Complexity measures and uncertainty relations of the high-dimensional harmonic and hydrogenic systems

In this work we find that not only the Heisenberg-like uncertainty products and the R\'enyi-entropy-based uncertainty sum have the same first-order values for all the quantum states of the $D$-dimensional hydrogenic and oscillator-like systems, respectively, in the pseudoclassical ($D \to \infty$) limit but a similar phenomenon also happens for both the Fisher-information-based uncertainty product and the Shannon-entropy-based uncertainty sum, as well as for the Cr\'amer-Rao and Fisher-Shannon complexities. Moreover, we show that the LMC (L\'opez-Ruiz-Mancini-Calvet) and LMC-R\'enyi complexity measures capture the hydrogenic-harmonic difference in the high dimensional limit already at first order

Summary statistics for key variables (mean/percent).

†<p>Reference levels in the Logistic regression.</p>‡<p>The uninsured is defined as those who did not purchase any medical insurance. Standard errors are in the parentheses.</p

Effect of URBMI on health services utilisation by the level of hospitals.

<p>Note: Chi-square test was used to testify the significant difference.</p

Comparison of analysis sample characteristics before and after matching (UEBMI and Uninsured).

<p>Comparison of analysis sample characteristics before and after matching (UEBMI and Uninsured).</p

Effect of basic medical insurance on health services utilisation.

<p>Note: Chi-square test was used to testify the significant difference for any outpatient visit in the past 2 weeks and any hospitalisation in the past year. T-test was used to testify the significant difference for outpatient visit rate in the past 2 weeks and hospitalisation rate in the past year.</p

Effect of UEBMI on health services utilisation by the level of hospitals.

<p>Note: Chi-square test was used to testify the significant difference.</p

Comparison of analysis sample characteristics before and after matching (URBMI and Uninsured).

<p>Comparison of analysis sample characteristics before and after matching (URBMI and Uninsured).</p

Urban Basic Medical Insurance Schemes in Shaanxi Province, China (Year 2008).

<p>Source: China Labour Statistical Yearbook 2009.</p><p>UEBMI - Urban Employee Basic Medical Insurance; URBMI - Urban Resident Basic Medical Insurance.</p

Logistic regression results for propensity scores.

<p>Note: *p<0.1, **p<0.05, ***p<0.01.</p

The L1 measure of imbalance before and after Coarsened Exact Matching.

<p>The L1 measure of imbalance before and after Coarsened Exact Matching.</p