esa-sceva/satcom-chunk-collection huggingface dataset:
# On the Impulse Response of Singular Discrete LTI Systems and Three Fourier Transform Pairs
## 5 Conclusions  
The frequency transfer function, \(H[k]\), of a linear time-invariant system is generally considered to be equivalent to the unit impulse response function \(h[n]\). The normal process of obtaining the impulse function from the frequency transfer function via the DFT, however, breaks down when the latter has singularities for discrete systems. This happens when the input time-domain function is a uniform train of pulses and the transfer function contains zeros on the unit cycle. We show that the frequency transfer function contains complete information to determine the IRF in such a case. A broader fundamental question to be answered is whether the IRF can always be determined from a frequency transfer function  
Figure 8: Same as Figure 7 except that, in this example, \(N=36\), \(L=4\) and \(L_{y}=6\). \(h[n]\) and \(h_{3}[n]\) are the same for \(n=0\):\(11\), while \(h[n]\) and \(h_{4}[n]\) are the same for \(n=0\):\(15\).  
Figure 9: An example plot for \(h[n]\), \(h_{3}[n]\) and \(h_{4}[n]\) with \(L=80\), \(L_{y}=149\) and \(N=320\). Each element in \(y[n]\) is a random integer from \(1\) to \(149\).  
containing singularities. If the answer is positive, the ensuring question is how to find \(h[n]\) from \(H[k]\) with any kind of pole in general.  
Our method to obtain \(h[n]\) from \(H[k]\) involves performing the inverse Fourier transform of the transfer function by excluding the poles to obtain a time-domain function, \(h_{1}[n]\). We show that a linear combination of \(h_{1}[n]\) and its shifts can yield \(h[n]\). It is important to note that the poles in the transfer function discussed here are all on the unit circle in the z-domain. Such systems are marginally stable and \(h[n]\) is periodic after \(max\big{(}L_{y}-L+1,\ 0\big{)}\) points. The number of independent points in \(h[n]\), \(M\), is the larger of \(L_{y}+1\) or \(L\). Our method requires the length of the discrete transfer function, \(N\), to be at least \(2M\) to correctly capture the first \(M\) points in \(h[n]\). It is of interest to explore whether it is possible to obtain the first \(M\) points of \(h[n]\) using \(N<2M\).  
In demonstrating that \(h[n]\) can be obtained using the DFT method, we have explored three interesting Fourier transform pairs. These DFT pairs are used not only for obtaining \(h[n]\) from \(H[k]\) but can be used to yield various trigonometric sums involving \(\frac{\sin(\pi k/N)}{\sin(\pi k/N)}\), where \(N\) is a multiple of integer \(L\) and \(k\) is the summing integer variable.  
The study is partially supported by the U.S. National Science Foundation grant AGS-2152109.  
No new data were created or analyzed in this study. Data sharing is not applicable to this article.  
The author declares no conflicts of interest.
# An Improved Galerkin Framework for Solving Unsteady High-Reynolds Navier-Stokes Equations
## 1 Introduction
This explicitly constructs a subgrid-scale model to address the numerical oscillation problem inherent in traditional Galerkin methods for convection-dominated regions. Furthermore, a new posteriori error estimator is designed based on dual residuals, which provides accurate error localization by dynamically weighting local momentum residuals, continuity residuals, and inter-element jump terms. This estimator guides a dynamic mesh refinement strategy, combining the longest-edge bisection method with local Delaunay re-triangulation to ensure mesh quality. The feasibility and superiority of this coupled approach are verified through numerical experiments on high-Reynolds-number flows, demonstrating its capability to provide a robust, accurate, and efficient solution for multiscale problems in computational fluid dynamics. The remainder of this paper is organized as follows. Section 2 details the mathematical model, presenting the strong and weak forms of the Navier-Stokes equations and discussing the theoretical foundation of the inf-sup condition for mixed finite element methods. In Section 3, the proposed numerical framework is elaborated upon, including the Taylor-Hood element discretization, the formulation of the VMS method, and the design of the posteriori error estimator that drives the adaptive mesh refinement strategy. Sections 4.1-4.4 present numerical experiments, focusing on the lid-driven cavity flow benchmark at both high and low Reynolds numbers, to validate the accuracy, stability, and efficiency of the method. Section 4.5 introduces a classical cylinder flow benchmark at \(\mathrm{Re}=5000\) to further demonstrate the framework's robustness in handling complex, non-steady flows. Finally, Section 5 concludes the paper with a summary of the findings and the key contributions of this work.
## 4 Conclusions  
In this paper, the method of matching terminal block schematic and physical information in substation secondary cabinets based on artificial intelligence is studied. Multi-layer object detection networks, tailored to the characteristics of schematic diagrams and physical entities in substation secondary systems, are designed for precise extraction of information. Network topologies oriented towards both schematic and physical systems are then established based on the Neo4j database. The branch-and-bound method is improved by employing a multi-modular graph convolutional network (MGCN) and deep Q-network (DQN), which are subsequently used to solve the maximum common subgraph (MCS), resulting in rapid matching of schematic-to-physical data. Experimental results demonstrate that the algorithm proposed in this paper significantly outperforms traditional algorithms in terms of information extraction in substations and rapid schematic-to-physical matching.  
Reflecting on the constructive feedback received, we acknowledge the importance of not only presenting our findings but also suggesting pathways for future enhancements. In light of this, we propose the exploration of innovative labeling techniques, such as the implementation of QR codes on labels, to streamline the identification and tracking processes of terminal blocks within substations further. This approach could potentially offer a more efficient and error-resistant method for managing and accessing detailed information about each component, thereby enhancing the overall effectiveness of our proposed model. We believe that integrating such technologies could serve as a valuable direction for future research, aiming to bridge the gap between current capabilities and the evolving needs of smart grid infrastructure.  
Conceptualization and methodology, W.C. and Z.C.; investigation and writing--original draft preparation, W.C. and C.W.; writing--review and editing, W.C. and T.L. All authors contributed substantially to the manuscript. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the State Grid Headquarters Science and Technology Project \"Research on Unified and Shared Modelling and Intelligent Application Technology for the Whole Secondary System of Substation\" (SGHEDK00 JYJS2200012).  
Not applicable.  
Data Availability Statement: Data is contained within the article.  
Author [PERSON] was employed by the company State Grid Economic and Technological Research Institute Co., Ltd. Author [PERSON] was employed by the company Power Science and Research Institute of State Grid Hebei Power Co. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.  
Figure 14: Visualization of subgraphs found by our model in substation secondary screen cabinet terminal block graphical and physical entities. (**a**) 1000. (**b**) 2000. (**c**) 3000.
## Calibration Process  
### Start Preset  
The initial position of the robot is a part of the floor with chessboards in front, where the robot is located from the very beginning, on which its camera is directed and the floorsurface is marked with aruco markers on the other side of it. An example of the initial position is illustrated in Figure 1.  
There can be any number of chessboards, determined by the amount of free space around the robot. To a greater extent, the accuracy of calibration is affected by the frames with different positions of the boards, e.g., two boards located at different distances from the robot and at different angles. It is important that they are located in a semicircle and directed approximately towards the robot. Additionally, their sizes should fully fit in the camera's field of view. The size and type of all the boards around the robot must be the same [10].  
Markers should be oriented towards the chessboards and begin as close to the robot as possible. The distance between the markers depends on camera's resolution, as well as its height and angle of inclination, but it must be such that at least three recognizable markers can simultaneously be in the frame. For Duckiebot-based experiments, the distance between the markers was set as 15 cm with a marker size of 6.5 cm. It is important to  
Figure 1: Initial position of the robot.  
note that the distance between the markers may not be very precise 15 cm. The calibration algorithm does not take into account the relative position of the markers against each other; however, the orientation of all markers must be strictly the same. The measurement accuracy depends to a large extent on this. In addition, the algorithm assumes that the markers are oriented towards the chessboards.  
The robot needs to be placed in front of the chessboards approximately in the center of the semicircle around which the chessboards are located. The exact position of the robot is not important, but initially there should be a specific board in the robot's field of view. It can be any of the boards, but later this information needs to be provided to the camera calibration script. To eliminate the statistical error and use images from the camera taken at different distances, at least two chessboards need to be used. Since the wheel calibration validation algorithm for this robot assumes deviations of no more than 10 cm by 2 m [11], and the accuracy of the error in determining the markers position does not exceed 1 cm, it is enough for the robot to drive at least 1/3 of the test distance during calibration, which is sufficient to detect the deflection of the robot.
# Continuous-Wave and Mode-Locked Operation of an In-Band Pumped Tm,Ho,LuCaGdAlO4 Laser
## 4 Mode-Locked (ML) Laser Results
The corresponding autocorrelation trace measured by noncollinear Second-Harmonic Generation (SHG) is shown in Figure 7b. The fit assuming a sech\({}^{2}\)-shaped pulse intensity gives a pulse duration (FWHM) of \(\tau\) = 218 fs. The resulting time-bandwidth product (TBP) amounts to 0.327. It deviates only slightly from the 0.315 value for the ideal, unchirped sech\({}^{2}\)-shaped pulses characteristic of a soliton laser. The soliton-like performance of this laser is confirmed by the almost ideal fitting of the spectral and temporal profiles in Figure 7. This pulse duration together with the average power give a peak power of roughly 7 kW. Figure 8a,b show the measured radio-frequency (RF) spectra of the fundamental beat note at \(\sim\)96.2 MHz with a resolution bandwidth (RBW) of 300 Hz and a 1-GHz-wide span (RBW: 100 kHz) to verify the stability of the ML laser. The extinction ratio of more than 68 dBc and the absence of any spurious modulation are evidence for stable steady-state ML operation of the Tm,Ho,Lu:CALGO laser. Attempts to further shorten the pulse duration with the optimum 0.2% OC were performed by modifying the cavity GDD. At a lower value of the negative round trip dispersion, e.g., \(-\)750 fs\({}^{2}\), the output spectrum broadened to 31 nm but no stable operation could be achieved. Figure 7: (**a**) Measured spectrum of the ML Tm,Ho,Lu:CALGO laser with \(T\)OC = 0.2% and (**b**) second-harmonic generation (SHG) based background-free autocorrelation trace: experimental data and fitted curve assuming sech\({}^{2}\)-shaped pulse intensity profile.
## 5 Experiment
### Experiment of Building the Map  
Firstly, in order to evaluate the positioning accuracy while mapping, we manually marked 6 positions in a real scene, as shown in Figure 8. The start point position 0 is specified as the original point (0,0) in the world coordinate system. As shown in Figure 8, the robot started from position 0 and stopped at position 5, and the blue arrow in each picture is the robot's moving direction. Table 2 shows the result of positioning in the SLAM system from position 1 to position 5.  
Figure 7: One example of the database: (**a**) The robot in the environment; (**b**) scan data obtained in the scene; (**c**) the RGB image; (**d**) the depth image.  
As can be seen from Table 2, for both methods, the initial error of positioning is small. However, while the robot was running further, the error increases with distance. Sooner or later, such error will be too large to be ignored, and finally cause failure to mapping. Such a situation may become worth for a low-cost LiDAR. That's why we need a loop closing module for thr SLAM system.  
We did further mapping experiment in a real scene compared with Karto-SLAM and Orb-SLAM. The result is shown in Figure 9. Figure 9a is the result of Karto-SLAM, the blue points are the estimated robot position during SLAM. Because of the growing cumulative error, the starting point and the ending point in the red coil cannot be fused together, the mapping failed. Figure 9b is the feature map constructed by orb-SLAM. It should be denoted that orb-SLAM is easy to lose tracking, and the robot should run and turn very slow while building the map. When tracking is lost, it needs a manual operation to turn back to find previous key-frames. As a result, orb-SLAM can't work directly with our recorded rosbag databases. Figure 9c is the grid map part of the proposed method, the green points are the robot positions estimated during SLAM. Because of the effective loop detection and optimization, the map is much better than compared methods. The final 2.5D map showing both grid and feature point is shown in Figure 10.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Position Number** & **Real Position (m)** & **Karto-SLAM (m)** & **Our Method (m)** \\ \hline
1 & (3,0) & (2.995,\(-\)0.002) & (2.994,\(-\)0.003) \\
2 & (6,0) & (5.987,\(-\)0.003) & (5.990,\(-\)0.005) \\
3 & (6,\(-\)8) & (6.025,\(-\)8.032) & (6.019,\(-\)8.021) \\
4 & (6,\(-\)16) & (6.038,\(-\)15.954) & (6.028,\(-\)15.973) \\
5 & (3,\(-\)16) & (2.949,\(-\)15.946) & (2.951,\(-\)15.965) \\ \hline \hline \end{tabular}
\end{table}
Table 2: The positioning result while Simultaneous Localization and Mapping (SLAM).  
Figure 8: The marked positions of the robot.
# Development of Analytical Model for Bonding of CFRP Rod in Concrete Subjected to Cyclic Loads
## 6 Analytical Approach
### Cohesive Elements  
Cohesive elements are employed to model the bond between CFRP and concrete, effectively defining the performance of the CFRP rod during pull-out tests. This performance can be influenced by factors such as geometry properties, type of industrial application, testing procedure, and load response. Numerous cohesive element models are available, but the traction separation response model was selected for this study. This model is particularly suitable when the adhesive thickness is negligible or considered zero. It assumes linear bonding performance before crack initiation and allows for the simulation of debonding initiation and damage propagation. This approach places significant emphasis on material properties, making it an excellent choice for simulating the cohesive zone. Although cohesive elements are considered to have negligible thickness, a thin layer was constructed for simulation purposes. This layer was assembled by combining parts with precise nodal coordination, a method particularly useful for forming complex configurations. This part's assembly is illustrated in Figure 20.
# Development of Dual-Axis MEMS Accelerometers for Machine Tools Vibration Monitoring
## 3 Calibration Methods and Performance Testing
### Testing of Linearity and Frequency Response  
As mentioned in the previous section, the PCB Model 353B15 was used as a standard reference PZT accelerometer. The test platform was fixed on the shaker (PCB type: 4810, New York, NY, USA), which is driven by a function generator (INSTEK AFG-2105, Taipei, Taiwan) and power amplifier (HP MT-1000, Palo Alto, CA, USA). The voltage output signals are recorded in LABVIEW auto-sweep programs by using a data acquisition card (NI 9234). The linearity and frequency response of the packaged MEMS accelerometer can be measured using the back-to-back calibration system. The linearity and cross-axis sensitivity characteristics of the MEMS accelerometer at 500 Hz are shown in Figure 6, where the slope denotes the measured sensitivity. As shown in Figure 6, the slope is 24.7 mV/g, which is close to the  
Figure 4: The first resonant frequency is 12.31 kHz and the related mode shape.  
Figure 5: The back-to-back calibration method. PZT: lead zirconate titanate; V\({}_{\text{MEMS}}\): the output voltage of MEMS accelerometer; V\({}_{\text{ref}}\): the output voltage of reference PZT accelerometer.  
sensitivity of the ADXL001 accelerometer, 24.5 mV/g, listed in the data sheet [16], with the maximum deviation of 0.003. The result of the frequency response is shown in Figure 7. Compared with that in Figure 1, the frequency response ranging from 10 Hz to 10 kHz is flatter because of the addition of a low-pass RC filter.
## 3 Case Analysis
### Prediction Accuracy with Factor Ablation
#### 3.2.6 Summary of Factor Ablation Experiments  
To observe the influence of different features on the prediction accuracy of each site more intuitively, we summarized all the feature ablation experiment results, as shown in Table 5.  
Figure 12: Predicted GPP vs. labeled GPP at a single site (no NDVI).  
Table 5 indicates that removing any feature from the AR site would result in a significant improvement in accuracy, with the largest improvement obtained after removing NDVI. The removal of any feature for the DXST, DXSW, and ZF sites would lead to a degradation of accuracy, with the DXST site showing a large accuracy decline and the  
Figure 13: Predicted GPP vs. labeled GPP at a single site (no LSWI).  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Site** & **AR** & **DXST** & **DXSW** & **GL** & **HBKO** & **HBSH** & **HBSW** & **NMC** & **ZF** \\ \hline R\({}^{2}\) & 0.663 & 0.853 & 0.843 & 0.879 & 0.935 & 0.868 & 0.856 & 0.879 & 0.758 \\ R\({}^{2}\) (no-Ta) & 0.899 & 0.226 & 0.196 & 0.777 & 0.952 & 0.901 & 0.879 & 0.271 & 0.505 \\ R\({}^{2}\) (no-PAR) & 0.736 & \(-\)0.262 & 0.556 & 0.718 & 0.913 & 0.880 & 0.905 & 0.685 & 0.568 \\ R\({}^{2}\) (no-EVI) & 0.847 & 0.326 & 0.408 & 0.648 & 0.943 & 0.899 & 0.895 & \(-\)0.385 & 0.080 \\ R\({}^{2}\) (no-NDVI) & 0.942 & 0.204 & 0.428 & 0.817 & 0.872 & 0.916 & 0.912 & 0.732 & 0.515 \\ R\({}^{2}\) (no-LSWI) & 0.874 & \(-\)0.991 & 0.377 & 0.702 & 0.905 & 0.918 & 0.884 & 0.590 & 0.203 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Results of all factor ablation experiments.  
lowest accuracy after removing LSWI. The DXSW site also shows a decline in accuracy, although it is smaller than that of the DXST site. The ZF site has a noticeable decline in accuracy after removing EVI. The NMC site has an abnormal increase in accuracy after removing NDVI and a decline after removing other features except NDVI. The GL site is insensitive to the removal of Ta or NDVI and shows slight decreases in accuracy after removing other features in addition to Ta and NDVI. The HBKO, HBSH, and HBSW sites are insensitive to the removal of any feature and have no obvious changes in accuracy.
## 4 Discussion
### Quantum Dot (QD) Modeling
Not only can excitonic levels in quantum dots be thermally stable, but they have very large, resonant oscillator strength at 1550 nm, too. Hence, the modeling explains the resonant absorption near 1550 nm of the quantum dot array, and why the switch devices can be driven with 1550 nm. However, it also suggests the long depopulation time T\({}_{1}\) (\(\approx\)T\({}_{\text{sp}}\) = 60 ns) even at room temperature. While this sheds light on the poor performance of photomixing results, it raises question on how the lifetime of the inversion of two energy levels can be shortened sufficiently for the fast electron relaxation and then the resulted THz emission. Superradiance provides an \"escape route\" for this. Under ultrashort strong laser pumping, the almost immediate inversion of QDs triggers spontaneous emission and the QDs cooperate with each other through the same radiated field. This is because the QD size is in the order of \(\sim\)2 nm, much shorter than the \(\sim\)1550 nm wavelength, and the QDs' distribution is dense [7]. The collective interaction of QDs with the same radiation field can reduce the spontaneous lifetime of QDs significantly, resulting in a build-up of the superradiant pulse.
## 6 Discussion and Limitations
### Study Limitations and Computational Considerations  
**Two-model training requirement**: The watermarking process of DICTION requires training two models (the target model and projection network), unlike methods such as those of [PERSON] et al. and DeepSigns, which only require single-model training. This represents the computational cost for ensuring robust watermarking properties. The impact is particularly significant for large models like GPT, but several mitigating factors exist: (i) **Offline processing**: Watermarking occurs in offline mode, eliminating runtime overhead for end users. (ii) **One-time cost**: The computational overhead is incurred only during watermarking, not during model deployment or inference. (iii) **Deployment efficiency**: Once watermarked and deployed, the model operates with identical performance characteristics to the original.