esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Recursive Formulation
### Recursive Subspace Identification (RSI)  
There are several ways to implement SI recursively and they can be roughly divided into two categories. One uses the matrix inversion lemma to update the orthogonal or oblique projection matrix [18; 19; 20; 21] and the other one uses an unconstrained criterion (known as [PERSON]'s criterion) to approximate the projections [22; 23; 24; 25]. Both of them introduce a forgetting factor, which is quite common in the recursive least squares (RLS) algorithm [34; 35], to keep fading out the past measurement and updating the newest information of system matrices.  
One of the significant results after introducing a forgetting factor is that the weighting of data is exponentially reduced as time goes on. There are pros and cons to using a forgetting factor; undoubtedly, the implementation is very easy, simple, and direct. On the other hand, the forgetting factors produce a time-varying weighting to the past data, as shown in Figure 1. To overcome the problem, constant weighting is preferable, such as a fixed moving window. [PERSON] proposed a recursive formulation based on a swap of matrices, called bona fide recursive algorithm [36; 37], and brought a moving window with fixed input and output data size, as shown in Figure 1. Definitely, the identified dynamic behaviors appeared only in the current window compared to the other algorithms using forgetting factors.  
The bona fide recursive algorithm is based on MOESP; admittedly, MOESP needs to implement Equation (9) at each step. Given a set of new measurement of input data, \(\mathbf{\mathrm{u}}_{k+1}\), and output data, \(\mathbf{\mathrm{y}}_{k+1}\), the vectors \(\mathbf{\mathrm{u}}_{k-i+2\,|\,k+1}\), \(\mathbf{\mathrm{y}}_{k-i+2\,|\,k+1}\), and \(\mathbf{\mathrm{\xi}}_{k-i+2\,|\,k+1}\) can be updated and the following relation holds  
\[\begin{bmatrix}\mathbf{\mathrm{U}}_{fk}&\mathbf{\mathrm{u}}_{k-i+2\,|\,k+1}\\ \mathbf{\mathrm{\Xi}}_{p,k}&\mathbf{\mathrm{\xi}}_{k-i+2\,|\,k+1}\\ \mathbf{\mathrm{Y}}_{f,k}&\mathbf{\mathrm{y}}_{k-i+2\,|\,k+1}\end{bmatrix}=\begin{bmatrix} \mathbf{\mathrm{u}}_{k-i-j+2\,|\,k-j+1}&\mathbf{\mathrm{U}}_{f,k+1}\\ \mathbf{\mathrm{\xi}}_{k-i-j+2\,|\,k-j+1}&\mathbf{\mathrm{\Xi}}_{p,k+1}\\ \mathbf{\mathrm{y}}_{k-i-j+2\,|\,k-j+1}&\mathbf{\mathrm{Y}}_{f,k+1}\end{bmatrix} \tag{15}\]  
Figure 1: The weighting of various forgetting factors and fixed window.
# Comparison of Machine Learning Methods to Up-Scale Gross Primary Production
## Materials and Methods
### Methods
#### 2.3.1 Up-Scaling GPP Using Machine Learning Methods  
Studies have shown that GPP is influenced by shortwave radiation (SWR), air temperature (Ta), vapor pressure deficit (VPD), soil moisture and nitrogen availability at canopy scale. While at ecosystem scale, GPP was well related to leaf area index (LAI), NDVI and canopy phenology [68]. In this paper, NDVI and FVC, which were selected as two of the inputs to describe the terrestrial photosynthetic vegetation activity to train the machine learning models to up-scale GPP at flux tower sites. Moreover, considering that SWR, Ta and RH characterized the condition of carbon storage under natural environment [9; 69], these factors were also taken into account when up-scaling GPP at flux tower sites. Daily GPP from the field carbon flux data, and corresponding remote sensing data (NDVI, FVC, land cover) and meteorological data (SWR, Ta, RH) were selected as the training datasets of machine learning methods. To make the input parameters comparable, the inputs of the training data were normalized firstly. Then five machine learning methods (Cubist regression tree [70; 71], RF [72], SVM [26], ANN [73], DBN [74]) were adopted to up-scale the GPP at flux tower sites.  
Figure 2: Flowchart of up-scaling and validation of GPP. Five machine learning methods were used to up-scale GPP from field to regional scale, then the results were validated at field scale, at footprint scale and at regional scale.
## 2 Methods
### Optimization Method
#### 2.4.1 Velocity Extension  
The normal velocity field on the entire level set mesh is required for each level set function to be evolved. However, since the sensitivities are only non-zero in the vicinity of the zero level sets (surfaces) and consequently the normal velocities (design variables) updated by the optimizer are also non-zero, these must be extrapolated to the rest of the design domain (LS mesh).  
For this purpose, a method is developed in this article with an analogous approach to the redistancing method described in [32]. Extrapolation is carried out in the developed method in a two-stage process, which is outlined in Figure 5. In the initialization phase, the surface described by the zero level set (\(\varphi(\mathbf{x})=0\)) is sampled. For this, the surface elements (triangles) belonging to the zero level set are derived from the FE mesh using the material IDs. The values of the normal velocities are then determined for each node of the surface mesh using linear interpolation with the FE basis functions from the LS mesh.  
The result of the initialization phase is a point cloud of the surface \(C_{s}=\{\mathbf{x}_{1},\mathbf{x}_{2},\ldots,\mathbf{x}_{n_{k}}\}\subset\mathbb{R}^{3}\) analogous to [32] with interpolated values and their adjacent triangles. The point cloud is also used to create a search data structure (kd tree).  
In the extrapolation phase, the projection of each vertex of the level set mesh (design domain) is identified on the discretized level set surface mesh. The search data structure  
Figure 4: Structure of the optimization loop with the individual components.  
Figure 5: Schematic representation of the velocity extension from the zero level set (blue) to the target vertex based on [33]. For this purpose, the pole of the target vertex is determined on the zero level set, and then, the normal velocity of the target vertex (orange) is calculated from the normal velocities of the triangle (green) using linear interpolation.  
and the list of adjacency triangles are used for this purpose. At the identified point, the normal velocity is interpolated using linear interpolation and assigned to the original node in the level set mesh.  
The two steps described can be parallelized straight-forwardly by means of multi-threading since both the interpolation step in the initialization phase for each vertex of the surface mesh and the extrapolation step for each vertex of the LS mesh can be carried out independently of each other.
# Fault Analysis and Protection Principle for the Distribution Networks Integrated with PV and BESS
## 3 The Proposed Fault Direction Detection Principle  
### Principle for Detecting Fault Direction Under Asymmetric Phase-to-Phase Faults  
#### 3.1.1 Voltage Blocking Criterion for Asymmetric Phase-to-Phase Faults  
The fault direction detection principle described in this section is specifically for two-phase short-circuit faults. Therefore, after the protection device is activated, it should first determine the type of fault according to the amplitude of the negative sequence voltage. When it is determined that the fault is not a two-phase short-circuit fault, the direction criterion should be blocked. At the same time, since the above analysis is carried out based on the FRT process of the PV and BESS, the direction criterion will only be enabled when the positive sequence voltage at the PCC is detected to be lower than 0.9 p.u. In summary, for PR4, when the detected positive sequence voltage and negative sequence voltage satisfy the equation shown in Formula (4), the negative sequence power direction criterion is activated; otherwise, the direction criterion will be blocked.  
The voltage blocking criterion is as follows:  
\[\left\{\begin{array}{l}U_{p4}^{+}<U_{\text{set}}^{+}=K_{\text{rel}}^{+}U_{ \text{max}}^{+}\\ U_{p4}^{-}>U_{\text{set}}^{-}=K_{\text{rel}}^{-}U_{\text{min}}^{-}\end{array}\right. \tag{4}\]  
Among them, \(K_{\text{rel}}^{+}\) and \(K_{\text{rel}}^{-}\) are reliability coefficients, with values of 0.98 and 0.95 respectively. \(U_{\text{max}}^{+}\) is the maximum value of the positive sequence voltage at the protection installation point, which is set according to the maximum positive sequence voltage when the PV and BESS enter the FRT state. \(U_{\text{min}}^{-}\) is the minimum value of the negative sequence voltage at the protection installation point, which refers to the negative sequence voltage measured at the protection relay location when a fault with the maximum fault resistance (10 \(\Omega\)) occurs at the end of the forward or reverse region under the maximum operating mode of the system. After substituting the system parameters for the calculation, \(U_{\text{max}}^{+}\) and \(U_{\text{min}}^{-}\) are set as 5.0964 kV and 0.2952 kV, respectively.
## 3 Results and Discussion
### Delimitation of Coastal Lakes  
The terrain ruggedness determined by the Riley formulation [21] enabled delimitation of the maximum extension of the lake basin. The surface areas were around 5% larger than those established with the 2017 orthophotograph (Figures 3, 4, 7, and 8). This finding indicates partial occupation of the actual surface area of the lakes, particularly by agricultural activities. The sectors present in each lake were estimated independently, and their characteristics are included in Table 3.  
Figure 2: Organic carbon vs pyrite S in lake sediments. Black solid lines represent the typical relation for marine sediments (C/S = 2.8 \(\pm\) 1.5; [23; 36]), while the blue solid line represent the same relation for freshwater environments with a reduce sulphate concentration [22]. For each location, the graph shows the results in surficial and deep samples (up to 100-110 cm in depth). The high relation C/S in all samples indicate that Xuno and Bodeira were always freshwater lakes.
## 4 Proposed MCA-IoT Design
### Hardware Component Selection with Justification  
The primary hardware components for network device construction are detailed in Table 2 and Figure 2c. For our MCA-IoT network, designed for deployment in diverse locations and harsh environmental conditions in Africa, the Raspberry Pi 3B+ (RPi 3B+) was deemed optimal. It offers robust operational stability under challenging conditions and features a built-in radio module supporting BLE 4.2 and dual-band WLANs (2.4 GHz and 5 GHz). With a 1.4 GHz processor, 1 GB SDRAM, a throughput of 300 Mbps, and a Power over Ethernet (PoE) port via a separate PoE HAT, the RPi 3B+ enables simplified cabling and remote access through a VNC server and Wi-Fi. Among various technologies, BLE 4.2 was selected for intra-cluster and inter-cluster communications due to its energy efficiency, compatibility with mobile units, support for cluster-based routing, and high throughput. Additionally, LoRa was chosen for edge CH-to-BS and BS-to-cloud communications due to similar advantageous characteristics. The technology selection justification matrix and power requirement metrics outlined in [10; 50] were utilized for this study. Further details on the selected hardware components are provided in Table 2.  
The devices in the MCA-IoT network, including the MNs, CH, RCH, and BS, were custom-built using RPi 3B+ controllers and various cross-platform hardware and software components tailored to their specific roles and demands, as shown in Figure 10. These devices are scalable and capable of role rotation. The MNs collect soil temperature and moisture data, which are transmitted to the CH. The CH processes the data by removing outliers, aggregating it, and then sending it directly or via an RCH to the BS for local decisions, while retaining a copy in The Things Network (TTN). Data from distant CHs are routed through BLE-based multihop for inter-cluster communications, while edge CHs (ECHs) use LoRa technology for data transmission to the BS. The two ECHs are equipped with LoRa end nodes to facilitate long-range communication. An actuation signal triggers the irrigation system to activate the water pump. The RPi 3B+ was chosen for its stability across various environmental conditions. The hardware and software design of the MCA-IoT was guided by the following considerations:  
1. **Architectural Support, Operational Simplicity, and Affordability:** Cost-effective and easy-to-operate components and technologies (e.g., BLE, LoRa, RPi 3B+) were selected to leverage the multihop cluster-based architecture. This choice ensures that the MCA-IoT network is infrastructure-less, battery-driven, deployable, manageable in any location, labor-saving, flexible, and easy to integrate into farm environments without fixed infrastructure. 2. **Effectiveness and Dependability:** Components were chosen based on their availability, ease of assembly, and market presence, which supports system maintenance and scalability.
# Advances in Random Fiber Lasers and Their Sensing Application
###### Abstract  
Compared with conventional laser, random laser (RL) has no resonant cavity, reducing the requirement of cavity design. In recent years, the random fiber laser (RFL), a novel kind of RL, has made great progress in theories and experiments. The RFL has a simpler structure, a more flexible design, and higher reliability. It has valuable applications for earth sciences, biological life sciences, and national defense security, due to these unique properties. This paper reviews the development of RFLs in the last decade, including their configurations based on various optical fibers and their output properties, especially the method of control. Moreover, we also introduce their applications in the optical fiber sensing system, which is a very important and practical orientation to study. Finally, this paper presents the prospects of RFLs.  
random fiber laser; fiber; random laser; optical fiber sensing +
Footnote †: journal: Sensors
## 3 Methodology
### Data Sources
#### 3.1.2 Validation Data  
Temporal changes were validated using a series of optical images from Google Earth Pro (version 7.3.6, Google LLC, Mountain View, CA, USA). Additionally, height data were validated through a comprehensive field study using a DJI Mavic 3 Pro drone (SZ DJI  
Figure 3: Temporal characteristics of the COSMO-SkyMed dataset (2012–2020). (**a**) Temporal distance (days) between consecutive SAR image acquisitions vs. time. (**b**) Stack duration distribution (%) of the total study period covered by each of the 13 sequential 28-image sub-stacks used in the analysis, illustrating the impact of acquisition frequency (e.g., Stack 5 accounts for 15.8% of the total time span). Percentages are individually rounded to one decimal place and may not sum to exactly 100%.  
Technology Co., Ltd., Shenzhen, China) in a spatially confined area of Hanyang district (Figure 4). This area was selected for its dynamic urban expansion and the variability in building heights, with structures ranging from 3 to approximately 150 m. Notably, since 2012, the area has witnessed a substantial increase in buildings over 100 m, with hundreds constructed by 2020.  
The drone surveys, conducted on 21 March 2024, with high-resolution imagery, covered approximately 504 buildings, collecting precise latitude, longitude, and building height data. While it may seem to be a limited validation dataset, it is worth noting that the surveyed buildings quantitatively provide a high spatial density of validation measurements in a rapidly expanding urban sector of Wuhan, where a multitude of PS candidates are present. The collection of such a dataset was already time-consuming. More extensive ground-truth surveys would have demanded an enormous effort, potentially reducing the overall cost-effectiveness of the research approach.. Thus, a trade-off was attempted, with consideration for the restrictions of drone flights over the urban areas in Wuhan. This robust dataset verified the heights recorded via PSInSAR and enhanced our understanding of the district's vertical development.  
Our empirical investigation revealed that most structures in the selected area of the Hanyang district typically range between 100 and 130 m, with some buildings reaching up to 150 m.  
Figure 4: Drone Imagery for Height validation within the Hanyang District: (**a–c**) Drone-captured images of tall buildings in Hanyang District, validating PSInSAR height measurements; (**d**) Author conducting drone operations for data collection.
## 2 Antenna Design  
The antenna design process started by accumulating the design specification based on the UHF nanosatellite application and the commercially available 1U nanosatellite structure. The proposed antenna was designed considering the inverted F antenna technique to avoid the deployment complexity of the current nanosatellite antenna system [22; 23]. The initial inverted F parameters and operating frequency were estimated using Equation (1), where \(h\) is the space between ground plane, \(c\) represents the velocity of light; and radiator patch, \(L1\) and \(L2\) are the patch length and height, respectively:  
\[f=\frac{c}{4(L1+L2+h)} \tag{1}\]  
The developed antenna addressed the inverse space accommodation relation between antenna and solar panel placement. The concept of the antenna over solar panels was adopted [24], and the antenna patch was modified to penetrate solar irradiance to the solar panel. The geometrical structure of the antenna was comprised of a rectangular-shaped patch with \(r_{1}\) and \(r_{2}\) net holes, two elliptical hollow spaces on the antenna patch, a shorting wall and a 50 \(\Omega\) coaxial feed. The equivalent inductance introduced by the feeding probe and shorting wall was reduced by etching two elliptical slots and net holes. As a result,maximum uncovered surface area for sufficient solar penetration was achieved to mount the solar panel. Figure 1 depicts the antenna geometry and the final design parameters are tabulated in Table 1. The Japan Aerospace Exploration Agency (JAXA) standard was followed to design the 1U nanosatellite structure and the antenna mounted on the z-plane of the structure. A GaAs base solar panel was considered in the simulation.  
Figure 1: (**a**) Antenna geometry and (**b**) Antenna structure integrated with 1U nanosatellite in simulation environment.
# Design of Novel Laser Crosslink Systems Using Nanosatellites in Formation Flying: The VISION
## 3 Concept of the Laser Crosslink Systems
### Optical Link Budget
#### 3.2.2 Signal-to-Noise Ratio Margin
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{5}{c}{**(a) PAT#1 and PAT#2—Search and Acquisition**} \\ \hline
**Elements** & **Budget** & **Available** & **Unit** & **Remarks** \\ \hline Tx Power & \(>\)\(-\)3 & 0.00 & dBW & 1 W output \\ Tx Gain & \(>\)56 & 56.98 & & Beam divergence, 8011.4 \(\upmu\)rad \\ Pointing Loss & \(>\)\(-\)5 & \(-\)0.68 & & Pointing error at Table 3 \\ Tx Optics Loss & \(>\)\(-\)7 & \(-\)2.00 & & Front-end, back-end optics \\ Path Loss & \(<\)\(-\)259 & \(-\)258.18 & & dB & 1000 km apart \\ Rx Gain & \(>\)111 & 111.71 & & Clear aperture diameter, 19 cm \\ Rx Optics Loss & \(>\)\(-\)7 & \(-\)7.00 & & Max. tracking sensor (CAM) \\ Rx Power & \(>\)\(-\)125 & \(-\)119.17 & dBW & Beam split, 99:1 \\ \hline
**SNR Margin** & \(>\)10 & 11.49 & dB & - \\ \hline \multicolumn{5}{c}{**(b) PAT#3—Detection**} \\ \hline
**Elements** & **Budget** & **Available** & **Unit** & **Remarks** \\ \hline Tx Power & \(>\)\(-\)3 & 0.00 & dBW & 1 W output \\ Tx Gain & \(>\)56 & 56.98 & & Beam divergence, 8011.4 \(\upmu\)rad \\ Pointing Loss & \(>\)\(-\)5 & \(-\)0.19 & & Pointing error at Table 3 \\ Tx Optics Loss & \(>\)\(-\)7 & \(-\)2.00 & & Front-end, back-end optics \\ Path Loss & \(<\)\(-\)259 & \(-\)258.18 & dB & Max. range, 1000 km \\ Rx Gain & \(>\)111 & 111.71 & & Clear aperture diameter, 19 cm \\ Rx Optics Loss & \(>\)\(-\)7 & \(-\)7.00 & & Max. tracking sensor (CAM) \\ Rx Power & \(>\)\(-\)125 & \(-\)118.69 & dBW & Beam split, 99:1 \\ \hline
**SNR Margin** & \(>\)10 & 11.81 & dB & - \\ \hline \multicolumn{5}{c}{**(c) PAT#4—Hand-off and Tracking**} \\ \hline
**Elements** & **Budget** & **Available** & **Unit** & **Remarks** \\ \hline Tx Power & \(>\)\(-\)3 & 0.00 & dBW & 1 W output \\ Tx Gain & \(>\)56 & 92.92 & & Beam divergence, 127.8 \(\upmu\)rad \\ Pointing Loss & \(>\)\(-\)5 & \(-\)0.03 & & Pointing error at Table 3 \\ Tx Optics Loss & \(>\)\(-\)7 & \(-\)2.00 & & Front-end, back-end optics \\ Path Loss & \(<\)\(-\)259 & \(-\)258.18 & dB & Max. range, 1000 km \\ Rx Gain & \(>\)111 & 111.71 & & Clear aperture diameter, 19 cm \\ Rx Optics Loss & \(>\)\(-\)7 & \(-\)7.00 & & Max. tracking sensor (QC) \\ Rx Power & \(>\)\(-\)125 & \(-\)82.58 & dBW & Beam split, 99:1 \\ \hline \hline
**SNR Margin** & \(>\)10 & 22.21 & dB & - \\ \hline \end{tabular}
\end{table} 
Table 4: Optical link budget and SNR margin for each PAT sequence in 1000 km of inter-satellite distance: (**a**) PAT#1 and PAT#2, (**b**) PAT#3; (**c**) PAT#4; (**d**) COM#1.
# Three Cube Packing for All Dimensions
## 4 Conclusions  
These results raise further questions. For example, if we are packing more than three cubes, are there multiple maximal packings and are there some identical cubes in maximal packing for some dimensions? There remains the unanswered question of \(V(d)\). We know \(V_{4}(2)=V_{5}(2)=\ldots=V_{11}(2)\) and \(V_{5}(3)=V_{4}(3)\). Is it true that for each dimension, the maximal packing volume does not change after a certain number of cubes?  
Our method of proof works great for three cubes. It helped that there is only one critical point on the boundary curves for the dimensions that suited us. This is not guaranteed for four or more cubes. It is possible that this method of proof would work for more cubes without some major improvements, but with each additional cube, it gets more complicated.  
The concept of maximal packing holds importance in various fields:  
* Geometry and packing problems: Maximal packing refers to arranging objects (such as spheres or cubes) within a given space in a way that maximizes their density or minimizes the empty space. In geometry, it is a fundamental question to determine how efficiently we can fill a region with identical objects. The study of maximal packing helps us understand the optimal arrangement of shapes in different dimensions.
* Materials science and crystal structures: In materials science, maximal packing is crucial for understanding the arrangement of atoms or molecules in crystalline structures. Crystals exhibit specific packing arrangements (e.g., face-centered cubic, hexagonal close-packed) that maximize the density of particles while maintaining stability. The efficiency of packing affects material properties such as hardness, conductivity, and optical behavior.
* Optimization and efficiency: Maximal packing problems often arise in optimization scenarios. Solving these problems has practical applications in logistics, manufacturing, and resource utilization.
* Computational complexity: Determining the optimal packing arrangement can be computationally challenging. Researchers use heuristics, algorithms, and mathematical techniques to approximate solutions. The study of maximal packing contributes to our understanding of computational complexity and algorithmic efficiency.
* In historical context: ancient civilizations (such as the Egyptians and Babylonians) were interested in efficient packing for practical reasons (e.g., storing grain, arranging bricks) and [PERSON]'s conjecture about the densest sphere packing in three dimensions dates back to the 17 th century.  
In summary, maximal packing plays a vital role in understanding spatial arrangements, optimizing resource usage, and solving complex problems across various disciplines.  
This research received no external funding.  
No new data were created or analyzed in this study. Data sharing is not applicable to this article.  
The authors declare no conflicts of interest.