Statistical computation of Boltzmann entropy and estimation of the optimal probability density function from statistical sample

In this work, we investigate the statistical computation of the Boltzmann entropy of statistical samples. For this purpose, we use both histogram and kernel function to estimate the probability density function of statistical samples. We find that, due to coarse-graining, the entropy is a monotonic increasing function of the bin width for histogram or bandwidth for kernel estimation, which seems to be difficult to select an optimal bin width/bandwidth for computing the entropy. Fortunately, we notice that there exists a minimum of the first derivative of entropy for both histogram and kernel estimation, and this minimum point of the first derivative asymptotically points to the optimal bin width or bandwidth. We have verified these findings by large amounts of numerical experiments. Hence, we suggest that the minimum of the first derivative of entropy be used as a selector for the optimal bin width or bandwidth of density estimation. Moreover, the optimal bandwidth selected by the minimum of the first derivative of entropy is purely data-based, independent of the unknown underlying probability density distribution, which is obviously superior to the existing estimators. Our results are not restricted to one-dimensional, but can also be extended to multivariate cases. It should be emphasized, however, that we do not provide a robust mathematical proof of these findings, and we leave these issues with those who are interested in them.Comment: 8 pages, 6 figures, MNRAS, in the pres

A systematic study on the binding energy of Λ\Lambda hypernuclei

In this paper, we calculated the binding energy per baryon of the $\Lambda$ hypernuclei systemically, using the relativistic mean field theory (RMF) in a statistic frame. Some resemble properties are found among most of the hypernuclei found in experiments. The data show that a $\Lambda$ hypernucleus will be more stable, if it is composed of a $\Lambda$ hyperon adding to a stable normal nuclear core, or a $\Lambda$ hyperon replacing a neutron in a stable normal nuclear core. According to our calculations, existences of some new $\Lambda$ hypernuclei are predicted under the frame of RMF.Comment: 8 pages, 6 figures, 3 table

Use of low-dose computed tomography to assess pulmonary tuberculosis among healthcare workers in a tuberculosis hospital

BACKGROUND: According to the World Health Organization, China is one of 22 countries with serious tuberculosis (TB) infections and one of the 27 countries with serious multidrug-resistant TB strains. Despite the decline of tuberculosis in the overall population, healthcare workers (HCWs) are still at a high risk of infection. Compared with high-income countries, the TB prevalence among HCWs is higher in low- and middle-income countries. Low-dose computed tomography (LDCT) is becoming more popular due to its superior sensitivity and lower radiation dose. However, there have been no reports about active pulmonary tuberculosis (PTB) among HCWs as assessed with LDCT. The purposes of this study were to examine PTB statuses in HCWs in hospitals specializing in TB treatment and explore the significance of the application of LDCT to these workers. METHODS: This study retrospectively analysed the physical examination data of healthcare workers in the Beijing Chest Hospital from September 2012 to December 2015. Low-dose lung CT examinations were performed in all cases. The comparisons between active and inactive PTB according to the CT findings were made using the Pearson chi-square test or the Fisher’s exact test. Comparisons between the incidences of active PTB in high-risk areas and non-high-risk areas were performed using the Pearson chi-square test. Analyses of active PTB were performed according to different ages, numbers of years on the job, and the risks of the working areas. Active PTB as diagnosed by the LDCT examinations alone was compared with the final comprehensive diagnoses, and the sensitivity and positive predictive value were calculated. RESULTS: A total of 1 012 participants were included in this study. During the 4-year period of medical examinations, active PTB was found in 19 cases, and inactive PTB was found in 109 cases. The prevalence of active PTB in the participants was 1.24%, 0.67%, 0.81%, and 0.53% for years 2012 to 2015. The corresponding incidences of active PTB among the tuberculosis hospital participants were 0.86%, 0.41%, 0.54%, and 0.26%. Most HCWs with active TB (78.9%, 15/19) worked in the high-risk areas of the hospital. There was a significant difference in the incidences of active PTB between the HCWs who worked in the high-risk and non-high-risk areas (odds ratio [OR], 14.415; 95% confidence interval (CI): 4.733 – 43.896). Comparisons of the CT signs between the active and inactive groups via chi-square tests revealed that the tree-in-bud, cavity, fibrous shadow, and calcification signs exhibited significant differences (P = 0.000, 0.021, 0.001, and 0.024, respectively). Tree-in-bud and cavity opacities suggest active pulmonary tuberculosis, whereas fibrous shadow and calcification opacities are the main features of inactive pulmonary tuberculosis. Comparison with the final comprehensive diagnoses revealed that the sensitivity and positive predictive value of the diagnoses of active PTB based on LDCT alone were 100% and 86.4%, respectively. CONCLUSIONS: Healthcare workers in tuberculosis hospitals are a high-risk group for active PTB. Yearly LDCT examinations of such high-risk groups are feasible and necessary. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s40249-017-0274-6) contains supplementary material, which is available to authorized users