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Bill & Melinda Gates Foundation.

Numerical simulation results show that the upper bound order of random packing densities of basic 3D objects is cube (0.78) > ellipsoid (0.74) > cylinder (0.72) > spherocylinder (0.69) > tetrahedron (0.68) > cone (0.67) > sphere (0.64), while the upper bound order of ordered packing densities of basic 3D objects is cube (1.0) > cylinder and spherocylinder (0.9069) > cone (0.7854) > tetrahedron (0.7820) > ellipsoid (0.7707) > sphere (0.7405); these two orders are significantly different. The random packing densities of ellipsoid, cylinder, spherocylinder, tetrahedron and cone are closely related to their shapes. The optimal aspect ratios of these objects which give the highest packing densities are ellipsoid (axes ratio = 0.8:1:1.25), cylinder (height/diameter = 0.9), spherocylinder (height of cylinder part/diameter = 0.35), tetrahedron (regular tetrahedron) and cone (height/bottom diameter = 0.8).packing, particle, nonspherical particle, cylinder, cone, spherocylinder, tetrahedron Citation:Li S X, Zhao J, Lu P, et al. Maximum packing densities of basic 3D objects.To pursue the densest packing has never lost its attraction to human beings. The earliest history of studies on packing problem can be traced back to the famous Kepler Conjecture (the problem of maximum packing density of identical spheres, 1661) and the debate between Newton and Gregory (the problem of maximum coordinate number of identical spheres, 1694). In 1900, Hilbert further presented the packing problem, especially the densest packing of spheres and regular tetrahedra, as the 18th problem in his celebrated list of 23 mathematical problems [1]. For centuries, packing problem has always been attractive since it is not only a basic problem of mathematics and physics, but also extensively applied to many branches of science, engineering and even in daily life. These applications range from the macroscale of celestial body motions to the microscale of molecular arrangements. According to the packing structures, packing problems can be classified into ordered packing and disordered packing. For ordered packing, Hales proposed a proof of the Kepler Conjecture in 1998 [2]. However, it still leaves a long way to the solution of the Hilbert's 18th problem. For disordered packing, random packing which is closely related to matter structure has been investigated extensively. The first systematic study on random packing was undertaken by Bernal in 1950s on the random packing of spheres [3]. Nowadays, numerical simulation has become the main means of random packing researches. Zhao et al.[4] gave a summarization and classification of numerical simulation approaches available on random packing. In respect of particle shapes, sphere is the most comprehensively studied particle shape on random packing, and the packing results are accepted widely within the academic community. Nonspherical particles are often simplified to equivalent spheres in engineering applications. However, recent investigations indicated that the packing properties of nonspherical particles ...

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BackgroundLeptospirosis is a water-borne and widespread spirochetal zoonosis caused by pathogenic bacteria called leptospires. Human leptospirosis is an important zoonotic infectious disease with frequent outbreaks in recent years in China. Leptospirosis’s emergence has been linked to many environmental and ecological drivers of disease transmission. In this paper, we identified the environmental and socioeconomic factors associated with leptospirosis in China, and predict potential risk area of leptospirosis using predictive models.MethodsLeptospirosis incidence data were derived from the database of China’s web-based infectious disease reporting system, a national surveillance network maintained by Chinese Center for Disease Control and Prevention. We built statistical relationship between occurrence of leptospirosis and nine environmental and socioeconomic risk factors using logistic regression model and Maxent model.ResultsBoth logistic regression model and Maxent model have high performance in predicting the occurrence of leptospirosis, with AUC value of 0.95 and 0.96, respectively. Annual mean temperature (Bio1) and annual total precipitation (Bio12) are two most important variables governing the geographic distribution of leptospirosis in China. The geographic distributions of areas at risk of leptospirosis predicted from both models show high agreement. The risk areas are located mainly in seven provinces of China: Sichuan Province, Chongqing Municipality, Hunan Province, Jiangxi Province, Guangdong Province, Guangxi Province, and Hainan Province, where surveillance and control programs are urgently needed. Logistic regression model and Maxent model predicted that 403 and 464 counties are at very high risk of leptospirosis, respectively.ConclusionsOur results highlight the importance of socioeconomic and environmental variables and predictive models in identifying risk areas for leptospirosis in China. The values of Geographic Information System and predictive models were demonstrated for investigating the geographic distribution, estimating socioeconomic and environmental risk factors, and enhancing our understanding of leptospirosis in China.

Few studies have examined nutrition transitions among the rural population of China, even though half of the Chinese population (about 700 million) is living in rural China. To fill this research gap, we examined temporal trends in dietary macronutrient intakes in members of the Chinese rural population aged 18–60 years. The analysis used data from consecutive three-day dietary recalls, collected from the China Health and Nutrition Surveys (CHNS). Mixed-effect models were constructed to obtain adjusted means and to examine temporal trends after adjusting for intra-class correlation within clusters and covariates, including age, sex, geographical region, urbanicity, and income. From 1991 to 2011, a downward trend in daily energy, protein, and carbohydrate intakes was seen in all categories, with a significant reduction among all rural people (p < 0.0001). In contrast, a significant increment in daily fat intake, the proportion of energy from fat, and the proportion of rural people consuming a diet with more than 30% of energy from fat, were observed in the present study (p < 0.0001). These results suggest that adults in rural China have been undergoing a rapid nutrition transition towards a high-fat diet. Therefore, more emphasis should be placed on the quality of fat and maintaining a balanced diet during the process of nutritional education.

BackgroundHemorrhagic fever with renal syndrome (HFRS) is an important public health problem in mainland China. HFRS is particularly endemic in Changsha, the capital city of Hunan Province, with one of the highest incidences in China. The occurrence of HFRS is influenced by environmental factors. However, few studies have examined the relationship between environmental variation (such as land use changes and climate variations), rodents and HFRS occurrence. The purpose of this study is to predict the distribution of HFRS and identify the risk factors and relationship between HFRS occurrence and rodent hosts, combining ecological modeling with the Markov chain Monte Carlo approach.MethodsEcological niche models (ENMs) were used to evaluate potential geographic distributions of rodent species by reconstructing details of their ecological niches in ecological dimensions, and projecting the results onto geography. The Genetic Algorithm for Rule-set Production was used to produce ENMs. Data were collected on HFRS cases in Changsha from 2005 to 2009, as well as national land survey data, surveillance data of rodents, meteorological data and normalized difference vegetation index (NDVI).ResultsThe highest occurrence of HFRS was in districts with strong temperature seasonality, where elevation is below 200 m, mean annual temperature is around 17.5°C, and annual precipitation is below 1600 mm. Cultivated and urban lands in particular are associated with HFRS occurrence. Monthly NDVI values of areas predicted present is lower than areas predicted absent, with high seasonal variation. The number of HFRS cases was correlated with rodent density, and the incidence of HFRS cases in urban and forest areas was mainly associated with the density of Rattus norvegicus and Apodemus agrarius, respectively.ConclusionsHeterogeneity between different areas shows that HFRS occurrence is affected by the intensity of human activity, climate conditions, and landscape elements. Rodent density and species composition have significant impacts on the number of HFRS cases and their distribution.