyper-IgE syndrome (AD-HIES), characterised by eczema, increased susceptibility to skin and lung infections, elevated IgE and skeletal abnormalities is associated with heterozygous STAT3 mutations. The autosomal recessive variant (AR-HIES) has similar immunological findings but mainly lacks extraimmune manifestations. Several AR-HIES patients have recently been shown to harbour mutations in the gene for dedicator of cytokinesis 8 (DOCK8). Here, we present the long-term outcome of a girl having received a hematopoietic stem cell graft for an at that time genetically undefined combined immunodeficiency associated with severe eczema, multiple food allergies, excessively elevated serum IgE levels and eosinophilia. She was recently found to carry a homozygous nonsense mutation in the DOCK8 gene. HSCT resulted in complete immunological correction, even though mixed donor chimerism occurred. Clinically, the outcome was characterised by disappearance of skin manifestations and severe infections, improvement of pulmonary function and constant decline of IgE levels. Outcome in untransplanted DOCK8 deficient patients is poor because of frequent life-threatening infections, CNS bleeding and infarction, and increased susceptibility to malignancy. This argues for early curative therapeutic approaches, supported by this report of successful long-term outcome after HSCT.

The newly developed "underwater" technique is superior to the conventional technique, since floating of the very thin donor cornea during the separation procedure prevents endothelial defects by guarding against folds. By enabling reliable keratoplasty in the mouse, this technique facilitates studies on the experimental allograft reaction.

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