Search results for: hypercubes

Authors: Dongqin Cheng

Abstract:

The n-dimensional balanced hypercube BHn (n ≥ 1) has been proved to be a bipartite graph. Let P be a set of edges whose induced subgraph consists of pairwise vertex-disjoint paths. For any two vertices u, v from different partite sets of V (BHn). In this paper, we prove that if |P| ≤ 2n − 2 and the subgraph induced by P has neither u nor v as internal vertices, or both of u and v as end-vertices, then BHn contains a Hamiltonian path joining u and v passing through P. As a corollary, if |P| ≤ 2n−1, then the BHn contains a Hamiltonian cycle passing through P.

Keywords: interconnection network, balanced hypercube, Hamiltonian cycle, prescribed edges

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Authors: Shih-Yan Chen, Shin-Shin Kao

Abstract:

In this paper, a thorough review about dual-cubes, DCn, the related studies and their variations are given. DCn was introduced to be a network which retains the pleasing properties of hypercube Qn but has a much smaller diameter. In fact, it is so constructed that the number of vertices of DCn is equal to the number of vertices of Q2n +1. However, each vertex in DCn is adjacent to n + 1 neighbors and so DCn has (n + 1) × 2^2n edges in total, which is roughly half the number of edges of Q2n+1. In addition, the diameter of any DCn is 2n +2, which is of the same order of that of Q2n+1. For selfcompleteness, basic definitions, construction rules and symbols are provided. We chronicle the results, where eleven significant theorems are presented, and include some open problems at the end.

Keywords: dual-cubes, dual-cube extensive networks, dual-cube-like networks, hypercubes, fault-tolerant hamiltonian property

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Authors: Xiaofang Wei

Abstract:

Harmful Algal Blooms are a recurrent disturbing occurrence in Lake Erie that has caused significant negative impacts on water quality and aquatic ecosystem around Great Lakes areas in the United States. Targeting the recent HAB events in western Lake Erie, this paper utilizes satellite imagery and hydrological modeling to monitor HAB cyanobacteria blooms and analyze the impacts of agricultural activities from Maumee watershed, the biggest watershed of Lake Erie and agriculture dominant.SWAT (Soil & Water Assessment Tool) Model for Maumee watershed was established with DEM, land use data, crop data layer, soil data, and weather data, and calibrated with Maumee River gauge stations data for streamflow and nutrients. Fast Line-of-sight Atmospheric Analysis of Hypercubes (FLAASH) was applied to remove atmospheric attenuation and cyanobacteria Indices were calculated from Landsat OLI imagery to study the intensity of HAB events in the years 2015, 2017, and 2019. The agricultural practice and nutrients management within the Maumee watershed was studied and correlated with HAB cyanobacteria indices to study the relationship between HAB intensity and nutrient loadings. This study demonstrates that hydrological models and satellite imagery are effective tools in HAB monitoring and modeling in rivers and lakes.

Keywords: harmful algal bloom, landsat OLI imagery, SWAT, HAB cyanobacteria

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Authors: Mario Tauzene Afonso Matangue, Ivan Andres Sanchez Ortiz

Abstract:

The Metropolitan area of Maputo (Mozambique Capital City) is located in semi-arid zone (800 mm annual rainfall) with 1101170 million inhabitants. On the west side, there are the flatlands of Infulene where the Mulauze River flows towards to the Indian Ocean, receiving at this site, the storm water contaminated with sanitary sewage from Maputo, transported through a concrete open channel. In Infulene, local communities grow salads crops such as tomato, onion, garlic, lettuce, and cabbage, which are then commercialized and consumed in several markets in Maputo City. Lettuce is the most daily consumed salad crop in different meals, generally in fast-foods, breakfasts, lunches, and dinners. However, the risk of infection by several pathogens due to the consumption of lettuce, using the Quantitative Microbial Risk Assessment (QMRA) tools, is still unknown since there are few studies or publications concerning to this matter in Mozambique. This work is aimed at determining the annual risk arising from the consumption of lettuce grown in Infulene valley, in Maputo, using QMRA tools. The exposure model was constructed upon the volume of contaminated water remaining in the lettuce leaves, the empirical relations between the number of pathogens and the indicator of microorganisms (E. coli), the consumption of lettuce (g) and reduction of pathogens (days). The reference pathogens were Vibrio cholerae, Cryptosporidium, norovirus, and Ascaris. The water quality samples (E. coli) were collected in the storm water channel from January 2016 to December 2018, comprising 65 samples, and the urban lettuce consumption data were collected through inquiry in Maputo Metropolis covering 350 persons. A non-parametric bootstrap was performed involving 10,000 iterations over the collected dataset, namely, water quality (E. coli) and lettuce consumption. The dose-response models were: Exponential for Cryptosporidium, Kummer Confluent hypergeomtric function (1F1) for Vibrio and Ascaris Gaussian hypergeometric function (2F1-(a,b;c;z) for norovirus. The annual infection risk estimates were performed using R 3.6.0 (CoreTeam) software by Monte Carlo (Latin hypercubes), a sampling technique involving 10,000 iterations. The annual infection risks values expressed by Median and the 95th percentile, per person per year (pppy) arising from the consumption of lettuce are as follows: Vibrio cholerae (1.00, 1.00), Cryptosporidium (3.91x10⁻³, 9.72x 10⁻³), nororvirus (5.22x10⁻¹, 9.99x10⁻¹) and Ascaris (2.59x10⁻¹, 9.65x10⁻¹). Thus, the consumption of the lettuce would result in greater risks than the tolerable levels ( < 10⁻³ pppy or 10⁻⁶ DALY) for all pathogens, and the Vibrio cholerae is the most virulent pathogens, according to the hit-single models followed by the Ascaris lumbricoides and norovirus. The sensitivity analysis carried out in this work pointed out that in the whole QMRA, the most important input variable was the reduction of pathogens (Spearman rank value was 0.69) between harvest and consumption followed by water quality (Spearman rank value was 0.69). The decision-makers (Mozambique Government) must strengthen the prevention measures related to pathogens reduction in lettuce (i.e., washing) and engage in wastewater treatment engineering.

Keywords: annual infections risk, lettuce, non-parametric bootstrapping, quantitative microbial risk assessment tools

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