esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Experimental Setup
### Ablation Study
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Model Variant** & \multicolumn{3}{c}{**JARVIS-DFT Dataset**} & \multicolumn{3}{c}{**Zenodo Dataset**} \\  & **PSNR** & **SSIM** & **RMSE** & **AUC** & **PSNR** & **SSIM** & **RMSE** & **AUC** \\ \hline w./o. Hybrid Stress-Strain Modeling Framework & 34.89 \(\pm\) 0.02 & 0.892 \(\pm\) 0.02 & 0.053 \(\pm\) 0.01 & 0.913 \(\pm\) 0.02 & 34.12 \(\pm\) 0.02 & 0.887 \(\pm\) 0.01 & 0.056 \(\pm\) 0.01 & 0.895 \(\pm\) 0.02 \\ w./o. Adaptive Learning with Physics-Consistency & 35.21 \(\pm\) 0.02 & 0.901 \(\pm\) 0.01 & 0.050 \(\pm\) 0.01 & 0.917 \(\pm\) 0.02 & 34.57 \(\pm\) 0.02 & 0.890 \(\pm\) 0.02 & 0.054 \(\pm\) 0.01 & 0.899 \(\pm\) 0.02 \\ w./o. Iterative Error Minimization & 34.67 \(\pm\) 0.02 & 0.994 \(\pm\) 0.01 & 0.052 \(\pm\) 0.01 & 0.911 \(\pm\) 0.02 & 34.02 \(\pm\) 0.02 & 0.885 \(\pm\) 0.02 & 0.057 \(\pm\) 0.01 & 0.892 \(\pm\) 0.01 \\ Full Model (Ours) & **37.12 \(\pm\) 0.02** & **0.918 \(\pm\) 0.02** & **0.044 \(\pm\) 0.01** & **0.955 \(\pm\) 0.02** & **36.25 \(\pm\) 0.02** & **0.911 \(\pm\) 0.02** & **0.049 \(\pm\) 0.01** & **0.908 \(\pm\) 0.02** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Ablation study results on model variants across JARVIS-DFT and Zenodo datasets. In the error analysis of this study, we compared the performance of different models across the JARVIS-DFT, Zenodo, ICME, and Materials Project datasets. As shown in Table 5, the errors of various models exhibit noticeable differences across datasets. ResNet and EfficientNet yielded errors of 0.056 and 0.062 on the JARVIS-DFT dataset, 0.061 and 0.059 on the Zenodo dataset, 0.071 and 0.069 on the ICME dataset, and 0.065 and 0.068 on the Materials Project dataset, indicating that EfficientNet achieved slightly lower errors on certain datasets but maintained similar overall performance to ResNet. U-Net demonstrated relatively lower errors, with values of 0.051 on JARVIS-DFT, 0.058 on Zenodo, 0.062 on ICME, and 0.059 on Materials Project, showing an improvement over ResNet and EfficientNet. Swin-Transformer further reduced the error, reaching 0.048 on JARVIS-DFT, 0.053 on Zenodo, 0.058 on ICME, and 0.061 on Materials Project, highlighting its better generalization ability. MobileNet exhibited comparatively higher errors across all datasets, with an error of 0.078 on the ICME dataset and 0.071 and 0.073 on the Zenodo and Materials Project datasets, respectively, suggesting potential limitations in handling complex structural mechanics problems. DenseNet showed error values similar to Swin-Transformer, with 0.055 and 0.060 on the JARVIS-DFT and Zenodo datasets, and 0.060 and 0.064 on the ICME and Materials Project datasets, respectively. Compared to these models, the proposed method consistently achieved the lowest error across all datasets, with values of 0.044 on JARVIS-DFT, 0.049 on Zenodo, 0.054 on ICME, and 0.057 on Materials Project. This
# Modeling of Historical Marine Casualty on S-100 Electronic Navigational Charts
## 3 Method: Data Modeling of Marine Casualty
### Application Schema Definition
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Feature** & **Attribute** & **Mult.** \\ \hline \multirow{6}{*}{HullAndEngineAccessoryDamage} & hullAndEngineAccessoryDamageType can have the following values: & \\  & 1. hull damage & \\  & 2. machineries and propulsion damage & [1..*] \\  & 3. other facility damage & \\  & 4. rudder damage & \\  & 5. outfit damage & \\ \hline \multirow{3}{*}{CollisionAndContact} & collisionAndContactType can have the following values: & \\  & 1. collision & \\  & 2. contact & [1..*] \\  & 3. floating object entanglement & \\ \hline \multirow{3}{*}{Navigationallssues} & navigationallssuesType can have the following values: & \\  & 1. drifting & \\  & 2. loss of direction & [1..*] \\  & 3. sailing hindrance & \\ \hline \multirow{3}{*}{FloodingAndSinking} & floodingAndSinkingType can have the following values: & \\  & 1. capsizing & \\  & 2. flooding & \\  & 3. sinking & \\ \hline \multirow{3}{*}{FireAndExplosion} & fireAndExplosionType can have the following values: & \\  & 1. explosion & \\  & 2. fire & \\ \hline \multirow{3}{*}{StrandingAndGrounding} & standingAndGroundingType can have the following values: & \\  & 1. grounding & \\  & 2. stranding & \\ \hline \multirow{3}{*}{OtherIncident} & otherIncidentType can have the following values: & \\  & 1. safety hindrance and near misses & [1..*] \\ \cline{1-1}  & 2. other incidents & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Specialized attributes and code lists for each marine casualty feature type. linked to under keel clearance management data models to support safer navigation in shallow or constrained waters. The _OtherIncident_ feature type accommodates incidents that fall outside predefined categories, such as near misses or potentially unsafe behaviors. Incident types emerging from evolving technologies such as smart ships can be represented by extending the associated code lists. This structured representation of marine casualty data can serve as a foundation for decision-support tools.
## 3 Expert Systems for Features Classification
### Artificial Neural Network  
ANN expert systems are based on the emulation of biological neuronal networks. An ANN is composed by a set of \"neurons\" distributed in several interconnected layers. Although there are several types of neural networks structures and configurations, the most used for features classification is the Multilayer Perceptron. Figure 4 shows the layer structure of a Multilayer Perceptron, with an input data terminal, no or some hidden layers, and one output layer.  
Figure 4: Scheme of Multilayer Perceptron neural network.  
Figure 3: Space of a 2-dimensional SVM (2 parameters on each failure representative feature) where a hyperplane is splitting the space in subspaces of healthy features and failure features.  
ANNs also must be trained before being able to correctly solve the problem. On ANN optimization, this learning is based on finding the best structure for a given problem (number of layers and number of neurons per layer) as well as the correct weight for each neuron within this network.  
Development of the Supra-System, a System Able to Generate and Optimize Failure Diagnostic Systems Improved with Expert Systems  
As presented in the previous sections, fault representative features finding methods and expert systems need to be optimized to obtain an acceptable diagnostic system. Finding the best fitting is not a trivial task since the accuracy of the expert system depends critically on the selection of its parameters. Therefore, to perform these tasks, in this paper, an autonomous system (the supra-system) is proposed. It is able not only of generating fault diagnostic systems, but also to optimize them through a set of fault representative features finding methods (Figure 5).
# Toward High Bit Rate LoRa Transmission via Joint Frequency-Amplitude Modulation
## 2 Preliminaries  
### LoRa Primer  
**Modulation:** A LoRa chirp encodes data by the initial frequency \(f_{0}\)[24]. The instantaneous frequency of the LoRa chirp is \(f(t)=f_{0}+kt,0\leq t\leq T\), where \(k\) is the slope and \(T\) is the duration of chirp. Then the instantaneous phase of LoRa chirp can be expressed as follows:  
\[\varphi(t)=2\pi\int_{0}^{t}f(t)\mathrm{d}t=2\pi\bigg{(}f_{0}t+\frac{1}{2}kt^{2 }\bigg{)},0\leq t\leq T \tag{1}\]  
The transmitted chirp can be expressed as  
\[s(t)=\mathrm{e}^{l2\pi\big{(}f_{0}t+\frac{1}{2}\frac{BW}{T}t^{2}\big{)}},0\leq t \leq T \tag{2}\]  
**Demodulation:** At the receiver, the LoRa demodulation involves two steps: multiplying the received signal \(r(t)\) with the downchirp and performing Fast Fourier Transform (FFT), which is called \"dechirp\". The dechirp operation makes the amplitude spectrum energy of the entire signal converge on a specific frequency bin (denoted by \(f_{0}\)), forming an energy peak. Specifically, let \(f_{0}=\frac{BW}{2}\), the upchirp can be obtained as \(upchirp(t)=e^{l2\pi\big{(}-\frac{BW}{2}t+\frac{1}{2}\frac{BW}{T}t^{2}\big{)}},0\leq t\leq T\). Let \(f_{0}=\frac{BW}{2}\) and replace the slope \(k=\frac{BW}{T}\) with \(-k=-\frac{BW}{T}\), the downchirp can be obtained as  
\[downchirp(t)=\mathrm{e}^{l2\pi\big{(}\frac{BW}{2}t-\frac{1}{2}\frac{BW}{T}t^{ 2}\big{)}},0\leq t\leq T \tag{3}\]  
Since \(s(t)\) and \(downchirp(t)\) are perpendicular to each other in the time-frequency diagram, the dechirp operation leverages their orthogonality to convert the chirp signal into a sinusoidal signal with a constant frequency, so that \(FFT[s(t)downchirp(t)]\) forms a spectral peak at the frequency point \(f_{0}\).
## 5 Conclusions and Future Work  
The extraction of the most influential nodes in a Complex Network is crucial for seeking more efficient data transmission within the network, evaluating its resilience, making better routing decisions, and gaining a deeper understanding of its dynamics. Our study arises from the need to find metrics that measure the influence of nodes in a DSCN, aiming to enhance the network's QoS metrics.  
Initially, we employed a network model that transformed the operation of OppMSN over time into a discretized time series of CSNs, to analyze the network's dynamic topology  
Figure 12: Overhead comparison of different routing protocols based on buffer size relative to the results of the S&W routing protocol: (**a**) comparison among all the analyzed routing protocols; (**b**) comparison of the proposed metrics and S&W.  
and the pattern of connections among devices. This approach provides a more accurate framework to analyze the evolution of these patterns, based on regression analysis, rather than using a single static aggregated network. In fact, the connections between devices have been analyzed from the perspective of dynamic centrality metrics, as well as from the perspective of a social complex network, extracting relationship patterns to detect the most influential devices over others throughout the network's operation.  
In this study, real datasets have been used for validation to showcase the effectiveness of the conducted experiments. The efficacy of different metrics employed on the datasets and potential correlations between them have been verified. Finally, based on influence dynamic rankings, our algorithms have facilitated better decision-making regarding the selection of nodes most suitable for routing data toward their destination in the datasets, leading to enhancements in standard QoS metrics.  
Moving forward, our future work involves analyzing the evolutionary characteristics of influence distribution using additional real datasets with more devices and enhanced connectivity among them. Furthermore, we will explore other combinations of centrality metrics and similarity indices to enhance the accuracy of classifying devices in an importance ranking. Additionally, we aim to investigate the concept of \"friend\" as a measure of temporal locality between each pair of nodes, evaluating its relationship with the connection capacity of a node with others.  
Conceptualization, F.J.R.-P.; Methodology, F.J.R.-P.; Formal analysis, F.J.R.-P.; Investigation, M.A.L.-R.; Resources, M.A.L.-R.; Data curation, M.A.L.-R.; Writing--review & editing, M.A.L.-R. and F.J.R.-P. All authors have read and agreed to the published version of the manuscript.  
This research was funded in part by TED2021-131699B-I00 / AEI/10.13039/501100011033/European Union NextGenerationEU/PRTR.  
Not applicable.  
The data presented in this study are available in the article.  
The authors declare no conflict of interest.
# Zero-Shot Detection of Visual Food Safety Hazards via Knowledge-Enhanced Feature Synthesis
## 3 Methodology
### Food Safety Knowledge Graph
#### 3.2.2 Knowledge Graph Embedding  
To leverage the structured knowledge in our FSKG for feature synthesis, we first need to obtain dense vector representations of the graph nodes and their relationships. Weemploy a knowledge graph embedding technique based on graph convolutional networks (GCNs) [45] to learn embeddings that preserve the graph's structural information.  
Let \(\mathbf{A}\in\mathbb{R}^{|\mathcal{N}|\times|\mathcal{N}|}\) be the adjacency matrix of the FSKG, where \(\mathbf{A}_{ij}>0\) if there is an edge between nodes \(i\) and \(j\), and \(\mathbf{A}_{ij}=0\) otherwise. For heterogeneous relationships, we create separate adjacency matrices \(\mathbf{A}^{(r)}\) for each relation type \(r\in\{FA,FF,AA\}\).  
We define the GCN-based embedding function \(\psi(\cdot)\) as follows:  
\[\mathbf{E}=\psi(\mathbf{X},\mathbf{A})=\tilde{\mathbf{A}}\sigma(\tilde{ \mathbf{A}}\mathbf{X}\mathbf{W}_{1})\mathbf{W}_{2} \tag{3}\]  
where \(\mathbf{X}\in\mathbb{R}^{|\mathcal{N}|\times d_{0}}\) is the initial feature matrix of the nodes (initialized with word embeddings for food categories and attribute definitions), \(\tilde{\mathbf{A}}=\mathbf{D}^{-\frac{1}{2}}\mathbf{A}\mathbf{D}^{-\frac{1}{2}}\) is the normalized adjacency matrix with \(\mathbf{D}\) being the diagonal degree matrix of \(\mathbf{A}\), \(\sigma(\cdot)\) is the ReLU activation function, and \(\mathbf{W}_{1}\in\mathbb{R}^{d_{0}\times d_{h}}\) and \(\mathbf{W}_{2}\in\mathbb{R}^{d_{h}\times d_{e}}\) are learnable weight matrices. Here, \(d_{0}\) is the dimension of the initial node features, \(d_{h}\) is the hidden dimension, and \(d_{e}\) is the embedding dimension.  
For each relation type \(r\), we compute the corresponding embeddings:  
\[\mathbf{E}^{(r)}=\psi(\mathbf{X},\mathbf{A}^{(r)}) \tag{4}\]  
The final node embeddings are obtained by aggregating embeddings across relation types:  
\[\mathbf{E}_{final}=\sum_{r\in\{FA,FF,AA\}}\alpha_{r}\mathbf{E}^{(r)} \tag{5}\]  
where \(\alpha_{r}\) are learnable attention weights that determine the importance of each relation type in the final embedding.
## 4 Experiment
### Ablation  
We conducted ablation experiments on MA-RPN and the feature reconstruction module DFRM. For the ablation experiment on MA-RPN, the traditional RPN structure was used to generate proposal regions instead of MA-RPN. For the ablation experiment on the DFRM, the original meta-features and ROI features from the query set were directly fused during the meta-test phase. The results are shown in Table 2. It can be seen that adding MA-RPN alone increased the mAP of defect components by 1.1%, and the defect detection performance of small-sized components such as pins was significantly improved, demonstrating that MA-RPN can not only effectively reduce noise in anchor boxes but can also generate more accurate candidate regions for small target objects by introducing low-level details. After adding the DFRM alone, the detection mAP increased by 2.0%, which was a significant improvement. This suggests that reconstructing meta-features based on the differences between defect and normal component features helps the model focus on defect-related features during classification in predictor head. Finally, the best detection performance was achieved with the model that combined both modules, verifying that the two modules do not conflict with each other and do not affect detection accuracy.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Optimization Method** & **Learning Rate** & **mAP (Base and Novel)** \\ \hline \multirow{4}{*}{SGD} & 0.01 & 72.4 \\  & 0.015 & 72.6 \\  & 0.02 & 72.8 \\  & 0.025 & 72.7 \\  & 0.03 & 72.5 \\ \hline Meta-SGD [34] & — & 73.0 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Performance in difference optimization method and learning rate.
## 1 Introduction
### Handover Tasks  
[PERSON] et al. explored the handover process from sociocognitive and physical perspectives [23]. The sociocognitive aspect consists of establishing an agreement on handover object (what), handover time (when), and handover location (where) between the two entities involved. The physical aspect involves the object handover actions, such as approach, reach, and transfer.  
Regarding the sociocognitive aspect, [PERSON] suggested that efficient collaboration requires common understanding of the task context between humans and robots and common expectations regarding the next step [27]. When two human working partners collaborate on an assembly task, they must be able to estimate the time required by their partner in the assembly process, including the effects of potential external and intrinsic factors (e.g., skill level, fatigue, and stress) that can affect the assembly rate [24]. [PERSON] et al. suggested that the precise and proactive estimation of handover time points by robots when handing over assembly parts to humans can minimize waiting times and maximize efficiency [28]. Robots with predictive capabilities can interact more effectively, intuitively, and naturally, and their operational efficiency is considerably greater than that of reactive robots. Additionally, experiment participants have reflected that interactions with robots are smoother when the robots are predictive rather than reactive [29,30]. Therefore, to ensure efficient and smooth collaboration, the handover time and position control during handovers are critical.  
Regarding the physical aspect, numerous scholars have explored the effect of robot handover posture, power, and path on handover efficiency. [PERSON] and [PERSON] conducted an experiment in which an object was handed by a humanoid robot with 29 degrees of freedom to a human [31]. The end effector of the humanoid robot used in the experiment had a complete sensing function that could detect an object's approach and the power supplied. The results demonstrated that the participants could respond to the robot's gestures and complete the handover process without any additional prompts. [PERSON] et al. used a Home Exploring Robotic Butler to investigate the effects of spatial contrast and temporal contrast of the robot before and after the handover process on handover intention [15]. The results revealed that temporal contrast is more beneficial to task fluency, reducing the time that a human worker must wait to receive the task. [PERSON] et al. investigated how trajectory and final handover posture can clearly indicate handover intention [23]. [PERSON] et al. suggested a handovermethod with which humans can most easily grasp an object; in this method, the robot should present the most appropriate part of the object (e.g., the handle) to the human [28]. [PERSON] and [PERSON] proposed that robotic verbal feedback improves team performance [32]. Other studies have focused on anthropomorphic social behavior within collaborative processes, such as visual fixation, which can improve HRI and thus ensure a smooth handover process [20,33].
# Dynamic Shortest Paths Methods for the Time-Dependent TSP
### Preliminaries  
The TDTSP is a generalization of the ATSP to the case of time-dependent cost functions. Specifically, we let \(D=(V,A)\) be a directed graph with \(n:=|V|\geq 3\) vertices, and \(\theta^{\max}\in\mathds{N}\) a fixed time horizon for \(\Theta:=\{0,\ldots,\theta^{\max}\}\). The travel time for an arc \(a\in A\) is given by a function \(c_{a}\colon\Theta\to\mathds{N}\). For each sequence of arcs \((a_{1},\ldots,a_{k})\) with \(a_{k}=(u_{k},v_{k})\) and \(v_{k}=u_{k+1}\), we can recursively define an arrival time  
\[\theta^{\text{arr}}(a_{1},\ldots,a_{k})\coloneqq\begin{cases}c_{u_{1},v_{2}}( 0),&\text{if $k=1$, and}\\ \theta^{\text{arr}}(a_{1},\ldots,a_{k-1})+c_{u_{k},v_{k}}(\theta^{\text{arr}}(a _{1},\ldots,a_{k-1}))&\text{otherwise.}\end{cases}\]  
A feasible solution of the TDTSP is a tour beginning at a source vertex \(s\in V\), visiting every other vertex exactly once, which then returns to \(s\). The TDTSP asks for a feasible solution \(T=(a_{1},\ldots,a_{n})\) minimizing the arrival time \(\theta^{\text{arr}}(a_{1},\ldots,a_{n})\) back at \(s\), which we will also denote by \(c(T)\). The specification of a source vertex is necessary for the TDTSP, as opposed to the ATSP, due to the time-dependency of the travel times \(c\). Several special properties of travel time functions play an important role in time-dependent versions of combinatorial problems: The first-in-first-out (FIFO) property stipulates that the traveler who first enters an arc is also the first to leave it again. Formally, it must hold for each \(a\in A\) that  
\[\theta+c_{a}(\theta)\leq\theta^{\prime}+c_{a}(\theta^{\prime})\quad\forall\, \theta,\theta^{\prime}\in\Theta,\,\theta\leq\theta^{\prime}.\]  
Shortest paths with respect to time-dependent costs can be computed efficiently using a variant of [PERSON]'s algorithm if the cost functions satisfy the FIFO property [6; 7].  
Secondly, several well-known results (e.g., [8; 9]) state that the symmetric version of the TSP can be approximated in the case of metric cost coefficients, that is, cost coefficients satisfying the triangle inequality. The definition of the triangle inequality can be easily generalized to the time-dependent case--a set of travel time functions satisfies the time-dependent triangle inequality if it holds for each \(u,v,w\in V\) with \(\theta,\theta+c_{uv}(\theta)\in\Theta\) that  
\[\theta+c_{uw}(\theta)\leq\theta+c_{uw}(\theta)+c_{vw}(\theta+c_{uw}(\theta)). \tag{1}\]
# Predicting Algorithm of Tissue Cell Ratio Based on Deep Learning Using Single-Cell RNA Sequencing
## 2 Materials and Methods
### Algorithm of Autoptcr Model  
The inputs of data are \(\dot{X}\), \(T\), and \(Z\). \(\dot{X}=\{\dot{x}_{1},\dot{x}_{2},\ldots,\dot{x}_{q}\}\) is a gene set of the trained ScRNA tissues, \(\dot{X}\) is a gene in the trained tissues, and q is the number of gene species in the trained tissues. \(T=\{t_{1},t_{2},\ldots,t_{p}\}\) is a gene set of the tested tissues, \(t\) is a gene in the tested tissues, and p is the number of gene species in trained tissues. \(Z\) is the proportion of cells corresponding to \(\dot{X}\). In the screening feature and data transformation work, the data are passed into the convolutional layer and the pooling layer of the feature extraction module, and \(r(\cdot)\) is the nonlinear activation function. We set \(\text{RELU}(\cdot)\) as the activation function. Then, we enter the predicted cell ratios obtained in the flattened and dense layers of the prediction module. The MSE loss between the real cell proportion and the predicted cell ratios is calculated, using the optimizer OA with a learning rate of LR to optimize the loss function LF of the Autoptcr model. The algorithm description is shown in Algorithm 1.  
```
Begin
1. Input: \(\dot{X}\) is the gene set of the trained ScRNA tissues; \(Z\) is the proportion of cells corresponding to \(\dot{X}\); \(T\) is the gene set of the tested tissues;
2. Set the hyperparameters of the Autoptcr model, \(LR=0.001\), \(OA=\text{Adam}\), \(LF=\text{MSE}\), \(D=1\), \(V=32\), \(S=2000\), \(BS=128\), \(X\leftarrow\varnothing\);
3. for\(c=1\)to\(q\)do
4. if feature variance of \(\dot{x}_{c}\leq 0.1\)
5. \(X\gets X\cup\{\varnothing\}\);
6. else
7. \(X\gets X\cup\{\dot{x}_{c}\}\);
8. endfor
9. \(X\gets X\cap T\); //Look for the same genes
10. Perform a data conversion on \(X\) to get \(X^{\prime}\), \(X\)\(\leftarrow\)\(X^{\prime}\);
11. for\(s=1\)to\(S\)do
12. Sample \(BS\) data from \(X\);
13. For\(j=1\)to\(4\)do
14. for\(v=1\)to\(V\)do//Determine the number of convolution filters \(V\)
15. \(Y^{j}\leftarrow\text{Relu}(\sum\limits_{d=1}^{D}W_{j}^{p}\cdot X_{f}^{d}+b_{j}^ {p})\); //Convolution layer processing
16. \(\widehat{Y}_{\overline{E}}^{j}\leftarrow\underset{\overline{E}\in O_{q}}{ \max}(Y_{\overline{E}}^{j})\); //Maxpooling layer processing
17. endfor
18. \(Y^{j+1}\leftarrow\widehat{Y}_{\overline{E}}^{j}\);
19. V\(\leftarrow\)V/2;
20. endfor
21. \(X^{\prime}\gets T(\widehat{Y}_{\overline{E}}^{j})\), get one-dimensional data;
22. Input \(X^{\prime}\) into two dense layers, get predicted cell ratio of tissue \(\hat{Z}\);
23. Calculate loss function, \(\text{MSE}=\frac{1}{l}\sum\limits_{i=1}^{l}(\hat{Z}_{i}-Z_{i})^{2}\);
24. Update the training parameters by \(OA\) and \(LR\);
25. endfor
26. Output: Final predicted cell ratio of tissue \(Z^{\prime}\); End
```  
**Algorithm 1** Autoptcr