esa-sceva/satcom-chunk-collection huggingface dataset:
## 5 Discussion  
### Performance Comparison  
#### 5.1.1 Informer Discriminator vs. Linear Discriminator  
In order to verify the influence of our proposed informer decoder-based discriminator on the multi-dimensional time series imputation results, we used the fully connected layer of AST and the informer encoder network we proposed as the discriminator of the model and conducted experiments on the electricity dataset. The experimental results (Table 10) show that when using the informer encoder, the time series imputation at each missing rate was better than using the fully connected layer as the discriminator, which had a significant effect on training a better time series imputation model. The goal of the discriminator is to fit a likelihood function that evaluates the imputation results. When the informer is used as the discriminator, it can make full use of the characteristics of the time series and learn more reasonable evaluation criteria than the linear discriminator. Therefore, the model of the discriminator is the practical choice.
# Embedding Equality Constraints of Optimization Problems into a Quantum Annealer +
## 3 Direct Approach  
We can solve (4) as an optimization problem. Conditions (C2) and (C3) can be implemented as linear constraints (since the problem variables are \(\mathbf{a}\), \(\mathbf{b}\), and \(\mathbf{c}\), while \(\mathbf{x}\) and \(\mathbf{t}\) are constants), but conditions (C1) is nonlinear because of the \(\exists\) predicate. To model (C1) as a linear constraint we define, for each \(\mathbf{x}\in\mathcal{C}\), a binary vector \(\mathbf{t}(\mathbf{x})\) (whose existence is guaranteed if (C1) is satisfied) and add the constraint \(Q(\mathbf{x},\mathbf{t}(\mathbf{x}))=\mu\). This creates \(|\mathcal{C}|m={n\choose k}m\approx n^{k}m/k!\) binary variables (for \(k\ll n\)). For \(k=1\) that number is \"only\" \(nm\), but it grows to \(\approx n^{2}m/2\) for \(k=2\) and to \(\approx n^{3}m/6\) binary variables for \(k=3\).  
Another factor that makes the optimization problem extremely hard is that the total number of constraints is proportional to \(2^{n+m}\), i.e., it grows exponentially with the number of the variables. For that reason, even for \(k=1\), we can solve the problem only for \(n=8\), \(m=8\) in reasonable time, while using the symmetry of the Chimera graph we are able to increase the size to \(n=12\), \(m=12\) for \(k=1\). The optimal value of the gap (the parameter \(\gamma\)) found in both cases is 4. Given that current D-Wave machines have more than thousand qubits and this number is doubling every couple of years or so, and the fact that the number of constraints grows exponentially with that number, it is clear that this approach is extremely limited in scalability and cannot handle any constraint of practical interest.  
For that reason, we look for an alternative approach whose idea is to solve several optimization problems that have similar structure as the one described above, but are limited to a single cell (\(n+m=8\)). Specifically, this approach has two levels. On the higher level, we define several types of cell properties that we refer to \"gadgets\" and a covering of the Chimera graph or a portion of it by these gadgets that will guarantee a correct solution of Problem 1 and a gap of at least 2, as long as the gadgets indeed satisfy the properties we have assumed for them. On the lower level, we show that such gadgets really exist by solving the corresponding optimization problems, which are easy because of the gadgets' sizes.
## 7 Conclusions  
A minimal number of sensor nodes are used by the proposed data routing system to cover a large area, which decreases the cost of node placement and makes it easy to track where land mines have been detonated. It is sensible and safe to monitor and dispose of the explosive material thanks to the GPS and camera-based data gathering, which provides the precise position of the sensed event. The complexity of processing and memory is decreased by using the LBT and Golomb + Multiple Quantization coders based image compression approach. Additionally, it can set up a T-based routing topology between the source and BS to allow event-driven based data gathering. And, it ensures a congestion-free data transmission by reserving the path based on the PRM-ACK mechanism. As a result, the suggested TRT mechanism effectively uses battery power and extends the network lifetime. It delivers better results in terms of average end-to-end delay, average energy consumption, packet delivery ratio and control overhead. Also, it is ideally suited for land mine detection and other applications of a similar nature. In the future, a test bed will be developed to evaluate the performance of proposed protocol for the real time applications.  
Conceptualization, K.K. and V.B.; methodology, K.K. and V.B.; software, K.K. and V.B.; validation, K.K., G.I., P.V., A.H., V.B., E.C. and P.S.M.; formal analysis, K.K., G.I., P.V., A.H., V.B., E.C. and P.S.M.; writing--original draft preparation, K.K., V.B. and P.S.M.; writing--review and editing, K.K., G.I., P.V. and A.H.; All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The data presented in this study are available on request from the corresponding author.  
Authors would like to thank and acknowledge Vellore Institute of Technology (VIT), Chennai-600127, India for their support and encouragement.  
The authors declare no conflict of interest.
## 4 Experiments and Results
### Parameter Estimation for Frequency-Modulated (FM) Sound Waves  
The experimental results of running the proposed LO algorithm are recorded in Table 10. In the same table, these findings are compared to those of thirteen different comparative algorithms. From Table 10, it can be shown that the LO algorithm performs similarly to five of the other compared algorithms in terms of attaining optimal outcomes when solving such problems. Furthermore, the LO algorithm is obtained the same best results at all times of runs, and this is similar to the GA-MPC algorithm. Thus, the effectiveness of the proposed LO in handling complex optimization problems is demonstrated. \begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Algorithm** & **Best** & **Mean** & **Median** & **Worst** & **Stdv** \\ \hline LO & 0.0220000 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) \\ HMA & 0.0220000 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) \\ DE & 0.0220000 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) \\ APS 9 & 0.0220000 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) \\ D0E-RHC & 0.0220000 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) & N/A & 0.0220000 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) \\ CHIO & 0.0220000 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) \\ ADE & 0.0220000 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) \\ IMO & 0.0220000 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) \\ KHABC & 0.0220000 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) \\ CDASA & 0.0220000 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) & 1.43290 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) \\ GA-MPC & 0.0220000 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) & 0.0220000 \(\times\) 10\({}^{4}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The performance of the LO algorithm against other comparative algorithms on transmission network expansion planning problems.
## 3 Materials and Methods
### Pediatric Pneumonia Performance Evaluation  
We assessed the performance of deep learning models for classifying pneumonia in chest X-ray images using precision, recall, specificity, F1 score, and accuracy, as defined in Equations (3)-(7). These metrics, calculated from the confusion matrix, provided a comprehensive evaluation of the models' diagnostic capabilities:  
\[\textit{Precision}= \frac{TP}{TP+FP}, \tag{3}\] \[\textit{Recall}= \frac{TP}{TP+FN},\] (4) \[\textit{Specificity}= \frac{TN}{TN+FP},\] (5) \[\textit{F1 score}=2\times\frac{\textit{Precision}\times\textit{ Recall}}{\textit{Precision}+\textit{Recall}},\] (6) \[\textit{Accuracy}= \frac{TP+TN}{TP+FP+TN+FN} \tag{7}\]  
We defined true positives (TP) as cases where the model correctly identified pneumonia and true negatives (TN) as cases without pneumonia that were accurately classified. Falsepositives (FP) occurred when the model incorrectly classified non-pneumonia cases as pneumonia, and false negatives (FN) represented missed pneumonia cases. Specificity measured the model's ability to correctly identify non-pneumonia cases, complementing recall, which focused on detecting pneumonia cases. Chest X-ray images with pneumonia typically showed patterns such as increased lung density, consolidation, or pleural effusion, while diagnostic errors often resulted from overlapping features with other conditions or artifacts in the images.
## 2 Materials and Methods
### Structure Prediction, Refinement, and Validation
#### 2.5.4 Structure Validation, Refinement, and Quality Assessment  
Ramachandran plots were then validated in all the predicted structures [48; 49] to find a good-quality model. The Ramachandran plot generated by PROCHECK provides a visual representation of the \(\varphi\) (phi) and \(\psi\) (psi) dihedral angles of amino acid residues in the protein backbone, enabling the evaluation of the model's conformational stability and structural integrity. If any of these predicted structures have more than 90% of their residues in the most favored regions of the Ramachandran plots, then we will select that structure. Otherwise, the 3D-predicted structures of VLP by I-TASSER, RoseTTAFold, and AlphaFold underwent refinement using the GalaxyRefine online web server ([[https://galaxy.seoklab.org/cgi-bin/submit.cgi?type=REFINE](https://galaxy.seoklab.org/cgi-bin/submit.cgi?type=REFINE)]([https://galaxy.seoklab.org/cgi-bin/submit.cgi?type=REFINE](https://galaxy.seoklab.org/cgi-bin/submit.cgi?type=REFINE)) (accessed on 30 July 2024)) [50]. This server conducted repacking and side-chain rebuilding processes to relax the structure through molecular dynamic simulations (MDS). Ramachandran plots, Z-scores, and MolProbity were then used to validate the refined 3D models. The quality of the modeled VLP structures was assessed using the ProSA tool ([[https://prosa.services.came.sbg.ac.at/prosa.php](https://prosa.services.came.sbg.ac.at/prosa.php)]([https://prosa.services.came.sbg.ac.at/prosa.php](https://prosa.services.came.sbg.ac.at/prosa.php)) (accessed on 1 August 2024)), which provided Z-scores to compare the models against experimental protein structures determined by X-ray crystallography and NMR [51]. Further validation was conducted using MolProbity ([[http://molprobity.biochem.duke.edu/](http://molprobity.biochem.duke.edu/)]([http://molprobity.biochem.duke.edu/](http://molprobity.biochem.duke.edu/)) (accessed on 1 August 2024)), which evaluated the overall model quality [52].
## 4 Illustrative Examples
### Cross-Section Analysis
#### 4.1.2 A Single-Cell Rectangular Cross-Section  
The thin-walled structure with a single-cell rectangular cross-section was analysed by the proposed approach to highlight its capability in coping with closed cross-sections. The cross-section was made of concrete, which was linear, elastic and isotropic, with the material parameters \(E\) = 21 GPa, \(v\) = 0.2 and \(\rho\) = 2500 kg/m\({}^{3}\). The cross-section had a width of \(b\) = 2 m, a height of \(h\) = 1 m and a constant thickness of \(t\) = 0.15 m. A cantilevered beam, having the cross-section and a length \(L\) = 15 m, was handled using the proposed approach to obtain the deformation modes, where the cross-section discretization was performed with five nodes on each width and three nodes on each height.  
The warping modes for the single-cell rectangular cross-section are displayed in Figure 10. These modes were derived from the first six eigenvectors of the thin-walled structure using the proposed approach. More concretely, modes v, vi and ix were derived from the first three eigenvectors (associated with the flexure), while modes iv and vii both were derived from the fourth eigenvector (associated with the rotation) and mode viii was related to the fifth eigenvector (associated with the uniform extension). From the point of hierarchy, mode iv belonged to the Primary family, while the others belonged to the Secondary family.  
Figure 11 presents the warping modes for the cross-section obtained by [PERSON] et al. [37]. The cross-section discretization was carried out in the same way. The modes were organized  
Figure 10: The first seven warping modes of the single-cell rectangular cross-section derived with the proposed approach: (**a**) Mode iv, (**b**) mode v, (**c**) mode vi, (**d**) mode vii, (**e**) mode viii, (**f**) mode ix and (**g**) mode x.  
hierarchically, where the first two represent shear-lag modes associated with the flexure modes, and the other two represent shear-lag modes associated with the extension and shear deformation, respectively. By comparison, the four deformation modes in Figure 11 correspond to modes vi, v, viii and ix, respectively. The difference occurred because the deformation modes in Figure 11 still contained the components of Classic modes, while those in Figure 10 eliminated these products. For example, the first mode in Figure 11 can be viewed as the combination of mode vi and Classic mode ii (flexure about the major axis) in the system of the proposed model. The same style goes for the remaining three modes. Thus, the two approaches were in well-agreement in the sense that all the warping modes obtained through the uncoupling procedure can be captured with the set of out-of-plane deformation modes derived with the proposed approach, although the priority assignments of two systems were not fully consistent. However, Primary warping mode iv (Vlasov warping) was not represented explicitly with the uncoupling procedure in [37], which goes against with mainstream theories.
# Probabilistic Shaping for Finite Blocklengths: Distribution Matching and Sphere Shaping
## 2 Preliminaries
### Fundamentals of Amplitude Shaping Schemes  
The amplitude shaper is a block that maps \(k\)-bit sequences to \(n\)-amplitude sequences in an invertible manner. The tasks of this block are (i) to create a _shaping codebook_\(\mathcal{A}^{\star}\subseteq\mathcal{A}^{n}\), and (ii) to realize a _shaping encoder_ to index these sequences. The former task is related to the properties of the desired set \(\mathcal{A}^{\star}\) while the latter deals with the algorithmic implementation of the mapping. This difference is discussed in detail in Section 2.4. In the remainder of this section, we introduce the concepts and parameters that are associated with the shaping techniques that will be investigated in this paper.  
The energy of a sequence \(a^{n}=(a_{1},a_{2},\ldots,a_{n})\) is given by  
\[e\left(a^{n}\right)=\sum_{j=1}^{n}a_{j}^{2}. \tag{3}\]  
When \(n\)-sequences are represented as points in an \(n\)-dimensional (\(n\)-D) space, the set  
\[\mathcal{A}^{\bullet}=\{a^{n}:e(a^{n})\leq E^{\bullet}\} \tag{4}\]  
consists of all amplitude sequences located inside or on the surface of the \(n\)-sphere of squared radius \(E^{\bullet}\). The zero-energy point is at the center of this sphere.  
The composition of a sequence \(a^{n}\in\mathcal{A}^{n}\) is defined as \(C=[n_{1},n_{2},\ldots,n_{|\mathcal{A}|}]\), where \(n_{j}\) denotes the number of times the \(j\)th element of \(\mathcal{A}\) occurs in \(a^{n}\). The number of \(n\)-sequences with the same composition \(C\) is given by the multinomial coefficient  
\[\text{MC}(C)=\frac{n!}{n_{1}!n_{2}!\cdots n_{|\mathcal{A}|}!}. \tag{5}\]  
For a set \(\mathcal{A}^{\star}\) of amplitude sequences with average amplitude distribution \(P_{A}(a)\) over \(\mathcal{A}\), the average energy per symbol is given by  
\[E=\sum_{a\in\mathcal{A}}P_{A}(a)a^{2}. \tag{6}\]  
The shaping rate of the set \(\mathcal{A}^{\star}\) is defined as  
\[R_{\text{s}}=\frac{\log_{2}|\mathcal{A}^{\star}|}{n} \tag{7}\]  
in bit/1-D. The input blocklength of a shaping algorithm that indexes sequences from the shaping set \(\mathcal{A}^{\star}\) is  
\[k=\lfloor\log_{2}\left(|\mathcal{A}^{\star}|\right)\rfloor \tag{8}\]  
in bits. It can be shown that the parameters of a shaping code \(\mathcal{A}^{\star}\) satisfy the following inequality  
\[\mathbb{H}(A)\stackrel{{\text{(a)}}}{{\geq}}\frac{\log| \mathcal{A}^{\star}|}{n}\stackrel{{\text{(b)}}}{{\geq}}\frac{k}{n} \tag{9}\]  
where (a) is due to the finite blocklength \(n\) and (b) is due to the binary-input nature of the shaping algorithm, i.e., the rounding in (8). Here \(\mathbb{H}(A)\) is the entropy of \(P_{A}\) in bits. In (9), both (a) and (b) are satisfied with equality when \(n\to\infty\) for asymptotically optimum amplitude shaping architectures. The rate loss of a shaping set \(\mathcal{A}^{\star}\) with average distribution \(P_{A}(a)\) can then be defined in bit/1-D as  
\[R_{\text{loss}}=\mathbb{H}\left(A\right)-\frac{k}{n}. \tag{10}\]
## 3 Materials and Methods
### Loss Function
Based on experience, supervised learning, when combined with semi-supervised methods, often requires a higher emphasis on labeled data to guide the learning process effectively. The CPS loss (\(\beta\)) and contrastive learning loss (\(\gamma\)) were given equal weights to balance their contributions, as both are essential for utilizing the unlabeled data to improve the model's generalization. This balanced approach ensures that the model benefits from both labeled and unlabeled data, leading to better overall performance. Therefore, in our experiments, we chose \(\lambda\) to be 0.4, \(\beta\) to be 0.3, and \(\gamma\) to be 0.3. The complete SemiPolypSeg optimization process is outlined in Algorithm 1. ```
0: Define the segmentation networks \(\{HTCSNet_{i}(\cdot)\}_{i=1}^{2}\), projectors \(\{Pro_{i}(\cdot)\}_{i=1}^{2}\), batch size \(B\), maximum epoch \(Epoch_{\max}\), labeled images \(X_{n}^{L}=\{(x_{i}^{L},y_{i}^{L})\}_{i=1}^{n}\), unlabeled images \(X_{m}^{ll}=\{u_{i}\}_{i=n+1}^{m}\), and all datasets \(X_{\text{All}}=X_{n}^{L}\cup X_{m}^{ll}\). Parameter:\(\{\theta_{i}\}_{i=1}^{2}\) of \(\{HTCSNet_{i}(\cdot)\}_{i=1}^{2}\) Output:\(\{HTCSNet_{i}(\cdot;\theta_{i})\}_{i=1}^{2}\). Initialization: Initialize network and projector parameters \(\{\theta_{i}\}_{i=1}^{2}\) and \(\{\mu_{i}\}_{i=1}^{2}\). 1:for epoch = 1 to \(Epoch_{\max}\)do
2:for all batches \(B\)do
3: Generate predictions for labeled data \(HTCSNet_{1}(x_{i}^{L})\) and \(HTCSNet_{2}(x_{i}^{L})\) for all \(x_{i}^{L}\in X_{n}^{L}\);
4: Generate predictions for unlabeled data \(HTCSNet_{1}(u_{i})\) and \(HTCSNet_{2}(u_{i})\) for all \(u_{i}\in X_{m}^{ll}\)
5: for all \(u_{i}\in X_{m}^{ll}\), Generate feature maps \(Pro_{1}(HTCSNet_{1}(u_{i}))\) and \(Pro_{2}(HTCSNet_{2}(u_{i}))\) from two projectors. 6: Let \(\text{Loss-Total}=\lambda\cdot\text{Loss-sup}+\beta\cdot\text{Loss-cps}+\gamma \cdot\text{Loss-sim}\), as defined in Equations (1)-(8). 7: Update \(\{\theta_{i}\}_{i=1}^{2}\) by applying gradient descent on Loss-Total. 8:endfor
9:endfor return\(\{HTCSNet_{i}(\cdot;\theta_{i})\}_{i=1}^{2}\). ```  
**Algorithm 1** SemiPolyPseg (training)
## 5 Validation of Surrogated MIMO-NARX Model
### Statistics for All Validation Cases  
The statistical information of the total 300 validation samples is further summarized for comparison of the Kriging/PCE/APC-NARX models and traditional MCS in Figure 19. Figure 19a shows the box plot for the mean fitness of the four outputs in reduced coordinates, in which the red line indicates the median, the blue box indicates the 25 th and 75 th percentiles, and the red plus symbol indicates outliers. It demonstrates that all three meta-model-surrogated MIMO-NARX models have nearly similar accuracy for most MCS validation cases except for some outliers. Figure 19b shows the histogram with a distribution fitting curve of the mean fitness of the four outputs in reduced coordinates, which illustrates that APC-NARX has more counts for higher fitness than the corresponding Kriging- and PCE-NARX models. Figure 19c-f shows the statistical information for the mean fitness of the nine-DOF absolute velocity and displacement responses. It can be observed from Figure 19c,e that the Kriging/PCE/APC-NARX strategy is quite accurate in velocity prediction while the accuracy of displacement obtained by integration decreases to a certain extent. Figure 19d,f indicates that PCE- and APC-NARX are superior to Kriging-NARX in terms of the counts of good fitness. Figure 19g-j shows the statistical information for the mean fitness of the nine inter-story responses of velocity and displacement. The accuracy is observed to decrease when compared with those in Figure 19c-f. Lower accuracy brings more outliers, which interferes with the comparison of the three meta-model surrogated MIMO-NARX models.  
Figure 20 shows the variation in the accuracy of Kriging/PCE/APC-NARX model prediction with respect to the mean ductility ratio of the nine inter-story Bouc-Wen hysteresis. The fitness and ductility in Figure 20 represent the mean value of the fitness and ductility ratio of the four outputs or nine responses. As shown in Figure 20a-e, the accuracy of the Kriging/PCE/APC-NARX strategy significantly decrease with the increase of inter-story ductility. Figure 20c,e illustrates this phenomenon again that the predicted accuracy of displacement is generally inferior to that of velocity due to the accumulation error. It can be demonstrated that the Kriging/PCE/APC-NARX strategy is basically accurate for most MCS validation cases within a certain nonlinearity range.  
Figure 18: Correlation coefficients for peak responses (300 samples). (**a**) Peak velocity; (**b**) Peak displacement.  
Figure 19: Boxplot and histogram of the mean fitness of different time history curves (300 samples). (**a**) The mean fitness of the four outputs in reduced coordinates: Boxplot; (**b**) Histogram; (**c**) The mean fitness of the nine-DOF absolute velocity responses: Boxplot; (**d**) Histogram; (**e**) The mean fitness of the nine-DOF absolute displacement responses: Boxplot; (**f**) Histogram; (**g**) The mean fitness of the nine inter-story velocity responses: Boxplot; (**h**) Histogram; (**i**) The mean fitness of the nine inter-story displacement responses: Boxplot; (**j**) Histogram.