Polynomial Kernels for Generalized Domination Problems

In this paper, we study the parameterized complexity of a generalized domination problem called the [${\sigma}, {\rho}$] Dominating Set problem. This problem generalizes a large number of problems including the Minimum Dominating Set problem and its many variants. The parameterized complexity of the [${\sigma}, {\rho}$] Dominating Set problem parameterized by treewidth is well studied. Here the properties of the sets ${\sigma}$ and ${\rho}$ that make the problem tractable are identified [1]. We consider a larger parameter and investigate the existence of polynomial sized kernels. When ${\sigma}$ and ${\rho}$ are finite, we identify the exact condition when the [${\sigma}, {\rho}$] Dominating Set problem parameterized by vertex cover admits polynomial kernels. Our lower and upper bound results can also be extended to more general conditions and provably smaller parameters as well.Comment: 19 pages, 6 figure

Parameterizing Path Partitions

We study the algorithmic complexity of partitioning the vertex set of a given (di)graph into a small number of paths. The Path Partition problem (PP) has been studied extensively, as it includes Hamiltonian Path as a special case. The natural variants where the paths are required to be either \emph{induced} (Induced Path Partition, IPP) or \emph{shortest} (Shortest Path Partition, SPP), have received much less attention. Both problems are known to be NP-complete on undirected graphs; we strengthen this by showing that they remain so even on planar bipartite directed acyclic graphs (DAGs), and that SPP remains \NP-hard on undirected bipartite graphs. When parameterized by the natural parameter ``number of paths'', both SPP and IPP are shown to be W{1}-hard on DAGs. We also show that SPP is in \XP both for DAGs and undirected graphs for the same parameter, as well as for other special subclasses of directed graphs (IPP is known to be NP-hard on undirected graphs, even for two paths). On the positive side, we show that for undirected graphs, both problems are in FPT, parameterized by neighborhood diversity. We also give an explicit algorithm for the vertex cover parameterization of PP. When considering the dual parameterization (graph order minus number of paths), all three variants, IPP, SPP and PP, are shown to be in FPT for undirected graphs. We also lift the mentioned neighborhood diversity and dual parameterization results to directed graphs; here, we need to define a proper novel notion of directed neighborhood diversity. As we also show, most of our results also transfer to the case of covering by edge-disjoint paths, and purely covering.Comment: 27 pages, 8 figures. A short version appeared in the proceedings of the CIAC 2023 conferenc

Quality of life in patients treated for COVID-19–associated mucormycosis at a tertiary care hospital

Objectives Coronavirus disease 2019 (COVID-19)–associated mucormycosis (CAM) has emerged as a formidable infection in patients with COVID-19. The aggressive management of CAM affects quality of life (QOL); thus, this study was designed to assess the QOL in patients with CAM at a tertiary healthcare institution. Methods This cross-sectional study of 57 patients with CAM was conducted over 6 months using a semi-structured standard questionnaire (the abbreviated World Health Organization Quality of Life questionnaire [WHO-BREF]) and a self-rated improvement (SRI) scale ranging from 0 to 9. Cut-off values of ≤52 and <7 were considered to indicate poor QOL and poor improvement, respectively. The correlations of QOL and SRI scores were evaluated using Spearman rho values. Results In total, 27 patients (47.4%; 95% confidence interval [CI], 34.9%–60.1%) and 26 patients (45.6%; 95% CI, 33.4%–58.4%) had poor QOL and poor SRI scores, respectively. The overall median (interquartile range) QOL score was 52 (41–63). Headache (adjusted B, −12.3), localized facial puffiness (adjusted B, −16.4), facial discoloration (adjusted B, −23.4), loosening of teeth (adjusted B, −18.7), and facial palsy (adjusted B, −38.5) were significantly associated with the QOL score in patients with CAM. Conclusion Approximately 1 in 2 patients with CAM had poor QOL and poor improvement. Various CAM symptoms were associated with QOL in these patients. Early recognition is the key to optimal treatment, improved outcomes, and improved QOL in patients with CAM

Open defecation among adults having household toilets and factors associated with it: An analytical cross-sectional study from rural Bihar, India

Background: Bihar is one of the focus states under Swachh Bharat Mission (SBM) in India. A study was conducted to estimate the prevalence and to determine the factors associated with the practice of open defecation among adults having household toilets, in rural Patna, Bihar. Methods: An analytical cluster cross-sectional study was conducted for a duration of one year among 609 participants using cluster sampling in rural block of Patna. The prevalence was calculated with 95 % confidence interval and binary logistic regression analysis was done to determine factors associated with open defecation. Results: Out of 609, 391(64.2 %, 95 % CI: 60–68 %) were practising open defecation despite having a household toilet. Male gender (AOR, 1.684; 95 % CI, 1.1–2.4), scheduled caste community (AOR, 2.168; 95 % CI, 1.3–3.4), family gross monthly income Rs. 35 years (AOR,1.453; 95%CI, 1.0–2.0), absence of government supply as water source (AOR: 2.106, 95 % CI: 1.088–3.410) were the independent factors associated with practice of open defecation. Conclusions: Nearly two-third of adults were practising OD despite having a household toilet. Male gender, schedule caste community, family gross monthly income Rs. 35 years, lack of government supply as water source were the factors associated with the practice ofOD

Enhancing microstructure and mechanical properties of nickel aluminium bronze alloy through tin addition

Abstract This article describes the changes in the microstructure, cooling curve characteristics and mechanical properties of cast Nickel Aluminium Bronze alloy (NAB) alloy that were produced by the addition of various amounts of Tin (Sn). The solidification parameters were recorded using a computer-aided cooling curve analysis setup, and optical and scanning electron microscopes were utilised to study the evolution of the microstructure. The chemical composition of different phases generated in the NAB alloy with and without Tin was investigated using an X-ray diffraction technique. With the addition of tin, the alloy's microstructure changed from columnar to equiaxed grain structures, and the ideal microstructure was produced at a Tin concentration of roughly 1.0 weight percent. The formation of the high temperature α and the grain boundary Sn rich phases across the alloy microstructure as a result of further addition has a considerable impact on the alloy's increased hardness (upto 69%) and tensile strength (upto 28.4%) compared to untreated NAB alloy. Influence of Sn on microstructure transformation is confirmed by the decline in alloy nucleation temperatures, the reduction in undercooling intensity, and the decrease in cooling rate during solidification. The addition of Tin to the NAB alloy caused morphological changes in the kappa (K) phases, which are also reported in the this article. In addition to this, the research makes an attempt to describe the mechanism underlying the formation of equiaxed grains and phase transformations in Sn-treated NAB alloys

Optimization of material removal rate and surface characterization of wire electric discharge machined Ti-6Al-4V alloy by response surface method

Wire electric discharge machining (WEDM) is one of the foremost methods which has been utilized for machining hard-to-cut materials like Titanium alloys. However, there is a need to optimize their important operating parameters to achieve maximum material removal rate (MRR). The present paper investigates the effect of control factors like current, pulse on time (Ton), pulse off time (Toff) on MRR of machining of Ti-6Al-4V alloy. The study showed that, increase in current from 2 A to 6 A results in a significant increase in MRR by 93.27% and increase in Ton from 20 μs to 35 μs improved the MRR by 7.98%, beyond which there was no improvement of MRR. The increase in Toff showed a counterproductive effect. Increase in Toff from 10 μs to 30 μs showed an almost linear decrease in MRR by 52.77%. Morphological study of the machined surface showed that cut surface consists of recast layer on which microcracks were present, and revealed the presence of globules, ridge-structured formations of recast layers and voids. In addition, a regression model was developed to predict the MRR with respect to the control factors, which showed a good prediction with an R2 value of 99.67%

Risk and associates of tobacco, alcohol and cannabis use among undergraduate university students – a Pan-India cross-sectional study

Introduction and aim. Substance abuse and its associated problems are a global concern. Young adults, particularly college-going students, remain among the highest at-risk groups for various substance use disorders. So, this study was conducted to find out the prevalence of substance use and its correlates among undergraduate (UG) university students. Material and methods. We did an online cross-sectional survey among 1003 undergraduate university students across India using a pre-structured, self-reported questionnaire consisting of basic demographic details, standard tool (WHO-ASSIST), and the results were tabulated. A multivariable binary logistic regression analysis was performed to find out the correlates of substance use and Pearson correlation to find a correlation between ASSIST scores. Significance was attributed to a p-value <0.05. Results. A total of 320 (31.9%), 167 (16.7%), and 125 (12.5%) among 1003 students used alcohol, tobacco, and cannabis respectively. 70 (21.9%), 116 (69.5%), and 62 (49.6%) were at moderate-high risk of abuse for alcohol, tobacco, and cannabis respectively. There was a strong positive statistically significant (p<0.001) correlation between all three substance-specific scores (Pearson’s Coefficients r = 0.643, 0.763, and 0.725 respectively). Conclusion. One, two, and three out of every ten students used cannabis, tobacco, and alcohol respectively. Many of them fall into the moderate-high risk category. The data suggest that a student at high risk for any one substance is also at a higher risk of using another substance as well. This calls for an integrated ‘bundle’ approach to focus on all substances together as one unit

Parameterizing Path Partitions

International audienc

Level of happiness among medical students in Bihar-An online survey

BACKGROUND: Happiness is a state of mental well-being and influences the learning and performance of an individual. Medical education due to its academic culture and longer course duration affects the performance and happiness of the students. So, this study was done to assess the level of happiness and the factors associated with it among medical students in Bihar.MATERIALS AND METHODS: A cross-sectional online survey was conducted among 321 medical students of all academic years from various medical colleges in Bihar. This study used a self-administered study tool using the online Google Form platform for data collection and assessed the level of happiness using Oxford Happiness Questionnaire. A multivariable binary logistic regression analysis was done to find out the predictors of happiness.RESULTS: A total of 34.6% (95% CI: 29.5–39.9%) medical students were happy. Male (38.2%) students were found to be happier than female (29.2%) students. Age, place of stay, physical activity, meditation and yoga, frequent socialization, absence of psychiatric illness, and stressful situation in the family were the independent predictors of happiness. Around 42.4% of students had another career option, and 32.1% had a second thought about a career due to the COVID-19 pandemic. The presence of any psychiatric illness had a significant effect on the happiness level of the students.CONCLUSION: Only one in three medical students is happy. Promotion of physical activity, meditation and yoga, and socialization will improve the happiness and thereby learning among medical students

Clinico-epidemiological and vaccination profile of patients attending flu clinic of a tertiary health care institution in Eastern India during the third wave of COVID-19 pandemic

Introduction and aim. With the third wave of COVID-19 hitting the country, there is an urgent need to systematically document the clinical-epidemiological and vaccination details of the patients to formulate evidence-based decisions. So, this study was planned to describe the profile of patients attending the flu clinic of a tertiary care hospital in eastern India. Material and methods. This hospital-based cross-sectional study was done for 6 weeks (Jan-Feb 2022) among 623 patients using a pre-tested, structured questionnaire related to COVID-19. An unadjusted odds ratio was calculated and statistical significance was attributed to a p-value <0.05. Results. Out of 623 patients, almost 90% of the patients were vaccinated against COVID-19 with at least one dose of any vaccine. Cough (57.8%) was the most common complaint. Patients aged > 60 years and those having one or more than one comorbidity suffered from moderate-severe COVID-19 infection when compared to their counterparts (p<0.001). Also, 2.1% of fully vaccinated, 3.8% of one dose vaccinated and 10.9% of unvaccinated patients suffered from moderate-severe COVID-19. Conclusion. During the third wave of the COVID-19 pandemic, a smaller number of elderlies compared to the previous two waves were affected indicating age shifting. The severity of COVID-19 was less among vaccinated individuals compared to unvaccinated highlighting the importance of COVID-19 vaccination