Regression Depth and Center Points

We show that, for any set of n points in d dimensions, there exists a hyperplane with regression depth at least ceiling(n/(d+1)). as had been conjectured by Rousseeuw and Hubert. Dually, for any arrangement of n hyperplanes in d dimensions there exists a point that cannot escape to infinity without crossing at least ceiling(n/(d+1)) hyperplanes. We also apply our approach to related questions on the existence of partitions of the data into subsets such that a common plane has nonzero regression depth in each subset, and to the computational complexity of regression depth problems.Comment: 14 pages, 3 figure

Optimal Point Placement for Mesh Smoothing

We study the problem of moving a vertex in an unstructured mesh of triangular, quadrilateral, or tetrahedral elements to optimize the shapes of adjacent elements. We show that many such problems can be solved in linear time using generalized linear programming. We also give efficient algorithms for some mesh smoothing problems that do not fit into the generalized linear programming paradigm.Comment: 12 pages, 3 figures. A preliminary version of this paper was presented at the 8th ACM/SIAM Symp. on Discrete Algorithms (SODA '97). This is the final version, and will appear in a special issue of J. Algorithms for papers from SODA '9

Age specific aetiological agents of diarrhoea in hospitalized children aged less than five years in Dar es Salaam, Tanzania

\ud This study aimed to determine the age-specific aetiologic agents of diarrhoea in children aged less than five years. The study also assessed the efficacy of the empiric treatment of childhood diarrhoea using Integrated Management of Childhood Illness (IMCI) guidelines. This study included 280 children aged less than 5 years, admitted with diarrhoea to any of the four major hospitals in Dar es Salaam. Bacterial pathogens were identified using conventional methods. Enzyme Linked Immunosorbent Assay (ELISA) and agglutination assay were used to detect viruses and intestinal protozoa, respectively. Antimicrobial susceptibility was determined using Kirby-Bauer disk diffusion method. At least one of the searched pathogens was detected in 67.1% of the cases, and mixed infections were detected in 20.7% of cases. Overall, bacteria and viruses contributed equally accounting for 33.2% and 32.2% of all the cases, respectively, while parasites were detected in 19.2% patients. Diarrhoeagenic Escherichia coli (DEC) was the most common enteric pathogen, isolated in 22.9% of patients, followed by Cryptosporidium parvum (18.9%), rotavirus (18.1%) and norovirus (13.7%). The main cause of diarrhoea in children aged 0 to 6 months were bacteria, predominantly DEC, while viruses predominated in the 7-12 months age group. Vibrio cholerae was isolated mostly in children above two years. Shigella spp, V. cholerae and DEC showed moderate to high rates of resistance to erythromycin, ampicillin, chloramphenicol and tetracycline (56.2-100%). V. cholerae showed full susceptibility to co-trimoxazole (100%), while DEC and Shigella showed high rate of resistance to co-trimoxazole; 90.6% and 93.3% respectively. None of the bacterial pathogens isolated showed resistance to ciprofloxacin which is not recommended for use in children. Cefotaxime resistance was found only in 4.7% of the DEC. During the dry season, acute watery diarrhoea is the most common type of diarrhoea in children under five years in Dar es Salaam and is predominantly due to DEC, C. parvum, rotaviruses and noroviruses. Constant antibiotic surveillance is warranted as bacteria were highly resistant to various antimicrobial agents including co-trimoxazole and erythromycin which are currently recommended for empiric treatment of diarrhoea.\u

Identification of diarrheagenic Escherichia coli isolated from infants and children in Dar es Salaam, Tanzania

<p>Abstract</p> <p>Background</p> <p>Relatively few studies have been done in Tanzania to detect and classify diarrheagenic <it>Escherichia coli </it>(DEC) strains among children with diarrhea. This study aimed at investigating DEC among children in Dar es Salaam aged less than five years hospitalized due to acute/persistent diarrhea.</p> <p>Methods</p> <p>DEC were isolated from stool samples collected from two hundred and eighty children with acute/persistent diarrhea at Muhimbili National Hospital and Ilala and Mwananyamala Municipal Hospitals in Dar es Salaam. A multiplex PCR system method was used to detect a species specific gene for <it>E.coli </it>and ten different virulence genes for detection of five pathogroups of DEC namely enteroaggregative- (EAEC), enteropathogenic- (EPEC), enterotoxigenic- (ETEC), enteroinvasive- (EIEC) and enterohemorghagic- <it>Escherichia coli </it>(EHEC).</p> <p>Results</p> <p>Sixty-four patients (22.9%) harbored DEC. Forty-one of them (14.6%) were categorized as EAEC. Most of the EAEC (82.9%) were classified as typical EAEC possessing the <it>aggR </it>gene, and 92.6% carried the <it>aat </it>gene. Isolates from thirteen patients were EPEC (4.6%) and most of these (92.3%) were typical EPEC with both <it>eae </it>and <it>bfpA </it>genes. Ten isolates were identified as ETEC (3.6%) with only the heat stable toxin; either <it>st1a </it>or <it>st1b </it>but not both. Age wise, EAEC and EPEC were significantly more prevalent among the age group 0–6 months (p < 0.05). Genes for EHEC (<it>stx</it>₁and <it>stx</it>₂) and EIEC <it>(ial</it>) were not detected in this study group.</p> <p>Conclusion</p> <p>The results show a high proportion of DEC among Tanzanian children with diarrhea, with typical EAEC and typical EPEC predominating. The use of primers for both variants of ST1 (st1a and st1b) increased the sensitivity for detection of ETEC strains.</p

Surface Reconstruction by Voronoi Filtering

We give a simple combinatorial algorithm that computes a piecewise-linear approximation of a smooth surface from a finite set of sampling points. The algorithm uses Voronoi vertices to remove triangles from the Delaunay triangulation. We prove the algorithm correct by showing that for densely sampled surfaces, where density depends on ''local feature size'', the output is topologically valid and convergent (both pointwise and in surface normals) to the original surface. We describe an implementation of the algorithm and show example outputs

Abstract A New Voronoi-Based Surface Reconstruction Algorithm

We describe our experience with a new algorithm for the reconstruction of surfaces from unorganized sample points inIR3. The algorithm is the first for this problem with provable guarantees. Given a “good sample ” from a smooth surface, the output is guaranteed to be topologically correct and convergent to the original surface as the sampling density increases. The definition of a good sample is itself interesting: the required sampling density varies locally, rigorously capturing the intuitive notion that featureless areas can be reconstructed from fewer samples. The output mesh interpolates, rather than approximates, the input points. Our algorithm is based on the three-dimensional Voronoi diagram. Given a good program for this fundamental subroutine, the algorithm is quite easy to implement

Surface Reconstruction by Voronoi Filtering

We give a simple combinatorial algorithm that computes a piecewise-linear approximation of a smooth surface from a finite set of sample points. The algorithm uses Voronoi vertices to remove triangles from the Delaunay triangulation. We prove the algorithm correct by showing that for densely sampled surfaces, where density depends on &quot;local feature size&quot;, the output is topologically valid and convergent (both pointwise and in surface normals) to the original surface. We describe an implementation of the algorithm and show example outputs. 1 Introduction The problem of reconstructing a surface from scattered sample points arises in many applications such as computer graphics, medical imaging, and cartography. In this paper we consider the specific reconstruction problem in which the input is a set of sample points S drawn from a smooth two-dimensional manifold F embedded in three dimensions, and the desired output is a triangular mesh with vertex set equal to S that faithfully represen..

The Crust and the Beta-Skeleton: Combinatorial Curve Reconstruction

We construct a graph on a planar point set, which captures its shape in the following sense: if a smooth curve is sampled densely enough, the graph on the samples is a polygonalization of the curve, with no extraeous edges. The required sampling density varies with the LOCAL FEATURE SIZE on the curve, so that area of less detail can be sampled less densely. We give two different graphs that, in this sense, reconstruct smooth curves: a simple new construction which we call the crust, and the B- skeleton, using a specific value of B

A New Voronoi-Based Surface Reconstruction Algorithm

We describe our experience with a new algorithm for the reconstruction of surfaces from unorganized sample points in IR3. The algorthim is the first for this problem with provable guarantees. Given a ''good sample'' from a smooth surface, the output is guaranteed to be topologically correct and convergent to the original surface as the sampling sensity increases. The definition of a good sample is itself interesting: the required sampling density varies locally, rigorously capturing the intuitive notion that featureless areas can be reconstructed from fewer samples. The output mesh interpolates, rather than approximates, the input points. Our algorithm is based on the three-dimensional Voronoi diagram. Given a good program for thsi fundamental subroutine, the algorithm is quite easy to implement