esa-sceva/satcom-chunk-collection huggingface dataset:
## 5 Distributed Algorithms for the Many-to-Many Maximum Weighted Matching Problem
### Approximation Ratio for the Distributed Algorithms
However, edge \((a,b)\) was selected as being locally heaviest, so Equation (33) holds even in the worst case, since: \[w\left(a,b\right)\geq w\left(a,c\right)\] \[w\left(a,b\right)\geq w\left(b,d\right)\]  
\(\square\)  
The following lemma mirrors Lemma 4 and is the key lemma in proving the equivalence of both centralized and distributed algorithms in the subsequent theorem. **Lemma 11**: _For every node \(i\) Algorithm LIC chooses all locally heaviest edges that are adjacent to it, if there is enough quota \(b_{i}\) available, or otherwise chooses the \(b_{i}\) of those that are heavier than any unchosen one._  
**Proof:** If there are less than \(b_{i}\) locally heaviest edges, algorithm LIC will choose all of them, since, by construction, it will continue to select them until there are no quota slots available at either endpoint. Otherwise, again by construction, it will choose the \(b_{i}\) heaviest of them for node \(i\). \(\square\)  
**Theorem 3**: _The LID algorithm is a \(\frac{1}{4}\left(1+b_{\max}^{-1}\left(1+\frac{1-b_{\max}^{-1}}{2s+b_{\max}^{- 1}}\right)\right)\)-approximation algorithm for the maximizing satisfaction b-matching problem, where \(b_{\max}\) is the maximum connection quota in the graph and \(s=\frac{L_{\max}}{L_{\min}}\) is the ratio of the maximum and minimum neighbor list sizes in the graph, \(L_{\max}\) and \(L_{\min}\), respectively._  
**Proof:** By Lemmas 11 and 4, we know that algorithms LIC and LID choose the same edges for each node and therefore produce the same solution. This means that the LID algorithm is also a \(\frac{1}{2}\)-approximation algorithm for the many-to-many maximum weighted matching (as Theorem 2 suggests for the LIC algorithm). Furthermore, the many-to-many maximum weighted matching we solve, by theorem 1, is a \(\frac{1}{2}\left(1+b_{\max}^{-1}\left(1+\frac{1-b_{\max}^{-1}}{2s+b_{\max}^{-1 }}\right)\right)\)-approximation of the corresponding b-matching problem. These two approximations combined give a \(\frac{1}{4}\left(1+b_{\max}^{-1}\left(1+\frac{1-b_{\max}^{-1}}{2s+b_{\max}^{- 1}}\right)\right)\)-approximation for the original maximizing satisfaction b-matching, where \(b_{\max}\) is the maximum connection quota in the graph. \(\square\) From the above theorem and Lemma 10, we also get the following theorem about the approximation ratio of AdaptiveLID:  
**Theorem 4**: _The AdaptiveLID algorithm solves the adaptive b-matching with preferences problem with \(\frac{1}{4}\left(1+b_{\max}^{-1}\left(1+\frac{1-b_{\max}^{-1}}{2s+b_{\max}^{- 1}}\right)\right)\)-approximation._
## 3 Results and Discussion
### Stability of Fe-Mn Nodules in the Soil  
Selective extraction methods can facilitate the analysis of As distribution within the distinct phases of Fe-Mn nodules. As depicted in Figure 7, HNO3 dissolved a minor fraction of As (0.78%), Fe (2.35%), Mn (3.63%), and Al (4.16%). NH2 OH-HCl, H2O2-HNO3, and CBD exhibited a strong affinity for Mn, extracting Mn within the range of 64.22-87.01%. However, the extractable As did not show a substantial increase when Mn was significantly dissolved in NH2 OH-HCl. The order of extractability for As and Fe remained consistent: CBD > H2O2-HNO3 > NH2 OH-HCl. Notably, the dissolution of Fe (21.69-67.05%) resulted in a marked increase in As extractability (22.62-51.40%) during CBD extraction. These findings indicate that As within Fe-Mn nodules is predominantly sequestered within Fe-(oxyhydr)oxides, such as goethite and hematite, which exhibit recalcitrance and remain undissolved. Arsenic associated with amorphous iron oxides can undergo dissolution through acid-enhanced, reductive, and chelant-enhanced mechanisms [43; 44], while As bound to crystalline iron oxides can only be dissolved via reductive processes [84]. CBD, functioning as a potent reducing agent, triggers the reductive dissolution of crystalline iron oxides [44]. In essence, under strongly reducing conditions in the soil (i.e., hypoxia), the reductive dissolution of Fe-(oxyhydr)oxides within Fe-Mn nodules can release As into the soil solution, potentially enhancing the uptake of As by rice [85; 86].  
The findings of the pH-dependent leaching assessments are depicted in Figure 8. Across a pH range from 2 to 11, the overall leaching of As remained notably low. At pH 2, the leached concentration of As was 0.05 mg/kg, constituting a mere 0.02% of the total concentrations within the Fe-Mn nodules. Similarly, at pH 11, the leached As concentration was 0.03 mg/kg, accounting for 0.01%. The dissolved As concentrations at other pH levels (3-10) were all less than 0.01% of the total concentrations in the Fe-Mn nodules, rendering them nearly negligible. Moreover, the trend of As variation mirrored that of Fe, underscoring the close association between As and Fe within the Fe-Mn nodules. In essence, the results suggest that Fe-Mn nodules exhibit a robust stability in storing As, with extremely acidic or alkaline conditions promoting the potenti  
Figure 7: Dissolution of As, Fe, Mn, and Al from Fe–Mn nodules using different selective extractions.  
nodules due to the desorption or dissolution of the Fe-(oxyhydr)oxides. The pH range of the karstic paddy soil (4.97-8.38) provides favorable conditions for the preservation of As within the Fe-Mn nodules.
# Concept, Design, Initial Tests and Prototype of Customized Upper Limb Prosthesis
## 3 Results  
### Results of Kinematic and Kinetosatic Analyses of Index Finger Mechanism  
The kinematic scheme of the designed prosthesis' fingers is shown in Figure 8 (where \(T,\ T_{1},\ T_{2},\ T_{3},\ T_{4}\) stands for each fingertip point).  
The designed mechanism enables two independent rotational motions for each finger and one rotation for each of the phalanges. Simulation of the fingertips' trajectories, as a result of kinematic analyses (with Matlab), is evidenced in Figure 9.  
Figure 7: The block scheme for the designed prosthesis.  
The kinetostatic analysis for the customized finger mechanisms was performed. For example, for the index finger mechanism (see Figure 10), there are three phalanges (P1, P2, P3) and the mechanism that enables the rotational motion of the tip and middle phalanx (P mechanism).  
Figure 8: Kinematic scheme of the hand’s fingers’ mechanisms.  
Figure 9: Simulation of fingertip trajectories.  
The mechanism is of triad structure, with B, E, and G being the input joints, and C, D, and F being the interior joints (Figure 11). For the index finger model, the kinetostatic calculation was done with Matlab software, assuming that each of the loading forces, \(Q_{i}\) (\(i=1\), 2, 3), are about 20 N (estimated value based on experiments with grasping relatively small objects). The simulation results are presented in Figure 12.  
Figure 11: Kinetostatic scheme of the index finger mechanism.  
Figure 10: Index finger mechanism.  
There were two methods (kinetostatic and virtual power) used for determining the driving torque values (in N\(\cdot\)m), both resulting in identical values. This proves the correct calculation results.
# Measuring Quality of Service in a Robotized Comprehensive Geriatric Assessment Scenario
## 3 Modelling QoS Metrics for the CLARC Scenario
### Observations  
An observation provides contextual evidence that the robot is optimal (or not) in terms of a property. It is defined as a context pattern whose occurrence improves (reinforces) or worsens (undermines) the QoS estimate of a property, to some degree (very high, high, medium, low, very low). In addition, the language offers a wide range of event sequence operators and aggregate functions that allow users to express complex contextual patterns.  
Listing 3 shows the observations specified for the CLARC scenario. We have captured fourteen observations that defines the relationship between contexts and non-functional properties. It is worth noting that we involved two experts (a physiotherapist and an engineer specialized in usability/accessibility of human-computer interfaces) to assist us in the modeling process.  
An observation will be triggered when its context pattern becomes true. For example, the O2 observation acts when the patient has answered a Barthel question on the first attempt or the test is finished. In this case, O2 impacts on Performance by increasing (reinforcing) its estimate. Moreover, the observations related to Performance and Interaction can be activated during the Barthel or Get Up & Go test. However, observations O13 and O14 are triggered only during the Barthel test, as they establish which interaction mechanism the patient is using.  
```
1 observationO1:TestState::RUNNNGorScoredor
2 PersonIsNextToChairorPersonIsSeatedor
3 PersonGetsUpreinforcesPerformancehigh
4 observationO2:FirstAttemptAnsweredorTestState::FINISHEDor
5 PersonDetectedreinforcesPerformancelow
6 observationO3:SecondAttemptAnsweredorTestState::RESTARTED
7 reinforcesPerformanceverylow
8 observationO4:BatteryLevel::VERY_LOWorTestState::STOPPEDorTestState::PAUSEDunderminesPerformanceveryhigh
9 observationO5:!Soredor!SecondAttemptAnsweredor
11 TestState::REPEATINGor!PersonIsNextToChairor
12!PersonIsSeatedor!PersonGetsUporCallingDoctor
13|mHerminesPerformancehigh
14 observationO6:!FirstAttemptAnsweredor!PersonDetected
15 underminesPerformancelow
16 observationO7:PersonIsSeatedorPersonIsNextToChairor
17 FirstAttemptAnswered
18 reinforcesInteractionhigh
19 observationO8:PersonDetectedorPersonGetsUp
20 reinforcesInteractionlow
21 observationO9:CallingDoctor underminesInteractionveryhigh
22 observationO10:!PersonIsSeatedor!SecondAttemptAnsweredor
23|PersonIsNextToChairunderminesInteractionhigh
24 observationO11:!PersonGetsUpor!FirstAttemptAnsweredor
25 TestState::PAUSEDorTestState::REPEATINGor
26!PersonDetectedunderminesInteractionlow
27 observationO12:SecondAttemptAnsweredorTestState::RESTARTED
28 reinforcesInteractionverylow
29 observationO13:UserInteraction::VOICE_RECOGNITION
30 reinforcesVoiceInteractionQualityhigh
31 observationO14:UserInteraction::REMOTE_CONTROLor
32 UserInteraction::TOUCH_SCREEN
33 underminesVoiceInteractionQualityhigh
```  
Listing 3: Observations for both tests.
## 3 Correction Method for Antenna Pattern Errors
### Correction of Antenna Pattern Multiplicative Errors  
The second step is to correct the visibility function multiplicative errors caused by antenna pattern differences and antenna pattern measurement errors. Since these antenna pattern errors are inseparable multiplicative errors, they cannot be corrected merely by accurately measuring the error of each individual term. To mitigate the impact of these multiplicative errors, it is essential to reduce the amplification factor associated with the antenna pattern. The antenna brightness temperature of each element can be obtained from the measured data. The average antenna brightness temperature \(\overline{T}_{A}\) is calculated by taking the mean of the BIs across all elements. The antenna pattern measured on the ground and the average antenna brightness temperature can be used to calculate the visibility function corresponding to the average antenna brightness temperature:  
\[V^{XX}_{T_{A}}=G^{CC}_{XX}\overline{T}^{XX}_{A},V^{YY}_{T_{A}}=G^{CC}_{YY} \overline{T}^{YY}_{A} \tag{24}\]  
Since the first step has corrected the contribution of cross-polarization, the above equation would contain only the product terms of the two co-polar antenna patterns.  
By subtracting the visibility function corresponding to the average antenna brightness temperature, the differential visibility function can be obtained:  
\[V^{XX}_{C2}=V^{XX}_{C1}-V^{XX}_{T_{A}},V^{YY}_{C2}=V^{YY}_{C1}-V^{YY}_{T_{A}} \tag{25}\]  
The differential visibility function of \(V^{XY}_{C1}\) and \(V^{YX}_{C1}\) is not considered. By reconstructing the BT from \(V^{XX}_{C2}\) and \(V^{YY}_{C2}\), the reconstructed BT \(T^{XX}_{B}-\overline{T}^{XX}_{A}\) and \(T^{YY}_{B}-\overline{T}^{YY}_{A}\) can be obtained. Therefore, the amplification factor can be reduced to \(T_{B}-\overline{T}_{A}\). The antenna errors would be amplified only by the difference between the BT and the average antenna brightness temperature. Consequently, the effect of antenna pattern differences and antenna pattern measurement errors is reduced. Finally, the average antenna brightness temperature is added back to the reconstructed BT in the end.  
After correction by the above two steps, the BT is reconstructed. Given that Equation (3) is underdetermined, a regularization method has been proposed in [26] to achieve a stable solution. In full polarization mode, the reconstructed BT obtained from the corrected visibility can be expressed as follows:  
\[invT=U^{*}Z{(J^{CC}_{pq})}^{-1}{(\hat{V}^{pq}-\Delta V^{pq}_{back}-\Delta V^{pq }_{cross}-\delta_{pq}V^{pq}_{T_{A}})}+\delta_{pq}T^{pq}_{A} \tag{26}\]  
\(J^{CC}_{pq}=G^{CC}_{pq}U^{*}Z\), U stands for discrete Fourier transform operator, and \(Z\) is the zero-padding operator. Since the cross-polarization has been corrected, only the co-polarization is considered for the G-matrix \(G^{CC}_{pq}\). \(\delta_{pq}\) is the Kronecker delta. \(\delta_{pq}=1\) if \(p=q\) and \(\delta_{pq}=0\) if \(p\
eq q\).
## 2 Models and Data
### Statistics  
We used correlation analysis to quantify the magnitude of dependence of GPP estimates with environmental variables and vegetation indices. Over the global scale, the correlation coefficient was calculated between GPP estimates of all LUE models with several environmental variables and vegetation indices.
# Stationary Target Identification in a Traffic Monitoring Radar System
###### Abstract  
Recently, as one of the intelligent transportation systems, radar systems that monitor traffic on the road have received attention. To ensure the reliable detection performance of the traffic monitoring radar, it is necessary to distinguish stationary road structures from moving vehicles. Therefore, in this paper, we propose a method for discriminating stationary targets in traffic monitoring radar systems. First, we install a frequency-modulated continuous wave radar system using a center frequency of 24.15 GHz on an overpass to monitor multiple lanes on the road. Then, we process the raw data obtained by the radar sensor to extract target information such as the distance, angle, velocity, and radar cross-section. Finally, we analyze the target characteristics in the angle-velocity domain to classify stationary targets and moving vehicles. In this domain, stationary targets appear as points lying around a straight line, and if we estimate that line, we can extract the stationary targets among all targets. To find the trend line, we use a random sample consensus-based estimation method, which can extract a dominant line component from a set of sample points. Through the proposed method, we can effectively remove the stationary targets in the field of view of the radar system.  
Keywords: intelligent transportation system (ITS); random sample consensus (RANSAC); road structure identification; traffic monitoring radar +
Footnote †: journal: Applied Sciences
## 2 Materials and Methods
### Experimental Setup  
The forklift used for this study is an electrically powered industrial truck with a lead-acid battery pack for energy storage with a nominal voltage of 80 V and a capacity of 450 Ah. This machine handles loads up to 1.6 tons with a double mast structure that allows load lifting up to 3.5 m. The forklift system includes three main electric motors fed by dedicated DC-DC converters as shown in Figure 1. The traction motor (TM) is an 8.6 kW DC series motor that drives forward and reverse movement, providing the necessary torque for propulsion, and in the case of breaking sends energy back to the battery pack through its bidirectional DC-DC converter. The lift motor (LM) is a 13.0 kW DC series motor that supplies power to the positive displacement hydraulic pump, which provides the pressurized fluid needed to activate and control the lift, tilt, and side shift hydraulic cylinders. When the load is dropped, the hydraulic system liberates pressure through a relief valve and therefore does not regenerate energy back to the battery pack during the process. The power steering motor (PM) is a 1.0 kW permanent magnet DC motor that manages the power steering system through a hydraulic pump, facilitating maneuvering and precise control of the forklift. Figure 1 shows that the TM and LM are DC series motors, which is one of the types of self-excited DC motor configurations. In this configuration, the field winding is internally connected to the armature winding and stands out for its robust starting torque.  
The three DC motors TM, LM, and PM are fed by buck (thyristor) DC-DC converters based on pulse width modulation (PWM). This switching control allows regulating and controlling the average voltage supplied to the motors by adjusting the duty cycle ratio. In this case the duty cycle of the three converters is fixed to 2.5 ms.  
For data acquisition, the forklift was equipped with the recorder DAS60 (SEFRAM Instruments, Saint-Etienne, France). This recorder has 6 analog channels, which were configured with a sample frequency of 50 kHz to measure the voltages and currents directly from sensors installed between each DC-DC converter and DC motor. The three voltage buses were directly connected to the recorder by dedicated cables while the currents where measured by DC current sensors AEMC MR416 (AEMC Instruments, Dover, NH, USA), which can measure up to 600 A with a bandwidth of 30 kHz. This data acquisition system captures real-time information on key electrical variables, which are essential for analysis and further estimation of the transported load weight. Figure 2a shows the forklift used in the investigation, including the data acquisition system mounted in the back side of the machine. Figure 2b shows the complementary equipment used for load weight measurement.  
Figure 1: Schematic diagram of forklift power system.  
Figure 2: Experimental setup (**a**) forklift and D&Q equipment, (**b**) tank for variable load implementation, and scale for load weighing.
# Spatio-Temporal Distribution of Deep Convection Observed along the Trans-Mexican Volcanic Belt
## 4 Results and Discussion  
### Spatio-Temporal Distribution of Cloud Fraction  
In the first step, the observed spatial and temporal distribution of cloud fraction is presented in Figure 2. The CF distribution represents the average of 10 years by grid point, where 1 means a zone completely covered by clouds and 0 represents a cloud-free region. In this analysis, high, middle or low clouds are not differentiated. The primary purpose is to establish the first impression on the cloudy situation in the region and relate these spatio-temporal distributions of clouds to dry and wet seasons. Such a behavior can be a result of the interaction of local static conditions (such as terrain features) and dynamic parameters (such as moisture fluxes, frontal activity, mesoscale systems or even climatic oscillations). From the analysis of the CF monthly climatologies, two principal phases have been identified. First, there is a wet season, from June-September, which mostly includes the summer months. The highest values of CF correspond to topographic features such as mountain ranges in the TMVB, Eastern and Western Sierra Madre and the coastal plains of the Gulf of Mexico and the Pacific Ocean. The other factor relating to this distribution is the sea breeze effect in coastal areas [52]. The impact of this type of circulation, for example, on cloud development, fog production and storm initialization, has been well-documented [53]. Second, the months from November to April are characterized by a constant decrease in CF values across the domain. CF values less than 0.3 are typical in most parts of the territory, except in the Gulf of Mexico. From November to February, these high values of CF are associated with the passage of cold winter fronts in this region of Mexico [54]. March and April are the drier months in this phase. Lastly, two smaller transition phases can be identified: first, in May as a dry transition; and second, in October as a wet transition. Maximum values of CF are located over the east during the May transition, while during the October transition, the maximum CF values are located over the central and the western portions of the domain. Such a situation suggests a transition from east to west as discussed above.
# Study on Bridge Displacement Monitoring Algorithms Based on Multi-Targets Tracking
## 3 Proposed Algorithm
Hole filling technology is explained in Equation (5), where \(A\) represents a binary image, \(A^{c}\) represents the complementary set of \(A\), \(B\) represents a 4-connected structural element, and \(X_{0}\) represents an all-black image except for a white spot in each hole. If \(X_{k}=X_{k-1}\), the algorithm ends at step \(k\) of the iteration. The parallel set of \(X\) and \(A\) is the image after hole filling:  
\[X_{k}=(X_{k-1}\oplus B)\cap A^{c},\ \ k=1,2,3,... \tag{5}\]  
Feature recognition's flowchart is shown in Figure 2. The main principle is to take the vertices of eight directions on the edge of the region and calculate the distances from them to the center of the region, respectively. Then, the standard deviation of these eight distances is calculated and a threshold is set. If the standard deviation is less than this threshold, the region is recognized as a circle. In this paper, the method of obtaining the center of a circle is the centroid location by first-order central moment method. It is a method of determining the centroid of image by using the geometric invariant first-order moment of a digital image. The concept of geometric moment was first proposed by [PERSON] in 1962, and it is shown in Equation (6):  
where \((u_{c},v_{c})\) means the coordinate of the region's center. Displacement calculation is to calculate the pixel displacement of the central coordinate of each circular target and determine the actual displacement distances according to the results of system calibration. Compared with other image displacement monitoring algorithms, the algorithm in this paper has two main advantages. The first advantage is that the algorithm designs specific region detection conditions directly according to the characteristics of the target without image correlation method so it eliminates a lot of repeated calculations. When there are more pixels in the image, the advantage of this algorithm will be more obvious. The second advantage is that the algorithm can monitor multiple targets at the same time, unlike [25; 26], where a camera can only monitor one target, which greatly reduces the cost of camera equipment. In summary, this algorithm is suitable for rapid displacement monitoring of large structures such as bridges.
## 4 Discussion
Future research could incorporate both nonlinear material models and time-dependent effects to more accurately describe the response under large deformations. Secondly, this study focused on three-point bending mechanical testing and simulation, without full feedback from motion and human body data. Future studies could include kinematic and biomechanical data to further improve the accuracy of the simulations. Lastly, the experimental shoes used in this study were selected for finite element (FE) validation purposes, rather than being dedicated carbon-plated running shoes. Using pre-made carbon-plated shoes might limit the benefits of FE modeling, whereas incorporating carbon plates into the shoe model allows for more cost-effective evaluations. Future research should refine the FE framework, simulate combinations of different sole materials and carbon plates (including variations in layer thickness and angles), and incorporate ankle-foot models and running biomechanics to better support the design of carbon-plated shoes.