Epidemiology and risk factors of chronic kidney disease in India – results from the SEEK (Screening and Early Evaluation of Kidney Disease) study

Background: There is a rising incidence of chronic kidney disease that is likely to pose major problems for both healthcare and the economy in future years. In India, it has been recently estimated that the age-adjusted incidence rate of ESRD to be 229 per million population (pmp), and >100,000 new patients enter renal replacement programs annually. Methods: We cross-sectionally screened 6120 Indian subjects from 13 academic and private medical centers all over India. We obtained personal and medical history data through a specifically designed questionnaire. Blood and urine samples were collected. Results: The total cohort included in this analysis is 5588 subjects. The mean ± SD age of all participants was 45.22 ± 15.2 years (range 18–98 years) and 55.1% of them were males and 44.9% were females. The overall prevalence of CKD in the SEEK-India cohort was 17.2% with a mean eGFR of 84.27 ± 76.46 versus 116.94 ± 44.65 mL/min/1.73 m2 in non-CKD group while 79.5% in the CKD group had proteinuria. Prevalence of CKD stages 1, 2, 3, 4 and 5 was 7%, 4.3%, 4.3%, 0.8% and 0.8%, respectively. Conclusion: The prevalence of CKD was observed to be 17.2% with ~6% have CKD stage 3 or worse. CKD risk factors were similar to those reported in earlier studies. It should be stressed to all primary care physicians taking care of hypertensive and diabetic patients to screen for early kidney damage. Early intervention may retard the progression of kidney disease. Planning for the preventive health policies and allocation of more resources for the treatment of CKD/ESRD patients are imperative in India

Metric dimension of directed graphs

A metric basis for a digraph G(V, A) is a set W⊂V such that for each pair of vertices u and v of V, there is a vertex w∈W such that the length of a shortest directed path from w to u is different from the length of a shortest directed path from w to v in G; that is d(w, u)≠d(w, v). A minimum metric basis is a metric basis of minimum cardinality. The cardinality of a minimum metric basis of G is called the metric dimension and is denoted by β (G). In this paper, we prove that the metric dimension problem is NP-complete for directed graphs by a reduction from 3-SAT. The technique adopted is due to Khuller et al. [Landmarks in graphs, Discrete Appl. Math. 70(3) (1996), pp. 217–229]. We also solve the metric dimension problem for De Bruijn and Kautz graphs in polynomial time

Rupture Degree Of Interconnection Networks

A well-designed interconnection network makes efficient use of scarce communication resources and is used in systems ranging from large supercomputers to small embedded systems on a chip. This paper deals with certain measures of vulnerability in interconnection networks. Let G be a non-complete connected graph and for S ⊆ V(G), let ω(G – S) and m(G – S) denote the number of components and the order of the largest component in G – S respectively. The Vertex-Integrity of G is defined as I(G) = min {│S │ + m(G – S) : S ⊆ V(G)}. A set S ⊆ V(G) is called an I-set of G if I(G) = │S│+ m(G – S). The rupture degree of G is defined by r(G) = max {ω ( G – S) – │S │ – m(G – S) : S ⊂ V(G), ω ( G – S) ≥ 2}. A set S ⊂ V(G) is called an R-set of G if r(G) = ω ( G – S) – │S│ – m(G – S). In this paper, we compute the rupture degree of split graphs, regular caterpillars and a class of meshes. We also study the relationship between an I-set and an R-set and also find an upper bound for the rupture degree of Hamiltonian graphs and a lower bound for the rupture degree of a complete binary tree

On Induced Matching Partitions of Certain Interconnection Networks

Abstract – The induced matching partition number of a graph G, denoted by imp(G), is the minimum integer k such that V(G) has a k-partition (V1, V2 … Vk) such that, for each i, 1 ≤ i ≤ k, G[Vi], the subgraph of G induced by Vi, is a 1-regular graph. The induced matching k-partition problem is NP-complete even for k = 2. In this paper we investigate the induced matching partition problem for butterfly networks. We identify hypercubes, cube-connected cycles, grids of order m x n, where at least one of m and n is even, as graphs for which imp(G) = 2. In the sequel we prove that imp(G) does not exist for grids of order m x n where m and n are both odd and Mesh of trees MT(n), n ≥ 2

Minimum Tree Spanner Problem for Butterfly and Benes Networks

The minimum tree spanner problem requires selecting a spanning tree of a fixed interconnection network that minimizes the cost of transmission between each pair of processors over the tree edges. In [8] we developed a technique to solve this problem for all parallel architectures including hypercube, CCC, wrapped butterfly, torus, star graphs which are classified under Cayley graphs. We introduced a new class of graphs called Diametrically Uniform Graphs and we provided a simple, efficient parallel algorithm to decide whether or not a parallel architecture is diametrically uniform. In this paper we consider the class of Butterfly and Benes networks, which are diametrically uniform and we solve the minimum tree spanner problem for this class

Super edge-magic total labeling of spiked fans, hyper x-trees, dew drops and prisms

E

Cordial labelling of butterfly networks and mesh of trees

E