esa-sceva/satcom-chunk-collection huggingface dataset:
## 5 Conclusions  
Circumferential PVI is a milestone in AF ablation treatment. This paper presented a comprehensive simulation study of the ablation characteristics of the MEU and MEB modes that could facilitate PVI. The MEU and MEB modes exhibit different trends of lesion growth, which can fulfill specific ablation requirements for clinical applications. The MEU mode is skilled in creating deep and broad lesion volume that ensure transmural lesions as long as sufficient RF power and ablation time are guaranteed. It is a feasible solution for patients with thick tissue around PVs. The MEB mode is proficient in creating durable contiguous lesions in a short time. It could be a first consideration for circumferential PVI. The cardiac tissue has a great chance to be irreversibly damaged due to high temperature generation. Further research may focus on other settings of power conditions, except the current two modes. This technology has the potential to accomplish and support complete PVI through a single application of RFCA.  
**Supplementary Materials:** The following are available online at [[http://www.mdpi.com/2076-3417/10/24/9081/s1](http://www.mdpi.com/2076-3417/10/24/9081/s1)]([http://www.mdpi.com/2076-3417/10/24/9081/s1](http://www.mdpi.com/2076-3417/10/24/9081/s1)). Figure S1: (a) Experimental apparatus of the in vitro validation and (b) the corresponding computational model with boundary conditions. Figure S2: Lesion growth in the MEU mode at 1.2, 9.5, 13, and 25.6 s of RFCA and MEB mode at 0.2, 2.4, 4.3, and 6 s of RFCA. Figure S3: Simulation of the MEU and MEB modes of a regular ablation catheter: (a) Modeling of the catheter, (b) maximum lesion depth, and (c) maximum temperature achieved under each active electrode and (d) Total lesion volume at 60 s of RFCA. The diameters of the electrode and the catheter body of the ablation catheter are 3.40 mm and 2.33 mm, respectively. The ablation catheter is placed at the same tissue model as that constructed in Section 2.2.  
**Author Contributions:** Conceptualization, S.Y. and X.W.; methodology, K.G. and S.Y.; software, K.G.; validation, K.G. and Y.W.; formal analysis, K.G.; investigation, K.G. and Y.W.; resources, K.G. and Y.W.; data curation,X.W.; writing--original draft preparation, K.G.; writing--review and editing, S.Y. and X.W.; visualization, K.G.; supervision, S.Y. and X.W.; project administration, X.W.; funding acquisition, X.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China, grant number 61801123 and 1171009; the China Postdoctoral Science Foundation Funded Project, grant number 2019M651367; the Shanghai Municipal Science and Technology Major Project, grant number 2017 SHZDZX01 and 16441907900; and the Shanghai Municipal Science and Economic and Information Commission Project, grant number GYQJ-2018-20-5. The authors are solely responsible for the content and writing of the paper.  
The authors declare no conflict of interest.
## 3 General Strategies for Energy Efficient BSN Hardware
### Supply Voltage Management
For instance, the TI MSP430 and other similar microcontrollers (MCUs), have on-board clock generation hardware that allows the MCU to programmatically change the operating clock frequency. This is accomplished in the MSP430 through the use of a Digitally Controlled Oscillator (DCO) that may be calibrated using a low frequency (32 kHz) watch crystal as a reference. Frequency agility is accomplished by switching different programmable constants into two clock control registers. The actual change in clock frequency occurs within approximately 10 \(\upmu\)s. Furthermore, this microcontroller operates over a wide range of voltages. The clock oscillator may be varied over a 16 to 1 range and the supply voltage over a 2 to 1 range. Within this envelope, a combination of processing rate and power requirements exist, making COTS embedded processors of this type ideal candidates for inclusion in a DVS scheme for BSNs. Figure 5 shows potential DVS operating points measured for the MSP430F2131 processor as explored in [9]. For longer lifetime BSN applications where the savings from Figure 5 are still inadequate, a similar DVS scheme can apply to a custom chip. Figure 6 compares a custom MCU design [7] to the MSP430. The custom design offers a 100\(\times\) improvement in energy per instruction. However, this does not come free of tradeoffs. In this case, the custom built MCU does not have its own clock generation hardware, and frequency agility is not as straight forward since there is only one, single frequency main clock. Though this custom designed MCU also operates over a wide range of voltages and is capable of supporting DVS, additional design effort is required to build in these operating modes. What's more, custom designed hardware does not enjoy the complete suite of mature and compatible peripherals as COTS components, which degrades custom hardware's flexibility. Figure 5: Operating points for a COTS MCU [9].
# Study on Dynamic Strain Distribution in Rock Broken by Abrasive Slurry Jet
## 6 Conclusions  
With a new approach, the non-contact strain measurement system, this paper carried out experiments to measure the dynamic rock strain to reveal the stress and strain field in rock under ASJ impacting. Theoretical analysis of stress propagation in rock had a similar result to the experiments, which can prove the correctness of the new approach. The paper reveals the dynamic strain distribution in rock broken by ASJ and provides a new idea and method to study the rock failure mechanics under ASJ impacting. The main conclusions are as follows.  
1. The non-contact strain measurement system has great potential in strain measurement with advantages of the simple measuring process and the full-field strain measurement. However, it has shortcoming that its accuracy will decrease when it is used to measure strains less than 10 \(\upmu\)m.
2. Dynamic strain will propagate in the form of spherical waves within the rock impacted by ASJ, the maximum value of those waves is proportional to the jet pressure and inversely proportional to the square of the propagation distance.
3. In the process of ASJ impacting rock, strain will increase from zero to a maximum value in milliseconds.
4. Dynamic strain in rock fluctuates due to the release of internal stress caused by the rock crushing, which can reflect that rock will be broken by ASJ in the form of stepped-failure.  
Conceptualization, C.G.; Data curation, F.W.; Formal analysis, F.W.; Funding acquisition, C.G.; Investigation, Z.M.; Methodology, C.G.; Resources, W.H.; Software, W.H.; Writing--original draft, F.W.; Writing--review & editing, C.G.  
This work is supported by the Fundamental Research Funds for the Central Universities (2017 XKZD02).  
The authors declare no conflicts of interest.
## 4 Experimental Setup
### Evaluation Protocol  
We considered two figures of merit to measure the performance of the proposal. For their definition, let us assume a set \(\mathcal{S}=\{(x_{i},\mathbf{z}_{i}):x_{i}\in\mathcal{X},\ \mathbf{z}_{i}\in \mathcal{Z}\}_{i=1}^{|\mathcal{S}|}\) of test data drawn from the same distribution as the train data \(\mathcal{T}\) but disjoint from it. Considering that, the two metrics are described below:  
* **Symbol Error Rate** (Sym-ER): computed as the average number of elementary editing operations (insertions, deletions, or substitutions) necessary to match the sequence predicted by the model with the ground truth sequence and normalized by the length of the latter. Mathematically, this is represented as follows: \[\text{Sym-ER }(\%)=\frac{\sum_{i=1}^{|\mathcal{S}|}\text{ED}\Big{(}\mathbf{z}_{i },\ \hat{h}(x_{i})\Big{)}}{\sum_{i=1}^{|\mathcal{S}|}|\mathbf{z}_{i}|}\] (2) where \(\text{ED}(\cdot,\cdot)\) represents the string edit distance [40].
* **Sequence Error Rate** (Seq-ER): ratio of incorrectly predicted sequences, i.e., the percentage of sequences of recognized symbols that have at least one error. Mathematically, this may be represented as follows: \[\text{Seq-ER }(\%)=\frac{\left|\left\{x\in\mathcal{S}:h(x)\
eq\hat{h}(x) \right\}\right|}{|\mathcal{S}|}\] (3)  
It must be noted that, while these figures of merit may be applied to any predicted sequence disregarding the label space considered, in the particular case of the \(\Sigma_{T}^{*}\) space of combined shape and height classes, some additional insights may be obtained by further analyzing the results. As commented upon in Section 3.1, each symbol in the \(\Sigma_{T}\) vocabulary is a 2-tuple \(\langle s_{i},h_{i}\rangle:s_{i}\in\Sigma_{S},\ h_{i}\in\Sigma_{H}\). Thus, for a given sequence \(\mathbf{z}_{i}=(z_{i1},z_{2},\dots,z_{iN})\in\Sigma_{T}^{*}\), we may decouple each symbol into its individual shape \(s_{i}\in\Sigma_{S}\) and height \(h_{i}\in\Sigma_{H}\) components and assess the model in terms of the sole prediction of those individual elements while trained for the combined prediction.
## 3 Results and Discussion
### Optical Characterization
For the latter samples, the absorption spectrum was indirectly evaluated from the reflection spectrum, assuming negligible transmittance through the Au-coated Si substrate within the employed electromagnetic spectral range. Extrapolations of the linear fitting domains within absorption spectra to intercept the energy axis allowed for assessment of the optical band gap energy values, with the estimated accuracy in the range of \(\pm\)0.01–0.03 eV. where \(\alpha\) is the absorption coefficient, \(\hbar\omega\) is the energy of the incident photons, and C is a constant. For all samples, \(\alpha\) could thus be directly evaluated by its dependence on the optical absorbance (A) and the film thickness (h):  
\[\alpha=\frac{\mathrm{A}}{\mathrm{h}} \tag{7}\]  
The calculated \(\mathrm{E_{g}}\) values of the CdTe films prepared by VTE, RF-MS and ECD are provided in Table 3, and were computed with a precision of \(\pm\)0.01-0.03 eV, as similarly estimated from the errors associated with the fits of the linear domains within absorption spectra, which is a typical accuracy demonstrated for [PERSON]'s method [44]. Notably, a good agreement with the theoretical optical band gap value of CdTe films, reported to be in the range of 1.40-1.44 eV [45], can be clearly noticed. Small variations of the band gap value with respect to the ideal bulk value of the CdTe (1.51 eV) can be explained by the contamination levels associated with each deposition method, which contribute to the formation of defects through doping within the crystalline structure and have a major impact on the electrical properties of the films, especially in terms of reducing the overall resistivity of the films and consequently their band gap energy. Nevertheless, the increasing tendency of the band gap can be observed, with the smallest value obtained for the evaporated CdTe film (1.43 eV) and the largest for the ECD-prepared CdTe film (1.48 eV). This result can be corroborated with the decreasing tendency of the crystallite size, from 81 nm for the VTE-deposited CdTe film to 21 nm for the electrodeposited CdTe film, respectively (see Table 3). This behavior can be explained in terms of quantum confinement effects, as a reduction in the crystallite size of the material can cause discretization of the energy levels, changing the density of states within the energetic band structure. As a consequence, the energy difference between the energy bands is increased, as is the band gap energy value. The largest band gap value of 1.48 eV, approaching the ideal value of the bulk CdTe material (1.51 eV), was obtained for the ECD-prepared CdTe thin film, additionally confirming that the latter \"bottom-up\" approach may represent a suitable low-cost and low-temperature synthesis method to produce good quality CdTe layers capable of penetrating the Cu NWs array under optimized processing conditions, thus allowing the fabrication of robust CdTe/Cu NWs interfaces for \"substrate\"-type photovoltaic structures based on semiconducting A\({}^{\mathrm{II}}\)-\(\mathrm{B}\)VI heterojunctions.
## 3 Numerical Simulations
### Numerical Method
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{3}{*}{**Mesh (Cells)**} & \multicolumn{8}{c}{**Angle of Attack (\({}^{\circ}\)) and Experiment Data of \(C_{d}\) and \(C_{l}\)**} \\ \cline{2-13}  & \multicolumn{4}{c}{**(C\({}_{d}\),\(C_{l}\)and Error Ratios)**} \\ \cline{2-13}  & \multicolumn{2}{c}{**0\({}^{\circ}\)**} & \multicolumn{2}{c}{**2\({}^{\circ}\)**} & \multicolumn{2}{c}{**4\({}^{\circ}\)**} & \multicolumn{2}{c}{**6\({}^{\circ}\)**} & \multicolumn{2}{c}{**8\({}^{\circ}\)**} & \multicolumn{2}{c}{**10\({}^{\circ}\)**} \\ \cline{2-13}  & **0.00809** & **0** & **0.00816** & **0.2125** & **0.00823** & **0.4316** & **0.00885** & **0.6546** & **0.0105** & **0.8873** & **0.01201** & **1.0707** \\ \hline \multirow{3}{*}{400,000} & 0.00792 & Approx. 0 & 0.00799 & 0.22065 & 0.00895 & 0.43996 & 0.01009 & 0.64220 & 0.01191 & 0.84574 & 0.01448 & 1.04173 \\ \cline{2-13}  & 2.16\% & / & 1.99\% & 3.83\% & 8.80\% & 1.94\% & 14.01\% & 1.89\% & 13.38\% & 4.68\% & 20.52\% & 2.71\% \\ \hline \multirow{3}{*}{590,000} & 0.00802 & Approx. 0 & 0.00822 & 0.21824 & 0.00886 & 0.43542 & 0.00997 & 0.64960 & 0.01165 & 0.85820 & 0.01403 & 1.05745 \\ \cline{2-13}  & 0.91\% & / & 0.79\% & 2.70\% & 7.68\% & 0.89\% & 12.66\% & 0.76\% & 10.95\% & 3.28\% & 16.80\% & 1.24\% \\ \hline \multirow{3}{*}{840,000} & 0.00801 & Approx. 0 & 0.00823 & 0.21810 & 0.00887 & 0.43504 & 0.01003 & 0.64861 & 0.01180 & 0.85991 & 0.01436 & 1.05249 \\ \cline{2-13}  & 0.96\% & / & 0.82\% & 2.64\% & 7.81\% & 0.80\% & 13.29\% & 0.91\% & 12.40\% & 3.54\% & 19.60\% & 1.70\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Grid independency study of three levels of different mesh with error ratios at a far-field distance of 16 m.  
The simulation parameters of convergence numerical results are as shown in Table 4. The turbulence model adopts SST k-omega and the turbulence specification method of the INLET boundary selects the intensity and viscosity ratios; the related values are 0.052% and 0.009. The turbulence model applies Spalart-Allmaras, the turbulence specification method of the INLET boundary selects the turbulent viscosity ratio, and the value is 3.
## 3 Theoretical Analysis and Proof
### Model Simplification  
In order to facilitate the subsequent analysis of the model, we focus on deriving a simplified neural dynamics model.  
**Theorem 1**.: _EAEND model (10) can be rewritten as_  
\[\varepsilon_{k+1}=(1.5-\mathrm{Y})\varepsilon_{k}-\varepsilon_{k-1}+0.5 \varepsilon_{k-2}-\Gamma\sum_{i=0}^{k}\varepsilon_{i}+\mathbf{O}(\sigma^{3}),\]  
_where \(\mathbf{O}(\sigma^{3})\) denotes the vector of truncation error \(O(\sigma^{3})\)._  
Proof.: First, by applying a [PERSON] numerical difference formula [48], we have  
\[\varepsilon_{k}=\frac{2\varepsilon_{k+1}-3\varepsilon_{k}+2\varepsilon_{k-1}- \varepsilon_{k-2}}{2\sigma}+\mathbf{O}(\sigma^{2}). \tag{11}\]  
Subsitituting the equation above into (6), one can further obtain:  
\[\frac{2\varepsilon_{k+1}-3\varepsilon_{k}+2\varepsilon_{k-1}-\varepsilon_{k- 2}}{2\sigma}+\mathbf{O}(\sigma^{2})=-\varphi\varepsilon_{k}-\varpi\sum_{i=0 }^{k}\varepsilon_{i}. \tag{12}\]  
Furthermore, (12) can be simplified as:  
\[\varepsilon_{k+1}-1.5\varepsilon_{k}+\varepsilon_{k-1}-0.5\varepsilon_{k-2}= -\mathrm{Y}\varepsilon_{k}-\Gamma\sum_{i=0}^{k}\varepsilon_{i}+\sigma \mathbf{O}(\sigma^{2}). \tag{13}\]  
Then, by simplifying the above formula, the equation can eventually be written as  
\[\varepsilon_{k+1}=(1.5-\mathrm{Y})\varepsilon_{k}-\varepsilon_{k-1}+0.5 \varepsilon_{k-2}-\Gamma\sum_{i=0}^{k}\varepsilon_{i}+\mathbf{O}(\sigma^{3}). \tag{14}\]  
The proof is complete.
# [PERSON] on Korean Block Ciphers
## 3 Proposed Method
### Cham
#### 3.2.2. Round Function  
In the second line of the round function from Equation (10), among the input \(X_{i}\) values, the values of \(X_{i}[1]\), \(X_{i}[2]\), and \(X_{i}[3]\) are used as new values of \(X_{i+1}\), but \(X_{i}[0]\) is not used after calculation. Therefore, the value of \(X_{i}[0]\) in the second line can be used by computing \(X_{i+1}[3]\) to save the qubits for a new value.  
In the second line of the round function, the constant \(i\) is XOR-ed to \(X_{i}[0]\). This is done by performing the X gate on the qubit according to the position where the bit of \(i\) is 1 in \(X_{i}[0]\). For example, if \(i=3=(1,1,0,0,\ldots,0)\), X gate is performed on the qubits \(X_{3}[0][0]\) and \(X_{3}[0][1]\).  
The round function of CHAM is expressed in Equations (10) and (11). The detailed circuit design process is shown in Algorithm 9, and the overall quantum circuit for CHAM-64/128 is shown in Figure 12.  
```
0:\(RK,X_{i}\), Round \(i\)
0:\(X_{i+1}\)
1:if\(i\) is odd then
2:\(X_{i}[1]\gets X_{i}[1]\lll 1\)
3:\(X_{i}[1]\leftarrow\)CNOT(\(RK[i\bmod 2m],X_{i}[1]\))
4:\(X_{i}[0]\leftarrow\)X gate(\(i,X_{i}[0]\))
5:\(X_{i}[0]\leftarrow\)ADD(\(X_{i}[1],X_{i}[0]\))
6:\(X_{i}[1]\leftarrow\)CNOT(\(RK[i\bmod 2m],X_{i}[1]\)) (reverse)
7:\(X_{i}[1]\gets X_{i}[1]\gg 1\) (reverse)
8:\(X_{i+1}[3]\gets X_{i}[0]\lll 8\)
9:\(X_{i+1}[j]\gets X_{i}[j+1],\quad j=0,1,2\)
10:else
11:\(X_{i}[1]\gets X_{i}[1]\lll 8\)
12:\(X_{i}[1]\leftarrow\)CNOT(\(RK[i\bmod 2m],X_{i}[1]\))
13:\(X_{i}[0]\leftarrow\)X gate(\(i,X_{i}[0]\))
14:\(X_{i}[0]\leftarrow\)ADD(\(X_{i}[1],X_{i}[0]\))
15:\(X_{i}[1]\leftarrow\)CNOT(\(RK[i\bmod 2m],X_{i}[1]\)) (reverse)
16:\(X_{i}[1]\gets X_{i}[1]\gg 8\) (reverse)
17:\(X_{i+1}[3]\gets X_{i}[0]\lll 1\)
18:\(X_{i+1}[j]\gets X_{i}[j+1],\quad j=0,1,2\)
19:endif
20:return\(X_{i+1}=\{X_{i+1}[0],X_{i+1}[1],X_{i+1}[2],X_{i+1}[3]\}\)
```  
**Algorithm 9** Round function of CHAM.
## 3 Results  
### QSM and F-Scores for Patients with Early PD and HCs  
Figure 2 shows representative QSM images of HC and early PD. By visual inspection, QSM images of early PD shows brighter signals in basal ganglia areas than HC, demonstrating iron accumulation in early PD.  
Mean QSM values for the seven ROIs in patients with PD and HCs are shown in Table 2. The mean QSM values for early PD patients were approximately 10% higher (range, 0.070-0.142 ppm) than the values for HCs (range, 0.059-0.134 ppm). In comparisons of F-scores for patients with PD and HCs, GP demonstrated the highest F-score, and PUT demonstrated the lowest, meaning that the largest difference between patients with PD and HCs was in the GP.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline \multirow{2}{*}{**ROI c**} & \multicolumn{2}{c}{**Mean QSM k Value \(\pm\) SD, ppm**} & \multirow{2}{*}{**F-score l**} \\ \cline{2-2} \cline{4-4}  & **Patients with Early PD (_n = 24_)** & & & \\ \hline GP d  & 0.142 \(\pm\) 0.034 & 0.134 \(\pm\) 0.038 & 14.634 \\ DN e  & 0.101 \(\pm\) 0.031 & 0.095 \(\pm\) 0.026 & 11.461 \\ SNr f  & 0.131 \(\pm\) 0.044 & 0.115 \(\pm\) 0.044 & 11.261 \\ SNc g & 0.130 \(\pm\) 0.043 & 0.125 \(\pm\) 0.041 & 9.349 \\ RN h  & 0.102 \(\pm\) 0.032 & 0.097 \(\pm\) 0.034 & 9.251 \\ CN i  & 0.070 \(\pm\) 0.025 & 0.059 \(\pm\) 0.021 & 7.497 \\ PUT j & 0.109 \(\pm\) 0.049 & 0.094 \(\pm\) 0.025 & 6.910 \\ \hline \hline \end{tabular}
\end{table}
Table 2: QSM Values and F-scores for Patients with Early PD a and HCs b.  
Figure 2: Representative quantitative susceptibly mapping (QSM) images of healthy control and patient with the early stage of [PERSON]’s disease. The patient shows brighter signals in basal ganglia areas than the healthy control, demonstrating iron accumulation in the early stage of [PERSON]’s disease.
# Interference Alignment in Multi-Hop Cognitive Radio Networks under Interference Leakage
## 4 Ergodic Capacity
### Ergodic Capacity For Perfect IA  
Using (11), after replacing \(\gamma_{th}\) with \(\gamma\), the cdf of the \(i\)th hop can be expressed as:  
\[F_{\Gamma_{R_{i}\to R_{i+1}}}(\gamma)=1-\exp\bigg{(}\frac{-\gamma}{\tilde{ \gamma}_{R_{i}\to R_{i+1}}}\bigg{)}. \tag{23}\]  
By substituting (23) into (22), \(\mathbb{E}[\Gamma_{R_{i}\to R_{i+1}}]\) can be found as \(\tilde{\gamma}_{R_{i}\to R_{i+1}}\). Hence, \(\mathcal{C}^{\text{up}}_{erg}\) can be expressed as:  
\[\mathcal{C}^{\text{up}}_{erg,P}\leq\frac{1}{K}\log_{2}\big{(}1+\min\big{(} \tilde{\gamma}_{S\to R_{1}},\tilde{\gamma}_{R_{1}\to R_{2}},\ldots,\tilde{ \gamma}_{R_{K-1}\to D}\big{)}\big{)}. \tag{24}\]  
Note that \(\mathbb{E}[\Gamma_{S\to R_{1}}]\) and \(\mathbb{E}[\Gamma_{R_{K-1}\to D}]\) can be found similarly.
## 3 Results and Discussion
### Verification of Predictive Models  
After calculating the new formulation for the mixture of the three proteins, the predicted concentration (21.21% pea, 32.78% lentils, and 46.01% fava beans) was tested in the laboratory, and the analyses were repeated for comparison with the values predicted by the program (n = 3). The (experimental) values obtained in the laboratory are shown in Table 6.  
It can be noted that the values obtained are close to those predicted by the mathematical optimization model, with the exception of EAI, and therefor  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Dependent Variable Response** & **Goal** & **Lower Limit** & **Upper Limit** & **Predicted Value** & **Experimental Value** & **Relative Error (\%)** \\ \hline EAI (m\({}^{2}\)/g) & Maximize & 16.00 & 32.00 & 16.09 & 23.75 \(\pm\) 1.18 & 41.0 \\ Zeta potential (mV) & Minimize & \(-\)28.00 & \(-\)31.00 & \(-\)30.9 & \(-\)29.16 \(\pm\) 1.46 & 0.90 \\ Coalescence stability (\%) & Minimize & 4.0 & 7.0 & 3.56 & 2.53 \(\pm\) 0.69 & 0.91 \\ D\({}_{4,3}\) (nm) & Minimize & 400.00 & 420.00 & 421.28 & 436.16 \(\pm\) 16.06 & 3.56 \\ HCT (min) & Maximize & 18.00 & 26.00 & 24.69 & 22.40 \(\pm\) 2.54 & 6.73 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Predicted and experimental values for optimization parameters of the protein mixture.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sample 1** & **Sample 2** & **Correlation** & **\(p\)-Value** \\ \hline EAI (m\({}^{2}\)/g) & Centrifugal stability (\%) & 0.759 & 0.024 \\ EAI (m\({}^{2}\)/g) & IPD & 0.695 & 0.002 \\ HCT (min) & Centrifugal stability (\%) & 0.725 & 0.008 \\ Coalescence stability (\%) & Flocculation stability (\%) & 0.765 & 0.000 \\ Coalescence stability (\%) & Flocculation index (\%) & 0.845 & 0.000 \\ Flocculation stability (\%) & Flocculation index (\%) & 0.725 & 0.000 \\ Flocculation stability (\%) & D\({}_{4,3}\) (nm) & 0.758 & 0.008 \\ Zeta Potential (mV) & ESI (min) & 0.657 & 0.005 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Pearson correlation analysis between the tested variables that were significant.  
considered valid for the formulation. Through the desirability function, it is possible to optimize each parameter independently, as shown in Table 3, to modulate, maximize, or minimize each response variable, in addition to optimizing multiple responses to obtain the ideal formulation.  
The predicted value and the experimental value are close in most analyses, with a relative error of less than 5%. It can be concluded that the mathematical optimization model, with the exception of EAI, is considered valid for the formulation. The equation-predicted formulation showed better results for the tested dependent variables than the mixture formulations and even better than the isolated protein.