esa-sceva/satcom-chunk-collection huggingface dataset:
## 7 Conclusions  
In this article, we detailed the concept of sinusoidal parameter estimation using quadratic interpolation over three bins of a power-scaled DFT surrounding a magnitude spectrum peak. This method, the XQIFFT, improves on existing quadratic interpolation methods based on linear and logarithmic scaling. We presented a heuristic for optimizing the XQIFFT power-scaling exponent \(p\) for a particular window type/window length/zero-padding factor. We presented an analysis of noise sensitivity of the proposed estimator, the dependency of the optimal exponent on window length, and a comparison with competing methods in noisy conditions under twelve common window types. We observed that across the entire tested SNR range, the proposed XQIFFT had a lower bin estimate MSE than the state-of-the-art direct estimates of Duda and Candan for ten of the twelve tested windows. From examining the high SNR regions we can also say that for ten of the twelve tested windows the XQIFFT has a lower systematic bias than the state-of-the-art methods as well. For the remaining two windows tested (Hann and Tukey), the XQIFFT has a lower MSE only at low SNR.  
When implementing the XQIFFT, the reader may choose the correct value of \(p\) in one of two ways depending on their application. For common windows whose lengths are between 512 and 4096 samples, linear interpolation between the values of \(p\) reported in Table 2 may be used to approximate the optimal value of \(p\) to five decimal places. For even more precision or for window types or lengths  
Figure 10: Testing different window types. (**a**) [PERSON] window; (**b**) [PERSON]–[PERSON] window; (**c**) [PERSON] window; (**d**) [PERSON] window; (**e**) [PERSON] window; (**f**) [PERSON]–[PERSON] window; (**g**) [PERSON] window; (**h**) DPSS window; (**i**) Kaiser–[PERSON] window; (**j**) [PERSON] window; (**k**) [PERSON] window; (**l**) [PERSON] window (50%).  
not reported in Table 2, the reader may use the generalized procedure reported in Section 5.3 to produce an optimal value of \(p\).  
Future work should consider applying the XQIFFT-style magnitude spectrum scaling to types of estimators that rely on techniques other than parabolic interpolation. We expect that for other approaches that rely in some way on main lobe shape, the main-lobe-shaping philosophy of the XQIFFT may yield improvements.  
**Acknowledgments:** Thank you to the anonymous reviewers who contributed valuable suggestions for refining this work.  
**Author Contributions:** [PERSON] contributed the central concept of the article. [PERSON] was the main contributor to the \"Problem Statement,\" \"Invariance Properties of QIFFFT Methods,\" and \"Sensitivity to Noise\" sections and the material on the asymptotic behavior of the XQIFFT. [PERSON] was the main contributor to the \"Results\" section and created Figures 1-4. Otherwise the authors contributed equally to the manuscript.  
**Conflicts of Interest:** The authors declare no conflict of interest.
## 3 Results of Numerical Simulations and Case Studies
### Case of a Circular Reference Orbit  
In this last part of Section 3, we analyze the limiting case of a circular reference orbit. Accordingly, consider the scenario in which \(e_{0}=0\) and the semilatus rectum is equal to \(1\,\mathrm{AU}\). In this case, Equation (4) simplifies as  
\[\widetilde{r}(\widetilde{t}_{0})=1,\quad\theta(\widetilde{t}_{0})=0,\quad \widetilde{v}_{r}(\widetilde{t}_{0})=0,\quad\widetilde{v}_{t}(\widetilde{t}_ {0})=1 \tag{15}\]  
where the initial true anomaly \(v_{0}\) was set to zero for symmetry reasons (the initial orbit is circular). On the other hand, the final constraints given by Equation (7) now become  
\[\widetilde{r}(\widetilde{t}_{f})=1,\quad\theta(\widetilde{t}_{f})=\widetilde{ t}_{f}+\Delta\phi,\quad\widetilde{v}_{r}(\widetilde{t}_{f})=0,\quad\widetilde{v}_{t} (\widetilde{t}_{f})=1 \tag{16}\]  
The dimensionless angular velocity of the virtual point along the (circular) reference orbit is a constant of motion with a value equal to \(1\) so that the polar angle \(\theta_{p_{f}}\) of the virtual point at the (dimensionless) final time is simply equal to \(\widetilde{t}_{f}\).  
Using the initial and final conditions given by Equations (15) and (16), respectively, the (dimensionless) optimization problem modeled by the equations of motion (6) and the Euler-Lagrange Equation (9) can be solved with a standard method as a function  
Figure 11: Minimum flight time as a function of \(a_{c}\) for a phasing ahead and behind in an Earth-based mission scenario when \(v_{0}=0\,\mathrm{deg}\). **(a)** Phasing ahead case; **(b)** phasing behind case.  
of the characteristic acceleration \(\widetilde{a}_{c}\) and the phasing angle \(\Delta\phi\). For example, assuming \(a_{c}=0.1\,\mathrm{mm}/\mathrm{s}^{2}\), i.e., \(\widetilde{a}_{c}\simeq 0.0169\), the variation of the minimum flight time with the phasing angle \(\Delta\phi\in[-60,\,60]\) deg is reported in Figure 12. This figure shows, as expected, clear similarities with the graphs reported in Figure 8.  
This aspect confirms that a preliminary study of the performances in the phasing maneuver in the case of an Earth-based scenario can be carried out using the simplified circular orbit model. The transfer strategy in the simplified circular case is similar to that obtained in the Earth-based mission scenario. For example, assuming again \(a_{c}=0.1\,\mathrm{mm}/\mathrm{s}^{2}\) and \(\Delta\phi=\pm 60\,\mathrm{deg}\), the optimal trajectories for the sailcraft reported in Figure 13 are obtained. The corresponding optimal control law \(\tau=\tau(t)\) is shown in Figure 14. In particular, the specific form of the curve drawn in Figure 14 suggests a simplified form of the control law, which originates from the fundamental work by [PERSON] (2016). This simplified, non-optimal form of the control law is illustrated in the next section.  
Figure 12: Minimum flight time for a phasing ahead and behind when the reference orbit is circular with a radius equal to \(1\,\mathrm{AU}\), and \(a_{c}=0.1\,\mathrm{mm}/\mathrm{s}^{2}\). (**a**) Phasing ahead case; (**b**) phasing behind case.
# A Scientific Document Retrieval and Reordering Method by Incorporating HFS and LSD
## 4 Experimental Process and Result Analysis
### System Experiment  
#### 4.2.1 Matching Results of Mathematical Expression Based on HFS  
To ensure the reliability of the mathematical expression similarity evaluation method relying on HFS, an extensive array of experiments was carried out, encompassing diverse types of mathematical expressions. Subsequently, to illustrate the effectiveness of the proposed method, a series of statistical analysis experiments were conducted. These experiments revolved around 10 randomly selected query expressions, intentionally chosen to encompass a variety of mathematical symbols and structures, as outlined in Table 2.  
Figure 3: Text semantic similarity calculation.  
In the experiment, the evaluation of the recall and precision of the retrieval results is conducted using the MAP (Mean Average Precision) metric for ten different query combinations. The calculation method for AP (Average Precision) is  
\[AP=\frac{1}{r}\sum_{i=1}^{r}\frac{i}{pos(i)}, \tag{7}\]  
where \(i\) represents the index of the relevant document, \(pos(i)\) signifies the position of the document, and \(r\) denotes the total number of relevant documents.  
MAP is a widely used metric in information retrieval, calculated as the average of AP scores. It provides a comprehensive assessment of retrieval performance. Table 3 presents the MAP scores for different 'k' values in both the Chinese and English datasets. As shown in the table, the MAP decreases gradually as the 'k' value increases. This trend is attributed to the smaller number of similar expressions available for certain complex mathematical expressions in the dataset. For some of these intricate or less-common expressions, there are fewer than 20 similar candidates, which results in relatively lower MAP_20 values.
## 2 Materials and Methods
### Modified Membrane Characterization--Analytical Methods  
Contact Angle (CA) and Surface Free Energy (SFE): Static and dynamic contact angles (CA) measurements were performed at room temperature using the goniometer PG-X (FibroSystem AB) and deionized water (18 M\(\Omega\) cm) and glycerin as testing liquids. CAs were determined for pristine and grafted membranes, based on sessile drop (static CA) and the tilting plate (dynamic CA) methods described elsewhere [44; 45]. The apparent CA values were calculated by ImageJ software (Image), NIH--freeware version), with an accuracy of \(\pm 2^{\circ}\). Additionally, a contact goniometric analysis was implemented for surface free energy (SFE) assessment for planar ceramic membranes. SFE was  
Figure 1: Ceramic membrane modification by alkylsilanes grafting agent and differences in hydrophobicity level (contact angle and water liquid entry pressure (LEPw)) before (left) and after (right) hydrophobization process.  
calculated based on the Owens-Wendt method [PERSON] and [PERSON] (1985). The results are presented as an average value obtained from 20 to 30 measurements (average accuracy of \(\pm\)5%).  
Atomic force microscopy (AFM): This technique was used for surface analysis (topography and phase analysis) of planar membranes (NanoScope MultiMode SPM System and NanoScope IIIa Quadrex controller--Veeco, Digital Instrument, Saint Ives, Cambridgeshire, UK). Tip scanning mode was applied for surface roughness analysis. Ambient temperature conditions were kept during all experiments. The root mean squared (RMS) roughness was used as a parameter describing heterogeneity of the samples. Scan size areas were equal to 5 \(\times\) 5 \(\upmu\)m. All samples were analyzed at least five times and an average value of RMS was calculated (accuracy \(\pm\)5%).  
Liquid entry pressure (LEPw): The grafting effectiveness of tubular membranes was assessed by liquid entry pressure determination (LEPw)--Equation (1). LEPw is a pressure value at which liquid penetrates across open pores of the membrane and is transported through the hydrophobic layer on the permeate side [PERSON] _et al._ (2011); [PERSON] _et al._ (2011); [PERSON] _et al._ (2011); [PERSON] _et al._ (2011). According to the Laplace-Young equation (Equation (1)), it can be noticed that LEPw value refer to the surface tension (\(\gamma_{\mathrm{L}}\)), contact angle (\(\theta_{\mathrm{ef}}\)) on membrane surface, pore radius (r), and tortuosity factor (B).  
\[\mathrm{LEP_{w}}=-\mathrm{B}\frac{2\gamma_{\mathrm{L}}}{\mathrm{r}}\cos\theta _{\mathrm{ef}} \tag{1}\]  
The LEPw measurements were realized using a laboratory experimental rig presented in detail elsewhere [PERSON] _et al._ (2011). LEPw values were determined for all tubular membrane samples, prior to the membrane characterization in membrane distillation process. During the LEP measurements, the time interval between each pressure step was equal to 60 min.
###### Abstract  
We designed and fabricated a telecentric f-theta imaging lens (TFL) to improve the imaging performance of spectral domain optical coherence tomography (SD-OCT). By tailoring the field curvature aberration of the TFL, the flattened focal surface was well matched to the detector plane. Simulation results showed that the spot in the focal plane fitted well within a single pixel and the modulation transfer function at high spatial frequencies showed higher values compared with those of an achromatic doublet imaging lens, which are commonly used in SD-OCT spectrometers. The spectrometer using the TFL had an axial resolution of 7.8 \(\upmu\)m, which was similar to the theoretical value of 6.2 \(\upmu\)m. The spectrometer was constructed so that the achromatic doublet lens was replaced by the TFL. As a result, the SD-OCT imaging depth was improved by 13% (1.85 mm) on a 10 dB basis in the roll-off curve and showed better sensitivity at the same depth. The SD-OCT images of a multi-layered tape and a human palm proved that the TFL was able to achieve deeper imaging depth and better contrast. This feature was seen very clearly in the depth profile of the image. SD-OCT imaging performance can be improved simply by changing the spectrometer's imaging lens. By optimizing the imaging lens, deeper SD-OCT imaging can be achieved with improved sensitivity.  
SD-OCT; imaging depth; roll-off; field curvature aberration; spectrometer +
Footnote †: journal: Applied  
1
# Few-Shot Steel Defect Detection Based on a Fine-Tuned Network with Serial Multi-Scale Attention
## 3 Methodology
### Enhanced Semi-Supervised Learning Algorithm
The methodology can be explained through the following steps (see Algorithm 2). ```
1:Employ labeled data for initial model training. 2:while no desired performance achieved and no pre-established iterations reached do
3: Utilize the trained model to generate predictions for unlabeled data, treating them as pseudo-labels. 4: Integrate labeled data and pseudo-labels to create an augmented training dataset. 5: Further train the model with the augmented dataset. 6:endwhile
```  
**Algorithm 2** Steps of pseudo-label-based SSL  
The accuracy of pseudo-labels significantly affects the performance of the model. Consequently, thorough consideration must be given to the selection of high-quality pseudo labels, such as by establishing confidence thresholds or utilizing regularization techniques to mitigate the impact of noise. In our study, high-dimensional feature maps were extracted during the training phase of SSL. These feature maps were subjected to dimensionality reduction via the locally linear embedding (LLE) algorithm, transitioning to a two-dimensional space. This refined the workflow of the pseudo-label-based SSL algorithm, which, supported by the LLE algorithm, unfolded as follows:  
(1) A limited number of labeled data were employed to initiate model training. (2) Following the initial model training, high-level features were obtained, which were then dimensionally reduced and visualized through the LLE algorithm. A subsequent data cleansing stage involved the identification and removal of images with incorrect labels, which were then redlassified as unlabeled data. (3) The trained model was applied to predict unlabeled data, and the resulting predictions were utilized as pseudo-labels. (4) The labeled data and pseudo-labels were combined to form an extended training set, which was used to continue training the model. (5) Steps 2 and 3 were executed in cycles until the model either converged, fulfilled the performance criteria, or reached the maximum number of training iterations, resulting in the final model.
# VPP Participation in the FCR Cooperation Considering Opportunity Costs
## 1 Introduction
### FCR Activation and VPP Participation
The concept of the VPP downward reserve provision is illustrated in Figure 4, still using the frequency evolution presented in Figure 2.  
Likewise, the HE upward reserve provision is illustrated in Figure 5.  
Figure 4: VPP downward reserve provision and associated opportunity costs. From these examples it can be concluded that opportunity costs may be occurring in every instant _for the VPP as a whole_, but only half of the time for each of its participants, allowing them to operate with no headroom. It must be taken into account that this example has extreme variations in the frequency for demonstration purposes, but in reality, the frequency is closer to 50 Hz most of the time, allowing the VPP participants to dedicate their units to the energy market in normal conditions and only incur opportunity costs when contingencies happen. One relevant question that arises is, thus, what is the volume of opportunity costs in this case? To answer this question, it is necessary to assess the usage of upward and downward reserves in existing grids. For instance, the data from three years of market sessions in France spanning data from mid-2020 to the end of 2022 [10] is organized from the highest to lowest percentage of reserves activated in Figure 6. The value read on the y-axis is the ratio between the activated energy (MWh) to the contracted power (MW) of the upward/downward reserve. This plot shows that the maximum value of either upward and downward reserves that were measured was around 40% and the minimum was close to 0%. The average and mean values were around 10%. Whether this small percentage translates into low or high opportunity costs for participants in a VPP was one of the motivations behind this study. Figure 5: VPP upward reserve provision and associated opportunity costs. Figure 6: Percentage of upward and downward reserves used in France.
## 3 Application Examples and Comparative Analysis
### Calculation Results and Comparative Analysis
Based on the results in Table 2 and the comparative analysis in Figures 10 and 11, the formulas derived in this study (Equations (20)-(22) and (25))--which account for instantaneous detonation axial pressure and rock mass damage--demonstrate greater accuracy and rationality than existing models. Figure 11: Variation patterns of triaxial stresses at calculation point A with different damage factors. Figure 10: Comparison of radial and axial stresses with and without considering relevant factors q(t) and D.
## 4 Experiment and Results
### Generalization Experiments of SIT-Conversion
#### 4.2.1 Datasets and Parameter Setup  
The CIFAR10 dataset consists of 60,000 samples, divided into 10 categories, where each sample is a 32 \(\times\) 32 pixel RGB image. These 60,000 samples are further split into 50,000 training samples and 10,000 testing samples. The CIFAR100 dataset is similar to CIFAR10, except it has 100 categories, with each category containing 500 training images and 100 testing images. The ImageNet-1K dataset contains 1.2 million training samples, 50,000 validation samples, and is divided into 1000 categories.  
The models were trained in parallel using two NVIDIA RTX4090 GPUs, and one was employed during the SNN inference phase. The input size of the model was set to 224 \(\times\) 224, with a batch size of 256. All experiments were conducted using the AdamW optimizer [72] with a cosine learning rate schedule, as detailed in Table 5. The pretrained model (EdgeNeXt-S) obtained from the ImageNet-1K dataset was fine-tuned on CIFAR10 and CIFAR100 datasets. By default, the EdgeNeXt model had learning rate and weight decay set to \(6\times 10^{-3}\) and 0.05, respectively, and was fine-tuned for 100 epochs on both CIFAR10 and CIFAR100. For the Next-ViT model, pretrained model weights (Next-ViT-S) were loaded and fine-tuned on CIFAR10, CIFAR100, and ImageNet-1K datasets. By default, the learning rate and weight decay were set to \(5\times 10^{-6}\) and 0.1, respectively, with a gradual decay in the learning rate. The model was fine-tuned for 20 epochs on the ImageNet-1K dataset with a weight decay of \(1\times 10^{-8}\). Fine-tuning was performed for 100 epochs on CIFAR10 and CIFAR100 with a learning rate of \(5\times 10^{-4}\) to achieve better convergence. For the UniFormer model, pretrained model weights (UniFormer_XXS) were loaded and fine-tuned on CIFAR10, CIFAR100, and ImageNet-1K datasets. By default, the learning rate and weight decay were set to \(4\times 10^{-5}\) and 0.05, respectively, with a gradual decay in the learning rate. To prevent overfitting, the model was fine-tuned for 25 epochs on the ImageNet-1K dataset. Fine-tuning was conducted for 100 epochs on CIFAR10 and CIFAR100 with a learning rate of \(5\times 10^{-4}\). For the fine-tuned ANNs of EdgeNeXt, Next-ViT, and UniFormer models, we employed SIT-conversion to obtain corresponding converted SNNs models, and inference was conducted on different datasets to validate the effectiveness of SIT-conversion.
## 5 Analysis on Bearing Capacity of PHC Modular Pile
### Effect of Inclination Angle of Nodule  
Apart from the nodular diameter and nodular length, the inclination angle of the nodule will also affect the bearing capacity of the PHC nodular pile. The tangent value of the inclination angle of nodule (tan \(\alpha\)) was set as 0, 0.5, 1, 1.5, and 2 (\(\alpha=0^{\circ},26.6^{\circ},45^{\circ}\), \(56.3^{\circ}\), and \(63.4^{\circ}\)), respectively, as presented in Figure 11. The calculated load-displacement responses of the PHC nodular pile with different inclination angles are arranged as shown in Figure 12.  
Figure 10: Effect of nodular diameter on bearing capacity of PHC nodular pile.  
Figure 12 shows that the pile head displacements of the PHC nodular pile with different inclination angles all increased stably with pile head load, and the ultimate bearing capacity of the PHC nodular pile decreased with the increase in inclination angle of nodule. The ultimate bearing capacities of the PHC nodular pile were 3186 kN, 2882 kN, 2719 kN, 2467 kN and 2357 kN, respectively, as the value of tan \(\alpha\) increased from 0 to 2. However, it should also be noted that the disturbance induced by pile installation would increase with the decrease in the inclination angle of the nodule. When the inclination angle of the nodule was 90\({}^{\circ}\), the PHC nodular pile would become a PHC pipe pile. When the inclination angle of nodule decreased to 0\({}^{\circ}\), the inclination angle of nodule would become a right angle and the installation effect of the PHC nodular pile would become the largest.  
The nodular spacing, nodular length, nodular diameter and inclination angle of nodule will not only affect the bearing capacity of the PHC nodular pile, but also change the degree and extent of the installation effect. In the design of the driven PHC nodular pile in engineering projects, the relationship between the disturbance induced by pile installation and the ultimate bearing capacity of the PHC nodular pile after the recovery of soil strength should be comprehensively considered to select the appropriate value of nodular diameter.  
Figure 11: Schematic of nodule with different inclination angles.  
Figure 12: Effect of inclination angle of nodule on bearing capacity of PHC nodular pile.
## 2 Methodology
### Conceptual Framework on Vulnerability
#### 2.1.4 Crisis Management Vulnerability  
In the context of crisis management, several crucial indicators are mapped and analyzed to enhance emergency response preparedness. These indicators include the distance to the nearest hospital, the presence of fire brigades in the vicinity, and the proximity to intervention brigades. By correlating these indicators with the evaluation of different zones and infrastructures in terms of the Fire Inception Index (representing the likelihood of a fire ignition), a comprehensive assessment of the potential vulnerabilities and risks within the study area can be achieved.  
Moreover, the incorporation of the Fire Inception Index of each building into the analysis allows for more detailed and nuanced visualization of the results. This data-driven approach enables emergency planners and authorities to identify areas and infrastructures with higher probabilities of fire ignition, thereby prioritizing resources and interventions accordingly.  
By combining these indicators with vulnerability mapping and fire risk analysis, decision-makers gain valuable insights into the spatial distribution of risks and critical points. This information is crucial in formulating effective emergency plans and strategies to minimize potential damage and ensure the safety of residents and the preservation of the city's invaluable cultural heritage in the event of extreme fire events.