esa-sceva/satcom-chunk-collection huggingface dataset:
# A Novel Bayesian Linear Regression Model for the Analysis of Neuroimaging Data
## Appendix A DBL-FS Variational Inference
### Mean Field Approximation of \(\mathbf{a}\)  
Using the mean field approximation over variable \(\mathbf{a}\), we find that the logarithm of its approximate posterior is:  
\[\ln\left(q(\mathbf{a})\right)=\mathbb{E}[\ln\left(p(\mathbf{y}|\mathbf{X}, \mathbf{a},\tau)\right)]+\mathbb{E}[\ln\left(p(\mathbf{w}|\mathbf{a},\mathbf{ a})\right)]+const. \tag{11}\]  
If we develop the first term in the equation, we have:  
\[\ln\left(p(\mathbf{y}|\mathbf{X},\mathbf{a},\tau)\right) =\sum_{n=1}^{N}\ln p(y_{n}|\mathbf{x}_{n,:},\mathbf{a},\tau)= \sum_{n=1}^{N}\ln\mathcal{N}\Big{(}\mathbf{x}_{n,:}\mathbf{X}^{T}\mathbf{a}, \tau^{-1}\Big{)}\] \[=\sum_{n=1}^{N}\left(\frac{1}{2}\ln\left(\tau\right)-\frac{\tau}{ 2}(y_{n}-\mathbf{a}^{T}\mathbf{X}\mathbf{x}_{n,:}^{T})(y_{n}-\mathbf{x}_{n,:} \mathbf{X}^{T}\mathbf{a})\right)+const\] \[=\frac{N}{2}\ln\left(\tau\right)-\frac{\tau}{2}\sum_{n=1}^{N} \left(y_{n}^{2}-2y_{n}\mathbf{x}_{n,:}\mathbf{X}^{T}\mathbf{a}+\mathbf{a}^{T} \mathbf{X}\mathbf{x}_{n,:}^{T}\mathbf{a}\right)+const, \tag{12}\]  
and, calculating the expectation of this expression, we obtain:  
\[\mathbb{E}_{\tau}[\ln\left(p(\mathbf{y}|\mathbf{X},\mathbf{a},\tau)\right)]= \frac{N}{2}\ln(\langle\tau\rangle)+\langle\tau\rangle\mathbf{y}\mathbf{Ka}- \frac{\langle\tau\rangle}{2}\mathbf{a}^{T}\mathbf{K}^{T}\mathbf{Ka}+const. \tag{13}\]  
Equivalently, the second term can be calculated as:  
\[\ln\left(p(\mathbf{w}|\mathbf{a},\mathbf{a})\right) =\sum_{d=1}^{D}\ln p(w_{d}|\mathbf{a}_{d,}\mathbf{a})=\sum_{d=1} ^{D}\ln\mathcal{N}\Big{(}0,\mathbf{a}_{d}^{-1}\Big{)}\] \[=\sum_{d=1}^{D}\left(\frac{1}{2}\ln\left(\mathbf{a}_{d}\right)- \frac{1}{2}\mathbf{a}^{T}\mathbf{x}_{:}\mathbf{a}_{d}\mathbf{x}_{:}^{T} \mathbf{a}\right)+const\] \[=\frac{1}{2}\sum_{d=1}^{D}\ln\left(\mathbf{a}_{d}\right)-\frac{1 }{2}\sum_{d=1}^{D}\left(\mathbf{a}^{T}\mathbf{x}_{:}\mathbf{a}_{d}\mathbf{x}_{ :}^{T}\mathbf{a}\right)+const, \tag{14}\]  
and, we if we use the expectation, we have:  
\[\mathbb{E}_{\alpha}[\ln\left(p(\mathbf{w}|\mathbf{a},\mathbf{a})\right)]= \frac{1}{2}\sum_{d=1}^{D}ln\left(\langle\mathbf{a}_{d}\rangle\right)-\frac{1 }{2}\mathbf{a}^{T}\mathbf{X}\mathrm{diag}(\langle\mathbf{a}\rangle)\mathbf{X} ^{T}\mathbf{a}+const. \tag{15}\]  
Now, joining Equations (13) and (15), we obtain:  
\[\ln\left(q(\mathbf{a})\right)=\langle\tau\rangle\mathbf{y}^{T}\mathbf{Ka}- \frac{\langle\tau\rangle}{2}\mathbf{a}^{T}\mathbf{K}^{T}\mathbf{Ka}-\frac{1}{ 2}\mathbf{a}^{T}\mathbf{X}\mathrm{diag}(\langle\mathbf{a}\rangle)\mathbf{X} ^{T}\mathbf{a}+const. \tag{16}\]Therefore, we can identify the parameters of the \(q\) distribution on this equation, having:  
\[q(\mathbf{a})=\mathcal{N}(\mathbf{a}|\langle\mathbf{a}\rangle,\mathbf{\Sigma}_{a}) \tag{10}\]  
where the mean is:  
\[\langle\mathbf{a}\rangle=\tau\mathbf{\Sigma}_{a}\mathbf{K}^{\mathbf{T}}\mathbf{y} \tag{11}\]  
and the variance is:  
\[\mathbf{\Sigma}_{a}^{-1}=\mathbf{X}\mathrm{diag}(\langle\mathbf{\alpha} \rangle)\mathbf{X}^{\mathbf{T}}+\langle\tau\rangle\mathbf{K}^{\mathbf{T}} \mathbf{K} \tag{12}\]
###### Abstract  
The world is facing the global challenges of insecurity, poverty and climate change, which can impede food availability, production and nutritional security. Due to these factors, the production and availability of crop species such as legumes, pulses and cereals are declining, while some are gradually becoming extinct, which affects consumption. To meet global food demands, efforts should be geared towards promoting the cultivation and utilization of underexploited and neglected crops, which have the potential to improve food and nutrition security. However, the exploitation and utilization of crops mostly depend on existing knowledge. Therefore, this review gives an overview of the current knowledge regarding lima beans (_Phaseolus Iunatus_ L.), an underutilized legume that can serve as a promising potential food crop. While there are some studies on lima beans, they cannot compare to the abundance of studies on other legumes. It is essential to exploit the nutritional and health properties of this crop, as well as to explore processing techniques such as cooking, soaking, fermentation and germination for transforming them into other food forms. Despite the dearth of information on this crop compared to other legumes, there is a case for the promotion of lima beans, especially where there are incessant food shortages, as they will allow for dietary diversity. This is vital considering the vulnerability of world food systems, coupled with an ever-growing population, necessitating a focus on other neglected crops to improve food security.  
food security; legume; underutilized crop; nutritional benefits +
Footnote †: journal:  
the cultivation, domestication and use of an underutilized legume such as the lima bean could help to ameliorate the current global over-dependence on other legumes such as soybeans and common beans. Such an over-dependence can have a negative ecological, nutritional, economic and agronomic impact. As few scientific reviews exist on lima bean utilization [6; 7; 8; 9], this review provides updated information on this crop as a vital, yet underutilized legume crop for improving food and nutrition security. Available literature was sourced from major databases (Scopus, Web of Science and Google Scholar). In addition to providing up-to-date information, this review also describes the nutritional, anti-nutritional and health composition of the crop, an overview of its microstructure, the impact of food processing on these constituents and the utilization of the lima bean for food use.
## 6 Discussion  
### Results Obtained from ASMAG  
#### 6.1.1 Snow Cover Ratio SCR and AAR  
The mapped SCR for each glacier depends very much on the acquisition date of the scene and will be larger than the AAR in all years where the week of maximum ablation is not met. As this is seldom the case, our SCR values are generally higher. However, with very few exceptions, the ranking is identical indicating that glacier specific differences in the ablation pattern are well captured by the ASMAG mapping. On the other hand, in years where (cloud-free) scenes from near the end of the ablation period are available (mostly after 1997) very good matches of the SCR with the AAR have been achieved for all three glaciers. This indicates the high potential of the method for high quality results when denser time series of satellite data are available. Despite the high year-to-year variability, a negative and nearly identical trend of AAR values is observed over the two study periods (1985-2000, 2001-2016) for the three glaciers (from \(-0.06\) to \(-0.08\)). Such trends were also found before 1998 [60] and are in line with a temperature increase since 1979 at the climate station in Vent (0.07 \({}^{\circ}\)C /year) [58] and a general decrease of SC in the Alps [61; 62].  
Less or even no SC on glaciers is expected to become more frequent in the future especially for mid-latitude glaciers. One example representing such conditions was the very hot summer in 2003, where the measured ELA was above the highest point of the glacier. Under such conditions, ASMAG is expected to produce erroneous results from arbitrary snow patches or bright spots on the glacier,  
Figure 9: (**a**) Visual versus automatic SLA for Abramov glacier in Kyrgyzstan. As in the Öztal region, an r\({}^{2}\) of nearly 90% is also obtained. In (**b**), (**c**) and (**d**) a comparison of the ASMAG snow cover classification (red outlines) and the manual digitized SLA (yellow outlines) obtained from [PERSON] et al. (2017) [59] is shown for three different years.  
although in our case ASMAG worked well in 2003 as only images from mid and end of July (still with snow on glaciers) were available.
# A Self-Calibration Method for Robot End-Effector Using Spherical Constraints
## 1 Introduction
They applied forces of varying magnitudes and directions to the end-effector and measured the resulting deformation coefficients. [PERSON] et al. [12] examined the combined effects of static errors, link flexibility and joint flexibility on the robot's end-effector pose, validating the model's feasibility through simulation. [PERSON] et al. [13] proposed a non-linear control technique that investigates the effects of torque oscillations in a permanent magnet synchronous motor (PMSM) on control precision. This method was applied to a two-degree-of-freedom robotic arm, leading to enhanced position control accuracy for the robot's end-effector. In parallel, [PERSON] et al. [14] conducted a thorough analysis of errors in robotic kinematics and dynamics parameters, considering joint angle errors induced by end loads. Their research significantly improved the robot's positioning accuracy, reducing it from 7.52 mm to 1.29 mm. Among the three constraint methods discussed, calibration methods based on distance and plane constraints are typically large, cumbersome and involve complex processes requiring numerous data points. The point constraints calibration method, which necessitates manually aligning the robot end-effector to a specific point, introduces significant uncertainty due to the difficulty of ensuring consistent alignment. This results in low calibration efficiency and longer time consumption. In real industrial robot applications, various end-effectors are mounted on the manipulator to address different operational needs. The deformation of the robot end-effector is inevitable and can lead to a reduction in positioning accuracy. To address this issue, this paper proposes a self-calibration method based on spherical constraints that accounts for end-effector deformation. This method features a compact and portable calibration device, eliminates the need for manual alignment and offers high calibration accuracy and efficiency. The remainder of this paper is organized as follows. Section 2 derives the error models for geometric errors of the robot and deformation errors of the end-effector. Section 3 presents a method for identifying error parameters using spherical constraints. Section 4 describes the design of simulation calibration experiments conducted in MATLAB. Section 5 details the implementation of error calibration and compensation on a KUKA robot. Conclusions and future research are addressed in Section 6.
# Employing Ray-Tracing and Least-Squares Support Vector Machines for Localisation +
## 2 Experimental Setup and Methodology
### Least-Square Support Vector Machines  
Least-Squares Support Vector Machine (LSSVM) is a reformulation of the standard SVMs in order to solve linear kernel-based systems. They were first proposed by [PERSON] and [PERSON] [15]. They are typically used for classification and regression as is the case in [2; 16]. The regression capability is exploited in many applications that require function estimation. In such applications, one moves from a large data set of observations, and tries to construct a model from the data, which is generally counter-intuitive to common engineering approaches where one builds a model and then apply it to new data. The function estimation methodology seeks to construct a function \(\Re^{n}\rightarrow\Re\) of the form:  
\[y(x)=\sum_{i=N}^{N}\alpha_{i}\psi(x,x_{i})+b, \tag{1}\]  
given a training set of \(N\) data points \(\{x_{i}y_{i}\}_{i=1}^{N}\) where \(x_{i}\in\Re^{n}\) is the \(i^{th}\) input and \(y_{i}\in\Re\) is the corresponding \"output\" to be used for training the regressor. \(\alpha_{i}\) are positive real constants and \(b\) is a real constant, and both these 2 constants form the parameters of the regressor. The function \(\psi(x,x_{i})\) is called the Kernel and it is typically taken to be \(x_{i}^{T}x\) for linear SVMs, or \(\psi(x,x_{i})~{}=~{}\exp\Bigl{\{}-\frac{\|x-x_{i}\|^{2}}{\sigma^{2}}\Bigr{\}}\) for Radial Basis Function (RBF) SVMs, with \(\sigma\), being a constant. The LS-SVM formulation leads to a linear system that can be written in matrix form as:  
\[\left[\begin{array}{cc}0&1_{N}^{T}\\ 1_{N}&\Omega+\gamma^{-1}I_{N}\end{array}\right]\left[\begin{array}{c}b\\ \alpha\end{array}\right]=\left[\begin{array}{c}0\\ Y\end{array}\right], \tag{2}\]  
where \(Y=\left[y_{1},~{}\ldots,y_{N}\right]^{T}\), \(\alpha=\left[\alpha_{1},~{}\ldots,\alpha_{N}\right]^{T}\) and \(\mathrm{I}_{N}=\left[1,~{}\ldots,1\right]^{T}\), \(I_{N}\) is an \(N\times N\) identity matrix and \(\Omega\) is the kernel matrix. The parameter \(\gamma\) tunes the trade-off between model complexity and level of tolerable training errors. The parameters of the regressor \(\alpha\) and b are obtained by solving the above linear system (Equation (2)). These parameters are then fed into the regressor (Equation (1)). In this study we choose the Radial Basis Function (RBF) kernel because it gives the best validation and test set performance [17]. The LSSVM formulation and detailed options are available from [PERSON]'s original formulation [18].  
Figure 3: Ground reflected multipath (red dashed path).
# Predicting Saudi Stock Market Index by Using Multivariate Time Series Based on Deep Learning
## 2 Literary Survey
The experimental findings using publicly available benchmark datasets demonstrated that the model not only outperformed state-of-the-art baselines in terms of prediction accuracy but also identified the dynamic link between input and output variables. Next, to make the regression coefficients adjustable for each time step, RNNs were used to reparameterise the basic model. A simple linear regression and statistical test were used to establish the base model. In time-dependent fields like finance and economics that depend on variables, explaining dynamic relationships between input and output variables is one of the most crucial challenges ([PERSON] et al. (2022)). According to [PERSON] et al. (2022), the Prophet model based on logistic regression had the lowest RMSE value of all the other algorithms; therefore, it was the most effective. A firm's growth and advancement can be easily predicted by examining its stock market performance, which paves the way for the advancement of stock-price projection technology to determine the effects of any event occurring in the modern world. Four supervised ML models, Facebook Prophet, multivariate linear regression, autoregressive integrated moving average (ARIMA), and LSTM, were used to predict the closing stock price of Tata Motors, a major Indian automaker, while RMSE was used to determine efficacy ([PERSON] et al. (2022). The introduction of an automated system which can predict potential stock prices with significant precision is important as it is not humanly possible for stock market traders and investors to comprehend the nature of fluctuations in prices. Forecasting future stock-market trends is unfortunately quite difficult due to the unpredictable, nonlinear, and volatile character of stock-market values. [PERSON] et al. (2022) demonstrated the promising potential of their proposed architecture by examining data from the Dhaka Stock Exchange. In order to reduce investment risks, it is crucial for the interested parties and stakeholders to possess suitable and insightful trends of stock prices ([PERSON] et al. (2022). Using an RNN and discrete wavelet transform (DWT), [PERSON] and [PERSON] (2019) sought to forecast Saudi stock price trends based on historic prices. A comparison indicated that the proposed DWT-RNN method provided for a more precise estimation of the day's closing price using MAE, mean squared error (MSE), and RMSE than the ARIMA method. The developed RNN was trained using the backpropagation through time (BPTT) approach to assist in forecasting the closing price of the Saudi market's stocks for the selected sample of firms for the upcoming seven days. The noise around the data collected from the Saudi stock market was reduced with the help of the DWT technique. The results were then analysed and compared to that of more conventional prediction algorithms, such as ARIMA ([PERSON] et al. (2022)). Appendix A summarizes the details of the literary survey.
## 2 Principle and Design of Wave Field Synthesis 3D Imaging System
### Optical System Principle
The origin is located at the corresponding lens center, \(x_{n}\) indicates the pixel coordinate relative to the lens center, \(A_{n}\) represents the amplitude provided by the pixel and \(k=2\pi/\lambda\) is the wave number. In addition, the lens modulation based on the thin lens approximation can be described as  
\[M_{L}(x,y)=\exp\left[-\mathrm{i}\frac{k}{2f}x^{2}\right]. \tag{2}\]  
By multiplying Equation (1) and (2), the perceived wave function of the pixel after passing through the lens can be written as  
\[U(x,z)=U_{S}\cdot M_{L}=\frac{A_{n}}{d}\mathrm{exp}\left[i\frac{k}{2}\left( \frac{1}{d}-\frac{1}{f}\right)x^{2}+\mathrm{i}kd\right]\cdot\mathrm{exp}\left[ -\mathrm{i}\frac{kx_{n}}{d}x\right], \tag{3}\]  
where the first exponential term with square in \(x\) indicates the curvature, and the second term linear in \(x\) represents the average propagation direction of the corresponding spherical wave cutout, which forms behind the lens. By comparing Equation (1) and (3), the spherical wave can be assumed to originate from a point source in a distance \(d_{v}\) behind the lens array, which depends on \(d\) and \(f\) according to  
\[d_{v}=\frac{fd}{f-d}. \tag{4}\]  
Please note that due to their limited aperture, the lenses only produce a cutout of a spherical wave rather than the entire wave field. This effect is an important requirement for the spherical wave field synthesis. It enables creating the effect of object occlusions, i.e., when one object in the front blocks parts of the spherical waves originating from an object behind it. At this point, the main direction in which the spherical wave cutout propagates shall be derived. According to Figure 2, one can find the geometrical relation  
\[\cot\alpha=\frac{x_{n}}{d}=\frac{x_{0}}{d_{v}}. \tag{5}\]  
Within the paraxial approximation, this is equivalent to  
\[\cos\alpha=\frac{x_{n}}{d}. \tag{6}\]  
Inserting Equation (6) turns the second exponential term in Equation (3) into a plane wave travelling along the direction \(\alpha\) with respect to the lens plane. The angle \(\alpha\) therefore defines the direction in which the spherical wave cutout propagates. The Equations (4) and (6) are crucial for the design of the desired wave field to depict an object in a virtual distance \(d_{v}\) behind the lens' plane. Finally, in our experiments, each LCD pixel was associated to the lens in front of it (in the direction of the optical axis). We avoided crosstalk between neighboring lenses by a 3D-printed parallax barrier.
# Fresher Experience Plays a More Important Role in Prioritized Experience Replay
## 5 Experiment  
### Discrete Control  
Discrete control tasks refer to tasks with discrete action spaces. The number of actions is countable and one-hot vectors can indicate whether an action is executed [35]. Herein, we select two Atari games based on OpenAI Gym [36] to evaluate the performance of FPER in discrete control tasks: LunarLander-v2 and CartPole-v1, shown in Figure 2.  
In our experiments, two hidden layers are included in the common part of Dueling DQN. There are 512 and 128 hidden units in the first and second layers respectively. We use Root Mean Square Propagation (RMSprop) [37] to optimize the neural network parameters with a learning rate of \(5\times 10^{-4}\). The discounted factor is set as 0.99. The freshness discounted factor is set as 0.90. The buffer size is set as \(10^{4}\), and the mini-batch size is  
Figure 2: From left to right: LunarLander-v2, CartPole-v1.  
set as 32. Additionally, dynamic \(\epsilon\)-greedy strategy is used to help the agent explore the environment efficiently. The value of \(\epsilon\) is initially set as 1.0, which decreases to 0.1 smoothly in 20,000 steps.  
In order to compare the performance of Algorithm 1, PER and CER are embedded in Dueling DQN. Moreover, FPER is combined with a lifetime pointer in these two discrete control tasks to stabilize the learning process. Each task runs the same episodes and is evaluated after each episode. Each episode reports the average reward over 10 episodes without exploration strategy. Results are shown over five random seeds of Gym simulator and the network initialization.  
Figure 2(a) shows the experimental plots of FPER, CER and PER applied in LunarLander-v2. The rewards of these three approaches are quite different. FPER performs the greatest reward, and PER obtains the least. Figure 2(b) depicts the experimental outcomes of FPER, CER, and PER applied in CartPole-v1. The rewards of CER and PER are almost the same i.e., CER could not improve the performance of PER in this case. The performance of FPER is obviously high in reward in the same episode than CER and PER. As shown in Figure 3, FPER could obtain higher reward and achieve better performance in the same episode than CER and PER. This shows that fresh experiences are more effective during the learning process in discrete control tasks.  
Table 1 lists the implemented time taken by the agent for different algorithms in different discrete control tasks. Compared to other algorithms, FPER achieves the same reward with the fewest time steps in different environments. So the learning speed and learning capacity of FPER are comparatively high than CER and PER.  
Figure 3: Learning curves in discrete control tasks. The shaded region represents the standard deviation of the average evaluation over five trials, and the thick line represents the mean of the average evaluation over five trials. (**a**) LunarLander-v2. (**b**) CartPole-v1.
## 4 Results and Discussion
### Parametric Studies  
As described in the previous paragraph, the proposed FE model showed relatively accurate predictions for the RC beams strengthened with the Fe-SMA strip. Parametric analyses were performed with this FE model, to investigate which variable affected the flexural strength of the RC beam strengthened with the Fe-SMA strip using the NSM method. The variables considered in this parameter analysis were the concrete compressive strength, recovery stress level, amount of Fe-SMA strip, and ratio of tensile reinforcement of the specimen SL-90S-4. The parametric studies were conducted in terms of the crack load, yield load, and ultimate load on each parametric variable. In addition, the displacement ductility index was considered to investigate the serviceability of the RC beam reinforced with the Fe-SMA strip. The displacement ductility index was calculated using Equation (4) below.  
\[\mu_{\delta}=\frac{\mu_{u}}{\mu_{y}} \tag{4}\]  
where, \(\mu_{\delta}\) represents the displacement ductility index, \(\mu_{u}\) and \(\mu_{y}\) represent the displacement at the yielding load and ultimate load, respectively.  
Figure 11: Comparison of load- displacement curves for B2 & B6: (**a**) B2; (**b**) B6.  
Figure 12: Comparison of experimental and numerical prediction results.