esa-sceva/satcom-chunk-collection huggingface dataset:
## 5 Discussion  
The techniques and studies which are discussed in Section 2, shows a trend of applying machine learning techniques and gaining gradual recognition and acceptance for solving insurance-related issues in the healthcare industry. The focus of most of the research is more on cost efficiency and fraud detection. The designs are based on prediction, analysis and evaluation of healthcare services, operations and resources. It is observed that the data-driven analysis using probability distributions is the most helpful platform for analyzing existing loopholes. Optimization is an interdisciplinary term, which combines mathematics, computer science, economics and engineering. There is a pervasive requirement of the applicability of optimization approaches to healthcare-related problems. The optimization approaches improve the provision of healthcare services by making them more cost-effective and efficient. It is a good practice to perform experimentation, using different values for the parameters considered in the optimization problem, to verify the robustness of the optimization results. For this purpose, intensive experimentation is performed on medical benefits amount in a considered case study using the concepts of data clustering and a probability distribution model. After the detailed literature review in Section 2, we observed that there is a requirement of an efficient methodology to generate insurance packages that must not be designation specific rather evenly distributed fairly in all employees of an organization. None of the existing methodologies are focused on generating insurance packages and optimization of medical benefits using machine learning techniques. Our proposed methodology use machine learning concepts and perform data-driven analysis of original transactional data using probability distribution concepts. Table 20 shows the novelty of our proposed methodology.  
Figure 19: Data Driven Analysis using Gamma Distribution.  
This data-driven analysis is helpful in ensuring longterm sustainability of the insurance programs. The main purpose of using Kmeans is to get a group of all similar employees in each category. Further processing on centroids is performed to get better premium amounts for packages. Subsequently, the gamma probability distribution is applied to optimize the amount according to the requirement. There is a chance that any employee's group can be changed, and accordingly, the amount can be optimized. The probability distribution for each category is computed again.
## 4 Numerical Simulations
### Simulation Comparisons  
In order to demonstrate the advantages of the proposed control, the results of the proposed control are compared with those of the sliding mode control (SMC) and adaptive SMC (ASMC). The SMC is presented in (6), (9), (10) and (11). The ASMC is computed by (6), (9), (10), (12) and (13).  
**Remark 1**.: _The parameters of the three controllers are presented in Table 2. As the SMC is designed based on the manipulator dynamics, the ASMC is developed from the SMC and the proposed control inherits from the ASMC, so the parameters of the ASMC inherit from the SMC and the parameters of the proposed control inherit from the ASMC to maintain the fairness in comparisons._  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Variable** & **Description** & **Variable** & **Description** \\ \hline \(l_{1}=0.46\) m & Length of the 1 st link & \(m_{1}=0.7\) kg & Mass of the 1 st link \\ \(l_{2}=0.4\) m & Length of the 2 nd link & \(m_{2}=0.6\) kg & Mass of the 2 nd link \\ \(l_{3}=0.2\) m & Length of the 3 rd link & \(m_{3}=0.3\) kg & Mass of the 3 rd link \\ \(g=9.81\) ms\({}^{-2}\) & Gravity constant & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters of the 3-DOF robotic manipulator.  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Controllers** & **Parameters** \\ \hline SMC & \(\lambda=10I_{3\times 3}\), \(\textbf{k}=3I_{3\times 3}\), \(\textbf{\eta}=15 diag\Big{(}\left[\begin{array}{ccc}2&1&1\\ \end{array}\right]^{T}\Big{)}\) \\ ASMC & \(\lambda=10I_{3\times 3}\), \(\textbf{k}=3I_{3\times 3}\), \(\varepsilon_{1}=0.001\), \(\kappa_{1}=10^{-2}\left[\begin{array}{ccc}2.5&2.5&1\\ \end{array}\right]\), \(\kappa_{2}=5\cdot 10^{-4}\left[\begin{array}{ccc}1&1&1\\ \end{array}\right]\) \\ Proposed control & \(\lambda=10I_{3\times 3}\), \(\textbf{k}=3I_{3\times 3}\), \(\varepsilon_{1}=0.001\), \(\kappa_{1}=10^{-2}\left[\begin{array}{ccc}2.5&2.5&1\\ \end{array}\right]\), \(\kappa_{2}=5\cdot 10^{-4}\left[\begin{array}{ccc}1&1&1\\ \end{array}\right]\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Coefficients of the SMC, ASMC, and the proposed control.  
**Remark 2**.: _The data are multiplied with a constant to convert from radian units to degree units before they are plotted in the figures of Section 4.3._  
**Remark 3**.: _In order to improve the ability of the Nussbaum functions in control direction detection, the Nussbaum function in the simulation is modified as follows:_  
\[N(\zeta_{i})=sign\Big{(}\frac{e^{\zeta_{i}^{2}}}{\cos\Big{(}\frac{\pi}{2}\zeta_ {i}\Big{)}}\Big{)} \tag{28}\]
## 5 Experiment Conclusions
### Experimental Results and Analysis
#### 5.3.3 Monotonicity
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Network** & **DNC** & **CI** & **KS** & **CC** & **KSGC** & **LGM** & **LGC** & **SC** & **IGC** \\ \hline Dolphins & 0.9958 & 0.9613 & 0.3769 & 0.9737 & 0.9852 & 0.9821 & **0.9979** & 0.9675 & 0.3124 \\ Polbooks & **1.0000** & 0.9993 & 0.4949 & 0.9847 & 0.9985 & 0.9967 & **1.0000** & 0.9887 & **1.0000** \\ Adjnoun & 0.9994 & 0.9846 & 0.5990 & 0.9837 & 0.9981 & 0.9961 & **1.0000** & 0.9920 & 0.9997 \\ Jazz & 0.9993 & 0.9980 & 0.7944 & 0.9878 & 0.9994 & 0.9991 & **0.9996** & 0.9983 & 0.9994 \\ C\_elegans & 0.9977 & 0.9949 & 0.6094 & 0.9893 & 0.9974 & 0.9972 & **0.9979** & 0.9955 & 0.9977 \\ USAir97 & 0.9951 & 0.9433 & 0.8114 & **0.9892** & 0.9935 & 0.9933 & 0.9981 & 0.9928 & 0.9951 \\ Vote & 0.9956 & 0.9100 & 0.7265 & 0.9988 & 0.9994 & 0.9993 & 0.9999 & 0.9887 & 0.9997 \\ Email & 0.9993 & 0.9649 & 0.8088 & 0.9988 & 0.9982 & 0.9977 & 0.9999 & 0.9943 & **0.9999** \\ Yeast & 0.9856 & 0.9111 & 0.7737 & 0.9988 & 0.9988 & 0.9986 & **0.9996** & 0.9873 & 0.9992 \\ Hamsterster & 0.9819 & 0.9641 & 0.8714 & 0.9851 & 0.9848 & 0.9844 & **0.9957** & 0.9829 & 0.9857 \\ Kohonen & 0.9954 & 0.9332 & 0.7306 & 0.9980 & 0.9965 & 0.9960 & **0.9997** & 0.9943 & 0.9984 \\ Dmela & 0.9491 & 0.8583 & 0.7083 & 0.9996 & 0.9996 & 0.9995 & **0.9999** & 0.9905 & 0.9998 \\ Average & 0.9914 & 0.9533 & 0.6883 & 0.9908 & 0.9957 & 0.9950 & **0.9988** & 0.9879 & 0.9414 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The M value of DNC and the baseline methods. The largest M values in the different networks are shown in bold.
## 3 Results and Discussion
### Remote Sensing Applications
#### 3.4.4 Water Management
[PERSON] et al. [98] assessed spectral indices for detecting water stress in fruit trees, revealing the effectiveness of UAV-based imagery in capturing water stress conditions. [PERSON] et al. [99] studied water status in a large almond farm in California using high-resolution multispectral imagery from a small UAV, predicting SWP through NDVI. [PERSON] et al. [100] measured SWP and CWSI, assessing water status and providing guidance for irrigation management based on crop development and economic factors. Another UAV study focused on a different topic, where [PERSON] et al. [101] assessed irrigation effects on almond tree transpiration, revealing variations in transpiration rates among different irrigation treatments. Figure 12a shows that satellites were the most frequently used platform in 63% of the studies, followed by UAVs in 20% and MAVs in 17%. Different methods have been employed in WM studies (Figure 12b), with an emphasis on VIs such as NDVI (used in 38% of studies), CWSI (employed in 28% of studies), and the combined application of both (found in 5% of studies). The TSEB method also stands out, being employed in 14% of the studies. The METRIC and S-SEBI methods, applied for evapotranspiration estimations, were also extensively used in 10% and 5% of studies, respectively.
### Literature Review
References [24; 42] use a differential evolution (DE) algorithm for the optimal coordination of bi-directional OC relays in the closed-loop distribution networks. In [31], a non-dominated sorting genetic algorithm-II (NSGA-II) is proposed for the coordination of DOC relays to minimize the total operating time of primary and backup relays with a multi-objective function. More recently, heuristic techniques, such as Cuckoo optimization algorithm [38], Electromagnetic Field Optimization (EFO) algorithm [41], the Hybrid GA-NLP Approach [44], evolutionary algorithm and linear programming [45], a biogeography-based optimization (BBO) algorithm [46], Symbiotic Organism Search Optimization technique [48], seeker algorithm [49], ant colony optimization (ACO) [43], bee colony optimization (BCO) [70], an Imperialistic Competition Algorithm [71], teaching learning-based optimization (TLBO) [72], harmony search algorithm [73], or firefly algorithm [74] are also used as powerful tools to solve the optimization coordination problem of DOC relays in the distribution network. In general, it can be concluded that many recent studies on coordination algorithms are performed for DOC relays in a DG-integrated distribution network because the presence of DGs leads to the directional change of fault currents. The operation characteristic of DOC relays is similar to that of OC relays excepting for the directional-change detection of fault currents [75; 76; 77; 78; 79; 80]. In conclusion, it should be noted that the purpose of this survey is to provide a more comprehensive view of many recent protection coordination algorithms for DOC relays in the DN. The directional-change detection functions of fault currents are out of the research scope so that this study will only focus on the development of an adaptive and scalable protection coordination system of overcurrent relays in a DG-integrated DN.
## 3 Results
### Spatial Variability in 'Dry' and 'Wet' Conditions
#### 3.2.2 SMAI and LST During Wet Conditions  
The years 2010 and 2014 are characterized by above-normal precipitation for prolonged periods or for the whole growing season. Year 2010 is characterized by precipitation equal to or above the monthly norms for March, April (small exceptions in eastern parts), May (for most parts of the region), June, July, September (50-150% of norms). The only exception is in August when, in most parts of the country, precipitation is between 0% and 50% of the climatic norms.  
Spatial distribution of SMAI for the 50 cm soil layer indicates optimum soil moisture availability from March to July with a slight decrease in August when 'risk of drought' is observed over the whole region (Figure 5a-c). SMAI spatial distribution at the 20 cm layer (Figure 5d-f) is also considered because it is more sensitive to evaporative losses of water in wet conditions. For the upper 20 cm soil surface, SMAI indicates 'risk of drought' in some regions still in June/July, becoming 'orange/dry' for the whole region in August. The distribution of SMAI at 20 cm soil depths more closely corresponds to the increase of LST as a result of high insolation in June-July, and its increases up to 30-35 \({}^{\circ}\)C in some parts during August (Figure 5g-i). While during dry periods, there is a good agreement between the spatial distribution of LST and SMAI for 50 cm soil depth (Figure 4), in wet periods, LST spatial distribution is more closely related to SMAI variability at 20 cm soil depth, and LST is lower as shown in Figure 5.  
Figure 5: Spatial distribution of SMAI (50 cm soil layer) monthly mean over Bulgaria in 2010 for (**a**) June, (**b**) July, and (**c**) August, and of SMAI (20 cm soil layer) for (**d**) June, (**e**) July, and (**f**) August. LSASAF LST for (**g**) June, (**h**) July, and (**i**) August.  
For all months (March-October) of 2014 and for almost all parts of Bulgaria precipitation is above climatic monthly norms (NIMH Hydrometeorological Bulletin, 2014), sometimes 3-3.5 times the norm in July and August that leads to a full soil moisture capacity. The results are consistent with the findings for 2010 (Figure 5), that in 'wet' conditions, the LST spatial variability is more closely related to SMAI distribution for 20 cm soil depth than SMA for 50 cm soil depth (because of similarity, maps with the SMAI and LST spatial distribution are not presented here).
## 4 Results and Discussion
### Flow Analysis of Viscosity Conditions in Simulation
#### 4.1.2 High Viscosity Condition  
When the slot is filled with fluid, the flow viscosity remains constant below 13 m/s, and no rotational vortices occur within the slot. In the flow trajectory, the fluid spreads evenly from the center to the left and right, enabling a consistent extrusion. This phenomenon indicates that the slot's internal space temporarily stores the fluid and allows for stable and controlled output during extrusion. With a mass inflow of 0.1 kg/s and a maximum viscosity ranging from 20,000 to 35,000 cps, stable extrusion is achievable.
## 2 The Topology Optimization Problem  
### Problem Formulation  
The discrete mathematical model of the topology optimization formulation of a compliance minimization problem with consideration of the material volume and buckling constraints can be expressed as  
\[\begin{array}{l}Find:\mathbf{x}=\{x_{1},x_{2},\cdots,x_{n}\}\\ min:C=\mathbf{F}^{T}\mathbf{U}\\ s.t.:\left\{\begin{array}{c}\mathbf{K}\mathbf{U}=\mathbf{F}\\ \min\lvert\lambda_{j}\rvert\geq\underline{\lambda}>0\\ \sum_{e=1}^{n}V(x_{e})\leq fV_{0}\\ 0<x_{min}\leq x_{e}\leq 1\end{array}\right.\end{array} \tag{1}\]  
where \(x_{i}\) (\(i=1,\,2,\,3,\,\ldots,\,n\)) are the design variables of the relative material density, n is the number of design variables, \(C\) is the compliance, \(\mathbf{F}\) represents the nodal force vectors obtained after the boundary search, \(\mathbf{U}\) is the corresponding global displacement vector, \(\lambda_{j}\) is the \(j\)-th buckling factor of the structure in the optimization process, \(\underline{\lambda}\) is the lower bound of the first-order buckling factor of the structure, \(V\) is the total volume of the structure in the optimization process, \(V_{0}\) is the volume of the initial design \(\text{domain},f\) is the upper bound of the given volume fraction, and \(x_{min}\) is a non-zero lower bound introduced to ensure the positive definiteness of the total stiffness matrix of the structure. The model is the same as the models used in the literature [14; 15].  
For convenience of calculation, the Kresselmeier-Steinhauser (K-S) aggregation function is used to convert the multi-constraint problem of Equation (2) into a single-constraint problem13. The new topology optimization formulation can be expressed as:  
\[\begin{array}{l}Find:\mathbf{x}=\{x_{1},x_{2},\cdots,x_{n}\}\\ min:C=\mathbf{F}^{T}\mathbf{U}\\ s.t.:\left\{\begin{array}{c}\mathbf{K}\mathbf{U}=\mathbf{F}\\ \int_{1}^{KS}[g_{V},g_{\lambda}](x)\leq 0\\ 0<x_{min}\leq x_{e}\leq 1\end{array}\right.\end{array} \tag{2}\]  
where we used the K-S function to aggregate multiple constraints [13]. Explicitly, the constraint functions that are aggregated in Equations (1) and (2) can be expressed as:  
\[\begin{array}{l}g_{V}(\mathbf{x})=f(\mathbf{x})/\overline{f}-1\\ g_{\lambda}(\mathbf{x})=1-\underline{\lambda}^{KS}[\mu_{i}](\mathbf{x})\end{array} \tag{3}\]  
where \(f(\mathbf{x})\) is the volume fraction of the optimized structure, f is the upper bound of the given volume fraction, and \(J^{KS}[\mu_{i}](x)\) is a K-S aggregation function defined below:  
\[J^{KS}[\mu_{i}](\mathbf{x})=\mu_{1}(\mathbf{x})+\frac{1}{\rho}\ln(\sum_{i=2}^{q}e^{ \rho(\mu_{i}(x)-\mu_{1}(x))}) \tag{4}\]  
where \(\rho\) is the aggregation parameter, \(\rho\in\ [1,\infty]\), and \(\mu_{i}\) is expressed as the \(i\)-th order eigenvalue. Equation (4) produces an upper bound and a smooth approximation for \(\mu_{1}=\max\limits_{i\in[1,12]}\lvert\mu_{i}\rvert\). Therefore, a smooth lower bound for \(\underline{\lambda}\) is indirectly obtained.
# Natural Frequency Prediction Method for 6R Machining Industrial Robot
## 2 Materials and Methods
### Sample Preparation
#### 2.1.3 Sample Data Acquisition  
Experimental modal test (EMT) is applied so that the natural frequency data of sample configurations can be identified accurately. According to principle of modal test, any element of frequency response function (FRF) can be written as  
\[h_{ij}(\omega)\ =\ \sum_{k\ =\ 1}^{n}\left(\frac{a_{ijk}}{(j\omega-p_{k})}+ \frac{a_{ijk}^{*}}{(j\omega-p_{k}^{*})}\right), \tag{3}\]  
which presents the response of \(i\) point caused by the excitation at \(j\) point. \(a_{ijk}\) and \(a_{ijk}^{*}\) are related to mode shapes, their values are depending on relevant combination of excitation and response. \(p_{k}\) and \(p_{k}^{*}\) contain the information of natural frequency and damping, which are global characteristics independent of excitation and response combinations. Theoretically, one combination of excitation and response is enough to identify all the natural frequencies, provided the excitation and response points avoid the nodes.  
The sample configurations selected by CCD design vary greatly, for the convenience of implementing all the trials in the CCD design, hammer excitation is chosen, and a three-direction  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Factors** & \(q_{2}\) & \(q_{3}\) & \(q_{4}\) & \(q_{5}\) \\
**Levels** & **(Deg)** & **(Deg)** & **(Deg)** & **(Deg)** \\ \hline \(-1\) & \(-55\) & \(-140\) & \(-180\) & \(-70\) \\ \(-0.5\) & \(-30\) & \(-95\) & \(-92.5\) & \(-30\) \\ \(0\) & \(-5\) & \(-50\) & \(-5\) & \(10\) \\ \(+0.5\) & \(20\) & \(-5\) & \(82.5\) & \(50\) \\ \(1\) & \(45\) & \(40\) & \(170\) & \(90\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Factors and Levels of central composite design (CCD).  
Figure 3: Partial variable range.  
accelerometer is fixed on the flange of robot to acquire response signal. In this way, the extra mass brought by EMT device can be negligible as the accelerometer is small and light compared to the robot. Excitations are generated from three directions for each trial, which are corresponding to the three directions of the accelerometer, as shown in Figure 4. Then three FRFs will be obtained for natural frequency identification, avoiding incomplete excitation or excitation on the nodes. Moreover, for each direction, five groups of excitation and response signals are acquired to decrease the signal-to-noise ratio through average algorithm. With FRFs the natural frequencies are preliminarily identified, then complex modal indicating function is used to confirm the accurate values of natural frequencies.  
With the ABB IRB4600 industrial robot being the object, a EMT system for sample data acquisition is set up, including a LIXIE hammer, a PCB three-direction accelerometer, an ECON device for vibration signal processing and a PC (as shown in Figure 5). The configuration of robot is adjusted according to the CCD design in turn. All the identified natural frequency information will be used as the sample data to construct a prediction model.
## 4 Experiments
### Experimental Settings  
#### 4.1.1 Datasets  
Table 3 gives the prepared six datasets across two languages. PBE is the sum of three Chinese datasets (PEP, BNU, EEP) provided in [17]. The PEP dataset is collected from textbooks for primary students published by People's Education Press in 2018, while the BNU dataset is collected from textbooks published by Beijing Normal University in 2018, both in China, respectively. EEP is a dataset that includes problems from entrance exam papers for middle schools in 34 provinces of China from 2010 to 2019. PBE contains 3262 AWPs after the aggregation and cleaning of duplicate problems. Math23a and APECa are subsets of the math word problem datasets Math23k [37] and APE-clean [31], respectively, filtered to remove unsolvable and non-arithmetic types of problems, retaining only high-quality Chinese AWPs.  
AGG is an English dataset proposed by [34], containing 1492 AWPs that cover several typical scenes. MAMPS is an English dataset proposed in [38] and widely used in problem-solving research, containing 2373 AWPs. GSM8K is a popular English dataset [22] and contains 1319 AWPs for testing, widely used to evaluate foundational mathematical abilities of large language models.  
In addition to the aforementioned characteristics, this paper also calculated the average length of problem text (counted by number of words) and the average length of operation steps (counted by number of operators), represented as 'AvgLen' and 'AvgOp', respectively, in Table 3. These characteristics have been used in a previous study [1] to help assess the difficulty of problems within the dataset.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Dataset** & **Size** & **AvgLen** & **AvgOp** & **Source** & **Language** \\ \hline PBE [17] & 3262 & 33.76 & 2.95 & textbook, exam & CN \\ Math23a [37] & 20,160 & 27.68 & 2.70 & web & CN \\ APECa [31] & 15,245 & 29.32 & 2.82 & textbook, web & CN \\ AGG [34] & 1492 & 26.96 & 1.30 & web, exam & EN \\ MAMPS [38] & 1987 & 30.28 & 1.47 & web & EN \\ GSM8K [34] & 1319 & 42.25 & 3.29 & web & EN \\ \hline \hline \end{tabular}
\end{table}
Table 3: Datasets for evaluating solving accuracy.
## 2 Materials and Methods
### Auxiliary Datasets
#### 2.3.1 Sentinel-1  
To assist in the detection of regions of open water, ESA Sentinel-1 C-band radar imagery was used, provided as monthly median backscatter composites of Radiometrically Terrain Corrected (RTC) expressed in gamma-nought [44].  
Sentinel-1 VV, VH, and Normalised Polarisation Difference Index of VV and VH (NPDI) data were generated using the Microsoft Planetary Computer [39] covering the central Amazon region. In this case, NPDI is defined as (VV-VH)/(VV+VH).