esa-sceva/satcom-chunk-collection huggingface dataset:
## 4 Vehicle State Estimation, Localization, and Sensors
### Wheel Odometry Algorithm  
The wheel odometry works based on data from encoders coupled to the rear wheels. Every single encoder generates 100 sets of pulses for a revolution of the tire (encoder resolution). A revolution of the tire makes the single revolution in the encoder (1 by 1 coupling). Each rotary incremental encoder provides a least two output signals (usually A and B), which are in form of digital square waves. The rate of occurrence in the signal represents the shaft speed rotation, while the quantity of pulses shows the covered distance. Encoder output signals are sent to a processor board. The processor samples the encoder's signal every 5 milliseconds. Vehicle kinematic state can be defined using vehicle position (\(X\), \(Y\)) in the world coordinate frame (with an index point) and the vehicle heading \(\Psi\). Whenever the vehicle starts to turn, it must follow a circular path (see Figure 2). The integration time is so insignificant that we can consider the curvature of the path as a constant curvature. In Figure 2, \(X_{i}\) and \(Y_{i}\) are initial points and \(X_{f}\) and \(Y_{f}\) are final points.  
Length of the arcs for the right wheel \(\Delta_{dr}\) and the left wheel \(\Delta_{dl}\) are calculated using encoder measurement from the encoder (\(\Delta c_{r}\),\(\Delta c_{l}\)), the radius of the wheels (WRr, WRI), and resolution of the encoder (\(E_{res}\)) as follows:  
\[\Delta d_{r} =\frac{2\pi(WR_{r}\Delta c_{r})}{E_{res}} \tag{23}\] \[\Delta d_{l} =\frac{2\pi(WR_{l}\Delta c_{l})}{E_{res}} \tag{24}\]  
Figure 2: Wheel odometry model.  
Considering \(W_{dis}\) as the distance between wheels, the radius of curvature for each wheel and center can be calculated using the following relations:  
\[R_{right}=\frac{\Delta d_{r}W_{dis}}{\Delta d_{r}-\Delta d_{l}} \tag{25}\]  
\[R_{center}=\frac{W_{dis}}{2}*\frac{\Delta d_{r}+\Delta d_{l}}{\Delta d_{r}- \Delta d_{l}} \tag{26}\]  
\[R_{left}=\frac{\Delta d_{l}W_{dis}}{\Delta d_{r}-\Delta d_{l}} \tag{27}\]  
Using the above parameters, change of heading angle (\(\Delta_{\Psi}\)) and \(\left(\Delta_{x},\Delta_{y}\right)\) increments can be calculated as:  
\[\Delta_{\Psi}=\frac{\Delta d_{r}-\Delta d_{l}}{W_{dis}} \tag{28}\]  
\[\Delta_{x}=R_{center}(\cos(\Psi)\sin(\Delta_{\Psi})-\sin(\Psi)(1-\cos(\Delta_ {\Psi}))) \tag{29}\]  
\[\Delta_{y}=R_{center}(\sin(\Psi)\sin(\Delta_{\Psi})-\cos(\Psi)(1-\cos(\Delta_ {\Psi}))) \tag{30}\]  
Finally, the position and orientation of the vehicle are updated as follow:  
\[\Psi_{i+1}=\Delta_{\Psi}+\Psi_{i} \tag{31}\]  
\[x_{i+1}=\Delta_{x}+x_{i} \tag{32}\]  
\[y_{i+1}=\Delta_{y}+y_{i} \tag{33}\]  
Table 1 depicts the vehicle parameters (in our designed vehicle in this study) used in the wheel odometry model.
## 5 Evaluation Results and Discussion
### System Overview and Limitations
The alternative of head-mounted display (HMD) eye-trackers was also deemed unusable as were uncomfortable for the users and distorted their performance and subjective feedback during focus group trials. To resolve the above issue, video recordings were used to track the drivers' eye-gaze, head position, and body posture, yet the derived information was not included in the analysis, as not all the drivers consented to be recorded, introducing confounders. A large number of users could alleviate this issue in future evaluations. The second reason is that a driver's attention is not necessarily where his/her eyes are gazing. Various objects (in-vehicle and externally), events, or thoughts could distract the driver whilst he/she phenomenically gaze in the right direction. As such, it remains unclear the potential impact of the driver's attention captured by the HUD interface, namely percent road centre (PRC) which could affect the driver's response times (RTs) [65; 66]. Although in the particular motorway scenarios and the current AR HUD system, the PRC might have a negligible effect to the driver, in an urban environment the multilateral movement and positioning of pedestrians, crossings, could increase the PRC with direct impact on driver's and surrounding road users' safety. Thus, the interface is primarily designed and tested for motorway driving and performing to the requirements of an urban environment was outwith the remit of the current investigation but remains within our future development plans. The collision avoidance braking and manoeuvring performed by the user in the evaluation provided a suggestive appraisal of their actual ability to focus on the driving task manifested by the reduced collisions. Yet, some of these responses could have been instinctively performed. Detection response tasks (DRT) could be introduced seemingly on the following evaluations to check, at frequent intervals, the driver's actual attention on the road [67; 68]. The driving simulation investigated the driver's behaviour with and without the proposed system, on a typical British motorway environment and simulated specific accident scenarios as provided by the local traffic police. As stated previously, the digital twin model of the city of Glasgow and the extended motorway network had to be optimised to facilitate optimal software and hardware performance. Additionally, the neighbouring vehicles' AI offers limited driving behaviour which is developed primarily to fulfil the traffic flow needs and the specific accident scenarios' formation. Additional characteristics could be included to challenge further driver's ability to respond. Finally, the number of users (30), although sufficient to provide statistically significant results and in par to similar studies [2; 25; 50; 51; 62], could be increased in the future to improve the accuracy of the results and acquire a better understanding of driver's future requirements related to the incorporation of emerging technologies in the daily vehicular environment.
## 4 Results and Analysis
### Variance Analysis and Significance Test  
Variance analysis is widely used in data processing of the orthogonal test and can compensate for the deficiencies of the range analysis. The corresponding sum of squared variance and sum of squared errors need to be calculated for the experiment data when the variance analysis is applied. Based on the calculation results of the elastic modulus and UCS at different influencing factor levels in the orthogonal test, the corresponding sums of deviations squares, errors squares, and degrees of freedom for each factor were calculated with the help of an orthogonal design assistant. Moreover, the mean square is the ratio of the sum of squares of deviation to the degree of freedom. The F ratio is the ratio of the mean square of each factor to the mean square of error, respectively. Therefore, the mean square and the F ratio of each factor could be calculated for the elastic modulus and UCS, as shown in Figure 7. Finally, the F-ratios were compared with the critical values of \(F_{0.01}(2,\;6)\) and \(F_{0.05}(2,\;6)\). If \(F>F_{0.01}(2,\;6)\), the factor was highly significant, denoted by **. If \(F_{0.01}(2,\;6)>F>F_{0.05}(2,\;6)\), the factor was significant, denoted by *. If \(F<F_{0.05}(2,\;6)\), the factor was highly insignificant. Among them, \(F_{0.01}(2,\;6)=10.93\) and \(F_{0.05}(2,\;6)=5.14\).  
As shown in Figure 7, the results demonstrated that the sensitivity of the rock mass elastic modulus to the four influencing factors was not significant. The main reason is that the elastic modulus is an inherent characteristic of the rock mass, which is mainly related to the chemical composition of material and not its structural state. Besides, the sensitivity of the rock mass elastic modulus to the four influencing factors was in the order of trace  
Figure 6: Extreme difference values of the elastic modulus and UCS under various influencing factors.  
Figure 7: F ratio and significance levels of the elastic modulus and UCS under various influencing factors.  
length \(>\) bulk density \(>\) inclination \(>\) dip angle. The sensitivity analysis of rock mass UCS to the trace length of fracture was significant, while the sensitivity analysis to the inclination, dip angle, and bulk density of the fracture was insignificant. The sensitivity degree of the rock mass UCS to the four influencing factors was in the order of trace length \(>\) inclination \(>\) bulk density \(>\) dip angle, which is also consistent with the results of the range analysis.
# A Two-Step Algorithm for Handling Block-Wise Missing Data in Multi-Omics
## 6 Conclusions  
In this research, we addressed the methodological framework introduced in [6] to tackle multi-class classification challenges in the context of block-wise missing data. Our two-stage approach, implemented in the bvm R package, proved effective across two real-world multi-omics datasets: breast cancer and exposome data.  
For the breast cancer dataset, our approach maintained high classification performance, with accuracy around 80% in most scenarios. However, as the proportion of missing blocks increased, we observed a decline in performance, particularly for the Her2 and LumB subtypes. The misclassification between LumA and LumB aligns with known biological challenges, as these subtypes share molecular similarities [18].  
In the exposome dataset, our method effectively handled missing values while predicting children's BMI z-scores. The structured partitioning of exposure blocks provided a robust way to assess environmental influences on health, reinforcing the importance of multi-source integration in exposure studies.  
Despite these promising results, our approach presents some limitations. When missing data exceeded 30%, performance deterioration became evident, particularly for underrepresented classes. Future work should explore adaptive imputation strategies or uncertainty quantification techniques to mitigate these effects. Additionally, further benchmarking against other missing data strategies could provide deeper insights into the method's comparative strengths and weaknesses.  
Overall, this study underscores the potential of structured missing-data handling in multi-omics research, providing a scalable and interpretable approach for complex biological and environmental datasets.  
S.B.-M.: Software, Formal analysis, Writing, F.R.: Conceptualization, Writing, Data analysis, A.S.: Supervision, E.V.: Conceptualization, Writing, Data analysis. All authors have read and agreed to the published version of the manuscript.  
Our research group has public funding (Ministerio de Ciencia, Innovacion y Universidades, PID2023-148013 OB-C22/AEI DOI:10.13039/501100011033) which finances all the group's production, including but not limited to this work.  
All relevant data can be downloaded from public repositories. Breast cancer data repository: [[https://github.com/hyr0771/DiffRS-net](https://github.com/hyr0771/DiffRS-net)]([https://github.com/hyr0771/DiffRS-net](https://github.com/hyr0771/DiffRS-net)) (accessed date 16 February 2025), Exposome repository: [[https://github.com/isglobal-exposomeHub/ExposomeDataChallenge2021/](https://github.com/isglobal-exposomeHub/ExposomeDataChallenge2021/)]([https://github.com/isglobal-exposomeHub/ExposomeDataChallenge2021/](https://github.com/isglobal-exposomeHub/ExposomeDataChallenge2021/)) (accessed date 16 February 2025).  
We are grateful to everyone at the TCGA Consortium and ISGlobal Exposome 2021 Data Challenge.  
The authors have declared that no competing interests exist.
# Factors Affecting Rear-End Collisions in Underground Road Junctions Using VISSIM
## 2 Literature Review
### Evaluating the Effectiveness of Underground Roads  
Driving simulators are an effective method for collecting data from subjects driving in a virtual environment to analyze behavioral patterns based on different driving conditions [13]. Several researchers have employed driving simulators to observe driver behavior in underground roads or tunnel environments similar to underground roads, focusing on how design factors influence driver behavior [10; 14; 15; 16]. Driving simulators have also been utilized to evaluate safety under varying conditions, including weather, lighting, and human factors [17; 18; 19].  
However, analyzing complex interactions between drivers can be challenging with driving simulators, as it typically involves one or two users at a time. In contrast, microscopic traffic simulation is well suited for analyzing intricate interactions between vehicles [13]. Therefore, traffic simulation is necessary to evaluate complex systems, such as underground road junctions.  
Some studies have employed traffic simulation to assess operational effectiveness in underground roads, and many others have used it to evaluate safety in underground roads and tunnels [20; 21; 22; 23; 24; 25]. Factors such as speed variance, traffic volume, travel time, and queue length have been analyzed to assess safety [20; 21; 22; 23]. Existing research has significantly contributed to understanding underground road safety, including aspects like road design, lighting, and secondary crash risks. However, there remains a gap in research concerning the safety and operation of junctions, which are crucial components of the underground road network. Therefore, this study aims to conduct an in-depth analysis of underground road junctions and their related safety factors using traffic simulation, focusing on assessing accident risk through surrogate safety measures (SSMs) such as time-to-collision (TTC), crash potential index (CPI), and deceleration rate to avoid the crash (DRAC).
# Empirical Evaluation on Utilizing CNN-Features for Seismic Patch Classification
## 2 Related Work
### CNN-Features  
CNN-features are composed of values taken from the activation unit of the first FC layer of the CNN architecture [8]. Various studies have been conducted using CNN-features in many applications. In [24], it was evaluated whether the CNN weights obtained from large-scale source tasks could be transferred to a target task with a limited amount of training material. Along with this study, many other studies related to the extraction and utilization of CNN-features have been conducted [6; 9; 10].  
In [25], it was reported that reusing a previously trained CNN as a generic feature extractor leads to a state-of-the-art result, meaning that CNNs are able to learn generic feature extractors that can be used for different tasks. Thus, some studies have recently been reported in the industry on the techniques of extracting, and classifying feature vectors with this approach [7; 11]. In [7], top-performing hand-crafted descriptors, including the LBP (local binary pattern) and the HOG (histogram of oriented gradients), were compared with CNN-based models using variants of AlexNet [26]. Experiments on three datasets reported that CNN-based models were superior to other models. However, it was also pointed out that, to extract meaningful features from raw data, the approach requires huge amounts of training data. In case the generation of data is expensive, it might not be appropriate, as in [27].  
In the meantime, CNNs have improved performances while building deeper and wider networks [28]. In a different way, there are studies to improve the performance by simply using a pooling based on quadratic statistics, such as covariance, rather than sum (mean) or max pooling. A few examples are: second-order pooling (O2P) [15]; bilinear pooling (BiP) [12]; compact BiP [29]; deep architecture for O2P [30]; improved BiP [31]; matrix power normalized covariance (MPN-COV) [32]; and the iterative matrix square root normalization of covariance pooling (iSQRT-COV) [33].  
In [12], an effective architecture, called a bilinear CNN (B-CNN), was developed for visual classification. B-CNNs represent an image as a pooled outer product of features, derived from two CNNs, which capture the localized feature interactions. The work in [31] shows that feature normalization and domain-specific fine-tuning provide additional benefits, improving the accuracy using identical networks. In subsequent studies, various methods were proposed, in turn, to overcome the disadvantages of the B-CNN, such as the high dimensionality of the feature vectors, or GPU-unfriendly algorithms.
# From Phase Space to Non-Equilibrium Dynamics: Exploring [PERSON]'s Theorem and Its Implications
## 2 The Equation of Motion for Physical Quantities
### Foundations of Hamiltonian and Liouville Dynamics  
The equation of motion for any arbitrary physical quantity \(F\), which could represent energy, momentum, or any other observable of the system, is given by:  
\[\dot{F}=\frac{\partial F}{\partial q}\dot{q}+\frac{\partial F}{\partial p}\dot {p}=[H,F], \tag{1}\]  
where \([H,F]\) denotes the Poisson bracket. These brackets encode the algebraic structure of Hamiltonian mechanics and are central to **[PERSON]'s theorem**, which governs the evolution of phase-space distributions.  
A cornerstone of classical mechanics, [PERSON]'s theorem states that for a Hamiltonian system, the phase-space density \(\rho(q,p,t)\) evolves according to:\[\frac{\partial\rho}{\partial t}=-[H,\rho]=0, \tag{2}\]  
implying that the phase-space volume is preserved under time evolution (\(d\rho/dt=0\)). This theorem arises directly from the symplectic structure of Hamiltonian dynamics, where the second-form \(\omega=\sum_{i}dp_{i}\wedge dq_{i}\) ensures volume conservation. While foundational, this framework assumes isolated, equilibrium systems-a limitation we address in this work through entropy-driven modifications.
# Energy and Distance Based Multi-Objective Red Fox Optimization Algorithm in Wireless Sensor Network
## 6 Results and Discussion
### Performance of Network Lifetime  
ED-MORFO and existing methodologies were used to compare the performance of the lifetime of a network. Figure 6 depicts the existing MCH-EOR [24] and RDSAOA-EECP [25] assessments. Figure 6 illustrates that, when compared to existing approaches, ED-MORFO produces better outcomes. In contrast to the existing MCH-EOR [24] and RDSAOA-EECP [25], there is an increase in the longevity of ED-MORFO. As the network's node count grows, additional sensor nodes begin steering packets indiscriminately, and there is a significant chance that nodes perish at some point. Only the optimal node is assigned to transfer packets in the ED-MORFO approach, resulting in increased battery life and network longevity. Table 5 summarizes the results of the lifetime performance analysis. When compared to existing methodologies, the suggested ED-MORFO improves the network lifetime at a specific node, as shown in the table. The suggested ED-MORFO achieves a network lifetime of 3719 s, compared to 3500 s for the MCH-EOR [24], and 3000 s for the RDSAOA-EECP [25].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Number of Nodes**} & \multicolumn{3}{c}{**Throughput (Mbps)**} \\ \cline{2-4}  & **Existing MCH-EOR [24]** &
\begin{tabular}{c} **Existing** \\ **RDSAOA-EECP [25]** \\ \end{tabular} & **Proposed ED-MORFO** \\ \hline
100 & 0.97 & 0.94 & 0.99 \\
200 & 0.92 & 0.90 & 0.97 \\
300 & 0.89 & 0.84 & 0.96 \\
400 & 0.85 & 0.81 & 0.93 \\
500 & 0.79 & 0.75 & 0.91 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Performances of throughput.  
Figure 5: Performance analysis of throughput for proposed EDMORFO and Existing MCH-EOR [24], RDSAOA-EECP [25].
# NTT and Inverse NTT Quantum Circuits in CRYSTALS-Kyber for Post-Quantum Security Evaluation
## 2 Background
### Number Theoretic Transform (NTT)  
**Theorem 1**.: _The Fourier transform (FT) is a mathematical transformation that translates a function from its original domain (often time or space) to a representation in the frequency domain. For instance, an audio signal can be decomposed into multiple sine and cosine waves through the Fourier transform (FT). For an oscillation function, \(f(t)\), which changes over time \(t\), the oscillation encompasses various frequency components. If the frequency component is extracted and expressed as the frequency intensity distribution \(F(\omega)\) for the frequency \(\omega\), the nature of vibration can be easily analyzed. The mathematical expression for FT follows:_  
\[F(\omega)=\frac{1}{\sqrt{2\pi}}=\int_{-\infty}^{\infty}f(t)e^{-i\omega t}dt\]  
**Theorem 2**.: _The discrete Fourier transform (DFT) operates on finite \(N\) complex fields, in contrast to the continuous interval (\(-\infty\),\(\infty\)) addressed by the Fourier transform (FT). The \(N\) complex number sequence \(x_{N}=x_{0},\ldots,x_{(n-1)}\) is converted into another complex number sequence \(X_{k}=X_{0},\ldots,X_{t}\). Equation (1) shows the DFT process of a complex number field. \(k\) is the index of frequency, \(n\) is the index of the time sample, and \(N\) is the total number of samples in the input signal._  
\[X_{k}=\sum_{n=0}^{N-1}x_{n}e^{-2\pi ikn/N} \tag{1}\]  
_The number theoretic transform (NTT) generalizes the domain of the discrete Fourier transform (DFT) to operate over integer fields. It uses the \(n\)-th primitive root of unity based on a quotient ring instead of the complex field of DFT. When performing multiplication on two \(n\)-bit length polynomials, typical schoolbook multiplication has a computational complexity of \(O(n^{2})\) whereas that of NTT multiplication is \(O(nlogn)\). In lattice-based ciphers, NTT is used for efficient multiplication. The NTT multiplication of two polynomials, \(a\) and \(b\), is calculated as follows: \(NTT^{-1}(NTT(a)\cdot NTT(b))\). For the polynomial transformation, \(a\in Z_{q}[X]/(X^{256}+1)\) is split into \(a_{L}^{(1)}\in Z_{q}[X]/(X^{256}-\zeta^{128})\) and \(a_{R}^{(1)}\in Z_{q}[X]/(X^{256}+\zeta^{128})\). The \(a_{L}^{(1)}\in Z_{q}[X]/(X^{256}-\zeta^{128})\) and \(a_{R}^{(1)}\in Z_{q}[X]/(X^{256}+\zeta^{128})\) polynomials that are split into sub-rings are transformed, as seen in Equation (2)._  
\[a\in Z_{q}[X]/(X^{256}+1)\begin{cases}a_{L}^{(1)}=(a_{0}+\zeta^{128}a_{128})+( a_{1}+\zeta^{128}a_{129})+\cdots\\ a_{R}^{(1)}=(a_{0}-\zeta^{128}a_{128})+(a_{1}-\zeta^{128}a_{129})+\cdots\end{cases} \tag{2}\]