Upper Dimension and Bases of Zero-Divisor Graphs of Commutative Rings

For a commutative ring R with non-zero zero divisor set Z∗(R), the zero divisor graph of R is Γ(R) with vertex set Z∗(R), where two distinct vertices x and y are adjacent if and only if x y = 0. The upper dimension and the resolving number of a zero divisor graph Γ(R) of some rings are determined. We provide certain classes of rings which have the same upper dimension and metric dimension and give an example of a ring for which these values do not coincide. Further, we obtain some bounds for the upper dimension in zero divisor graphs of commutative rings and provide a subset of vertices which cannot be excluded from any resolving set

Improved lung function and body mass index associated with long-term use of Macrolide antibiotics

AbstractBackground: A number of studies have suggested that the non-antimicrobial actions of macrolide antibiotics may be valuable in treating patients with cystic fibrosis. The use of long-term macrolide antibiotics for the management of CF patients colonised by Pseudomonas aeruginosa and progressive pulmonary disease was introduced into our clinic in 1997. A retrospective study was undertaken to assess of the impact of this therapy. Methods: Twenty patients with progressive pulmonary disease (>10% fall in FEV1 over 12 months despite optimising conventional therapy) were commenced on Azithromycin, 250 mg daily during a 21-month period. At the time of assessment they had remained on therapy for a mean of 0.9 years. Changes in lung function, weight, body mass index (BMI) and frequency of pulmonary exacerbations were assessed. A group of 20 patients with stable lung function and matched as far as possible for age and sex was identified for comparison. Results: Pulmonary function increased significantly in the Azithromycin group with FEV1% predicted increasing from a mean of 50.2–59.1% (P=0.001) while FVC% predicted increase from 64.5 to 76.1% (P=0.002). There was small but non-significant fall in lung function in the comparison group. Body mass index increased by a mean of 1.1 in the Azithromycin group but remained unchanged in the comparison group. The number of pulmonary exacerbations requiring intravenous antibiotics declined by 48.3% in macrolide treated subjects compared to the pre-treatment period (P<0.025); frequency of exacerbations in the control group was unchanged. Conclusion: Long-term Azithromycin treatment in patients with progressive deterioration in lung function appears to have led to an improvement in pulmonary function, increased body mass index and decreased the frequency of pulmonary exacerbations requiring intravenous antibiotics

Automated quantification of non-calcified coronary plaques in cardiac CT angiographic imagery

The high mortality rate associated with coronary heart disease (CHD) has driven intensive research in cardiac image analysis. The advent of computed tomography angiography (CTA) has turned non-invasive diagnosis of cardiovascular anomalies into reality as calcified coronary plaques can be easily identified due to high intensity values. However, detection and quantification of the non-calcified plaques in CTA is still a challenging problem because of their lower intensity values, which are often similar to the nearby blood and muscle tissues. In this work, we propose Bayesian posterior based model for precise quantification of the non-calcified plaques in CTA imagery. The only indicator of non-calcified plaques in CTA is relatively lower intensity. Hence, we exploited intensity variations to discriminate voxels into lumen and plaque classes. Based on the normal coronary segments, we computed the vessel-wall thickness in first step. In the subsequent step, we removed vessel wall from the segmented tree and employed Gaussian Mixture Model to compute optimal distribution parameters. In the final step, distribution parameters were employed in Bayesian posterior model to classify voxels into lumen or plaque. A total of 18 CTA volumes were analyzed in this work using two different approaches. According to the experimental results, mean Jaccard overlap is around 88% with respect to the manual expert. In terms of sensitivity, specificity and accuracy, the proposed method achieves 84.13%, 79.15% and 82.02% success, respectively. Conclusion: According to the experimental results, it is shown that the proposed plaque quantification method achieves accuracy equivalent to human experts