## 4 Discussion  
### Body Temperature and iPRV  
Since humans are warm-blooded animals, we need to maintain our body temperature in a fixed range. However, while our bodies are infected by germs, to increase the power of immune body temperature, the corresponding organs should be regulated by ANS [20,25]. Increase heart rate by the sympathetic nervous system (SNS) and vasoconstriction, for example. Some studies showed the relationship between thermoregulation and HRV [26,27]. Their result showed that the very low frequency band power (VLF) had a corresponding change, while the core body temperature or the environment temperature changed. However, they did not discuss the situation of fever. Moreover, to indicate a meaningful VLF, the signal length should be longer [1]. Our previous studies still showed that conventional nLF and nHF in patients with fever were different from those without fever [28]. Furthermore, we also examined whether the conventional frequency band indices in iPRV are similar to the indices in conventional HRV in our previous work in the time and frequency domain [14,15]. nLF and nHF calculated by iPRV actually showed the difference in ANS activity between patients with fever and people without fever. For non-linear dynamic analysis, the higher resolution time series can present much detail about the complexity of the time series. The CDF(E(\(k\) = 19)) of the iPR series also had a higher AUC than the CDF(E(\(k\))) of PPi, whatever \(k\). Therefore, the following term CDF(E(\(k\) = 19)) is denoted as the one of iPR series. Tables 4 and 5 show the AUC calculated by time- and frequency domains of iPRV and PRV. Only pulse rate and mean (PPi) had a higher AUC than CDF(E(\(k\) = 19)). In addition to Mean(PPi), Mean(iPR) also had a high AUC, but it is because they are directly correlated with pulse rate. Although pulse rate differences are found between patients with fever and non-fever (\(p\) < 0.001), only pulse rate to find patients with fever is not enough. Influencing pulse rate is so easy. For example, the pulse rate of someone after exercise also possibly had a high pulse rate which is similar to the pulse rate of patients with fever. The pulse rate distribution is shown in Figure 6a. The pulse rate in the fever group is significantly higher than in the non-Fever group. The difference between pulse rate and CDF(E(\(k\) = 19)) is that CDF(E(\(k\) = 19)) had a high correlation compared to body temperature in the ever group, but the correlation was low between pulse rate and body temperature in  
Figure 5: Distribution of AUC of E(\(k\)) of iPR (**left**), and CDF(E(\(k\))) of iPR (**right**). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variable** & **AUC** & **Sensitivity** & **Specificity** \\ \hline Mean(E(\(k\) = 1\(\sim\)20)) & 0.678 & 0.600 & 0.722 \\ std(E(\(k\) = 1\(\sim\)20)) & 0.689 & 0.800 & 0.667 \\ Max(E(\(k\) = 1\(\sim\)20)) & 0.678 & 0.800 & 0.611 \\ Min(E(\(k\) = 1\(\sim\)20)) & 0.678 & 0.800 & 0.556 \\ Area(E(\(k\) = 1\(\sim\)20)) & 0.678 & 0.600 & 0.722 \\ E(\(k\) = 4) & 0.689 & 0.800 & 0.611 \\ CDF(E(\(k\) = 19)) & 0.745 & 0.733 & 0.722 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The AUC of the variables related to the entropy value of PPi. the fever group (Figures 4c and 6d). For patients suffering from fever, autoregulation of not only their ANS but also peripheral response. The CDF(E(\(k\) = 19)) may correspond to this reflection of autoregulation or the severity of the disease. CDF(E(\(k\) = 19)) had a higher absolute correlation \(|\)r\(|\) compared to pulse rate in each group and total subjects (Total: 0.757 vs. 0.726; Non-fever group: 0.287 vs. 0.05; Fever group: 0.830 vs. 0.267). It showed that CDF (E (\(k\) = 19)) is not directly affected by pulse rate. Body temperature, ANS activity, or peripheral response may be the possible factors that affect the CDF(E(\(k\) = 19)), especially in the Fever group. Applying logistic regression using pulse rate and CDF(E(\(k\) = 19)) can increase AUC.