esa-sceva/satcom-chunk-collection huggingface dataset:
## 5 Evaluation of Scale Effects in the Validation of GOCI-Derived SSC
### Limitations of Traditional Validation Methods  
For instance, as shown in Figure 8, the coefficient of variation (CV) of SSC within a \(3\times 3\) window for the 500 m GOCI image is 0.0528, whereas the corresponding CV calculated from a 50 \(\times\) 50 array of 30 m HJ CCD SSC pixels (covering the same area) is  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Sensor**} & \multicolumn{2}{c}{**Spatial**} & \multicolumn{3}{c}{**CV**} \\  & **Resolution (m)** & **Minimum** & **Maximum** & **Mean** & **Standard Deviation** \\ \hline HJ CCD & 500 & 0.0043 & 0.3500 & 0.0638 & 0.0534 \\ GOCI & 500 & 0.0025 & 0.3499 & 0.0564 & 0.0441 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Spatial variability of SSC retrieval results from HJ CCD and GOCI imagery.  
Figure 7: Frequency distribution of the coefficient of variation in a 3 \(\times\) 3 window for GOCI and HJ CCD retrieval results.  
0.0944. This indicates that the higher spatial resolution of the HJ CCD more accurately captures the true spatial variability.  
Figure 9 further illustrates the spatial distribution and differences in CV between the 500 m GOCI and 30 m HJ CCD images, after resampling the GOCI CV image to 30 m resolution for direct comparison. As detailed in Table 3, the average CV in the 3 \(\times\) 3 window for the 30 m HJ CCD data is nearly twice that of the GOCI data, highlighting significant differences in spatial variability.  
Table 4 presents the validation results of SSC at an in situ station for both HJ CCD and GOCI images. Despite the superior atmospheric correction and higher R\({}^{2}\) of the GOCI  
Figure 8: Distribution of SSC in neighboring pixels around the measured station: (a) GOCI SSC retrieval results in a 3 \(\times\) 3 window (CV = 0.0528); (b) HJ CCD SSC retrieval results in a 50 \(\times\) 50 window within the 3 \(\times\) 3 GOCI pixel area (CV = 0.0944).  
\begin{table}
\begin{tabular}{c c c} \hline
**CV** & **3 \(\times\) 3 Window Mean** & **Standard Deviation** \\ \hline
30 m HJ & 0.1078 & 0.0355 \\
500 m GOCI & 0.0564 & 0.0441 \\ HJ-GOCI & 0.0514 & \(-\)0.0086 \\ \hline \end{tabular}
\end{table}
Table 3: Statistical values of the coefficient of variation in a 3 \(\times\) 3 window for GOCI and HJ CCD.  
Figure 9: Differences in the coefficient of variation between 500 m GOCI and 30 m HJ CCD in a 3 \(\times\) 3 window.  
SSC inversion model, the validation accuracy of the GOCI SSC is lower than that of the HJ CCD data, likely due in part to scale effects. The 30 m resolution HJ CCD data are less affected by scale effects than the 500 m GOCI data. Table 5 compares SSC from different window sizes of the HJ CCD image with in situ measurements at station S02, showing that the average SSC derived from a 17 \(\times\) 17 window is closer to the measured value than that from a 3 \(\times\) 3 window. However, due to the limited number of validation points, further analysis with a larger dataset is required.
## 4 Methodology
### 8-Parameter Transformation
#### 4.4.1 Transformation Parameters
In this case, order of the unknown parameters is \(t_{x}\), \(t_{y}\), \(t_{z}\), \(\alpha_{x}\), \(\alpha_{y}\), \(\alpha_{z}\), \(\mu_{xy}\), and \(\mu_{z}\), so coefficients \(a_{ij}\) in the design matrix have the following values [8]:\[a_{14}^{i} =-\mu_{xy}^{0}r_{13}^{0}Y_{i}^{i}+\mu_{z}^{0}r_{12}^{0}Z_{i}^{i} \qquad a_{17}^{i} =r_{11}^{0}X_{i}^{i}+r_{12}^{0}Y_{i}^{i}\] \[a_{24}^{i} =-\mu_{xy}^{0}r_{23}^{0}Y_{i}^{i}+\mu_{z}^{0}r_{22}^{0}Z_{i}^{i} \qquad a_{27}^{i} =r_{21}^{0}X_{i}^{i}+r_{22}^{0}Y_{i}^{i}\] \[a_{34}^{i} =-\mu_{xy}^{0}r_{33}^{0}Y_{i}^{i}+\mu_{z}^{0}r_{32}^{0}Z_{i}^{i} \qquad a_{37}^{i} =r_{31}^{0}X_{i}^{i}+r_{32}^{0}Y_{i}^{i}\] \[a_{15}^{i} =-\cos\alpha_{Z}^{0}(\mu_{xy}^{0}r_{31}^{0}X_{i}^{i}+\mu_{xy}^{0} r_{32}^{0}Y_{i}^{i}+\mu_{z}^{0}r_{33}^{0}Z_{i}^{i}) \qquad a_{18}^{i} =r_{13}^{0}Z_{i}^{i}\] \[a_{25}^{i} =\sin\alpha_{Z}^{0}(\mu_{xy}^{0}r_{31}^{0}X_{i}^{i}+\mu_{xy}^{0} r_{32}^{0}Y_{i}^{i}+\mu_{z}^{0}r_{33}^{0}Z_{i}^{i}) \qquad a_{28}^{i} =r_{23}^{0}Z_{i}^{i}\] \[a_{35}^{i} =\mu_{xy}^{0}\cos\alpha_{Y}^{0}X_{i}^{i}+\mu_{xy}^{0}r_{31}^{0} \sin\alpha_{X}^{0}Y_{i}^{i}-\mu_{z}^{0}r_{31}^{0}\cos\alpha_{X}^{0}Z_{i}^{i} \qquad a_{38}^{i} =r_{33}^{0}Z_{i}^{i}\] \[a_{16}^{i} =\mu_{xy}^{0}r_{21}^{0}X_{i}^{i}+\mu_{xy}^{0}r_{22}^{0}Y_{i}^{i}+ \mu_{z}^{0}r_{23}^{0}Z_{i}^{i}\] \[a_{26}^{i} =-\mu_{xy}^{0}r_{11}^{0}X_{i}^{i}-\mu_{xy}^{0}r_{12}^{0}Y_{i}^{i} -\mu_{z}^{0}r_{13}^{0}Z_{i}^{i}\] \[a_{36}^{i} =0\]
## 4 Discussion
### Challenges and Limitations
#### 4.4.1 Data Reliability  
Our simulation assumes that returns are correctly identified and recorded by the retailer, and that the recycler accurately records output. In practice, human errors or intentional misreporting could occur. Blockchain can ensure data is not changed after the fact, but it cannot guarantee the data was true when entered (often termed the \"garbage in, garbage out\" problem). Mitigating this might involve IoT integration, e.g., scanning returned items with RFID to automatically log their identity, using weight sensors to log recycled material quantities, etc. These would add to the system's complexity but increase trust in the on-chain data.
# Combining the Transformer and Convolution for Effective Brain Tumor Classification Using MRI Images
## 3 Research Methodology
### Datasets Explanation
#### 3.5.1 BraTS 2018 Dataset  
To assess the model's effectiveness, we choose the BraTS 2018 dataset, which is a commonly used benchmark dataset. This dataset consists of 1425 MRI images, of which 998 MRI images are used for training, 285 MRI images for validation, and 142 MRI images for testing, and included total MRI images of four modalities, those being 356 T1, 355 T2, 356 T1 CE, and 358 FLAIR. Sample images of the BraTS 2018 dataset are shown as images in Figure 8.  
Figure 8: Sample images of the BraTS 2018 dataset.
# Freeform Wide Field-of-View Spaceborne Imaging Telescope: From Design to Demonstrator
## 4 Discussion and Future Perspectives
### Long-Term Perspectives towards Future Space Missions  
As a possible application, the pushbroom telescope might be complemented with a spectrometer unit, for example, for climate change and/or pollution monitoring [14]. Recently, the need for compact spectrometers for enhanced climate and pollution monitoring has been put forward, as highlighted by, for example, the CHAPS instrument that targets the monitoring of local pollution in urban areas [21]. Possible integration with an 1100-1700 nm spectrometer might enable greenhouse gas monitoring [14; 15; 16; 17]. Also, as our telescope achieves an RMS spot diameter of the order of 30 \(\upmu\)m or less at the detector plane, this telescope would be compatible with other spectrometers operating within wavelength ranges exceeding 1700 nm, while keeping a diffraction-limited design for the telescope. In particular, the thermal infrared region (8-14 \(\upmu\)m) could be of interest for the monitoring of trace gases in the atmosphere, while highlighting the direct link between greenhouse gases and the Earth's outgoing longwave radiation.  
From a long-term perspective, we foresee launching the proposed telescope on board a small satellite at a Low-Earth-Orbit altitude of 700 km. The satellite could, for example, be a CubeSat companion to the Earth Climate Observatory (ECO) pursuing improved radiation monitoring at the top-of-atmosphere [22; 23]; while, alternatively, a SmallSat platform (such as a PROBA satellite) can be considered. The use of CubeSat or SmallSat satellite platforms holds promise for a faster development time at a reduced cost, implying that, for the same cost as a large space mission, multiple copies of this satellite, i.e., a constellation of satellites, can be realized leading to improved monitoring of our planet.
# Jamming Analysis between Non-Cooperative Mega-Constellations Based on Satellite Network Capacity
## 2 System Model  
In this section, the main jamming region is introduced. Then, we discuss the jamming scenario and propagation model. Finally, the transmission rate is calculated. Table 1 gives the summary of the mathematical notations.  
Figure 1: Scene diagram of jamming between mega-constellations \(\Psi_{A}\) and \(\Psi_{B}\).
## 2 Materials and Methods
### Experimental Set-Up and Testing Procedures
#### 2.6.1 Testing Procedure for the Transmitter Block  
In this section, we detail the procedure used to verify the proper functioning of the transmitter block in the system, as illustrated in Figure 28. This subsystem is situated in the internal interface PCB.  
The testing process involved generating a 4 MHz sine signal using the FPGA, as shown in Figure 29. This signal was transmitted via an LED to the Thorlabs PDA10A2 PD [28], which spans a spectral range from 200 nm to 1100 nm and possesses a bandwidth of 150 MHz. The PD was connected to a Tektronix 2012 oscilloscope to observe the received signal, as depicted in Figure 28.  
Figure 28: Scheme of the testing procedure for the transmitter block.  
Figure 27: Set-up carried out to test every module of the system.  
These tests were conducted using both the visible LED and the IR LED, as the system's uplinks and downlinks employ visible and infrared channels.  
Figure 29a illustrates the set-up for testing the transmitter block, using the LUW CN7N-KYLX-EMKM OSRAM LED, which was bought on [[https://eu.mouser.com/](https://eu.mouser.com/)]([https://eu.mouser.com/](https://eu.mouser.com/)) (accessed on 5 September 2024). The distance between the visible LED and the Thorlabs PDA10A2 PD was 7 cm. The Tektronix 2012 oscilloscope screen in Figure 29a shows the signal received by the PD, which measured 4 MHz--the same frequency as the sine signal transmitted through the transmitter block.  
Likewise, Figure 29b depicts the test set-up of the transmitter block using the HSDL-4250 Lite-On IR LED. The distance between the infrared LED and the Thorlabs PDA10A2 PD was 6 cm. The oscilloscope screen shown in Figure 29b indicates that the PD-received signal frequency was 4 MHz, identical to the frequency of the sinusoidal signal transmitted through the transmitter block.
# IMU-Aided High-Frequency Lidar Odometry for Autonomous Driving
## 3 The Proposed Approach
### Pre-Processing Step 2: Intra-Frame Correction
#### 3.4.2 Rectification by Previous Registration Results  
This approach assumes that the motion of the vehicle is constant during \(\left[t_{\rm k-2}^{\rm L},t_{\rm k}^{\rm L}\right]\). Thus, it can assume that the relative transformation \(\triangle\,T_{\rm k-1,k-2}^{\rm B}\) between frame \(\mathbf{f}_{\rm k-1}^{\rm L}\) and \(f_{\rm k-2}^{\rm L}\) is the same as the relative transformation \(\triangle\,T_{\rm k,k-1}^{\rm B}\) between frame \(\mathbf{f}_{\rm k}^{\rm L}\) and \(\mathbf{f}_{\rm k-1}^{\rm L}\). Therefore, we can linearly interpolate the relative transformation \(exp\left(\triangle\,\xi_{\rm k-1,k-2}^{\wedge}\right)\) to rectify the raw distorted points in frame \(\mathbf{f}_{\rm k}^{\rm L}\) as:  
\[\mathbf{\hat{X}}_{\rm(i,b,k)}^{\rm B}=\exp\left(\triangle\,\xi_{\rm k-1,k-2}\cdot \frac{i}{S_{b}}\right)^{\wedge}\cdot\mathbf{X}_{\rm(i,b,k-j)}^{\rm B}\,. \tag{14}\]
# S seaweed Polysaccharides in Agriculture: A Next Step towards Sustainability
## 2 Seaweed Polysaccharides
### Agar  
Agar (Figure 2) is a very important polysaccharide industrially extracted from the red seaweeds genus _Gracilaria_ and _Gelidium_, from the phylum Rhodophyta [27; 28; 29]. Generally, the industrial extraction method is based on a thermal treatment of the seaweed biomass in an aqueous solution (between 2-4 h at 105-110 \({}^{\circ}\)C) for immediate filtration while the extract is hot (as the agar gels very quickly at 50 \({}^{\circ}\)C). After the filtration process, the extract either gels or is maintained in a viscous solution due to the amount of agar present in the solution. However, the gel itself is normally yellowish or brown in color because some of its constituents are degraded (proteins, monosaccharides). Therefore, the freezing/thawing technique is used to obtain a concentrated agar with a clear color, as this technique allows the agar to be washed with water, avoiding pre-treatment to reduce impurities during extraction. Finally, the agar obtained is dried in an oven with air circulation and then milled for later application in industry [23; 30; 31].  
Figure 1: Chemical structure of alginic acid [14] Legend: G—gluturonic acid; M—mannuronic acid.  
It is a gel-forming polysaccharide consisting of 70% agarose and 30% agaropectin molecules, composed of residues of (1-4)-3, 6-anhydro-L-galactose and \(\beta\) 9 (1-3)-d-galactose [27]. To date, there is no evidence that its molecular weight has any significance for food safety, and therefore, it is considered safe regardless of its molecular weight [28]. However, the quality of the agar differs greatly between species belonging to these two orders. For example, agar extracted from _Gelidium convenum_ (Gelidiales) is considered more suitable for pharmaceutical applications, [29]. On the other hand, agar extracted from _Gracilaria gracilis_ (Gracilariales) is normally used, almost exclusively, in the food industry. However, normally, this agar has one more step in the industrial extraction system, which consists of an alkaline pre-treatment with sodium hydroxide, to increase the quality of the rheological properties of the agar obtained [30].  
Agar is considered safe for human consumption by regulatory authorities in the United States of America (FDA) and the European Union (EFSA). Despite the inclusion of agar (E406) in the list of approved food additives, its application in food products is regulated and limited. It is estimated that approximately 90% of commercialized agar is destined for the food industry [30].
## 3 Results
### Optical Emission Spectrum  
Optical emission spectrometry (OES) is an important technique used in plasma diagnostics. The distribution and internal states of various species within the plasma can be determined by observing the plasma-emitted light. Figure 1b shows the compact air-cooled coaxial DBD plasma generated at an applied power of 60 W and an air flow rate of 20 L min-1. A collimating lens was mounted under the emission hole of the compact  
Figure 2: Voltage and current waveforms according to the applied power. Power consumption was calculated from the values of V\({}_{\mathrm{rms}}\) and A\({}_{\mathrm{rms}}\). (**a**) 40 W, (**b**) 50 W, (**c**) 60 W, (**d**) 70 W, (**e**) 80 W.  
air-cooled coaxial DBD. Emission analyses were performed at the center of the discharge gap. The excited nitrogen and oxygen species are expected to be measured in the air at the DBD [22]. Figure 3 shows the optical spectrum in the range 200-900 nm for the coaxial DBD plasma. The spectrum was found to be dominated by N\({}_{2}\) (C\({}^{3}\)I\({}_{\mathrm{u}}-\) B\({}^{3}\)I\({}_{\mathrm{g}}\)) second positive system emissions at 300-450 nm as well as by N\({}_{2}\)\({}^{+}\) (B\({}^{2}\Sigma_{\mathrm{u}}-\) X\({}^{2}\Sigma_{\mathrm{g}}\)) first negative system emissions 300-450 nm as a result of the direct or step-wise electron impact excitations and the pooling reaction of the nitrogen metastable state [23]. In addition, the OH band was not observed in the range 306-312 nm, along with the absence of lines associated with oxygen atoms in the air at the DBD. Ozone generated in a compact air-cooled coaxial DBD is formed via a three-body reaction of oxygen atoms [13; 14; 15; 16], as shown below:  
\[\mathrm{e}+\mathrm{O}_{2}\rightarrow\mathrm{e}+\mathrm{O}+\mathrm{O} \tag{3}\]  
\[\mathrm{O}+\mathrm{O}_{2}+\mathrm{O}_{2}/\mathrm{N}_{2}\rightarrow\mathrm{O}_{ 3}+\mathrm{O}_{2}/\mathrm{N}_{2} \tag{4}\]  
Reactive oxygen and nitrogen in a metastable state for ozone production can play a significant role in the three-body reaction. The quenching of the oxygen atoms is responsible for the absence of oxygen atom peaks during the generation of air plasma. [PERSON] et al. reported that the quenching of oxygen atoms is faster than the radiative processes of oxygen atoms \({}^{5}\)S\({}_{0}\)-\({}^{5}\)P and \({}^{3}\)S\({}_{0}\)-\({}^{3}\)P [24]. In this sense, in the compact air-cooled coaxial DBD, which produces a large amount of ozone, oxygen-related peaks were not detected because of the reaction of ozone formation.
## 1 Introduction
### From Rank Products to Entropic Ranks  
The rank product method partially addresses these issues through a frequentist approach, by measuring the consistency of behavior across the sample groups, using the fold change (FC) criterion. When testing for up-regulation, the Rank Product \(RP_{g}^{up}\) of a gene \(g\)) is calculated as:  
\[RP_{g}^{upp}=\prod_{i=1}^{k}\left(\frac{r_{i,g}^{up}}{N_{i}}\right) \tag{1}\]  
where \(N_{i}\) is the total number of features and \(r_{i,g}^{up}\) (for single-colour transcriptomics) is the rank of gene \(g\) in the decreasing-FC-ordered list of genes in the \(i\)th pair of control vs. case samples (i.e., \(r^{up}=1\) for a gene consistently more overexpressed than any other in all cases vs. all control samples). Similarly calculated is the \(RP_{g}^{down}\), over the increasing-FC-ordered lists. The percentage of false positive (pfp) value for each rank product (RP) score is estimated through a permutation-based procedure outlined in the initial publication of the method [4].  
The initial Rank Product implementation in Bioinformatics, whilst addressing a number of the aforementioned issues, retains arbitrariness by trimming the final list either by a calculated pfp/\(p\)-value thresh-holding or by directly choosing the number of genes. Moreover, it tends to behave over-optimistically with increasing data dimensionality, as shown in recent works [7] (see also \"Supplementary Material 1--Method\").  
Our work aims to measure the information content of the RP distribution, implement a data-driven, non-parametric partitioning, provide a workflow for high-throughput data analysis and unbiased information extraction (Figure 1), and generalize the approach to various data types. We introduce the calculation of entropy over a transformation of the RP distribution, followed by a clustering procedure in order to identify the most consistent cutoff point successfully separating information-rich features from noise-dominated ones, without human intervention. The methodology operates upon the non-parametric RP distribution, relegating pfp and the \(p\)-value (which may be calculated empirically or parametrically) to quality indicators of the analysis instead of decision criteria. Consequently, it allowsfor improvement of the pfp calculation methods and adoption of new approaches [7; 8], ensuring result reproducibility and comparability as long as the RP calculation process itself remains unchanged.
## 2 Overview of the IEEE 802.15.4e Protocol  
The IEEE 802.15.4e standard defines the Physical layer (PHY) and MAC sublayer specifications for the devices having a low data rate, low power and short-range communication, which is quite good enough for the wireless ZigBee networks. The IEEE 802.15.4e-enabled devices operate in the license-free 868\(\sim\)868.6-MHz, 902\(\sim\)928-MHz and 2400\(\sim\)2483.5-MHz bands with a data rate of 250 kb/s to satisfy a set of applications. Two types of devices, a Full-Function Device (FFD) and a Reduced-Function Device (RFD), are present in the IEEE 802.15.4e-based network. Both star and peer-to-peer networks are supported by the IEEE 802.15.4e standard, and both topologies work in either a beacon-enabled mode or non-beacon-enabled mode. In a star topology, communication is normally made with the PAN coordinator only, whereas any device can communicate with any other one in its communication range in the peer-to-peer network.  
The IEEE 802.15.4e standard defines the slotted medium access control scheme for the short-range communication devices with low data rates. There are many MAC schemes defined by IEEE 802.15.4e, such as Time Slotted Channel Hopping (TSCH), Low Latency Deterministic Networks (LLDN), Deterministic and Synchronous Multi channel Extension (DSME), Radio Frequency Identification blink (RFID) and Asynchronous Multi-Channel Adaptation (AMCA). However, the standard specifies the optional use of the general superframe structure under beacon-enabled mode for low duty cycle devices in the network as described in the following subsection.
# Multiple PUE Attack Detection in Cooperative Mobile Cognitive Radio Networks
## 3 DNN Detection of Multiple PUE Attacks
### Cooperative Energy Detection  
The Centralized Control of FC simplifies decision-making and coordination. Centralized data collection can enhance the accuracy of detection algorithms, such as those using DNN. Nevertheless, some issues need to be addressed. High traffic to the FC can slow down response times and add delays, especially under heavy attack scenarios.  
In Decentralized Control, each SU operates independently, maintaining network functionality even if some nodes fail, and does not need a central system. However, ensuring that SUs effectively share detection information can be more complex without a central authority, and maintaining up-to-date knowledge of PUE attacks across a decentralized network may require robust protocols. In this case, a centralized control is implemented to keep a database of the attackers.  
The energy detection system aims to identify a threshold that enables an MCRN to differentiate a PU from a PUE. However, as the users move, the energy detector alone cannot determine if there is a PU or a PUE.  
In this model, the energy detector identifies a possible PU/PUE signal. It releases the channel and initiates the detection process. If there is a PU, it is permanently released while it is transmitting, but if the system recognizes a PUE, it can continue using the channel.  
The energy detector is shown in Equation (1) [15].  
\[f(t)=\begin{cases}n(t)&SU\\ i(t)*s(t)+n(t)&PU/PUE\end{cases} \tag{1}\]  
where \(n\) is the noise, \(i\) represents the impulse, and \(s\) is the received signal. Then, a binary hypothesis is used as described in Equation (2).  
\[F(n)=\begin{cases}a(n)&H0\\ s(n)+a(n)&H1\end{cases} \tag{2}\]  
Figure 2: Model for multiple PUE attack detection.  
where \(a\) is the noise channel, \(n\) is the sample index, and \(s\) is the signal. In the energy calculation, N is the number of samples of the energy [16].  
\[Z(F_{n})=\frac{1}{N}\sum\limits_{n=1}^{N}{\left|F(n)\right|^{2}} \tag{3}\]  
Compared to a threshold \(\lambda\), the value of \(Z\) decides the \(\mathrm{PU}/\mathrm{PUE}\) signal presence. The probabilities of false alarm (\(P_{fa}\)) and detection (\(P_{d}\)) for a CSS are given by [17]:  
\[P_{d} =P\{T(X)>\lambda/H1\}\] \[Q_{d} =1-\prod\limits_{i=1}^{K}{\left(1-P_{d,i}\right)} \tag{4}\] \[P_{fa} =P\{T(X)>\lambda/H0\}\] \[Q_{fa} =1-\prod\limits_{i=1}^{K}{\left(1-P_{fa,i}\right)} \tag{5}\]  
The energy detected is then sent to the FC, and the frequency is released while the whole process is carried out.
## 3 Results and Discussion
### Fitting the Models  
Based on the statistical processing of data regarding the effects of two factors, particle size and addition level, predictive models for FN index of quinoa-wheat composite flour and dough rheological properties in terms of Mixolab parameters were evaluated. The most fitting quadratic models were obtained for the following parameters: Falling number (FN), water absorption (WA), dough stability (ST), dough development time (DT), C2 torque as minimum consistency during protein weakening stage (C2), difference between torques C1 and C2 (C1-2), C3 torque as maximum consistency during starch gelatinization stage (C3), difference between torques C3 and C2 (C3-2), C4 torque as minimum consistency corresponding to hot starch stability gel (C4), C3-4--difference between torques C3 and C4, C5 torque as maximum consistency during starch retrogradation stage (C5) and difference between torques C5 and C4 (C5-4). The coefficients of determination (\(R^{2}\)) values (0.69-0.97), indicated the fitted models represented the experimental data well, elucidating the relationships between factors and responses.