## 3 Results
### Results of Grain-Size Unmixing  
For grain-size distribution, a multi-mode pattern is observed, which agrees well with marine surface samples (Figure 3c). Because grain-size distribution of all samples consists of three components, the Weibull-based function formula for partitioning can be expressed as follows:  
\[\begin{split} f(x,\alpha_{1},\beta_{1},m_{1},&\alpha_ {2},\beta_{2},m_{2},\alpha_{3},\beta_{3})\\ &=m_{1}\frac{\alpha_{1}}{\beta_{1}^{\alpha_{1}}}x^{\alpha_{1}-1} e^{-(\frac{x}{\beta_{1}})^{\alpha_{1}}}+m_{2}\frac{\alpha_{2}}{\beta_{2}^{\alpha_{2}}} x^{\alpha_{2}-1}e^{-(\frac{x}{\beta_{2}})^{\alpha_{2}}}+(1-m_{1}\\ &-m_{2})\frac{\alpha_{3}}{\beta_{3}^{\alpha_{3}}}x^{\alpha_{3}-1} e^{-(\frac{x}{\beta_{3}})^{\alpha_{3}}}\end{split} \tag{3}\]  
The values \(\alpha_{1}\) and \(\beta_{1}\) are parameters of the distribution function of the coarse-grained component, \(\alpha_{2}\) and \(\beta_{2}\) represent the medium-grained component, and \(\alpha_{3}\) and \(\beta_{3}\) are parameters of the fine-grained component. The percentages of each component in a sub-population are given by \(m_{1}\), \(m_{2}\), \((1-m_{1}-m_{2})\), respectively. Here, \(x\) is a variable representing grain size.  
Figure 4: Down-core variation of unmixed components of core YDZ–3 with modes and contents. The right panel shows decomposition R\({}^{2}\) (bold green line), R\({}^{2}_{\text{adj}}\) (dashed black line), and standard error of the regression (_SE_) (thin purple line) were employed for helping choosing the best fit of partitioning estimations. Comp–1, -2, -3 are three components by unmixing.  
Using the measured grain-size data from Malven Mastersizer 2000 analyzer (MalverP-ANalytical, Malvern, UK), i.e., one hundred grain-size classes between 0.3 \(\upmu\)m and 300 \(\upmu\)m, these eight parameters can be estimated following the General Least Square Fitting, setting the squared sum of the residual error to the minimum in multiple dimensions [37]. Three statistics, including R-squared (R2), adjusted R-squared (R2\({}_{\text{adj}}\)), and standard error of the regression (\(SE\)), were employed for choosing the best fit of estimations (Figure 4).  
As a result, all samples have been well unmixed. Modal sizes of each component (labelled Comp-1, -2, -3) are 61.1 \(\pm\) 28.9 \(\upmu\)m, 30.0 \(\pm\) 23.9 \(\upmu\)m, and 2.8 \(\pm\) 1.6 \(\upmu\)m, respectively, and their relative percentages are 57.6 \(\pm\) 19.4%, 32.0 \(\pm\) 17.0%, 10.4 \(\pm\) 5.9%, respectively. All regressions are significant in statistics, and R2 and R2\({}_{\text{adj}}\) are over 0.997 with \(SE\) of 0.395 \(\pm\) 0.127 (Figure 4), illustrating the reliability of unmixing processes.  
Specifically, changes in modal sizes of each component are similar, while changes in contents are different (Figure 4). Prior to \(\sim\)6400 yr BP, all parameters changed little, and after that, all changes were amplified, consistent with other grain-size parameters (Figure 2). Eight intervals can be similarly identified according to changes in modal sizes, and between each interval, all transitions are abrupt. A negative correlation between Comp-1 and Comp-2 contents is also evident. Integrating these findings, it is inferred that although modal sizes and contents of the three components are different, all parameters are closely correlated, indicating only one major factor controlling sedimentary dynamics of core YDZ-3 in the Holocene.