esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Results
### Dataset Construction  
From the previously described experiments, a total of 600 original PTCs curves were produced, with each category consisting of 200 curves. This dataset, referred to as the original dataset, was utilized for generating synthetic PTCs curves via the AoT-DCGAN model and for subsequent comparative experiments in the classification model. A novel weight optimization strategy was employed to ensure the model's production of high-quality PTCs curves, facilitating asynchronous updates of the discriminator and generator weights. This strategy aimed to prevent the discriminator's loss function from becoming too small during early training stages, which could hinder weight updates. The AoT-DCGAN model generated a total of 600 synthetic PTCs curves using the original dataset,  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Make-Up Conditions** & **Curve Description** \\ \hline Standard & Acceptable (AC) \\ Thread Damage & Abnormal Thread Interference (ATI) \\ Misalignment & None Defined Torque (NDT) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Detailed dataset information.  
Figure 10: Examples of the PTCs curves from the experiments.  
Figure 9: Experimental equipment and flowchart.  
with each category containing 200 curves. The newly generated data was added to the original dataset, resulting in datasets with varying data augmentation ratios of 1.5, 1.75, and 2. In other words, the augmented datasets were 1.5 times, 1.75 times, and 2 times the size of the original dataset.  
Figure 11 displays the artificial PTCs curves produced by the AoT-DCGAN under different operational conditions, with corresponding real data also presented. It can be observed that the curves generated by the model exhibit features similar to those of the real data. For instance, as shown in the ATI curves, the fluctuation characteristics of the real sample are accurately represented in the generated sample. Therefore, by this operation, it is possible to expand dataset with similar characteristics.
# Service-Oriented Cooperation Policies for Intelligent Ground Vehicles Approaching Intersections
## 3 Fundamental Traffic Models and Cooperation Procedure
### Modeling Heterogeneous Intelligent Vehicles and Their Behaviors  
(1) Model of Intelligent Vehicles  
Considering that intelligent vehicles serve as diverse mobile carriers in the coming C-ITS, we have designed a vehicular model with service-related properties as a tuple \(v_{i}:=<id=i,<\zeta,p>,\mathbb{E},<\ell,\gamma,s,a>,<\widetilde{\gamma}, \widetilde{\tau}>>\), as detailed in Table 1. In this model, service properties are indicated by the first sub-tuple. The classic physical properties are presented by \(\mathbb{E}\), including vehicular length (\(v.l\)), width (\(v.w\)), current acceleration (\(v.a\)) and velocity (\(v.v\)), length between both axes \(v.\Delta l_{w}\), maximum velocity (\(v.\overline{v}\)), and the kinematic model etc. Current vehicular position and behavior status are indicated by the second sub-tuple, and the reserved vector of S-CS and the corresponding tokens are in the last element. Our previous study has implemented this parameter-customizable model and demonstrated that this model is effective enough.  
(2) Reservation-based Vehicular Actions and States  
For the reservation-based passing-through problem, whether one vehicle is allowed to pass through a critical section or not primarily depends on if it can successfully obtain the token of this section. So, vehicular behaviors will be closely related to reservation and authorization. In our previous work, we have abstracted different vehicular motions as a uniform event-triggered action model. Concretely, \(i^{th}\) action \(\alpha_{i}\) is presented as a tuple \(<id=i,\mathit{name},\zeta_{s},M_{si},M_{ci}>\). On this basis, a group of PTI-related vehicular actions has been designed, covering Initialization \(\alpha_{0}\), Cruise with reservation \(\alpha_{1}\), Entering \(\alpha_{2}\), Cruise \(\alpha_{3}\), Lane-changing \(\alpha_{4}\), Overtaking \(\alpha_{5}\), Passing \(\alpha_{6}\), Parking \(\alpha_{7}\), and Termination \(\alpha_{8}\). All these proposed actions and their conditions are detailed in [15].  
With these new action models, any vehicular behavior can be essentially presented as a scheduling sequence of actions. Consequently, we employed the concept of behavior state \(S\) and an event-triggered sate-automata \(\mathbb{A}_{S}\) to represent any special maneuver case and any vehicular movement procedure, separately. The automata \(\mathbb{A}_{S}\) is composed of an action set \(\zeta_{\alpha}^{S}\), an event-based action-transition matrix \(M_{A}\) and a state-transition matrix \(M_{S}\). After normalizing all possible maneuver stages, eight vehicular states have been designed to present anyone traveling procedure, and the state-switch logic of \(\mathbb{A}_{S}\) as shown in Figure 3. More details are presented in [5,7,15].  
Figure 2: Intersection and Its Composed S-CSs. (**a**) Intersection and Its Four Critical Sections. (**b**) Positions for One Static Critical Section.
# Feature Point Matching Method Based on Consistent Edge Structures for Infrared and Visible Images
## 1 Introduction
Due to the consistency of edge structures of infrared and visible images, edge properties including orientation and length are consistent as well. In the process of establishing feature descriptions by the edge orientation, the edge length should be used to improve the ability of describing the global structure of infrared and visible images further. In order to overcome these deficiencies of edge-based methods, a feature detection and description method based on consistent edge structures of images (DDCE) is proposed. The main contributions are listed as follows. (1) Consistent edges are extracted by selecting long edges to present global structures, which are similar in both infrared and visible images. (2) Common feature points are detected according to the constraints of consistent edge structures. (3) By using the edge properties including edge length and edge orientation, the edge length weighted edge orientation histogram is computed to build feature descriptions. The remainder paper is organized as follows. In Section 2, the proposed matching method is described including consistent edge extraction, common feature detection, feature description, and feature matching. In Section 3, experimental results and corresponding analyses are given out. In Section 4, this paper is concluded.
## 6 Actor-Critic Methods
### Proximal Policy Optimization (PPO)
#### 6.3.5 Self-Learned Vehicle Control Using PPO  
[PERSON] and [PERSON] [45] proposed a method that enhances PPO for vehicle control by combining minimal path planning with reinforcement learning to achieve efficient and generalizable vehicle control in obstacle-rich environments. The key innovation lies in using PPO to learn vehicle control policies that follow a pre-computed approximate path while adapting to unforeseen obstacles and optimizing for faster completion times.  
The environment is framed as a POMDP, where the state \(s_{t}\) includes relative positions of the next \(n\) checkpoints, vehicle velocity, and simulated LiDAR data. The action \(a_{t}\) consists of continuous control variables, such as throttle and steering for cars, and x-axis and z-axis movements for drones. The policy \(\pi_{\theta}\) is parameterized by a neural network, mapping the observed state \(s_{t}\) to an action \(a_{t}\):  
\[a_{t}\sim\pi_{\theta}(a_{t}|s_{t}). \tag{201}\]  
The reward function balances three objectives: checkpoint progress, collision avoidance, and minimizing time. The total reward \(r_{t}\) at time \(t\) is defined as follows:  
\[r_{t}=r_{t}^{\text{chk}}+r_{t}^{\text{time}}+r_{t}^{\text{col}}, \tag{202}\]  
where  
\[r_{t}^{\text{chk}} = \begin{cases}1+\sum_{i=1}^{k}\delta_{i},&\text{if checkpoint $i$ is passed,}\\ 0,&\text{otherwise,}\end{cases} \tag{203}\] \[r_{t}^{\text{time}} = -\beta\cdot\Delta t,\] (204) \[r_{t}^{\text{col}} = \begin{cases}-3,&\text{if collision occurs,}\\ 0,&\text{otherwise.}\end{cases} \tag{205}\]  
The policy is trained using PPO with a clipped surrogate objective:  
\[L_{\text{PPO}}(\theta)=\mathbb{E}_{t}[\min(\rho_{t}A_{t},\text{clip}(\rho_{t},1-\epsilon,1+\epsilon)A_{t})], \tag{206}\]  
where \(\rho_{t}=\frac{\pi_{\theta}(a_{t}|s_{t})}{\pi_{\theta_{\text{old}}}(a_{t}|s_{ t})}\) is the probability ratio, and \(A_{t}\) is the advantage function:  
\[A_{t}=r_{t}+\gamma V_{\theta}(s_{t+1})-V_{\theta}(s_{t}). \tag{207}\]  
The training process employs curriculum learning, progressively increasing the complexity of generated maps by adjusting the proportion of obstacles and randomizing the initial orientation of the vehicle. Early training stages use simpler maps with fewer obstaclesand optimal starting orientations. The difficulty gradually increases as the agent improves, enhancing generalization to unseen environments.  
Additionally, the method introduces a fractional factorial design to optimize hyperparameters and state representations. This approach ensures the efficient evaluation of different configurations without exhaustive testing, reducing overall computational costs during training. By combining minimal path planning, curriculum learning, and PPO-based control, the proposed method eliminates the need for detailed motion planning while achieving high performance in generalizable navigation tasks.
# Wearable Light-and-Motion Datalogers for Sleep/Wake Research: A Review
## 2 Methods  
Sources for the dataloggers selection for this review were existing practical knowledge of the authors on several research-grade dataloggers, an author's (K.D.) database of the articles on chronobiological studies, and the PubMed library. The search in PubMed was performed using word string (actimet* OR actigraph* OR accelerometer) AND (\"light sensor\" OR \"ambient light\" OR \"illumination\") and filter \"Humans\"; 65 records were retrieved. Several review articles were also analyzed (e.g., [11; 12; 13; 1], others). The selection criteria were as follows: (1) currently available wearable devices; (2) that continuously record the levels of both human motion and ambient light; (3) the recorded data available for later computational analysis.  
According to the first criterion, the review did not consider devices that are (or were/remained) in the development, pre-commercial stage. They include either zero-cycle-developed prototypes (e.g., Eco-Mini [14; 15], closed project [16]; an unnamed device [17]) or predecessor-based upgrading dataloggers (e.g., Sleep Watch 2.0 instead of Motionlogger Watch announced by Ambulatory Monitoring, Ardsley, NY, USA [18]; Speck instead of Daysimeter-D under joint development by Light and Health Research Center, New York, NY, USA and Blue Iris Labs, Fairfax, CA, USA [19; 20]). There is one more device not included by the first criterion--AC10, or \"Tempatilumi\" (Guarulhos, Sao Paulo, Brasil) [21] because there is no evidence for its current production (existence of a manufacturer) and use in recent studies. The vast majority of existing dataloggers--mainly contemporary, smartphone-compatible--did not meet the second criterion: they do not record either human motion (e.g., LYS button, Lido) or ambient light (light sensor that they have is used exclusively to adjust the screen brightness: Oura Ring, Apple Watch, Fitbit, Withings devices, others).  
In the result of the search, 17 dataloggers produced by 14 manufacturers were chosen for this review. The sources to collect their technical and functional characteristics for comparison were the authors' practical knowledge of several devices, manufacturers' websites (descriptions of device specifications, pdf instructions to users), and email communication with the manufacturers. The authors have experience with five reviewed devices: Activwatch 2 [22], MotionWatch 8 [23], LightWatcher [24], Daqtometer 2.4 [25; 26], ActTrust 2 (ongoing \"Light-Arctic\" project [27])--each produced by different manufacturers. An email request to specify some features of the devices was sent to 10 manufacturers (and one researcher--in the case of the ActiTrac device), and all responded, providing almost all necessary information.
## 3 Influence of Boundary Distance in the Integral Response Deformation Method
### Influence of the Bottom Artificial Boundary Distance
#### 3.2.1 Internal Forces and Deformations  
Figure 7 presents the variation in the relative errors of the internal forces and lateral deformations of the underground structure with the \(R_{\text{B}}\). Overall, the errors significantly increase with increasing \(R_{\text{B}}\). Specifically, as \(R_{\text{B}}\) increases from 0.5 to 5.0, the axial force errors at Sections A and B decrease from \(-\)30.02% to \(-\)3.70%; the shear force error at Section E decreases from \(-\)20.38% to \(-\)3.06%; the bending moment error at Section F decreases from \(-\)18.19% to \(-\)2.63%; and the lateral deformation error of the central column decreases from \(-\)8.49% to \(-\)2.04%.  
Figure 7: Computational accuracy of the IRDM under different \(R_{\text{B}}\) values, where \(R_{\text{B}}\) is a dimensionless bottom boundary distance ratio \(R_{\text{B}}=H_{\text{B}}/H\).  
Further analysis reveals that for \(R_{B}\) between 0.5 and 3.0, errors in internal forces and lateral deformations decrease markedly with increasing \(R_{B}\). However, when \(R_{B}\geq 3.0\), the error variations stabilize and remain consistently below 5%.
## 3 Materials and Methods
### Data Analysis
#### 3.2.2 Descriptive Statistics  
To gain a better understanding of the dataset, we conducted descriptive statistics on the abstracts. The average length of the abstracts was found to be 215 (SD = 90) words for English and 190 (SD = 77) words for German abstracts. It is noteworthy that, while English abstracts have a higher word count, German abstracts tend to be longer in terms of character count. This observation is due to the nature of the German language, where words often contain more characters compared to English [36]. Specifically, the average character count for English abstracts was 1480 (SD = 585), while, for German abstracts, it was 1587 (SD = 616) characters. Additionally, the annotations were accompanied by significant statistical insights. The average annotation time for each document was 176 (SD = 73) seconds, highlighting variability in annotation durations. The annotation process was also conducted at an average rate of 113 (SD = 12) words per minute (WPM), emphasizing diverse annotation speeds, which is consistent with [PERSON] et al.'s study [37]. Furthermore, the mean intraclass correlation coefficient (ICC) for annotations was found to be 0.81 (SD = 0.08) (according to [PERSON] et al. guideline [38], ICC values below 0.5, between 0.5 and 0.75, between 0.75 and 0.9, and exceeding 0.90 indicate poor, moderate, good, and excellent reliability, respectively), indicating substantial consistency and agreement among the annotations provided by medical professionals.  
\begin{table}
\begin{tabular}{c|c c c c c} \hline \multirow{2}{*}{**Category**} & \multicolumn{2}{c}{**Med. Student**} & \multicolumn{2}{c}{**Med. Doctor**} & \multirow{2}{*}{**Total**} \\ \cline{2-2} \cline{4-5}  & **Junior** & **Senior** & **Junior** & **Senior** & \\ \hline \multirow{2}{*}{Participants} & 70 & 59 & 59 & 28 & 216 \\ \cline{2-5}  & 32.4\% & 27.3\% & 27.3\% & 13\% & 100\% \\ \hline \end{tabular}
\end{table}
Table 1: Annotation process participants’ distribution among four categories.
## 3 Results
### Effect of Kinematic Parameters and Computational Fluid Dynamics Simulations
#### 3.2.2 Effect of the Flight Velocity in Forward Free Flight  
This simulation aims to investigate the effect of kinematics parameters of the model with rotation in addition to the translational motion. In Case 2, \(V_{\infty}\) is taken as 0.6, 0.8, 1.0, and 1.2 m/s. A kinematic parametric study on flight velocity is presented to explore its influence on aerodynamic performance. We simulate free flights of the butterfly model with rotation (body pitch motion). The kinematics of thoracic motion is simplified to a time-varying cosine function. The initial position and amplitude of the thoracic pitch  
Figure 8: (**a**) The instantaneous aerodynamic forces of the butterfly accompanied by the change of \(B_{0}\) in four flapping cycles; and (**b**) the average aerodynamic forces at different fixed pitch angles.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameters** & **Case 1** & **Case 2** & **Case 3** & **Case 4** \\ \hline \(f\) (Hz) & 10 & 10 & 10 & 10 \\ \(A_{f}\) (deg.) & 60 & 60 & 60 & variable \\ \(A_{p}\) (deg.) & 0 & 30 & 30 & 30 \\ \(A_{0}\) (deg.) & 20 & 20 & 20 & 20 \\ \(B_{0}\) (deg.) & variable & 34 & 34 & 34 \\ \(C_{0}\) (deg.) & \(-35\) & \(-35\) & \(-35\) & \(-35\) \\ \(\gamma\) (rad) & \(\pi/2\) & \(\pi/2\) & variable & \(\pi/2\) \\ \(V_{\infty}\) (m/s) & 1 & variable & 1 & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Kinematic parameters K set-ups of four cases.  
angle are certain values. The simulation model of the body can rotate in the longitudinal direction, while it does not rotate in the yawing and rolling directions. The simulation results are shown in Figure 9.  
As the velocity increases, the lift and drag generated by flapping wing increase synchronously, and their instantaneous peaks increase accordingly. \(\bar{F}_{x}\) and \(\bar{F}_{y}\) of the butterfly at the velocity of 1.0 m/s are 4.7 \(\times\) 10\({}^{-4}\) and 2.7 \(\times\) 10\({}^{-3}\) N (approximately 80% of butterfly gravity), respectively. The lift reaches the instantaneous maximum 9.5 \(\times\) 10\({}^{-3}\) N at the mid-downstroke of the DS (approximately 0.025-0.03 s). The thrust reaches the instantaneous maximum 1.7 \(\times\) 10\({}^{-3}\) N at the mid-downstroke of the DS (approximately 0.075-0.08 s). The effect of flight velocity on lift and drag is relatively linear within the test velocity range. According to previous kinematic observations, the butterfly has fluctuations in the \(Y\)-axis direction, and the velocity in the \(X\)-axis direction is also time-varying. \(v_{x}\) and \(v_{y}\) will be set as a periodic change function in further research.
## 2 Materials and Methods
### Cultivation of Biodegrading Microorganisms  
Bacterial Salt Medium (BSM; [21]) comprising of KH\({}_{2}\)PO\({}_{4}\) 0.17 g\(\cdot\)L\({}^{-1}\), K\({}_{2}\)HPO\({}_{4}\) 0.13 g\(\cdot\)L\({}^{-1}\), (NH\({}_{4}\))\({}_{2}\)SO\({}_{4}\) 0.71 g\(\cdot\)L\({}^{-1}\), MgCl\({}_{2}\) - 6H\({}_{2}\)O 0.034 g\(\cdot\)L\({}^{-1}\) and a trace metal solution (MnCl\({}_{2}\) cdot 4H\({}_{2}\)O 1 g\(\cdot\)L\({}^{-1}\), CaCl\({}_{2}\) \(\cdot\) 2H\({}_{2}\)O 26 g\(\cdot\)L\({}^{-1}\), FeSO\({}_{4}\) \(\cdot\) 7H\({}_{2}\)O 0.6 g\(\cdot\)L\({}^{-1}\) and Na\({}_{2}\)MoO\({}_{4}\) \(\cdot\) 2H\({}_{2}\)O 2 g\(\cdot\)L\({}^{-1}\)) dosed at 1 mL\(\cdot\)L\({}^{-1}\) was used for cultivation of biodegrading bacteria. The BSM was supplemented with 1% diesel oil (summer diesel for moderate climate compliant with EN590 [22] purchased from an OMV petrol station, sterilised by filtering through a 0.45 \(\upmu\)m filter) as a sole source of carbon and energy. Cultivations were carried out with aeration in batch mode at 25 \(\pm\) 1 \({}^{\circ}\)C. For experiment A the intensively aerated fermenter (20 L) was used, for experiment B Erlenmeyer flasks (V = 250 mL, 6 \(\times\) 60 mL of media) on rotary shaker were used. Cultivation of the culture for experiment A was carried out perpetually throughout the experiment. Each week, after withdrawal of the biodegradation culture for bioaugmentation (see Section 2.4 for details), the bioreactor was refilled by a fresh BSM and sterile diesel in order to have a permanently high amount of biomass for bioaugmentation available (see Section 2.5 for details).  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Concentration** \\ \hline Hydrocarbon content & \\ Aliphatics C\({}_{10}\)-C\({}_{40}\) [g\(\cdot\)kg\({}^{-1}\) dwt] & 80.7 \(\pm\) 2.2 \\ Sum of PAHs [mg\(\cdot\)kg\({}^{-1}\) dwt] \({}^{1}\) & 95 \(\pm\) 29 \\ \hline Water extractable elements \({}^{2}\) & [mg/kg dwt] \\ Al & 68.2 \(\pm\) 1.2 \\ As & \textless{}0.1 \\ Ba & 46.3 \(\pm\) 1.1 \\ Ca & 67478 \(\pm\) 713 \\ Cd & \textless{}0.02 \\ Co & \textless{}0.02 \\ Cr & \textless{}0.02 \\ Cu & 11.4 \(\pm\) 0.4 \\ Fe & 161.1 \(\pm\) 5.1 \\ K & 3253 \(\pm\) 40 \\ Li & \textless{}0.1 \\ Mg & 2444 \(\pm\) 46 \\ Mn & 242 \(\pm\) 1.6 \\ Mo & 5.8 \(\pm\) 0.4 \\ Na & 1652 \(\pm\) 81 \\ Ni & 9.4 \(\pm\) 0.0 \\ P & 2.6 \(\pm\) 0.3 \\ Pb & \textless{}0.07 \\ S & 2480 \(\pm\) 51 \\ Sb & \textless{}0.1 \\ Se & \textless{}0.1 \\ Sn & \textless{}0.3 \\ Sr & 244.5 \(\pm\) 5.0 \\ Ti & \textless{}0.02 \\ Zn & 159.4 \(\pm\) 4.8 \\ Zr & \textless{}0.02 \\ \hline Chemical properties & \\ TOC [g/kg dwt] & 14.3 \(\pm\) 0.4 \\ pH & 7.76 \(\pm\) 0.10 \\ \hline \hline \end{tabular} dwt = dry weight; TOC = Total organic carbon; PAH = polyaromatic hydrocarbons; \({}^{1}\) [PERSON] et al. 2017 [20];  
\({}^{2}\) Presummably bioavailable = first fraction of sequential BCR extraction (see Section 2.5.)  
\end{table}
Table 1: Soil characteristics (average \(\pm\) standard deviation, n = 4).
## 2 Methodology
### The Three-Phase Hysteresis Model for Residual Trapping  
Although conventional two-phase hysteresis models assume the reversibility of permeability during the drainage process following the previous imbibition cycle, this assumption is invalid for three-phase fluid flow because the relative permeability of gas is lower when displacing a water-oil mixture than when displacing oil only [29]. The three-phase hysteresis model proposed by [PERSON] and [PERSON] [30] is adopted in the present study and has shown better matching to experimental data than the two-phase model [31; 32].  
The gas permeability during the drainage process is calculated using Equation (1):  
\[k_{rg}^{\text{drain}}\Big{(}S_{g},\ S_{w}^{\text{I}},S_{g}^{\text{start}}\Big{)} =\Big{[}k_{rg}^{\text{input}}\Big{(}S_{g}\Big{)}-k_{rg}^{\text{input}}\Big{(} S_{g}^{\text{start}}\Big{)}\Big{]}\Bigg{(}\frac{S_{wi}}{S_{w}^{\text{I}}} \Bigg{)}^{\alpha}+k_{rg}^{\text{limb}}\Big{(}S_{g}^{\text{start}}\Big{)} \tag{1}\]  
We clarify that a list of symbols is given in the Nomenclature.  
The relative permeability of the gas with decreasing gas saturation (i.e., non-wetting phase in the imbibition process) is denoted by \(S_{gf}\) and is estimated by Equations (2) and (3):  
\[k_{rg}^{\text{limb}}\Big{(}S_{g}\Big{)}=k_{rg}^{\text{drain}}\Big{(}S_{gf}+S_{ g}^{\text{end}}\Big{)} \tag{2}\]  
\[S_{gf}=\frac{1}{2}\Bigg{\{}\Big{(}S_{g}-S_{gr}\Big{)}+\sqrt{\Big{(}S_{g}-S_{ gr}\Big{)}^{2}+\frac{4}{C}\Big{(}S_{g}-S_{gr}\Big{)}}\Bigg{\}} \tag{3}\]  
where the trapped gas saturation, \(S_{gr}\), and Land's parameter [33], \(C\), are estimated from Equations (4) and (5), respectively:  
Figure 1: Schematic diagram of the multiple contact miscibility process during CO\({}_{2}\)-enhanced oil recovery (EOR).  
\[S_{gr}=S_{gc}+\frac{S_{gm}-S_{gc}}{1+C\Big{(}S_{gm}-S_{gc}\Big{)}} \tag{4}\]  
\[C=\frac{1}{S_{gr,\max}-S_{gc}}-\frac{1}{S_{g,\max}-S_{gc}} \tag{5}\]  
\(S_{gr,\max}\) is the maximum trapped gas saturation and can be approximated using an empirical correlation with the porosity, \(\phi\)[34], in accordance with Equation (6):  
\[S_{gr,\max}=0.5473-0.9696\phi \tag{6}\]  
To determine the relative permeability of the oil, the [PERSON]'s first model modified by [PERSON] and [PERSON] [35] is applied. The minimum residual oil saturation, designated \(S_{om}\), is modified to reflect the effect of trapped gas on oil relative permeability, as shown in Equation (7):  
\[S_{om}^{\rm mod}=S_{om}-a\Big{(}S_{g}-S_{gf}\Big{)} \tag{7}\]  
where \(S_{g}\) and \(S_{gf}\) are the total and free gas saturations respectively, and \(a\) is input parameter of 0.68 for mimicking a strongly water-wet condition [36].