Filling in pattern designs for incomplete pairwise comparison matrices: (quasi-)regular graphs with minimal diameter

Multicriteria Decision Making problems are important both for individuals and groups. Pairwise comparisons have become popular in the theory and practice of preference modelling and quantification. We focus on decision problems where the set of pairwise comparisons can be chosen, i.e., it is not given a priori. The objective of this paper is to provide recommendations for filling patterns of incomplete pairwise comparison matrices (PCMs) based on their graph representation. Regularity means that each item is compared to others for the same number of times, resulting in a kind of symmetry. A graph on an odd number of vertices is called quasi-regular, if the degree of every vertex is the same odd number, except for one vertex whose degree is larger by one. If there is a pair of items such that their shortest connecting path is very long, the comparison between these two items relies on many intermediate comparisons, and is possibly biased by all of their errors. Such an example was previously found, where the graph generated from the table tennis players' matches included a long shortest path between two vertices (players), and the calculated result appeared to be misleading. If the diameter of the graph of comparisons is low as possible (among the graphs of the same number of edges), we can avoid, or, at least decrease, such cumulated errors. The aim of our research is to find graphs, among regular and quasi-regular ones, with minimal diameter. Both theorists and practitioners can use the results, given in several formats in the appendix: graph, adjacency matrix, list of edges.Comment: 68 pages, 28 figure

Determinants of early marriage among female children in Amhara Region, Ethiopia

Background: Early Marriage is one of the global problems that undermine the personal development and the rights of women seriously. It is delicate among the developing countries such as Ethiopia. It has major consequences for public health, national security, social development, human rights, economic development, and gender equality. Methods: The analyzed data were obtained from the 2016 EDHS and 1120 samples were considered in this analysis. Both bivariate and multivariable binary logistic regression model were used to identify the determinants of early marriage practice. Results: The prevalence of early marriage practice was 48.57% in the study area. The odds of early marriage practice were 2.04(AOR=2.04, 95% CI: 1.88, 2.45) times higher among rural residents compared to urban. The odds of early marriage practice was 0.94(AOR=0.94, 95%CI: 0.57, 1.98) times lower among women who had primary education compared to uneducated women. Those who did not know the legal marital age were 1.61(AOR=1.61, 95%CI: 1.26, 2.07) times more likely to practice early marriage compared to parents who knew the legal marital age. Conclusion: Education level, family monthly income, residence, literacy level and knowledge of legal marital were significant determinants of early marriage practice

Determinants of neonatal mortality in Ethiopia: an analysis of the 2016 Ethiopia Demographic and Health Survey

Background: The first 28 days of life, the neonatal period, are the most vulnerable time for a child\u2019s survival. Neonatal mortality accounts for about 38% of under-five deaths in low and middle income countries. This study aimed to identify the determinants of neonatal mortality in Ethiopia. Methods: The study used data from the nationally representative 2016 Ethiopia Demographic and Health Survey (EDHS). Once the data were extracted; editing, coding and cleaning were done by using SAS 9.4.Sampling weights was applied to ensure the representativeness of the sample in this study. Both bivariate and multivariable logistic regression statistical analysis was used to identify determinants of neonatal mortality in Ethiopia. Results: A total of 11,023 weighted live-born neonates born within five years preceding the 2016 EDHS were included this in this study. Multiple logistic regression analysis showed that multiple birth neonates (Adjusted Odds Ratio (AOR)=6.38;95%-Confidence Interval (CI):4.42-9.21), large birth size (AOR=1.35; 95% CI: 0.28-1.62), neonates born to mothers who did not utilize ANC (AOR=1.41; 95% CI: 1.11-1.81), neonates from rural area (AOR=1.88; 95% CI: 1.15-3.05) and neonates born in Harari region (AOR=1.45; 95% CI: 0.61-3.45)had higher odds of neonatal mortality. On the other hand, female neonates (AOR=0.60; 95% CI: 0.47-0.75), neonates born within the interval of more than 36 months of the preceding birth (AOR=0.56; 95% CI: 0.43-0.75), neonates born to fathers with secondary and higher education level (AOR=0.51; 95%CI:0.22-0.88) had lower odds of neonatal mortality in Ethiopia. Conclusion: To reduce neonatal mortality in Ethiopia, there is a need to implement sex specific public health intervention mainly focusing on male neonate during pregnancy, child birth and postnatal period. A relatively simple and cost-effective public health intervention should be implemented to make sure that all pregnant women are screened for multiple pregnancy and if positive, extra care should be given during pregnancy, child birth and postnatal

Prevalence and associated factors of anemia among children aged 6 to 59 months in Ethiopia: Evidence from the Ethiopian demographic and health survey

Anemia is one of the most widely spread public health problems, especially in developing countries including Ethiopia. The aim of this study was to assess the prevalence and associated factors of anemia among children aged 6-59 months in Ethiopia. A community-based cross-sectional study (the Ethiopian Demography and Health Survey 2016) was used as a source of data. Participants were 8385 children aged from 6 to 59 months selected in a two-stage stratified cluster sampling. The level of hemoglobin was determined by HemoCue analyzer. The risk factors of anemia were computed by logistic regression (α=0.05). The result revealed that more than half (57.3%) of children aged 6-59 months were found anemic of which 3.1% had severe anemia, 29.2% had moderate and 25% mild anemia. The anemia status of the children’s mother (OR: 3.01, CI: 0.34, 6.75), living in Somali region (OR: 5.73, CI: 1.86, 17.71), living in rural areas (OR: 1.84, CI: 1.38, 2.83), age of study participants (OR: 0.82, CI: 0.29,1.45) among 24-42 months old children (OR: 0.53, CI: 0.16,1.08) among 43-59 months old children, rich and medium parents (OR: 0.29, CI: 0.20,0.73), smoker mother (OR: 0.02, CI: 0.00, 0.05) were the risk factors of anemia among Ethiopian children aged 6-59 months. The overall prevalence of anemia among Ethiopian children aged 6–59 months was high. It is argued that measures that prevent childhood illnesses and maternal anemia need to be put in place in order to reduce anemia among Ethiopian children

200 kHz Sonication of Mixed-Algae Suspension from a Eutrophic Lake: The Effect on the Caution vs. Outbreak Bloom Alert Levels

For effective ultrasonic algae removal, several studies have considered the ultrasound equipment linked factors, such as power and frequency. However, studies on the response of mixed algal cultures and associated water quality parameters to ultrasound are limited. In this lab-scale sonication, the removal of cyanobacteria at a pre-set frequency of 200 kHz on mixed algae suspensions collected from a eutrophic lake was investigated. The caution (17.5 µg/L) and outbreak (1450 µg/L) alert levels in terms of chlorophyll-a (Chl-a) concentrations of the initial samples were each sonicated for 10, 15, and 20 min, and then kept in an incubator. Fifteen minutes of sonication resulted in best removal efficiency of 0.94 and 0.77, at an ultrasonic dose of 30 kWh/m3 at the outbreak and caution level concentrations, respectively. Immediately after 15 min sonication, and after standing in the incubator for a day, chlorophyll-a removal efficiencies of 0.28 and 0.90 were achieved in the outbreak level, respectively, and the matching removal efficiencies for the caution level were 0.23 and 0.64. Even though the removal was substantial in both cases, the final 147 µg/L chlorophyll-a concentration of the outbreak, which is itself still in the outbreak level range, shows that ultrasonication is not effective to satisfactorily remove algae from a concentrated suspension. Total dissolved nitrogen and chemical oxygen demand were reduced, overall, due to sonication. However, total dissolved phosphorus of the concentrated level was increased during the treatment. Although sonication needs further replicated experimental testing in whole-lake systems, our results show that 200 kHz sonication was able to reduce chlorophyll-a concentrations in small-scale laboratory tests

Constrained Eigenvalue Minimization of Incomplete Pairwise Comparison Matrices by Nelder-Mead Algorithm

Pairwise comparison matrices play a prominent role in multiple-criteria decision-making, particularly in the analytic hierarchy process (AHP). Another form of preference modeling, called an incomplete pairwise comparison matrix, is considered when one or more elements are missing. In this paper, an algorithm is proposed for the optimal completion of an incomplete matrix. Our intention is to numerically minimize a maximum eigenvalue function, which is difficult to write explicitly in terms of variables, subject to interval constraints. Numerical simulations are carried out in order to examine the performance of the algorithm. The results of our simulations show that the proposed algorithm has the ability to solve the minimization of the constrained eigenvalue problem. We provided illustrative examples to show the simplex procedures obtained by the proposed algorithm, and how well it fills in the given incomplete matrices

A numerical comparative study of completion methods for pairwise comparison matrices

In the context of some multi-criteria decision-making methods, such as the Analytic Hierarchy Process, an expert is required to compare entities, e.g. alternatives and criteria. However, often, for various reasons, the expert cannot provide judgments on all pairs of entities. For these cases, several completion methods have been proposed in the literature to estimate the missing values of pairwise comparison matrices. In this paper, we study the similarity of eleven completion methods on the basis of numerical simulations and hierarchical clustering. We perform simulations for matrices of different orders considering various numbers of missing comparisons. Finally, the results suggest the existence of a cluster of five extremely similar methods, and a method significantly dissimilar from all the others

Spatial Frailty Survival Model for Multidrug-Resistant Tuberculosis Mortality in Amhara Region, Ethiopia

Tuberculosis (TB), a disease caused by Mycobacterium tuberculosis (MTB), is the main cause of death. It disproportionally affects those living in the different regions of countries and within the region. The aim of this study was to examine spatial variation of mortality and the risk factor of death on multidrug-resistant tuberculosis patients treated in different MDR-TB hospitals of Amhara region. The data for this study was used from multidrug-resistant tuberculosis patients’ record charts and analyzed using STATA software. The result of this study shows that 61 (29.47%) of the patients died, and the rest, 146 (70.53%), of the patients were censored at the time of the study. Out of 207 MDR-TB, 146 (70.53%) were males and 61 (29.5%) were females. This study revealed that there was no heterogeneity for death in patients treated in different hospitals. Older patients, therapeutic delay, alcohol use, any clinical complication previously not treated, HIV coinfection, and presence of any chronic disease were the risk factors that influenced the death of multidrug-resistant tuberculosis patients

Geographical disparities and determinants of infant mortality in Ethiopia: mapping and spatial analysis using EDHS data

Abstract Background Infant mortality remains a public health challenge in Ethiopia. Exploring infant mortality will aid in tracking the progress toward achieving sustainable development goals. Objective The study aimed to explore the geographical variations and associated factors of infant mortality in Ethiopia. Method A total of 11,023 infants from the 2016 Ethiopian Demographic and Health Survey (EDHS) data were extracted and included in the analysis. EDHS used a two-stage cluster sampling design with a census enumeration area as the primary sampling unit and households as the secondary sampling unit. Arc GIS software was used for spatial analysis using clusters for exploring geographical variations in infant mortality. A binary logistic regression was employed using R software to identify the significant determinants of infant mortality. Results The study revealed that the spatial distribution of infant mortality was non-random in the country. Infants whose mothers not receiving ANC (AOR = 1.45; 95%CI: 1.17, 1.79), not breastfed status (AOR = 3.94; 95%CI: 3.19, 4.81), poor wealth index (AOR = 1.36; 95%CI: 1.04, 1.77), male infants (AOR = 1.59; 95%CI: 1.29, 1.95), birth order of six or above (AOR = 3.11; 95%CI: 2.08, 4.62), small birth size (AOR = 1.27; 95%CI: 1.26, 1.60), birth spacing [(≤ 24 months (AOR = 2.29; 95%CI: 1.79, 2.92), 25–36 months (AOR = 1.16; 95%CI: 1.12, 1.49)], multiple births (AOR = 6.82; 95%CI: 4.76, 10.81), rural residence (AOR = 1.63; 95%CI: 1.05, 2.77) and regions [Afar (AOR = 1.54; 95%CI: 1.01, 2.36), Harari (AOR = 1.56; 95%CI: 1.04, 2.56), and Somali (AOR = 1.52; 95%CI: 1.03, 2.39)] were the determinants of infant death in Ethiopia. Conclusions There is a great geographical disparity in infant mortality rates across regions. Afar, Harari, and Somali regions were verified as hot spot areas. ANC usage, breastfed status, wealth index, sex of the infant, birth order, birth size, birth spacing, birth type, residence, and region were the determinants of infant death in Ethiopia. Therefore, appropriate interventions need to be implemented in the hot spots to alleviate the risk factors for infant mortality