Hadwiger Number and the Cartesian Product Of Graphs

The Hadwiger number mr(G) of a graph G is the largest integer n for which the complete graph K_n on n vertices is a minor of G. Hadwiger conjectured that for every graph G, mr(G) >= chi(G), where chi(G) is the chromatic number of G. In this paper, we study the Hadwiger number of the Cartesian product G [] H of graphs. As the main result of this paper, we prove that mr(G_1 [] G_2) >= h\sqrt{l}(1 - o(1)) for any two graphs G_1 and G_2 with mr(G_1) = h and mr(G_2) = l. We show that the above lower bound is asymptotically best possible. This asymptotically settles a question of Z. Miller (1978). As consequences of our main result, we show the following: 1. Let G be a connected graph. Let the (unique) prime factorization of G be given by G_1 [] G_2 [] ... [] G_k. Then G satisfies Hadwiger's conjecture if k >= 2.log(log(chi(G))) + c', where c' is a constant. This improves the 2.log(chi(G))+3 bound of Chandran and Sivadasan. 2. Let G_1 and G_2 be two graphs such that chi(G_1) >= chi(G_2) >= c.log^{1.5}(chi(G_1)), where c is a constant. Then G_1 [] G_2 satisfies Hadwiger's conjecture. 3. Hadwiger's conjecture is true for G^d (Cartesian product of G taken d times) for every graph G and every d >= 2. This settles a question by Chandran and Sivadasan (They had shown that the Hadiwger's conjecture is true for G^d if d >= 3.)Comment: 10 pages, 2 figures, major update: lower and upper bound proofs have been revised. The bounds are now asymptotically tigh

Boxicity of Series Parallel Graphs

The three well-known graph classes, planar graphs (P), series-parallel graphs(SP) and outer planar graphs(OP) satisfy the following proper inclusion relation: OP C SP C P. It is known that box(G) <= 3 if G belongs to P and box(G) <= 2 if G belongs to OP. Thus it is interesting to decide whether the maximum possible value of the boxicity of series-parallel graphs is 2 or 3. In this paper we construct a series-parallel graph with boxicity 3, thus resolving this question. Recently Chandran and Sivadasan showed that for any G, box(G) <= treewidth(G)+2. They conjecture that for any k, there exists a k-tree with boxicity k+1. (This would show that their upper bound is tight but for an additive factor of 1, since the treewidth of any k-tree equals k.) The series-parallel graph we construct in this paper is a 2-tree with boxicity 3 and is thus a first step towards proving their conjecture.Comment: 10 pages, 0 figure

Loss of correction in unstable comminuted distal radius fractures with external fixation and bone grafting -a long term followup study

Over the years, management of complex distal radius fractures by closed means has often failed leading to late collapse. We have chosen the principle of ligamentotaxis using external fixation and bone grafting in this study to prevent late complications. Eighty one patients with complex distal radius fractures belonging to Type IV A, IV B, IV C of Universal classification were treated with an AO external fixator between 1995 and 2001. Mean age group was 38. 47 years with longest follow up of 7 years. Bone grafting was done primarily in 20 patients and early grafting (within 3 weeks) in 5 patients. Statistically significant differences were observed between the two groups(with or without bone grafting) with respect to postoperative values of (radial length, radial tilt and volar tilt). Results were assessed based on Sarmientos criteria. 56 patients had excellent results, 9 had good results and 16 had poor results. Late collapse with decreased radial length was observed in 18 patients who did not undergo bone grafting. Mean grip strength was 63 percent. Osteoarthritic changes were noted in 20 patients. We conclude that accurate anatomic reduction is necessary for achieving good to excellent functional and cosmetic results. Bone grafting is the mainstay of treatment in comminuted distal radius fractures along with fracture stabilisation

A clinical study on maternal and fetal outcome in twin pregnancy at KIMS hospital, Hubli, Karnataka, India

Background: Development of two fetus inside the uterus is called twin gestation. Twin gestation is considered as high-risk pregnancy due to associated high maternal morbidity and perinatal mortality in comparison with singleton pregnancies. The past two decades have witnessed a sharp rise in the incidence of twin and higher order gestations.Methods: Prospective analytical study of all women admitted in Obstetrics and Gynaecology department with twin pregnancy at KIMS Hubli, over a period of one year between November 2016 and October 2017.Results: There were 11,127 deliveries occurred in study period of one year, out of which there were 174 twin deliveries accounting for 1.56% of prevalence rate. Anemia was the commonest complication occurring in 160 cases contributing around 90%. Preterm delivery was the second complication occurring in 124 cases accounting for 71%. Among 348 babies, there were 40 perinatal death accounting 11%. There was no maternal death.Conclusions: Twin pregnancy is a high-risk condition, should have mandatory hospital delivery. Early detection, proper treatment improves both maternal and neonatal outcome

Study on Relationship of Psychopathology on Childhood Obesity among School Children in South India

AimTo study the relationship of psychopathology on obesity among school children of Davangere district, South India.Settings and designSchool children studying in V-VII standard of Davangere dist in Karnataka, south India. Stage-I cross sectional study for identification of obese children. Stage-II Case control study to find out the relationship of psychopathology and obesity among school children.Material and MethodsBody mass index (BMI) was calculated using BMI charts based on NCHS standards. 421 obese children and 842 controls (1:2 ratios) were studied by using Childhood Psychopathology Measurement Schedule (CPMS) tool developed and standardized by Malhotra et al.Statistical analysisData analysis was conducted at SPSS/ PC programme(Version 13)Results and conclusionsThe psychopathology was present in 44.2% of obese children by using CPMS tool as against only 13.8% of non obese children. The presence of psychopathology among obese boys was more (59.5%) than obese girls (49.4%).The obese children had the relationship of psychopathology 4.9 times more than nonobese children. The positive association of psychopathology with obesity was present in both sexes. The association was found to be stronger for boys in comparison to girls. Our study findings show that psychopathology have strong relationship on obesity among school children and psychopathology have a definite impact on childhood obesity

Political Economy of International Climate Finance: Navigating Decisions in PPCR and SREP

This working paper explores how countries can build their own 'climate finance readiness' by understanding their internal political economy and use that understanding to steer consensus-based decisions on climate finance investments. For climate finance to be effective, national leaders must build shared commitments. This involves considering the arguments, incentives and power dynamics at play to ensure priorities are more equitable and representative of a broader group of stakeholders. Doing so will also help to reduce the risk of implementation delays. This paper uses case studies from Bangladesh, Ethiopia and Nepal to explore how narratives and incentives within the political economy drive climate investment outcomes under the Pilot Programme for Climate Resilience (PPCR) and the Scaling up Renewable Energy Programme (SREP). It draws from broader analysis of the discourses around these investments, including 80 interviews with government; multilateral development banks (MDBs) and other stakeholders

PROTECTIVE EFFECT OF SAPONIN OF MOMORDICA CYMBALARIA FENZL ON HIGH-GLUCOSE INDUCED NEUROPATHY IN NB-41A3 MOUSE NEUROBLASTOMA CELLS

Objective: The natural product Momordica cymbalaria Fenzl has been in use considerably because of its antidiabetic activity. In this work, we have investigated the protective action of one of its phytoconstituent, a saponin, in peripheral neuropathy–a diabetic complication.Methods: The saponin was isolated and identified by preparative high-performance liquid chromatography (preparative HPLC) and thin layer chromatography TLC). High glucose (56 mM)-mediated neuropathy was induced in NB-41A3 mouse neuroblastoma cells and the neuroprotective activity of the saponin was assessed by evaluating its effect on the two polyol pathway enzymes–aldose reductase (AR) and sorbitol dehydrogenase (SDH). The accumulation of intracellular sorbitol, activity of Na+K+-ATPase and production of pro-inflammatory cytokines IL-6, IL-1β and TNF-α were also investigated.Results: The results showed a significant reduction in AR activity and intracellular accumulation of sorbitol on saponin treatment. Improvement in Na+K+-ATPase activity was evident with a noteworthy reduction in IL-6, IL-1β and TNF-α production.Conclusion: These results suggest that the saponin possesses neuroprotective activity in diabetic peripheral neuropathy.Keywords: Diabetic peripheral neuropathy (DPN), Saponin of Momordica cymbalaria (SMC), Neuroblastoma cells, Aldose reductase, Sorbitol dehydrogenase, Na+K+-ATPas

Performance Analysis of FinFET Based Inverter circuit, NAND and NOR Gate at 22nm and 14nm Node technologies.

The size of integrated devices such as PC, mobiles etc are reducing day by day with multiple operations, all of these is happening because of the scaling down the size of MOSFETs which is the main component in memory, processors and so on. As we scale down the MOSFETs to the nanometer regime the short channel effects arises which degrades the system performance and reliability. Here in this paper we describe the alternative MOSFET called FinFET which reduces the short channel effects and its performance analysis of digital applications such as inverter circuit, nand and nor gates at 22nm and 14nm node technologies. DOI: 10.17762/ijritcc2321-8169.15050

Stress-responsive pathways and small RNA changes distinguish variable developmental phenotypes caused by MSH1 loss.

BACKGROUND: Proper regulation of nuclear-encoded, organelle-targeted genes is crucial for plastid and mitochondrial function. Among these genes, MutS Homolog 1 (MSH1) is notable for generating an assortment of mutant phenotypes with varying degrees of penetrance and pleiotropy. Stronger phenotypes have been connected to stress tolerance and epigenetic changes, and in Arabidopsis T-DNA mutants, two generations of homozygosity with the msh1 insertion are required before severe phenotypes begin to emerge. These observations prompted us to examine how msh1 mutants contrast according to generation and phenotype by profiling their respective transcriptomes and small RNA populations. RESULTS: Using RNA-seq, we analyze pathways that are associated with MSH1 loss, including abiotic stresses such as cold response, pathogen defense and immune response, salicylic acid, MAPK signaling, and circadian rhythm. Subtle redox and environment-responsive changes also begin in the first generation, in the absence of strong phenotypes. Using small RNA-seq we further identify miRNA changes, and uncover siRNA trends that indicate modifications at the chromatin organization level. In all cases, the magnitude of changes among protein-coding genes, transposable elements, and small RNAs increases according to generation and phenotypic severity. CONCLUSION: Loss of MSH1 is sufficient to cause large-scale regulatory changes in pathways that have been individually linked to one another, but rarely described all together within a single mutant background. This study enforces the recognition of organelles as critical integrators of both internal and external cues, and highlights the relationship between organelle and nuclear regulation in fundamental aspects of plant development and stress signaling. Our findings also encourage further investigation into potential connections between organelle state and genome regulation vis-á-vis small RNA feedback

Experimental Investigations on Surface Topography in CNC Machining of Nickel-200 Alloy

ABSTRACT Now a day&apos;s Nickel material have growing applications in the manufacturing of various components and structure due to their inherent properties, the Nickel alloys are widely used in aerospace, marine, and nuclear power generation, chemical, petrochemical and process industries. Nickel is a versatile element and will alloy with most metals. At present very few researchers developed manufacturing technology for the production of highly precise Nickel products. Better surface topography can be achieved by the CNC turning process than with conventional grinding technique. The need of finding out machining characteristics of Nickel using high quality machine tools like CNC turning, the experiments were done according to Taguchi DOE. Present paper focuses the CNC turning experiments were conducted on one of the alloy of Nickel i.e. Nickel-200 for analyzing surface characteristics