esa-sceva/satcom-chunk-collection huggingface dataset:
## 4 Implementation
### Handling Constraints
#### 4.2.3 Calculating the Dependent Variable (\(p_{1}\))  
In order to satisfy the power balance requirement shown in Formula (6), \(p_{1}\) is regarded as a dependent variable. Thus, the violation of the power balance is converted into the violation of \(p_{1}\). Power outputs from the second to the last units are considered to be control variables and are provided by the duty of the proposed method, whereas \(p_{1}\) can be obtained by using Formulas (6) and (7). The formula below can find \(p_{1}\) exactly.  
\[p_{1}=\frac{-\left(B_{01}-1+2\sum\limits_{s=2}^{n}B_{1s}p_{n}\right)\pm\sqrt{ \Delta}}{2B_{11}} \tag{39}\]  
where  
\[\Delta=\left(B_{01}-1+2\sum\limits_{s=2}^{n}B_{1s}p_{n}\right)^{2}-4B_{11} \left(p_{d}+B_{00}-\sum\limits_{s=2}^{n}p_{s}+\sum\limits_{s=2}^{n}B_{0s}p_{s} +\sum\limits_{s=2}^{n}\sum\limits_{m=2}^{n}p_{s}B_{sm}p_{m}\right);\;\text{ and }\Delta\geq 0 \tag{40}\]  
Calculating \(p_{1}\) deals with the power balance constraint. However, sometimes it can violate other constraints such as power output limits and POZ. Power output of the first TGU is checked and violations of the upper and lower limits are penalized using the following equation:  
\[\Delta p_{1,k}=\left\{\begin{array}{ll}p_{1,\min}-p_{1,k}&if\quad\;\;p_{1, \min}>p_{1,k}\\ p_{1,k}-p_{1,\max}&if\quad\;\;p_{1,\max}<p_{1,k}\\ 0&else\end{array}\right. \tag{41}\]  
where \(\Delta p_{1,k}\) is the penalty for violation of the upper bound and lower bound of \(p_{1}\). If \(\Delta p_{1,k}\) is zero, it means there are no violations of the bounds; however, \(p_{1}\) would continue to be checked for POZ constraints by the following model:  
\[\Delta p_{1,k}=\left\{\begin{array}{ll}p_{1}-p_{1k}^{l}&if\quad\;\;p_{1k}^{ l}<p_{1}\leq\frac{p_{1k}^{l}+p_{1k}^{u}}{2}\\ p_{1k}^{u}-p_{1}&if\quad\left(p_{1}>\frac{p_{1k}^{l}+p_{1k}^{u}}{2}\right)&\& \left(p_{1}<p_{1k}^{u}\right)\\ 0&else\end{array}\right. \tag{42}\]
# Frequency-Domain Filtered-x LMS Algorithms for Active Noise Control: A Review and New Insights
## 4 Delayless Frequency-Domain ANC Algorithms
### Proposed Delayless Algorithm  
Several approaches have been proposed to remove the delay in the signal path or the weight update delay, but none of these algorithms can remove both kinds of delays. To address this problem, we propose a new delayless frequency-domain FxLMS algorithm as shown in Figure 5. First, we employ the modified filtered-x scheme to the frequency-domain ANC to remove the delay in the weight adaptation. Second, the delayless fast filtering approach in Section 4.2 is used to remove the signal path delay.  
The estimate of the control signal at the location of the error microphone is  
\[\begin{split}\mathbf{\hat{z}}(k)&=[\hat{z}(kL-L+1),...,\hat{z}(kL)]^{T}\\ &=[y(kL-L+1)*\hat{s},...,y(kL)*\hat{s}]^{T}\\ &=\mathbf{Q}^{01}\mathbf{F}^{-1}\sum_{p=0}^{P_{w}-1}\mathbf{Y}_{p }(k)\mathbf{\hat{S}}_{p},\end{split} \tag{44}\]  
where  
\[\mathbf{Y}_{p}(k)=diag\{\mathbf{F}\mathbf{y}_{p}(k)\} \tag{45}\]  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Operation** & **Complexity** \\ \hline (1) Compute the frequency-domain reference matrix \(\mathbf{X}_{0}(k)\) using (8) & One FFT \\ (2) Compute the filtered reference signal vector \(\mathbf{v}(k)\) using (11) & One FFT and \(4 LP_{\text{s}}\) multiplications \\ (3) Compute the FFT of \(\mathbf{v}_{0}(k)\) using (15) & One FFT \\ (4) Update \(\mathbf{\Lambda}(k)\) using (17) & 4\(L\) multiplications \\ (5) Compute the FFT of the error signal using (14) & One FFT \\ (6) Update the weight vector using (38) & \(2P_{w}\) FFTs and \(6 LP_{w}\) multiplications \\ (7) Compute \(\mathbf{b}(k+1)\) using (42) & One FFT and \(4L(P_{w}-1)\) multiplications \\ (8) Compute the cancelling signal \(\mathbf{y}(k+1)\) using (40) & \(2L^{2}\) multiplications \\ \hline \hline \end{tabular} Note: Steps (1)–(7) should be completed between \(kL\) and \(kL+L\); Average and peak multiplications: \((5+2P_{w})A/L+10P_{w}+4P_{k}+2L\).  
\end{table}
Table 7: [PERSON]’s delayless algorithm [46].  
is the frequency-domain cancelling signal matrix with \(\mathbf{y}_{p}(k)=\{y[(k-p-2)L+1],...,y[(k-p)L]\}^{T}\). Then, we can use (30) to estimate the disturbance signal vector \(\hat{\mathbf{d}}(k)\). The weight vector is updated as  
\[\hat{\mathbf{E}}(k)=\hat{\mathbf{D}}(k)+\mathbf{G}^{01}\sum_{p=0}^{P_{\rm w}-1 }\mathbf{V}_{p}(k)\mathbf{W}_{p}(k), \tag{46}\]  
\[\mathbf{W}_{p}(k+1)=\mathbf{W}_{p}(k)-\mu\mathbf{G}^{10}\mathbf{\Lambda}^{-1}( k)\mathbf{V}_{p}^{H}(k)\hat{\mathbf{E}}(k). \tag{47}\]  
Once we obtain the new weight vector \(\mathbf{W}_{p}(k+1)\), we can use (40) to calculate the control filter output. By doing so, the delay in the signal path is removed by using the hybrid fast filtering approach, and the delay in the weight update is removed by means of the modified filtered-x structure. Furthermore, the total complexity is distributed evenly in one block, which makes the algorithm practical. The proposed delayless algorithm is presented in Table 8.
## 2 Preliminary
### Support Vector Machine  
An SVM algorithm is used to find the best possible hyper-plane in K-dimensional feature space to separate the samples of different classes. The SVM classifier is popular because of its potential in solving for the global minimum. It can impressively control the over-fitting problem due to its feature generalization ability [52]. SVM can efficiently solve  
Figure 2: Architecture of the MLP network with a single hidden layer.  
the classification problem of non-linearly separable data with kernel approach. All these benefits of SVM make it the prime choice for classification tasks in the proposed work. The mathematical modelling of the Kernel approach is given below:  
The optimum hyperplane derived by the SVM classifier can be given by Equation (19):  
\[\sum_{i=1}^{N}\alpha_{i}y_{i}x^{T}x_{i}+b=0 \tag{19}\]  
where, N represents the number of samples, \(\alpha\) represents a Lagrange multiplier, and \(y_{i}\) represents the labelled value of \(i^{th}\) support vector, given as \(y_{i}\in\ \{1,-1\}\) and b represents bias. To classify the nonlinearly-separable data using a linear decision-plane, the kernel approach can be used in the following manner [53].  
With the help of Basis function \(\varphi\), the given data is transformed to higher dimensions. By using Equation (19), the hyper plane in a higher dimension can be given as:  
\[\sum_{i=1}^{N}\alpha_{i}y_{i}\ \varphi(x)^{T}\varphi(x_{i})+b=0 \tag{20}\]  
Equation (20) can be rewritten as:  
\[\sum_{i=1}^{N}\alpha_{i}y_{i}K(x,x_{i})+b=0 \tag{21}\]  
Here, K (x, xi) is kernel function, which is defined as:  
\[K(x_{i},x_{j})=\varphi(x_{i})\varphi(x_{j}) \tag{22}\]  
In the proposed work, the Linear kernel was used because of its ability to make SVM learn fast, the least risk of over-fitting, and the need for zero hyper parameters [54]. It is given by:  
\[K(x_{i},x_{j})=x_{i}\cdot x_{j} \tag{23}\]
## 3 Computational Methodology
### CORE-Clustering Algorithms
#### 3.2.1 Maximum Spanning Tree  
The maximum spanning tree of \(G\) is the simple and reliable modeling of the relationship between the graph nodes (only \(p-1\) links). One of the most famous algorithms developed to find such trees is called [PERSON]'s algorithm [25]. The maximum spanning tree is built by adding step by step partial associations so that there will be no cycle in the partial graph.  
We denote by \(G(N,T)\) the resulting graph, where \(T\) has a tree-like structure. Details of the algorithm are given in Algorithm 1. The algorithmic cost of the sort procedure (row 1) is \(\mathcal{O}(K_{E}\log{(K_{E})})\). Then, the for loop (rows 4 to 10) only scans the edges once. In this for loop, the most demanding procedure is the propagation of label \(L(N_{i})\), row 8. Fortunately, the nodes on which the labels are propagated are related to \(N_{j}\) in \(G(N,E)\). We can then use a depth-first search algorithm [26] for that task, making the average performance of the for loop \(\mathcal{O}(K_{E}\log{(p)})\).  
```
0: Graph \(G(N,E)\) with nodes \(N_{i}\), \(i\in 1,\cdots,p\) and edges \(E_{k}\), \(k\in 1,\cdots,K_{E}\).
0: Weight of edge \(E_{k}\) is \(W(E_{k})\).
1: Sort the edges by decreasing weights, so \(W(E_{1})\geq W(E_{2})\geq\cdots\geq W(E_{K_{E}})\).
2: Assign label \(L(N_{i})=i\) to each node \(N(i)\).
3: Initiate an edge list \(T\) as void.
4:for\(k=1:K_{E}\)do
5: We denote \(N_{i}\) and \(N_{j}\) the nodes linked by edge \(E_{k}\).
6:if\(L(N_{i})!=L(N_{j})\)then
7: Add edge \(E_{k}\) to the list \(T\)
8: Propagate the label \(L(N_{i})\) to the nodes that have label \(L(N_{j})\).
9:endif
10:endfor
11:return Graph with a tree structure \(G(N,T)\).
```  
**Algorithm 1** Maximum spanning tree algorithm
# A Study on the Roof-Cutting and Pressure Releasing Technology of Roof Blasting
## 4 Engineering Applications of Hard Roof Blasting
### Analysis of the Test Results
#### 4.3.2 Analysis of Microseismic Monitoring  
Figure 12 shows the microseismic events three days before and after blasting. According to the monitoring data, there were 25 microseismic energy events greater than 10\({}^{2}\) J before blasting and 14 microseismic energy events greater than 10\({}^{2}\) J after blasting. In the three days before and after blasting, 10\({}^{3}\) J-level events occurred 9 times, each near the working face. Combined with the location of the roof blasting, the larger events transferred to the working face, and the distribution was no longer concentrated, and the overall number of the larger energy events were lower than before blasting. The large-energy events were transferred to the tunnel face after the broken roof occurs, and the stress distribution was no longer concentrated. Overall, the rock formation in front of the working face was broken after blasting, which can release elastic energy accumulation and reduce the probability of rock bursts.  
Figure 13 shows the change law of energy events three days before and after blasting. A range of 10\({}^{2}\)-10\({}^{3}\) J-level energy events accounted for 56.25%, and 10\({}^{3}\)-10\({}^{4}\) J-level energy events accounted for 43.75% of events, both of which did not reach the orange warning level. The operating range was within the safety threshold. From Figure 13, the rock layer did not break immediately after blasting and still had partial bearing capacity. After a period of time, large deformation and breakage occur and then tend to stabilize.  
Figure 11: The relationship between the daily average stress changes of the stress gauges at different positions near the borehole.  
Figure 12: Energy distribution law of micro-seismic events.
# Cluster-Based Transmission Diversity Optimization in Ultra Reliable Low Latency Communication
## 4 Simulation Results
### Optimum Number of Cluster Evaluation
#### 4.3.1 Reliability for Three Packet Duplication  
In Figure 8, 3-packet duplication has more reliability when sensors are plotted in 4-clusters. At 5000 pkt/s, 4-clusters achieve reliability of 99.99045%. On the contrary, 2-, 3-, 5-, and 6-clusters at the same arrival conditions achieve the reliability of 99.9272%, 99.98703%, 99.96871%, and 99.8227% respectively.  
Figure 7: Determine reliability using 90 channels for both OFSMA and C-OFSMA scheme.
### Applications of Chaos by Virtue of the Noise-Like Properties  
Communications can benefit from the noise-like properties of chaotic systems. Some recent manuscripts have addressed this topic. For example, in [8], a key issue in radio wave communication systems has been discussed, i.e., how to exploit chaos with minimum modifications of conventional systems. In particular, the author of reference [8] have proposed the adoption of chaotic shape-forming filters as substitutes for conventional shape-forming filters. By using a suboptimal threshold, Bit Error Rate (BER) in both multi-path channel and system performance has been improved. Additionally, the removal of the complex algorithm for channel equalization has led to simply the software of the overall architecture [8]. The authors of reference [8] also suggest to readily use chaotic shape-forming filters in 5G or 6G communication systems, given that the shape-forming of baseband signals is of paramount importance in radio wave systems.  
In [9], suitable chaotic signals and matched filters are proposed for digital communications in wireless channels characterized by severe physical constraints. In particular, the behaviour of underwater acoustic channels is studied. The novelty in the communication system illustrated in [9] is twofold. On the one hand, hybrid systems are used as chaotic signal generators, including matched filters for maximizing the signal to noise ratio at the receiver side. On the other hand, matched filters are designed in order to reduce the noise effect when the information is decoded. The approach in [9] yields good communication capabilities, mostly if we consider the challenges posed by underwater acoustic channels. Moreover, the method is characterized by many advantages related to the properties of chaos, including robustness to narrowband interference. The method in [9] is also environment-friendly, given that noise-like chaotic signals do not disturb the whale's navigation system [10].
## 3 Simulation Results  
This section presents a comprehensive performance evaluation of five peak detection techniques--FFT thresholding, CA-CFAR, MPM (simplified), SVD-based, and the LTSP--under varying signal-to-noise ratio (SNR) and phase noise conditions. The primary objective is to compare the probability of detection (\(P_{d}\)) across algorithms for a simulated single-target FMCW radar beat signal.  
Simulations were conducted using a Monte Carlo approach to capture the statistical behavior of each method, particularly in the presence of additive white Gaussian noise and phase noise impairments. The comparison included both computationally lightweight methods (e.g., FFT, CFAR) and more advanced subspace techniques (SVD and LTSP) to explore their trade-offs in detection reliability, noise robustness, and algorithmic complexity.  
The simulation framework, signal generation process, and evaluation metrics are described in detail in the following subsection.
## 3 Metasurface Antennas in Small Cavities for Telemetry Applications
### Cavity Diameter of 0.15 \(\lambda_{0}\)
#### 3.1.2 Metasurface with Cavity Diameter \(a=20\) mm (0.15 \(\lambda_{0}\))  
The antenna structure is represented in Figure 11. The cavity thickness is \(h_{c}=14\) mm, and the optimized dimensions are given in Table 2. The external diameter of the cavity is 28 mm. Five layers of RO3010 are glued together, and four layers of metasurfaces are printed on the four upper ones. The rest of the volume is filled with Polypropylene (PP, \(\epsilon_{x}=2.26\) and \(\delta=0.002\)[15]), instead of air, to enhance its mechanical resistance.  
Figure 11: Side view of the cavity, showing a multilayer design of diameter 20 mm.  
Figure 10: Measured radiation patterns at \(f=2310\) MHz in the E- and H-planes of the metasurface antenna in a cavity of diameter 0.25 \(\lambda_{0}\).  
The manufactured antenna is well matched and resonates close to 2.3 GHz (Figure 12), as predicted by the simulation. The measured BW is 21 MHz, which is in good agreement with simulation results, but the measured gain is lower than the simulated one (\(-1\) dBi in experiment versus 0.8 dBi in simulation), indicating slightly higher loss due to the glue. The radiation characteristics are given in Table 2, and measured radiation patterns are represented in Figure 13. The beam is wider than for a diameter of 32 mm, especially in the E-plane (HPBW of 158\({}^{\circ}\)). The measured antenna efficiency is 37.7%. This drop is explained by the small size of the antenna (0.15 \(\lambda_{0}\)) in comparison to the previous antenna (0.25 \(\lambda_{0}\)). Indeed, the radiation efficiency of the small antenna is related to its volume (the sphere in which the antenna fits), and it decreases with the reduction of this volume [16; 1
## 2 Related Work
### AI-Assisted Behavior Recognition in Autism  
Action recognition is a significant branch in computer vision and pattern recognition, involving techniques that analyze video or image sequences to identify and classify human behaviors. Advances in AI technologies, particularly deep learning and MLLM, have enhanced action recognition algorithms' accuracy, leading to broader applications. Researchers have begun exploring the application of action recognition technologies for children with autism, creating specialized datasets and optimizing algorithms to enable more intelligent, automated screening and diagnosis of ASD.  
[PERSON] et al. [11] first collected a naturalistic dataset of self-stimulatory behaviors (SSBDs) in children with autism, including 75 videos with three types of behaviors: arm flapping, head banging, and spinning. They tested the dataset with baseline models using Bag of Words (BoW), STIP, and Harris3D feature extraction algorithms, though the approach struggled to differentiate the inherent periodic movements across behaviors, yielding low accuracy. [PERSON] et al. [29] enhanced the SSBD dataset and proposed a region-based behavior recognition framework, finding that a combination of I3D and MS-TCN yielded higher recognition performance. [PERSON] et al. [30] collected an expanded stereotypical behavior dataset (ESBD) comprising 141 videos across four types: spinning, arm flapping, hand action, and head banging. They introduced three recognition approaches, including local descriptor models, skeleton-based methods, and deep learning methods, with the local descriptor model based on optical flow histograms achieving the highest accuracy of 79%. However, these studies primarily focus on repetitive physical movements in children with autism, overlooking RRBs in object interaction and social interaction.  
To provide a more comprehensive evaluation of RRBs in children with autism, [PERSON] et al. [9] included object-tasting as a category of stereotypical behavior in their study. Through video recordings during diagnosis, they constructed a dataset called Activis, which comprises five behavior types, including clapping, arm flapping, object-tasting, jumping, and others. They proposed a two-stream fusion model based on 3D CNN, integrating RGB and optical flow features at a late-fusion stage, achieving an impressive accuracy of 85.6%, demonstrating the potential of action recognition systems in clinical ASD diagnostics. [PERSON] et al. [15] considered behaviors related to social difficulties in children with autism and incorporated auditory information as a data modality. They collected an audiovisual behavior dataset, AV-ASD, with 10 categories and 928 video clips, comparing baseline results from foundational models and MLLM. Although their fine-tuning significantly improved the recognition accuracy of MLLM, the advantage over foundational models was minimal, with overall accuracy still relatively low. Consequently, our study will delve into efficient applications of MLLM visual capabilities for RRB recognition.
# A Simple Model of Ballistic Conduction in Multi-Lead Molecular Devices
## 3 Multi-Lead Devices
### The Wide-Band Limit  
The wide-band limit (WBL) is a commonly used approximation for calculation of electron transport [41]. It is assumed that the wave-vector of the ballistic electron can be taken to be \(q=\pi/2\), and all other quantities in the expression for the transmission tend to their values for \(E=0\). In the SSP model of the symmetric two-lead device, the wide-band limiting transmission, \(T^{\mathrm{WBL}}\), for non-ipso devices reduces to a formula in terms of the tail coefficients of the characteristic polynomials of the four subgraphs induced by deletion of 0, 1, and 2 distinct connection vertices of the molecular graph \(G\)[55]. This expression has been used to develop selection rules for Fermi-level conduction of two-lead devices [60; 61].  
A similar approach can be used for many-lead devices. As an example, the WBL version of the sink transmission formula for lead 2 in the symmetric three-lead device is  
\[T^{\mathrm{WBL}}_{\mathrm{M}\to 2}=\frac{4\,\beta_{\mathrm{L}}^{2}\left( \beta_{\mathrm{L}}^{2}\,k_{12}^{2}+k_{13,23}^{2}\right)}{\beta_{\mathrm{L}}^{ 6}\,s^{2}+\beta_{\mathrm{L}}^{4}\left[(k^{(1)})^{2}-2\,s\,k^{(2)}\right]+ \beta_{\mathrm{L}}^{2}\left[(k^{(2)})^{2}-2\,k^{(1)}\,k^{(3)}\right]+(k^{(3)}) ^{2}} \tag{58}\]  
This can be expressed entirely in terms of the characteristic polynomials of the seven subgraphs induced by deletion of 0, 1, 2, and 3 distinct connection vertices as follows:  
\[T^{\mathrm{WBL}}_{\mathrm{M}\to 2}=\frac{4\,\tilde{\beta}_{\mathrm{L}}^{2} \left[(t_{1}\,t_{2}-s\,v_{12})+(v_{13}v_{23}-w_{123}\,t_{3})\,\tilde{\beta}_{ \mathrm{L}}^{2}\right]}{(s-V\,\tilde{\beta}_{\mathrm{L}}^{2})^{2}+(T-W\,\tilde {\beta}_{\mathrm{L}}^{2})^{2}\,\tilde{\beta}_{\mathrm{L}}^{2}} \tag{59}\]  
where \(\tilde{\beta}_{\mathrm{L}}=\beta_{\mathrm{LM}}^{2}/\beta_{\mathrm{L}}\), and we understand the lower-case symbols \(s,\,t_{i},\,v_{ij},\,w_{ijk}\) as the Fermi limits of the characteristic polynomials of the graphs \(G,G-i,G-i-j,G-i-j-k\), and the upper-case symbols \(T,V,W\) as their traces. This expression reduces to the corresponding two-lead equation (Equation (21) in [55]) when all SPs involving lead 3 are set to zero.  
It is straightforward to extend Equation (59) to arbitrary numbers of leads. As the seven polynomials in the three-lead case are linked by an identity for the principal minors of the \(2\times 2\times 2\) hyperdeterminant (see, e.g., Equation (2) in [78]), \(T^{\mathrm{WBL}}\) can be calculated from all seven or just six of them. In either case, the WBL approximation can be applied to this instance of a many-lead device to give the transmission from a knowledge of the graph itself and its connections. Only the tail coefficients of the characteristic polynomials are required; this will have particular significance for future development of multi-case selection rules based on the numbers of zero roots of the various polynomials.
###### Abstract  
Terahertz (THz)-band communications are a possible candidate for fast communication. Transmission power needs to be optimised in order to satisfy the requirements of such a network of nodes. Multi-hop communication can be used in THz communications to add relays when obstacles or other interference is evident. This paper investigates the domain of multi-hop THz communications, acknowledging the possibility of interference from other devices affecting the communication process and utilises interference cancellation. It formulates the Transmission Power Control (TPC) problem within a game-theoretic framework, specifically as a potential game, with the assurance of convergence to a Nash equilibrium in the majority of scenarios. Bounds of the Price of Anarchy (PoA) and the Price of Stability (PoS) are provided, given assumed factors. Also, asymptotic Lyapunov stability is shown. The findings from simulations conducted to assess the effectiveness of this approach are then discussed. In particular, the final utilities when utilising interference cancellation show an improvement compared to without-interference cancellation between 19.30 and 67.30% for five simulated players.  
Keywords:transmission power; SIC; terahertz; potential game; wireless +
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