Hyperorthogonal well-folded Hilbert curves

R-trees can be used to store and query sets of point data in two or more dimensions. An easy way to construct and maintain R-trees for two-dimensional points, due to Kamel and Faloutsos, is to keep the points in the order in which they appear along the Hilbert curve. The R-tree will then store bounding boxes of points along contiguous sections of the curve, and the efficiency of the R-tree depends on the size of the bounding boxes---smaller is better. Since there are many different ways to generalize the Hilbert curve to higher dimensions, this raises the question which generalization results in the smallest bounding boxes. Familiar methods, such as the one by Butz, can result in curve sections whose bounding boxes are a factor $\Omega(2^{d/2})$ larger than the volume traversed by that section of the curve. Most of the volume bounded by such bounding boxes would not contain any data points. In this paper we present a new way of generalizing Hilbert's curve to higher dimensions, which results in much tighter bounding boxes: they have at most 4 times the volume of the part of the curve covered, independent of the number of dimensions. Moreover, we prove that a factor 4 is asymptotically optimal.Comment: Manuscript submitted to Journal of Computational Geometry. An abstract appeared in the 31st Int Symp on Computational Geometry (SoCG 2015), LIPIcs 34:812-82

White Matter Injury and General Movements in High-Risk Preterm Infants

BACKGROUND AND PURPOSE: Very preterm infants (birth weight, MATERIALS AND METHODS: In this prospective study of 47 preterm infants of 24-30 weeks' gestation, brain MR imaging was performed at term-equivalent age. Infants underwent T1- and T2-weighted imaging for volumetric analysis and DTI. General movements were assessed at 10-15 weeks' postterm age, and neurodevelopmental outcomes were evaluated at 2 years by using the Bayley Scales of Infant and Toddler Development Ill. RESULTS: Nine infants had aberrant general movements and were more likely to have adverse neurodevelopmental outcomes, compared with infants with normal movements. In infants with aberrant movements, Tract-Based Spatial Statistics analysis identified significantly lower fractional anisotropy in widespread white matter tracts, including the corpus callosum, inferior longitudinal and fronto-occipital fasciculi, internal capsule, and optic radiation. The subset of infants having both aberrant movements and abnormal neurodevelopmental outcomes in cognitive, language, and motor skills had significantly lower fractional anisotropy in specific brain regions. CONCLUSIONS: Aberrant general movements at 10-15 weeks' postterm are associated with adverse neurodevelopmental outcomes and specific white matter microstructure abnormalities for cognitive, language, and motor delays

Treatment of resistant Raynaud's phenomenon with single-port thoracoscopic sympathicotomy:a novel minimally invasive endoscopic technique

OBJECTIVE: To assess the minimally invasive single-port thoracoscopic sympathicotomy feasibility and efficacy in patients with treatment-resistant RP. METHODS: Single-port thoracoscopic sympathicotomy was performed unilaterally on the left side in eight patients with RP (six males, two females, with a median age of 45.2 years). Five patients had primary and three had secondary RP. Perfusion effects in the hands were assessed at baseline and after 1 month by using a cooling and recovery procedure, and by using laser speckle contrast analysis. Number and duration of RP attacks were reported over a 2-week period. RESULTS: Patient satisfaction was 100% after surgery. After surgery, a unilateral improvement in perfusion was observed in the left hand compared with the right hand, with cooling and recovery (P = 0.008) and with laser speckle contrast analysis (P = 0.023). In addition, the number and duration of the attacks in the left hand decreased compared with the right hand (both P = 0.028). No serious adverse events occurred in a follow-up period of at least 10 months. CONCLUSION: Single-port thoracoscopic sympathicotomy is feasible and can be effective in improving hand perfusion in patients with RP. However, long-term efficacy needs to be established. CLINICAL TRIAL REGISTRATION NUMBER: NCT02680509