The structure of compact disjointness preserving operators on continuous functions

Let T be a compact disjointness preserving linear operator from C0(X) into C0(Y), where X and Y are locally compact Hausdorff spaces. We show that T can be represented as a norm convergent countable sum of disjoint rank one operators. More precisely, T = Snd ?hn for a (possibly finite) sequence {xn }n of distinct points in X and a norm null sequence {hn }n of mutually disjoint functions in C0(Y). Moreover, we develop a graph theoretic method to describe the spectrum of such an operator

The topography of DNA methylation in the non-neoplastic colonic mucosa surrounding colorectal cancers

The degree of gene hypermethylation in non-neoplastic colonic mucosa (NNCM) is a potentially important event in the development of colorectal cancer (CRC), particularly for the subgroup with a CpG island methylator phenotype (CIMP). In this study, we aimed to use an unbiased and high-throughput approach to evaluate the topography of DNA methylation in the non-neoplastic colonic mucosa (NNCM) surrounding colorectal cancer (CRC). A total of 61 tissue samples comprising 53 NNCM and 8 tumor samples were obtained from hemicolectomy specimens of two CRC patients (Cases 1 and 2). NNCM was stripped from the underlying colonic wall and samples taken at varying distances from the tumor. The level of DNA methylation in NNCM and tumor tissues was assessed at 1,505 CpG sites in 807 cancer-related genes using Illumina GoldenGate® methylation arrays. Case 1 tumor showed significantly higher levels of methylation compared to surrounding NNCM samples (P?

Validation of night blindness reports among children and women in a vitamin A deficient population in rural Tanzania.

OBJECTIVE: This study validates different definitions of reported night blindness (XN) in a vitamin A deficient African population with no local term for XN. DESIGN: Case-control study with follow-up after treatment. SETTING: Eight primary schools and health centres in rural Tanzania. SUBJECTS: A total of 1214 participants were screened for reported XN and other eye signs of xerophthalmia: 461 children aged 24-71 months, 562 primary school-age children and 191 pregnant or breast-feeding women. All 152 cases of reported XN were selected for the validation study and group matched with 321 controls who did not complain of XN. XN reports were validated against serum retinol concentrations and pupillary dark adaptation measurements in cases and controls. INTERVENTION: All children and women who reported XN or had other signs of active xerophthalmia were treated with vitamin A and followed up 3-4 weeks later. Half of the untreated control group who had their serum retinol examined in the baseline examination were also followed up. RESULTS: The overall prevalence of reported XN was 12.5%. At baseline, mean pupillary threshold (-1.52 vs -1.55 log cd/m(2), P=0.501) and median serum retinol concentrations (0.95 vs 0.93 micromol/l, P=0.734) were not significantly different in cases and controls either overall or in each population group. More restricted case definitions reduced the prevalence of reported XN to 5.5% (P<0.001), but there was still no significant difference between cases and controls although the results were in the expected direction. After treatment, the median serum retinol concentration improved significantly only in the most deficient group, the young children. Dark adaptation improved in all the subgroups but the difference was only significant for young children and primary school-age children when the restricted case definitions were used. CONCLUSIONS: XN reports are a poor indicator of vitamin A deficiency in this population. SPONSORSHIP: Task Force Sight and Life, Basel, Switzerland.