esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Solution to the Problem
### Thermal Stress and Electric Displacement Field  
According to the theory of solution of the equations, the solution of the in- homogeneous Equations (7) and (8) can be expressed as the sum of the general solution of the corresponding homogeneous equations and a particular solution of the in-homogeneous equation. Therefore, in the following discussion, we will construct the particular solution of Equations (7) and (8) and the corresponding general solution of homogeneous form.  
Similar to the solution process of temperature field, the solution of homogeneous Equation (9) can be expressed as  
\[\mathbf{U}_{p}=[W_{p},\Phi_{p}]^{T}=\text{Img}(z). \tag{50}\]Therefore, the stress and potential shift can be expressed as  
\[\mathbf{t}_{x}-i\mathbf{t}_{y}=\mathbf{L}^{(n)}\mathbf{G}(z). \tag{51}\]  
where  
\[\mathbf{G}(z)=\mathbf{g}^{\prime}(z).\]  
Substitute Equation (50) into Equations (7) and (8), we obtain  
\[\
abla^{2}W=-\frac{e_{15}^{(n)}\mathbf{p}}{c_{44}^{(n)}\epsilon_{11}^{(n)}+e_ {15}^{(n)}}[\text{Im}\mathbf{g}^{\prime}(z)-\text{Reg}^{\prime}(z)], \tag{52}\]  
\[\
abla^{2}\Phi=\frac{c_{44}^{(n)}\mathbf{p}}{c_{44}^{(n)}\epsilon_{11}^{(n)}+e _{15}^{(n)}}[\text{Im}\mathbf{g}^{\prime}(z)-\text{Reg}^{\prime}(z)]. \tag{53}\]  
where \(\mathbf{p}=[p_{1}^{(1)},p_{1}^{(2)}]^{T}\).  
By solving the Equations (52) and (53), we can obtain  
\[W=-\frac{e_{15}^{(n)}\mathbf{p}}{8(c_{44}^{(n)}\epsilon_{11}^{(n)}+e_{15}^{( n)})}[(1+i)\mathbf{g}(z)\overline{z}+(1-i)\mathbf{g}(\overline{z})z]+g_{w}(z)+ \lambda_{w}(\overline{z}), \tag{54}\]  
\[\Phi=\frac{c_{44}^{(n)}\mathbf{p}}{8(c_{44}^{(n)}\epsilon_{11}^{(n)}+e_{15}^{ (n)})}[(1+i)\mathbf{g}(z)\overline{z}+(1-i)\mathbf{g}(\overline{z})z]+g_{ \phi}(z)+\lambda_{\phi}(\overline{z}). \tag{55}\]  
where \(g_{w}(z)\), \(\lambda_{w}(\overline{z})\), \(g_{\phi}(z)\), \(\lambda_{\phi}(\overline{z})\) are holomorphic functions.  
According to the above discussion, the following functions may be taken as the special solutions of Equations (7) and (8)  
\[\mathbf{U}_{q}=[W_{q},\Phi_{q}]^{T}=\text{Im}\mathbf{f}(z). \tag{56}\]  
where  
\[\mathbf{f}(z)=\mathbf{f}_{n}(z)=\left[\begin{array}{c}-\frac{e_{1}^{(n)}p_{ 1}}{8(c_{44}^{(n)}\epsilon_{11}^{(n)}+e_{15}^{(n)})}[(1+i)g_{n}(z)\overline{z }+(1-i)g_{n}(\overline{z})z]+f_{n*}(z)\\ \frac{e_{44}^{(n)}p_{1}}{8(c_{44}^{(n)}\epsilon_{11}^{(n)}+e_{15}^{(n)})}[(1+ i)g_{n}(z)\overline{z}+(1-i)g_{n}(\overline{z})z]+f_{n*}(z)\end{array}\right],\]  
\[n=1,2. \tag{57}\]  
Here, \(f_{1*}(z)\) is a holomorphic function.  
For the non-homogeneous Equations (7) and (8), the relationship between stress and potential shift is also obtained  
\[\mathbf{t}_{x}-i\mathbf{t}_{y}=\mathbf{L}^{(n)}\mathbf{f}^{\prime}(z)+\left[ \begin{array}{c}0\\ p_{1}^{(n)}\end{array}\right]T(1-i). \tag{58}\]  
According to Equations (51), (57), the solutions of Equations (7) and (8) can finally be expressed as  
\[\mathbf{U}=\left[\begin{array}{c}W\\ \Phi\end{array}\right]=\mathbf{U}_{p}+\mathbf{U}_{q}=\text{Im}[\mathbf{f}(z)+ \mathbf{g}(z)]. \tag{59}\]
## Appendix C PN9 Coding  
The 9-bit pseudo-random number (\"PN9\") generator is shown at the top of Figure 14. The generator is described by the polynomial \(x^{9}+x^{5}+x^{0}\). The PN9 generates all the values between 1 through 511 (inclusively) in a pseudo-random order as it is clocked. The latches are all set to ones at the start of a whitening operation.  
Figure 15 illustrates the operation of the PN9 generator as it is clocked. The generator starts with a value of all ones \"111111111\". Bit 0 (the LSB) and bit 5 are XOR'd to produce 0 that is shifted into the MSB on the next clock. This results in the next value of the generator being \"01111111\". Again, bits 0 and 5 are XOR'd to give the next value of the MSB (again, 0) to produce the next value of the generator \"00111111\", and the process continues through all 511 states of the generator.  
The lower set of latches in Figure 14 contains the current byte of the data to be whitened. Recall that the preamble and sync words are not whitened, so the first byte of data to be whitened is either the packet length byte (in variable packet mode) or the first byte of user data.  
When the first byte of data is ready, it is XOR'd with the eight LSBs of the initial value of the PN9 generator, which are all ones. So, the PN9 generator is \"11111111\", and the dataare XOR'd with the eight LSBs of this, which is \"11111111\". This whitened data are then transmitted over the air. Next, the second byte of data is shifted into the data latches (eight shifts, one per bit), while the PN9 generator is also clocked eight times (once per bit). This means that the second byte of user data is not XOR'd with the next PN9 value but instead by the value eight later in the PN9 sequence. Thus, the PN9 generator contains \"11111111\" when the first byte is processed, while the PN9 generator state during the second byte of data is not \"01111111\" (the next PN9 value), but instead \"111100001\" (the ninth PN9 value).  
Suppose the (unwhitened) data sequence to be transmitted starts out as follows (these would be the bytes, for example, if a packet with a packet length byte of ten were transmitted, and the data were 0x00, 0x01,...): /0000 1010/0000 0000/0000 0001/0000 0010/... Remember that the values to XOR with the data are the eight LSBs of the PN9 sequence if every eighth value is used:  
1,1,1,1,1,1,1,1 *** Eight LSBs are 11111 1111  
0,1,1,1,1,1,1,1,1  
0,0,1,1,1,1,1,1  
0,0,0,1,1,1,1,1  
1,0,0,0,0,1,1,1,1  
1,1,0,0,0,0,1,1,1  
1,1,1,0,0,0,0,1,1  
1,1,1,0,0,0,0,1 *** Eight LSBs are 1110 0001  
0,1,1,1,1,0,0,0  
1,0,1,1,1,0,0,0  
1,0,1,1,1,1,0,0  
1,1,0,1,1,1,1,1  
0,0,0,1,1,1,0,1,1  
0,0,0,1,1,1,0,1,1  
0,0,0,1,1,1,0,1 *** Eight LSBs are 0001 1101
# Flattening the Curve of Flexible Space Robotics [PERSON]
## 1 Introduction
### Statements of Novelty
#### 1.2.1 Trade-Off Study on Application of Classical Methods  
Classical proportional plus integral plus derivative control is designed to satisfy the nominal performance specifications (e.g., rise time, overshoot, settling time, etc.). Following the well-documented methods of flexible system compensation. Second-order filters are sequentially applied to each flexible mode: notch filtering of resonant response and bandpass filtering of anti-resonant responses associated with free-free vibrations of on-orbit space robots. Classical procedures primarily focus on portions of flexible modes (either resonance or anti-resonance) that by generation of cross-over frequencies. Accordingly, only a single notch or bandpass filter is commonly used, which also helps limit system order, since addition of second-order filters in the feedback path increases the closed-loop system order. Trade-off studies are performed, evaluating both the performance and increase in system order for progressively more structural filtering, eventually seeking to \"flatten the curve\" (the magnitude response plots), essentially nullifying the flexible affects. While a predictable response can be tuned to the desired performance specification, these classical methods suffer from limited robustness to variation in system natural frequencies. Iterative application of classical structural filtering, as instantiated in this research, realizes an eleven to four hundred and twenty percent improvement in the gain margin and minus five to sixty-four percent improvement in the phase margin, with an up to twenty-four percent improvement in tracking error in response to step commands. On the downside, the methods increase the system order up to fifty, implying a high increase in computational burden.
## 5 Numerical Comparison of the Existing Mass-Rig Systems
### Numerical Modeling of the Inertial Systems
#### 5.1.1 Model I
However, this model replaces the stress-strain relationships in the zero-length section by an analogous stress-slip relationship for the steel and concrete fibers, as shown in Figure 13. The slip displacement at yield (\(S_{y}\)) in the steel fibers can be determined from the measurements of the linear variable differential transformers (LVDTs) located at the column base. For the purpose of comparing the three systems, a value of 0.76 mm for the slip displacement at yield is used in the distributed plasticity model based on the experimental results reported in [PERSON] et al. [9]. The steel fibers in the bond-slip zero-length element are modeled using the Guiffre-Menegotto-Pinto model because of its easy implementation. The same uniaxial concrete material model used in the concrete fiber section was adopted for the confined and unconfined concrete in the bond-slip zero-length element. To prevent discontinuities in the steel stresses and neutral axis location between the fibers of the non-linear beam/column element and the bond-slip section [23], the strains in this section were also modified. This adjustment was achieved by applying a scale factor of \(SF_{conc}=s_{y}/\varepsilon_{y}\) to the concrete strains. Although this scale factor is dimensionally incorrect, it increases the concrete strains to preserve consistency with the fiber sections. A scale factor of 17 is used for the analysis. Figure 13: Fiber stress-strain relations: (**a**) steel; (**b**) concrete. To represent the inertial forces transferred to the specimen, the IMS is modeled in OpenSees [10] using an equivalent elastic beam-column element with a pin support and a total height equal to the vertical distance from the pin at the base of the IMS to the longitudinal axis of the rigid link (i.e., 243.8 cm). Additionally, a truss element is used to represent the rigid link connecting the IMS and the specimen. The option of corotational transformation is assigned to the beam-column representing the IMS to capture P-\(\Delta\) effects.
## 4 Experimental Investigation of Aeroelastic Vibration and Harvesting Performance  
### Experimental Setup  
The experimental apparatus for the airfoil-based flutter piezoelectric energy harvester systems was constructed in a controlled laboratory environment, as illustrated in Figure 11.  
Figure 10: Velocity distribution diagram with the installation angle: (**a**) 0\({}^{\circ}\) installation angle; (**b**) 3\({}^{\circ}\) installation angle; (**c**) 6\({}^{\circ}\) installation angle; (**d**) 9\({}^{\circ}\) installation angle.  
The core component--an energy collection system--was mounted vertically in the test section using a specialized support mechanism to ensure stability and precise positioning.  
The experiments were conducted in an open-circuit wind tunnel facility housed within an enclosed laboratory space. To maintain accurate flow conditions, a calibrated pitot-static tube was installed at the tunnel inlet for continuous velocity monitoring. The experimental configuration was carefully designed to minimize flow interference, with adequate downstream distance between the test section and the laboratory wall to prevent flow recirculation. The energy harvesting system was installed in the test section through the access panel, with precise alignment relative to the freestream flow direction. To ensure reliable results and minimize wall interference effects, the system was designed with a blockage ratio below 5%, and no-slip boundary conditions were implemented on both the tunnel walls and airfoil-based surfaces.  
To validate the computational results presented in Section 3, the experimental protocol began with constraining the movable components of the energy harvester. Upon establishing steady-state flow conditions at the designated test velocity, the constraints were systematically removed to allow free oscillation of the system. The measurement apparatus consisted of a high-precision laser displacement sensor with a 0.1 mm resolution for tracking instantaneous motion, coupled with a microcontroller-based data acquisition system providing a 0.00081 V voltage resolution. This integrated system simultaneously recorded both displacement measurements from the laser sensor and voltage output from  
Figure 11: Wind tunnel experimental setup: **(a)** schematic diagram; **(b)** physical device.  
the piezoelectric sheet, with all experimental data continuously acquired and stored in a digital format for subsequent analysis and comparison with computational results.
###### Abstract  
Data clustering is an important research topic in data mining and signal processing communications. In all the data clustering methods, the subspace spectral clustering methods based on self expression model, e.g., the Sparse Subspace Clustering (SSC) and the Low Rank Representation (LRR) methods, have attracted a lot of attention and shown good performance. The key step of SSC and LRR is to construct a proper affinity or similarity matrix of data for spectral clustering. Recently, Laplacian graph constraint was introduced into the basic SSC and LRR and obtained considerable improvement. However, the current graph construction methods do not well exploit and reveal the non-linear properties of the clustering data, which is common for high dimensional data. In this paper, we introduce the classic manifold learning method, the Local Linear Embedding (LLE), to learn the non-linear structure underlying the data and use the learned local geometry of manifold as a regularization for SSC and LRR, which results the proposed LLE-SSC and LLE-LRR clustering methods. Additionally, to solve the complex optimization problem involved in the proposed models, an efficient algorithm is also proposed. We test the proposed data clustering methods on several types of public databases. The experimental results show that our methods outperform typical subspace clustering methods with Laplacian graph constraint.  
Keywords:subspace clustering; Sparse Subspace Clustering; low rank representation; Local Linear Embedding; manifold learning +
Footnote †: journal: Applied Sciences
# A Review of Explainable Deep Learning Cancer Detection Models in Medical Imaging
## 4 Discussion
### Future Directions  
There are numerous works that propose novel explanation methods but little focus on what makes an explanation suitable for the context it will applied. This is essential for domains such as cancer diagnosis. Furthermore, more studies are needed to identify what clinicians deem explainable and use these insights as a measuring stick for explanation methods for deep learning cancer detection systems. Another important direction is using these insights to derive quantitative explanation metrics. The majority of metrics used to measure explanation quality are designed without clinicians involved. To create explanation techniques suitable for clinician integration is is necessary to measure them in a way guided by end-user criteria. Explanation techniques also can be useful to extract clinically relevant features. There are studies that use explanation techniques to localize lesions but these models do not extract information such as shape, volume, area, and other relevant characteristics. A future opportunity is to extract these features without computationally expensive segmentation. With this, clinicians do not need to extract these features manually. If explanation techniques are implemented into clinical settings, the system can automatically extract these characteristics for the clinicians thus aiding in the diagnosis process.  
The common approach for providing an explanation for image classification is to produce a heatmap showing the most discriminative region. More work needs to be done to provide greater insight than using this direct approach. For example, it would provide more insight if explanation methods could should why a classification was not made and quantify the uncertainity of the explanation. Being able to reason for and against is also important to provide greater insight and explainability. More studies should be conducted on where current methods fail and why. This would provide the community more insight on how to create more robust explanation methods. It would also provide greater confidence the methods we currently have.  
Currently, the majority of cancer detection studies utilize post-hoc techniques. As stated in [33; 140] it is advantageous to develop intrinsically explainable (i.e., ad-hoc) deep learning models. Post-hoc explanation methods may be useful for diagnosing the deep network model but the insight gained is unsubstantial. A model suited for clinical implementation should be fully explainable with the predictive power of modern deep learning approaches. Post-hoc methods only explain where the network is looking which is not enough information for high stakes decision making. Post-hoc methods are fragile and easily manipulated [141; 142] and can provide misleading results which hinders clinical implementation. Some approaches attempting ad-hoc models were discussed in the paper with results that show that intrinsically explainable models can achieve accuracy similar to that of unexplainable models. More research is needed to verify this and evaluate the clinical performance.
# A Forecast Model of the Number of Containers for Containers by Voyage
## 3 Mixed Kernel Function SVM Prediction Model
### Construction of Mixed Kernel Function  
The assessment of the learning performance and generalization performance of the SVM depends on the selection of the kernel functions. Two types of kernel functions are widely used: (1) the \(q\) polynomial kernel function, \(K(x,x^{\prime})=[(x\cdot x^{\prime})+1]^{q},(q=1,2,\cdots)\) and (2) the Gaussian radial basis kernel function, \(K(x,x^{\prime})=\exp\Bigl{(}-\left\|x-x^{\prime}\right\|^{2}/\sigma^{2}\Bigr{)}, (\sigma>0)\)[35].  
The polynomial kernel function is a global kernel function with strong generalization ability but weak learning ability [36], whereas the Gaussian radial basis kernel function is a local kernel function with strong learning ability but weak generalization ability. It is difficult to obtain good results in regression forecasting [37] by using only a single kernel function. Moreover, there are certain limitations in using the SVM with a single kernel function to predict the non-linear change in the data of the number of allocated containers of the container ship for one voyage.  
A mixed kernel function is a combination of single kernel functions, integrating their advantages while compensating for the drawbacks, to obtain a performance that can not be achieved by a single kernel function. The mixed function proposed in this study is based on a comprehensive consideration of the local and global kernel functions. According to [PERSON]'s theorem, the convex combination of two Mercer kernel functions is a Mercer kernel function, and thus, the following kernel functions given by Equation (11) are also kernel functions:  
\[K\bigl{(}x,x^{\prime}\bigr{)}=(1-\rho)\exp\Bigl{(}-\left\|x-x^{\prime}\right\| ^{2}/\sigma^{2}\Bigr{)}+\rho\bigl{[}\bigl{(}x\cdot x^{\prime}\bigr{)}+1\bigr{]} ^{q} \tag{11}\]  
where \(0<\rho<1\), and \(\rho\) is the weight adjustment factor.  
In Equation (11), the flexible combination of the radial basis kernel function and polynomial kernel function is obtained by adjusting the value of \(\rho\)[38]. When \(\rho>0.5\), the polynomial kernel function is dominant and the mixed function shows strong generalization ability and when \(\rho<0.5\), the radial basis kernel function is dominant, and the mixed kernel function shows strong learning ability. Therefore, the mixed kernel function SVM exhibits a better overall performance in predicting the number of allocated containers of the container ship for one voyage.
# Semi-Supervised Manifold Alignment Using Parallel Deep Autoencoders
## 2 Semi-Supervised Manifold Alignment  
[PERSON] et al. [14] characterised manifold alignment using the correspondence information of two input datasets that have subsets of corresponding point pairs as semi-supervised manifold alignment. These subsets of corresponding points are employed to establish the alignment of the two latent low-dimensional manifolds. [PERSON] et al. [14] referred to points with correspondence information as \"labelled\" points. Among the semi-supervised manifold alignment methods, two approaches can be distinguished [38]:  
Approach I: Dimensionality reduction is followed by alignment [23].  
Approach II: A joint manifold is created to represent the union of the given manifolds, and then, the joint manifold is mapped to a lower-dimensional space [39].  
For experimental comparison with the new PDAE, we employed the following three methods. Each is an example of one of the above two general approaches and can be applied at the feature level (feat) and at the instance level (inst) [39]:  
Method 1 (MAPA), Manifold Alignment using Procrustes Analysis [23]: This method is a version of Approach I and in its second step applies Procrustes analysis to rescale and rotate manifold \(S_{Y}\) to align it with manifold \(S_{X}\). If Locality Preserving Projections (LPP) [40] are used in the dimensionality reduction step, it results in feature-level manifold alignment, and we refer to the method as MAPA-feat in the following sections. If Laplacian eigenmaps [41] are used in the dimensionality reduction step to obtain instance-level alignment, we refer to the method as MAPA-inst.  
Method 2 (MALG), Manifold Alignment preserving Local Geometry [39]: This method is a version of Approach II. First, a joint manifold \(Z\) is calculated using the graph Laplacians of the given manifolds. If, in the next step, eigenvalue decomposition of \(Z\) provides instance-level alignment, we refer to it as MALG-inst. If generalised eigenvalue decomposition of \(Z\) is used for feature-level alignment, we refer to the method as MALG-feat.  
Method 3 (MAGG), Manifold Alignment preserving Global Geometry [39]: This method is a version of Approach II. A joint manifold \(Z\) is generated using the global distances of corresponding pairs in \(X\cup Y\). Eigenvalue decomposition of \(Z\) provides dimensionality reduction to obtain the aligned low-dimensional manifolds in the case of instance-level alignment (MAGG-inst). Generalised eigenvalue decomposition is used instead in the case of feature-level alignment (MAGG-feat).  
In summary, this classification comprises six semi-supervised manifold alignment methods: MAPA-feat, MAPA-inst, MALG-feat, MALG-inst, MAGG-inst, and MAGG-feat. These will be used in the following for comparisons with the proposed PDAE.