I like your neat website, but I have one comment regarding your smooth noise-robust differentiation formulas. In the attached Excel spreadsheet I compare your formula for first-order differentiation for N = 5 with that for central differencing, either using no input noise (as when used in opti...
The first approach attempts to calculate the derivative through developing closed form formulas, such as techniques which approximate derivatives using the Taylor series [9,1,2,7,10], while the second approach calculates the derivative using the function data. In particular, regarding the methods ...
Secondly, the information entropy Ei and the weight Wi for the indicator i were calculated by the following formulas: Ei=−k∑j31fijln(fij)(where,fij=Zij′∑j=131Zij′;k=1ln31),iffij=0,fijln(fij)=0. Wi=1−Ei18−∑i=118Ei Thirdly, the weighted index was calculated as follows...
was determined by minimizing the false positive (FPL) and false negative (FNL) levels for upregulation SSMD-based decisions by solving for the intersection of the formulas:67 $$F_{t\left( {n - 1,\sqrt n \beta _2} \right)}\left( {\frac{{\beta _{\alpha _1}}}{k}} \right) =...
In Figure S4D, the fold-enrichment of Dpf2 in the vicinity (+/− 20Kb of the TSS) of up- and downregulated genes at sites exhibiting H3K27ac, Oct4 or Brg1 binding gain or reduction was calculated with the following formulas:(% Upregulated Dpf2 bound genes within region of interest) ...
The underlying formulas are quite simple and effective for quantitative and qualitative evaluations of vegetation cover, vigour, and growth dynamics (Xue and Su 2017). In real-world applications, SVIs are usually tailored to the specific application requirements coupled with appropriate validation tools...
IgG is a potent effector protein of the humoral immune response. Besides its role in antigen binding, IgG has been well established to regulate the activity of immune cells by binding to activating or inhibitory FcγR, mediating key effector functions of IgG such as the clearance of pathogens ...
Table 1. Data Calculation Formulas. 2.3. Research Methods The research methods consisted of three main parts, as illustrated in Figure 2. The first part involved the preparation of foundational data, including multi-source remote sensing imagery and data from open databases, followed by the prepro...