esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Proposed Methods
### Hyperspectral Data Acquisition and Preprocessing
#### 3.2.2 Spectral Data Preprocessing  
Signal noise interference is unavoidable in the process of soil hyperspectral data collection, and the proportion of noise will reduce the accuracy of soil moisture and organic matter identification. The wavelet with good time-frequency localization characteristics was changed to eliminate noise while retaining the characteristic peak of the signal [47]. The signal \(S(n)\) containing noise can be expressed as follows:  
\[S(n)=f(n)+\sigma e(n)\;\;n=0,\;1,\;\ldots,\;k-1 \tag{1}\]  
where \(f(n)\) is a useful signal, \(S(n)\) is a signal containing noise, \(e(n)\) is noise, and \(\sigma\) is the standard deviation of noise figure.  
Wavelet denoising includes signal decomposition, threshold setting, and wavelet reconstruction operations. These operations can suppress the noise part \(e(n)\) of the signal and restore the signal \(f(n)\) as much as possible. This experiment sets up a three-layer wavelet decomposition and reconstruction.  
The reconstructed hyperspectral data were processed by principal component analysis to reduce the dimensionality [48]. Principal component analysis can extract the main information from the original data with minimal loss. The set \(X\) with input dimensions was used as an example:  
\[X=[x_{1},\;x_{2},\ldots,x_{m}] \tag{2}\]  
As shown below, the focus was on each dimension:  
\[x_{1}\gets x_{i}-\frac{1}{m}\sum_{i=1}^{m}x_{1} \tag{3}\]  
Then, the covariance matrix XXT was calculated, and eigenvalue decomposition was performed. The eigenvalues were sorted as follows:  
\[\lambda_{1}\geq\lambda_{2}\geq\ldots\geq\lambda_{n} \tag{4}\]  
The largest eigenvector of first \(d\) (\(d\leq n\)) was used to form the eigenvalue of \(W\):  
\[W=[\omega_{1},\omega_{2},\ldots,\omega_{d}] \tag{5}\]  
Figure 2: Laboratory data acquisition device.  
\(W\) is called the feature transformation matrix, and the principal component matrix can be expressed as follows:  
\[A=W^{T}X \tag{6}\]  
\(T\) is the transpose of matrix. By retaining the previous principal components as a substitute for the original data, the dimensionality can be reduced, and the original information can be retained to the utmost extent.
### Heading Drift Correction Methods Based on Machine Learning  
In recent years, machine learning has become a very important technology with broad application prospects, and it has been applied to PNSs to achieve good performance. However, there are few studies on mitigating the heading drift of foot-mounted PNSs using machine learning methods. Most of the research mainly focuses on gait recognition [32], zero-velocity detection [19; 33], etc. There are many studies on heading estimation using waist-mounted or handheld IMUs. The authors of [3] reported that a decision tree model was trained to detect magnetic disturbances, and based on a waist-mounted IMU, the heading accuracy of their system was improved by combining the decision tree model and a Kalman filter. [PERSON] et al. [34] designed several machine-learning-based models to detect magnetic disturbances using the components of the international geomagnetic reference field model [35]. Among the machine learning models, the multi-layer perceptron achieved the best performance with a high accuracy. Then, heading estimates from multiple people walking in the same direction were filtered by their proposed magnetic disturbance detector and pedestrian clustering and were aggregated to provide a more accurate estimate of the common heading. The performance of their scheme exhibited a significant heading error reduction with respect to the conventional handheld PNS. Recent research by [PERSON] et al. [36] and [PERSON] et al. [37] showed the capability of an end-to-end neural-network-based model to obtain accurate 2D displacement and heading estimates using segments of IMU data from smartphones. The method proposed in [38] obtained good pose estimates of a smartphone-based PNS by concatenating neural-network-model-based inertial odometry and a conventional KF-based navigation system. However, machine-learning-based models are over-dependent on the dataset and are difficult to deploy to a real-time processing system. We tried to use a conventional optimal-estimation-theory-based framework to handle the problem.
# Analysis of 'Pre-Fit' Datasets of gLAB by Robust Statistical Techniques
## 4 Results, Discussion and Proposal for Further Work  
### Positioning Results  
This section illustrates how actual outliers present in the pre-fit residuals deteriorate the PVT estimated within the FILTER module. The coordinates of permanent stations are known with errors at the centimeter level. Then, because the magnitude of the outliers is at the few meters level, we can use the positions of permanent receivers as a reference truth to infer the impact of such outliers in the position estimates.  
Figure 6 depicts, at every epoch, the 3D errors of KIR0, computed with the norm of the difference between the XYZ coordinates estimated using the pre-fit residuals and the reference coordinates. The red color depicts the positioning error without taking any action to filter outliers, whereas the blue color shows the errors when outliers are identified and removed following the preliminary analysis with the LMS of Section 2 above. It can be seen how the original 3D errors grow up to 12 m, coincidentally with the time the GPS satellite 32 is observed in Figure 1. Figure 6 and its numerical counterpart Table 3, show that once these outliers are detected and removed, the 3D error is kept at the level of a few meters, as expected in the typical SPP.  
Figure 5: Comparison of computing times for LMS, LTS and FS on time windows of 10 epochs.  
Figure 7 depicts the 3D errors of HUEG, following the same method to produce Figure 6 for KIR0. In this case, the original 3D error obtained with SPP reaches almost 120 m, due to the presence of the outliers previously depicted in Figure 3. In contrast, 3D errors obtained with robust statistics present an accuracy of about one order of magnitude better in terms of RMS, as confirmed in Table 3. There are some discrepancies between the positioning errors obtained by the LTS, LMS and FS methods, which witness an overall good performance of all the three robust estimators and confirm the good trade-off between results and computational efficiency provided by the FS.  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multirow{2}{*}{**Station**} & \multirow{2}{*}{**Outlier Detection Method**} & \multicolumn{5}{c}{**3D Positioning Error (m)**} \\  & & **Mean** & **50\%** & **68\%** & **95\%** & **RMS** \\ \hline KIR0 & NONE & 2.21 & 1.61 & 2.13 & 6.83 & 2.93 \\ KIR0 & LMS & 1.55 & 1.44 & 1.76 & 2.90 & 1.70 \\ HUEG & NONE & 5.23 & 2.57 & 3.05 & 6.00 & 15.21 \\ HUEG & LMS & 2.23 & 2.15 & 2.67 & 3.84 & 2.41 \\ HUEG & LTS & 2.45 & 2.39 & 2.84 & 3.96 & 2.60 \\ HUEG & FS & 2.26 & 2.18 & 2.67 & 3.87 & 2.44 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Mean, median, 68 th and 95 th percentiles and RMS of the positioning errors obtained for the two permanent stations, KIR0 and HUEG, applying different outlier detection methods. Note that the ’NONE’ method only excludes satellites with an elevation lower than 5 degrees.  
Figure 6: 3D position errors of KIR0 using the SPP. In red, the original PVT obtained without detecting and removing outliers. In blue, the PVT achieved detecting and filtering the outliers with LMS.
## 2 Methodologies
### Prophet Forecasting Method  
A Prophet model is used with simple or complicated time-series data that includes single or multiple seasonality, holidays, and data trends. Multiple seasonality can include different patterns, such as days, weeks, months, and years. As reported by [PERSON] and [PERSON] [17], the mathematical representation of the decomposed time series model:  
\[y(t)=g(t)+s(t)+h(t)+\varepsilon_{t} \tag{1}\]  
where \(g(t)\) denotes the data trend function, \(s(t)\) denotes the seasonality, and \(h(t)\) denotes holidays effect that can be added within specific points of the data and as an extra regressor. The error term, \(\varepsilon_{t}\), denotes any distinctive features of the data that are not fitted by the model.  
Prophet trend function, \(g(t)\), can be signified by a piecewise linear growth model or a saturating growth model. Since the electrical generation does not exhibit a saturating growth, a piecewise linear growth model is utilized as:  
\[g(t)=(k+a(t)^{T}\delta)t+(m+a(t)^{T}\gamma) \tag{2}\]  
where \(k\) represents the growth rate, \(\delta\) represents adjustment rate, \(m\) represents the offset parameter, and \(\gamma\) is the trend changepoints, \(s_{j}\), and is set as \(-s_{j}\delta_{j}\), with \(a(t)\) defined as:  
\[a_{j}(t)=\left\{\begin{array}{ll}1&if\ t\geq s_{j}\\ 0&otherwise\end{array}\right. \tag{3}\]  
The change points allow the analyst in the loop to adjust the resulting forecast based on a previous experience. Therefore, the trend of the forecast can be hence fine-tuned and results in an enhanced forecast. The seasonality function \(s(t)\) can be modelled by Fourier series to represent daily, weekly,and yearly seasonality as well as to incorporate more complex seasonality patterns by higher order Fourier series. The seasonality function is hence written as:  
\[s(t)=\sum_{n=1}^{N}\Bigl{(}a_{n}\cos\Bigl{(}\frac{2\pi nt}{P}\Bigr{)}+b_{n}\sin \Bigl{(}\frac{2\pi nt}{P}\Bigr{)}\Bigr{)} \tag{4}\]  
where \(P\) is assumed to be 365.25 for yearly seasonality pattern. Furthermore, Prophet model allows adding extra regressors to enhance the forecast results. The holiday effects, as example, can be incorporated using \(h(t)\) function and define a list of holiday dates as a matrix of regressors \(Z(t)\) defined as:  
\[Z(t)=[1(t\;\epsilon\;D_{1}),\;\ldots,\;1(t\;\epsilon\;D_{\rm L})] \tag{5}\]  
\[h(t)=Z(t)\kappa \tag{6}\]  
with \(D\) as the set of holiday dates, \(\kappa\sim Normal\Bigl{(}0,v^{2}\Bigr{)}\) with \(v\) as the holiday smoothing parameter. In this work, additional regressors were utilized and defined as the temperature, the maximum load, the minimum load, and the population to result in a more reliable forecast that reflects the growth in population and Kuwait's average temperatures.
# Machine Learning for Decision Support and Automation in Games: A Study on Vehicle Optimal Path
## 2 Machine Learning Models
### Training Methods
#### 2.2.2 Soft Actor-Critic  
SAC, unlike PPO, is an off-policy reinforcement learning algorithm. It can learn from experiences collected at any time in the past by storing them in an experience replay buffer, from which samples are randomly drawn during training. This approach significantly enhances sample efficiency, often requiring 5-10 times fewer samples than PPO to achieve comparable performance. However, SAC typically necessitates more model updates, making it well suited for environments where each step takes longer, around 0.1 s or more [13]. As an off-policy actor-critic algorithm based on the maximum entropy RL framework, SAC's training objective is to maximize both entropy and reward. This dual objective differentiates SAC from traditional actor-critic methods that solely focus on maximizing cumulative rewards. SAC modifies the objective function by incorporating the expected entropy of the policy, favoring stochastic policies and thus enhancing exploration [25; 26].  
The main objective functions of SAC are as follows:  
1. Q-Function Update  
The Q-function parameters are updated to minimize the soft Bellman residual:  
\[J_{Q}(\theta)=\mathbb{E}_{(s_{t},a_{t})\sim\mathcal{D}}\bigg{[}\frac{1}{2} \big{(}Q_{\theta}(s_{t},a_{t})-\big{(}r(s_{t},a_{t})+\gamma\mathbb{E}_{s_{t+1} \sim p}[V_{\theta}(s_{t+1})]\big{)}\big{)}^{2}\bigg{]} \tag{3}\]  
In which, each component is defined as follows:  
* \(Q_{\theta}(s_{t},a_{t})\) is the Q-function parameterized by \(\theta\).
* \(r(s_{t},a_{t})\) is the reward received after taking action \(a_{t}\) in state \(s_{t}\).  
* \(\gamma\) is the discount factor.
* \(V_{\bar{\theta}}(s_{t+1})\) is the target value function.  
_2. Value Function Update_  
The value function is updated to minimize the difference between the Q-function and the expected value under the policy  
\[J_{V}(\bar{\theta})=\mathbb{E}_{s_{t}\sim\mathcal{D}}\bigg{[}\frac{1}{2}\Big{(} V_{\theta}(s_{t})-\mathbb{E}_{a_{t}\sim\pi_{\phi}}\big{[}Q_{\theta}(s_{t},a_{t})- \log\pi_{\phi}(a_{t}|s_{t})\big{]}\Big{)}^{2}\bigg{]} \tag{4}\]  
_3. Policy Update_  
The policy parameters are updated to maximize the expected return while also maximizing the entropy to encourage exploration:  
\[J_{\pi}(\phi)=\mathbb{E}_{s_{t}\sim\mathcal{D},a_{t}\sim\pi_{\phi}}\big{[}\log \pi_{\phi}(a_{t}|s_{t})-Q_{\theta}(s_{t},a_{t})\big{]} \tag{5}\]  
_Entropy Regularization_  
The entropy regularization term ensures that the policy does not become too deterministic:  
\[\mathcal{H}(\pi(\cdot|s))=-\mathbb{E}_{a\sim\pi}[\log\pi(a|s)] \tag{6}\]  
Combining these components, the SAC algorithm alternates between updating the Q-function, the value function, and the policy using experience replay to sample batches of data. This approach enables SAC to achieve stable and efficient learning by maintaining a balance between exploration and exploitation [27; 28; 29; 30].
# An Empirical Assessment of Performance of Data Balancing Techniques in Classification Task
## 4 Results and Discussion
### Performance of DBT
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Dataset** & **None** & **US** & **OS** & **HS** & **ROSE** & **SMOTE** & **CBUS** \\ \hline Pima & 0.679717 & 0.630189 & 0.693491 & 0.615189 & 0.652453 & 0.668491 & 0.692358 \\ \hline ecoli1 & 0.933333 & 0.941176 & 0.960784 & 0.95098 & 0.95098 & 0.927451 & 0.95098 \\ \hline segment0 & 0.989776 & 0.911392 & 0.969523 & 0.945472 & 0.736709 & 0.982181 & 0.903797 \\ \hline yeast3 & 0.820549 & 0.869318 & 0.863163 & 0.859375 & 0.875473 & 0.882102 & 0.878788 \\ \hline vowel0 & 0.944444 & 0.932961 & 0.994413 & 0.960894 & 0.96648 & 1 & 0.944134 \\ \hline glass2 & 0.512821 & 0.794872 & 0.884615 & 0.653846 & 0.666667 & 0.897436 & 0.628205 \\ \hline yeast-1\_vs\_7 & 0.5 & 0.703922 & 0.721569 & 0.668627 & 0.52549 & 0.709804 & 0.515625 \\ \hline ecoli4 & 1 & 0.960317 & 0.968254 & 0.968254 & 0.95098 & 0.992063 & 0.95098 \\ \hline glass-0-1-6\_vs\_5 & 0.5 & 0.614286 & 0.528571 & 0.928571 & 0.871429 & 0.985714 & 0.628571 \\ \hline page-blocks-1\_3\_vs\_4 & 0.788636 & 0.780682 & 0.854545 & 0.848864 & 0.6 & 0.971591 & 0.792045 \\ \hline yeast-1-4-5-8\_vs\_7 & 0.5 & 0.560606 & 0.670455 & 0.636364 & 0.617424 & 0.57197 & 0.583333 \\ \hline yeast-2\_vs\_8 & 0.875 & 0.809783 & 0.831522 & 0.782609 & 0.869565 & 0.793478 & 0.869565 \\ \hline yeast4 & 0.598252 & 0.737063 & 0.806294 & 0.792308 & 0.783566 & 0.899301 & 0.724825 \\ \hline winequality-red-4 & 0.5 & 0.536246 & 0.511489 & 0.630259 & 0.504207 & 0.522168 & 0.625243 \\ \hline poker-9\_vs\_7 & 0.5 & 0.521277 & 0.978723 & 0.93617 & 0.978723 & 0.957447 & 0.521277 \\ \hline yeast-1-2-8-9\_vs\_7 & 0.5 & 0.680328 & 0.531421 & 0.581967 & 0.520492 & 0.584699 & 0.510929 \\ \hline winequality-white-9\_vs\_4 & 0.5 & 0.828125 & 0.59375 & 0.625 & 0.84375 & 0.578125 & 0.515625 \\ \hline yeast5 & 0.8125 & 0.954861 & 0.980903 & 0.979167 & 0.961806 & 0.984375 & 0.956597 \\ \hline winequality-red-8\_vs\_6 & 0.5 & 0.511976 & 0.615768 & 0.567864 & 0.613772 & 0.543912 & 0.61477 \\ \hline ecoli-0-1-3-7\_vs\_2-6 & 0.5 & 0.527778 & 0.518519 & 0.518519 & 0.546296 & 0.518519 & 0.611111 \\ \hline abalone-21\_vs\_8 & 0.75 & 0.915929 & 0.99115 & 0.986726 & 0.995575 & 0.977876 & 0.938053 \\ \hline yeast6 & 0.641127 & 0.820811 & 0.90608 & 0.895699 & 0.854177 & 0.827731 & 0.885319 \\ \hline winequality-white-3\_vs\_7 & 0.5 & 0.676136 & 0.599432 & 0.710227 & 0.616477 & 0.571023 & 0.715909 \\ \hline winequality-red-8\_vs\_6-7 & 0.5 & 0.511976 & 0.615768 & 0.567864 & 0.613772 & 0.543912 & 0.61477 \\ \hline abalone-19\_vs\_10-11-12-13 & 0.5 & 0.561321 & 0.548742 & 0.528302 & 0.647799 & 0.597484 & 0.578616 \\ \hline Average AUC Score & 0.653846 & 0.731733 & 0.765558 & 0.765565 & 0.750563 & 0.779554 & 0.726057 \\ \hline Mean Rank & 5.92(7) & 4.66(6) & 2.80(1) & 3.74(4) & 3.66(3) & 3.24(2) & 3.98(5) \\ \hline [PERSON] test statistics & \multicolumn{4}{c}{Friedman chi-squared = 34.192, df = 6, \(p\)-value = 6.177 \(\times\) 10\({}^{-6}\)} \\ \hline \end{tabular}
\end{table} 
Table 3: Performance of DBT for kNN classifier.
# Optimizing Retransmission Threshold in Wireless Sensor Networks
## 4 Dynamic Programming-Based Distributed Algorithm for Optimal Retransmission Thresholds
\[\min \sum_{h=u_{i-1}-l_{i-1}+1}^{sum}C_{h}S_{h}+\sum_{v=i}^{n}p_{v}^{l_ {v}} \tag{11}\] \[s.t. \sum_{h=u_{i-1}-l_{i-1}+1}^{sum}a_{g(h)}C_{h}+\sum_{v=i}^{n}a_{v}l _{v}\leq\Delta^{\prime}\] \[C_{h}\in\{0,1\},h\in\{u_{i-1}-l_{i-1}+1,...,sum\}\]  
Based on the above analysis, knapsack Equation (11) is a special instance of Equation (9), where the 'object' set is \(\{S_{u_{i-1}-l_{i-1}+1},...,S_{sum}\}\) and the 'capacity' is bounded by \(\Delta^{\prime}\). Suppose \(C_{u_{i-1}-l_{i-1}+1}^{\prime},...,C_{sum}^{\prime}\) are the optimal solutions of Equation (11), then \(\sum_{l=u_{i-1}-l_{i-1}+1}^{u_{i}-l_{i}}C_{h}^{\prime}\) is the optimal retransmission threshold of node \(j_{i}\). The message exchanges among network nodes are enhanced to carry necessary information of link quality and queue length [6,11], so that each node can independently calculate the optimal retransmission threshold based on the path forwarding quality and the remaining time to deadline. Such a property enables the node to adaptively set the optimal retransmission threshold in a scalable manner. The proposed dynamic-based distributed algorithm for the optimal retransmission threshold is described in Algorithm 1. We present the analysis for the computational complexity of Algorithm 1. The recurrence process of the algorithm yields the time computation of \((\Delta^{\prime}-\sum_{h=i}^{n}a_{i}l_{i})\cdot(\sum_{h=i}^{n}u_{i}-l_{i})\). Thus, the time complexity of the proposed distributed algorithm is \(\mathcal{O}\left(n\Delta\cdot\max_{1\leq i\leq n}\{u_{i}\}\right)\). Space complexity can be similarly analyzed, that is \(\mathcal{O}\left(n\Delta\cdot\max_{1\leq i\leq n}\{u_{i}\}\right)\).
## 4 Fluid Dynamic Performance
### Factors
#### 4.1.3 Steady and Unsteady Blood Flows  
The blood flow is generally laminar, with a smooth and ordered fluid motion. The values of the Reynolds number in the human circulatory system can vary until seven orders of magnitude depending on the geometry of the vessel (Table 1), and also, in some cases when the flow emerges from a narrow opening into a larger region in the form of a jet, the blood flow can be considered turbulent, as happens in stenosed arteries. Although the blood flow is considered in most of the cases laminar, it is unsteady, especially at the capillary level.  
The pulsatile nature of the blood flow in arteries is due to the cyclic nature of the heart pump. The heart ejects and fills with blood in alternating cycles called _systole_ (blood is pumped out) and _diastole_ (no blood is pumped). Due to the different shape of the vessel of the circulatory system, the pressure and flow have different characteristic pulsatile shapes [75]. The Womersley number is defined as the ratio between the unsteady and viscous forces. For low values, viscous forces dominate, velocity profiles are parabolic in shape, and the centerline velocity oscillates in phase with the driving pressure gradient. On the other hand, for values \(\geq\)10, the unsteady inertial forces dominate, and the flow presents a flat velocity profile [76].  
Nevertheless, an steady flow could be an acceptable approximation for some experimental and numerical works. In addition, the fluid structure interaction (FSI) is commonly not taken into account for simplification. More information about the steady and unsteady hemodynamic flows can be found in [PERSON] et al. [57].
## 3 Case Studies
### Additional Data  
In order to carry out a simulation with an approximation to the reality of photovoltaic and wind energy production in Simulink, data were collected from the PVGIS (version 5.3) [27] and Wind Atlas (version 3.4) [28] platforms, which provide detailed information on solar radiation and wind speed, respectively. The study focused on obtaining representative data for one day in February in the town of Real, Amarante, specifically in the area of the data taken from the E-REDES Open Data Portal [26], in order to simulate realistic conditions for this time of year.  
The PVGIS platform [27] was used to collect average global solar irradiance data for a February day, as shown in Figure 10. This is essential for accurately modeling the behavior of solar panels throughout the day. These data are fundamental to understanding the performance of a photovoltaic system, since energy production depends directly on the amount of available sunlight.  
Figure 9: Load diagram taken from the E-REDES Open Data Portal  
On the other hand, Wind Atlas [28] was used to obtain data on the average wind speed at the site, which is crucial for simulating wind power generation. Using wind data from the IPMA (Portuguese Institute for the Sea and Atmosphere) [29], in the district of Porto, it was possible to extrapolate the wind speed for various hours of the day, as shown in Figure 11. Wind speed influences the amount of energy that wind turbines can produce, which makes it essential to model hourly variations.
###### Abstract  
Non-convex optimization problems often challenge gradient-based algorithms, such as Gradient Descent. Neural network training, a prominent application of gradient-based methods, heavily relies on their computational efficiency. However, the cost function in neural network training is typically non-convex, causing gradient-based algorithms to become trapped in local minima due to their limited exploration of the solution space. In contrast, global optimization algorithms, such as swarm-based methods, provide better exploration but introduce significant computational overhead. To address these challenges, we propose Multi-Agent Gradient Descent (MAGD), a novel algorithm that combines the efficiency of gradient-based methods with enhanced exploration capabilities. MAGD initializes multiple agents, each representing a candidate solution, and independently updates their positions using gradient-based techniques without inter-agent communication. The number of agents is dynamically adjusted by removing underperforming agents to minimize computational cost. MAGD offers a cost-effective solution for non-convex optimization problems, including but not limited to neural network training. We benchmark MAGD against traditional Gradient Descent (GD), Adam, and Swarm-Based Gradient Descent (SBGD), demonstrating that MAGD achieves superior solution quality without a significant increase in computational complexity. MAGD outperforms these methods on 20 benchmark mathematical optimization functions and 20 real-world classification and regression datasets for training shallow neural networks.  
on-convex optimization; gradient-based algorithms; multi-agent algorithms; adaptive optimization techniques; global optimization; computational cost; Swarm-Based Gradient Descent (SBGD); neural network training; mathematical benchmark functions