esa-sceva/satcom-chunk-collection huggingface dataset:
## 6 Validation. Testing the Simplification
### How to Check the Causal Dependency?  
To assure this feature the footprint matrix and fitness concepts from process mining techniques were applied. The footprint matrix represents the causal dependency between the activities in a log or in a model (more about this concept can be learned in [43; 44]). This concept is used in some process discovery algorithms, like the \(\alpha\)-algorithm [45], helping it to scan the event log for particular patterns. In this case, the footprint matrix will be calculated for a process model, containing the relation between each pair of activities in the workflow. Let \(M\) be a process model and \(a,b\) two activities that belong to the process model \(M\). It is possible to establish the following relationships:  
* \(a>_{M}b\) if only if there is a possible path \(p=\langle t_{1},t_{2},...,t_{n}\rangle\) and \(i\in 1,...,n-1\) such that \(p\in M\) and \(t_{i}=a\) and \(t_{i+1}=b\). This relation is also known as \"direct follows\" relation.
* \(a\rightarrow_{M}b\) if only if \(a>_{M}b\) and \(b_{M}a\)
* \(a\#_{M}b\) if only if \(a_{M}b\) and \(b_{M}a\)
* \(a\|_{M}b\) if only if \(a>_{M}b\) and \(b>_{M}a\)  
The footprint matrix is commonly used in basic conformance checking techniques providing a log-to-model comparison. However, this same approach can be used in log-to-log and model-to-model comparisons [46]. In our case, we will use the model-to-model comparison approach to quantify their similarity. The correct way is to compare the unsimplified model's footprint matrix (end of stage one) with the simplified model's footprint matrix (end of stage two). These two footprints matrix are calculated and compared using the fitness measure for each one of the 8102 inputs. The objective is to check that no wrong behaviour is introduced in the simplified model. The measurement that will be used for the comparison is the fitness. It represents the similarity between two footprints (belonging to two different process models \(M_{1}\) and \(M_{2}\)) using a 0.0 to 1.0 scale. In our case, a value of 1.0 in all comparisons will be the goal. In Equation (1) the fitness measurement for comparing two footprints (\(f_{M1}\) and \(f_{M2}\)) is defined [46].  
\[fitness=1-\frac{\text{different cells between $f_{M1}$ and $f_{M2}$}}{\text{total cells in $f_{M1}$ and $f_{M2}$}} \tag{1}\]  
For clarity, it is possible to visualise this procedure with an example. Take the process model from the end of stage one represented in Figure 8 as model \(M_{1}\). It must be compared with the process model from the end of stage two represented in Figure 10 (\(M_{2}\)). The reader can check the footprint matrix for both models. Table 1 contains the footprint for model \(M_{1}\) and Table 2 for model \(M_{2}\).  
In this example, both matrices contain the same values, and as a result, the fitness value is 1.0.
# Stable Throughput Analysis of Heterogeneous Hybrid FSO/RF Networks with Cognitive Radio Capability
## 3 Stable Throughput of Reference System (REF)
### Simultaneous Multipacket Transmission  
In this system, \(N=2\) for HY and \(N=1\) for RO, and \(v_{j,1,0}=v_{j,1,1}\) is given by  
\[v_{\texttt{HY,1,0}} = s_{f_{0},\texttt{HY}}(1-s_{f_{2},\texttt{HY}})+(1-s_{f_{0}, \texttt{HY}})s_{f_{2},\texttt{HY}}, \tag{12}\] \[v_{\texttt{HY,2,0}} = s_{f_{0},\texttt{HY}}s_{f_{2},\texttt{HY}}. \tag{13}\]  
The state transition diagram is shown in Figure 2. The balance equation for \(Q_{HY}\) is as follows:  
\[...\] \[\pi_{n}(\mu_{\texttt{HY,1}}+\mu_{\texttt{HY,2}})+\pi_{n+1}\mu_{ \texttt{HY,2}} = \pi_{n-1}\lambda_{\texttt{HY}}, \tag{14}\] \[...\]  
Figure 2: The buffer state transition diagram with one- or two-packet service in a single time slot.  
Simple manipulation of this system of equations provides a new representation that will be useful for deriving an explicit expression of the desired distribution. Rearranging Equation (14), we have  
\[\pi_{n} = \pi_{n-1}\frac{\lambda_{\texttt{HY}}-\psi_{n-1}}{\mu_{\texttt{HY,1} }+\mu_{\texttt{HY,2}}}, \tag{15}\]  
where \(\psi_{n}=\frac{\pi_{n+2}\mu_{\texttt{HY,2}}}{\pi_{n}}\). If \(\psi_{0}=\psi_{1}=\psi_{2}...=\psi\), then we have a closed form of \(\psi\) such that  
\[\psi = \frac{2\lambda_{\texttt{HY}}+\frac{(\mu_{\texttt{HY,1}}+\mu_{ \texttt{HY,2}})^{2}}{\mu_{\texttt{HY,2}}}}{2}-\frac{\sqrt{4\lambda_{\texttt{HY }}\frac{(\mu_{\texttt{HY,1}}+\mu_{\texttt{HY,2}})^{2}}{\mu_{\texttt{HY,2}}}+ \frac{(\mu_{\texttt{HY,1}}+\mu_{\texttt{HY,2}})^{4}}{\mu_{\texttt{HY,2}}^{2} }}}{2}. \tag{16}\]  
With \(\psi\) in Equation (16), the probability of \(Q_{\texttt{HY}}=0\) is given by  
\[\Pr(Q_{\texttt{HY}}=0)=\pi_{0}=\frac{\mu_{\texttt{HY,1}}+\mu_{ \texttt{HY,2}}-\lambda_{\texttt{HY}}+\psi}{\mu_{\texttt{HY,1}}+\mu_{\texttt{ HY,2}}}.. \tag{17}\]  
The service rate of \(Q_{\texttt{R}0}\) is the same to (10). Then, the stable region is finally obtained by  
\[R_{REF,\texttt{SMT}}=\{\lambda_{\texttt{HY}},\lambda_{\texttt{R} 0}|\lambda_{\texttt{HY}}<\mu_{\texttt{HY,1}}+\mu_{\texttt{HY,2}}+\psi,\lambda_ {\texttt{R}0}<\mu_{\texttt{R}0}\}. \tag{18}\]
# GSFedSec: Group Signature-Based Secure Aggregation for Privacy Preservation in Federated Learning
## 4 Security Analysis of the Proposed Algorithm
### Robustness against Various Attacks
#### 4.3.5 Honest-but-Curious Setting  
The honest-but-curious setting occurs when a communication party wants to learn sensitive information about other parties from legitimate messages. For example, suppose that the server receives messages from end devices. Devices send messages (including device updates and secret keys) to protect data and prevent the server from revealing the identity of the sending devices. The server must not be able to discover whether a particular user sends updates.  
In this study, the client first adds a secret component in the update, encrypts it, and then signs it from the GS as \((Upd_{se},\sigma_{GS})\). The server cannot determine whether the received \(\sigma_{GS}\) is signed by device \(A\) or \(B\). In addition, the original update cannot be obtained because it is secured using a secret key. Thus, the server will be unable to obtain any sensitive information that is intended to be kept secret.
## 4 Results
### Vegetation Vulnerability for the Near-Term and Distinct Future Period in MRB
#### 4.4.2 Local Moran's I  
The LISA cluster of vegetation vulnerability for the near future period and distinct future period in the MRB is shown in Figure 5. The cluster pattern of vegetation vulnerability was a high-high cluster upstream, low-low cluster downstream, not significant midstream for the near future period, and distinct future period in the MRB. There were no high-low outliers and low-high outliers, which indicated that the cluster of vegetation vulnerability was extremely concentrated for the near future period and distinct future period in the MRB. Specifically, the high vegetation vulnerability was in the high-high cluster upstream, the low vulnerability was in the low-low cluster downstream.  
From low to high emission scenarios, the area of high-high clusters increased, and the area of low-low clusters decreased. This changing trend was more obvious for the distinct future period. Under the SSP1-2.6, from the near future period to the distinct future period, the area of the high-high cluster decreased upstream, and the low-low cluster increased downstream. The situation was similar under the SSP2-4.5, but the changing areas were larger than the SSP1-2.6. Under the SSP5-8.5, from the near future period to the distinct  
Figure 4: Spatial distribution of vegetation vulnerability for the near future period and the distinct future period in the MRB.  
\begin{table}
\begin{tabular}{c l c c c c} \hline \hline
**Period** & **Scenario** & **Global Moran’s I** & _p_**-Value** & _Z_**-Value** & **Variance** \\ \hline \multirow{3}{*}{Near future period} & SSP1-2.6 & 0.5963 & \(p\) \(<\) 0.01 & 12.9971 & 0.0021 \\  & SSP2-4.5 & 0.6077 & \(p\) \(<\) 0.01 & 13.4134 & 0.0021 \\  & SSP5-8.5 & 0.6028 & \(p\) \(<\) 0.01 & 11.2632 & 0.0029 \\ \hline \multirow{3}{*}{Distinct future period} & SSP1-2.6 & 0.5024 & \(p\) \(<\) 0.01 & 11.0596 & 0.0021 \\  & SSP2-4.5 & 0.4108 & \(p\) \(<\) 0.01 & 8.8842 & 0.0021 \\ \cline{1-1}  & SSP5-8.5 & 0.4811 & \(p\) \(<\) 0.01 & 10.7101 & 0.0020 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Global Moran’s \(I\).  
future period, the area of high-high clusters and low-low clusters both increased. This indicated that from the near future period to the distinct future period, the vegetation vulnerability could be reduced under a low-emission scenario.
# A Phase Angle-Modulated Bat Algorithm with Application to Antenna Topology Optimization
## 4 Experimental Results and Discussions
### Compact Dual-Band Planar Monopole Antenna Design
#### 4.2.2 Antenna Topology Optimization Design
It starts from a simple initial geometry and exhibits superior electrical performance with a compact size. This section used a design example of a dual-band planar monopole antenna to confirm the advantages of P-AMBA in global optimization capabilities and the convergence rate. The results showed that the antenna structure designed by this method is novel and can be used for antenna designs in limited surrounding environment or unexplored areas. Figure 8: Schematic diagram of phase angle-modulated technology applied to antenna topology optimization. Figure 9: Comparison of the convergence curves of BPSO, BBA, AMBA, A-AMBA, and P-AMBA.
## 3 Validation of [PERSON]'s Resistance Integration Method (RIM) for Fire Design of Bonded Anchors  
The following validation has been presented partially in a previous publication by [PERSON] et al. [28]. This paper provides an extended database for the validation of the resistance integration method thanks to the tests conducted at TU Kaiserslautern [20]. To investigate the validity of [PERSON]'s RIM, pull-out fire tests were selected from two projects (Table 1). Figures 11-13 show a comparison between fire tests and the outcome of [PERSON]'s method for one example of each of the three adhesives used in this study. The figures show calculated resistances using [PERSON]'s method (resistance integration) at 15, 30, 60, 90, 120, 180 and 240 min of ISO 834-1 fire exposure in addition to the times where pull-out failure in fire tests occurred. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Adhesive**} & **Anchor Geometry** & **Applied Load** & **Pull-Out Failure Time** & **Pull-Out Resistance acc.** & **Pull-Out Resistance acc.** \\  & **(Size \(\times\) Embedment** & **[xN]** & **under Fire Conditions** & **[PERSON]’s RIM Results** & **[PERSON]’s RIM Results** \\  & **[mm]** & **[xN]** & **[cmi]** & **[cmi]** & **[xN]** \\ \hline \multirow{8}{*}{
\begin{tabular}{c} Adhesive-1 \\ (epoxy) \\ \end{tabular} } & & 0.50 & 41 & 0 & 0.45 \\  & & 0.50 & 53 & 0 & 0.20 \\  & M\(\mathrm{I}0\times 50\) & 0.75 & 38 & 0 & 0.51 \\  & & 0.75 & 39 & 0 & 0.49 \\  & & 0.75 & 44 & 0 & 0.38 \\ \cline{2-5}  & M\(\mathrm{I}0\times 60\) & 1.00 & 38 & 0.50 & 0.95 \\ \cline{2-5}  & M\(\mathrm{I}2\times 55\) & 1.00 & 45 & 0 & 0.50 \\  & & 1.00 & 56 & 0 & 0.27 \\ \cline{2-5}  & M\(\mathrm{I}6\times 70\) & 0.75 & 61 & 0 & 0.74 \\ \cline{2-5}  & & 1.00 & 82 & 0 & 0.75 \\  & & 2.50 & 52 & 0.68 & 1.71 \\  & & 2.50 & 67 & 0 & 1.15 \\  & & 2.50 & 82 & 0 & 0.75 \\ \cline{2-5}  & M\(\mathrm{I}24\times 95\) & 2.00 & 75 & 0 & 1.77 \\ \cline{2-5}  & M\(\mathrm{I}00\times 120\) & 9.00 & 83 & 0 & 3.79 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of the data of the study (fire tests and simulation results). Figure 10: Bond stress vs. temperature relationship for Adhesive-3 according to EAD 330087-00-0601 [15]. Table 1 summarizes the data of this study: fire test data (applied load and pull-out failure time under fire conditions), [PERSON]'s RIM results considering the bond stress vs. temperature curve with/without considering temperatures beyond \(T_{max}\).
## 3 Results
### Fat-Free Body Parameters  
The mean values of the parameters in the V group are listed in Table 4. SLM, FFM, SMM, BCM and protein increased, while minerals and BMC decreased under the influence of the vibration procedure. However, it should be emphasized that these changes were minor, and did not exceed 0.3% of the initial value and were not statistically significant for any of the parameters (Tables 4 and 5). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Before Vibrations or before 6 Weeks**} & \multicolumn{4}{c}{**After Vibrationsor after 6 Weeks**} & \multicolumn{2}{c}{**Before–After**} \\ \hline  & **Group** & **Mean** & **SD** & **Min** & **Max** & **Mean** & **SD** & **Min** & **Max** & **Mean** \\ \hline \multirow{2}{*}{FM [kg]} & V & 15.27 & 6.06 & 6.30 & 44.50 & 15.25 & 6.11 & 4.20 & 45.10 & 0.02 \\ \cline{2-10}  & C & 14.68 & 6.89 & 5.60 & 46.00 & 14.73 & 6.88 & 4.40 & 44.40 & \(-\)0.05 \\ \hline \multirow{2}{*}{PBF [\%]} & V & 25.25 & 6.52 & 12.80 & 48.10 & 25.19 & 6.62 & 9.30 & 48.00 & 0.06 \\ \cline{2-10}  & C & 24.23 & 7.20 & 10.70 & 48.40 & 24.25 & 7.18 & 9.30 & 46.40 & \(-\)0.02 \\ \hline \multirow{2}{*}{VFA [cm\({}^{2}\)]} & V & 53.64 & 22.56 & 6.80 & 177.40 & 52.36 & 21.47 & 5.00 & 166.30 & 1.28 \\ \cline{2-10}  & C & 63.62 & 34.96 & 17.00 & 220.50 & 63.67 & 33.98 & 9.70 & 207.80 & \(-\)0.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._ \begin{table}
\begin{tabular}{c c c} \hline \hline  & **ANOVA Effects** & **F** & \(p\) \\ \hline \multirow{4}{*}{Body mass [kg]} & Group (V vs. C) & 0.154 & 0.695 \\ \cline{2-5}  & Intervention (Before vs. After) & 2.055 & 0.153 \\ \cline{2-5}  & Intervention * Group & 1.012 & 0.315 \\ \hline \multirow{4}{*}{BMI [kg/m2]} & Group (V vs. C) & 0.15 & 0.695 \\ \cline{2-5}  & Intervention (Before vs. After) & 2.32 & 0.129 \\ \cline{2-5}  & Intervention * Group & 1.23 & 0.269 \\ \hline \multirow{4}{*}{FM [kg]} & Group (V vs. C) & 0.447 & 0.505 \\ \cline{2-5}  & Intervention (Before vs. After) & 0.021 & 0.885 \\ \cline{2-5}  & Intervention * Group & 0.096 & 0.757 \\ \hline \multirow{4}{*}{PBF [\%]} & Group (V vs. C) & 1.250 & 0.265 \\ \cline{2-5}  & Intervention (Before vs. After) & 0.014 & 0.906 \\ \cline{2-5}  & Intervention * Group & 0.047 & 0.828 \\ \hline \multirow{4}{*}{VFA [cm\({}^{2}\)]} & Group (V vs. C) & 8.849 & 0.003 \\ \cline{2-5}  & Intervention (Before vs. After) & 0.597 & 0.440 \\ \cline{1-1} \cline{2-5}  & Intervention * Group & 0.692 & 0.406 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: ANOVA results with group effect (V vs. C), intervention (Before vs. After) and interactions between them (Intervention * Group) for body mass, BMI, and fat tissue parameters.
## 3 Materials and Methods
### Evaluation Metrics and Feedback Adjustment Strategies  
Feedback from the evaluation metrics is used to adaptively adjust the optimization process and fine-tune the weight coefficients, ensuring that the system remains aligned with the sustainability goals. The feedback adjustment process is divided into two main components: reward-based feedback and constraint-based feedback.  
Note on reward definitions:  
Equation (12) is used _only during offline RL training_ and measures the _incremental gains_\(\Delta ESI_{I}\), \(\Delta EGI_{t}\), and \(\Delta SWI_{I}\). After deployment, the system switches to the absolute index reward in Equation (14), which relies on \(ESI(t)\), \(EGI(t)\), and \(SWI(t)\) and a system-wide trade-off term \(P_{t}\) to guide the real-time weight refinement. This distinction prevents reward-scaling drift between the training and inference.
# Integrated Sensing and Communication Using Random Padded OTFS with Reduced Interferences
## 2 The OTFS Waveform
The inverse DFT is performed on its rows, i.e., along the Doppler direction, and then the TD matrix \(\mathbf{S}\) is obtained. Then, the entries of the matrix \(\mathbf{S}\) are transmitted column by column. Figure 1: Graphical explanation of the relationship between OTFS and OFDM. Denotations: IR/FR-impulse/frequency response, F—Fourier transform, SFT—2D symplectic Fourier transform, STFT—short time Fourier transform, ZT—Zak transform. Like in the case of the OFDM waveform, OFTS needs to have pilots on the DD grid to estimate the CSI. The mutual arrangement of the pilots and the data can vary, but the DD grid is usually divided into two zones: the pilot zone and the data zone. In the lower part of Figure 2, different types of OTFS are compared with respect to different allocation strategies of pilot elements (\(P_{k}\)) and data elements (\(D_{k}\)) in the matrix \(\mathbf{X}\). \(D_{k}\) are used to transmit data bits, while pilots (\(P_{k}\)) are used for OTFS frame synchronization and channel equalization. The pilots do not necessarily occupy all subcarriers in the pilot zone, and some of the subcarriers can be inactive (the so-called guard carriers, which have a form of a strip, box, or cross). The guard interval is denoted by 0s in Figure 2. Also, depending on the configuration, the shape of the pilot zone and positions of the active (non-guard) carriers could be different. Guard carriers are used to reduce the interference between pilots and data carriers, but the drawback of many zero-value guard carriers is the reduction in pilot power. RP-OTFS [22; 23; 24; 25; 26] does not use guard carriers and offers better channel estimation characteristics. In this paper, RP-OTFS is discussed in its original form version [22; 23; 24; 25; 26] and in an improved form in the context of the ISAC system. The RP-OTFS represents a completely different approach in the OTFS design, since in its original proposition, the zero guard zone is missing and the pilots have randomly chosen values. In the remaining part of the paper, we will use the following denotations: \(M\) is the number of rows of the \(\mathbf{X}\) matrix (aka the number of elements in the delay direction of the DD grid), \(N\) is the number of columns of the \(\mathbf{X}\) matrix (aka the number of elements in the Doppler direction of the DD grid). Figure 2: Principle of generation of the OTFS modulated waveform and different OTFS types.
## 4 The Measurement Setup and Scenarios
### The NB-IoT Operational Scenarios and Settings  
Measurement-based investigations were carried out by testing the performance of both NB-IoT uplink channels (i.e., NPUSCH and NPRACH) in standalone deployment. To yield representative results, attention and special care were paid to carry all the experiments out in a systematic manner. For this reason, a set of 15 measurement scenarios was created, each corresponding to a different combination of the [MCS;Nrep] pair for NPUSCH performance, and a set of 4 measurement scenarios was proposed to cover NPRACH performance verification of the detection success ratio in the function of the repetition number. By being able to control the link attenuation between the eNB and NB-IoT UE with the aforementioned <1 dB precision, its magnitude for each scenario was first set to a relatively low value of 145 dB, for which the entire set of uplink messages in both analyzed channels could be received with a 100% success rate. Then, the attenuation (pathloss) was increased in 2 dB steps until connectivity was completely lost, which corresponded to 0% of successful detections of NPUSCH or NPRACH messages at the eNB.  
Such a procedure allowed us to obtain smooth profiles of the passages between 0% and 100% of the successfully received NPUSCH uplink messages (see Figure 3). Each profile represented one of the  
Figure 2: A measurement setup for emulating extreme maximum coupling loss (MCL) conditions.  
aforementioned combinations of two adjustable transmission factors, namely the MCS (its three settings being 0, 5, and 10) and the number of repetitions (with 5 settings of N1, N4, N16, N64, and N128), being the key parameters determining the effective NB-IoT NPUSCH coverage.  
NPRACH measurements focused on determining the boundary coverage profiles obtained for the edge values of repetitions (i.e., N1 and N128).  
A complete list of other crucial operational parameters used in the experiment can be found in Table 1.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline NB-IoT eNB output power, P\({}_{\text{out}}\) & 43 dBm \\ NB-IoT UE transmission power & 23 dBm \\ Type of diversity & Transmit, MISO (\(2\times 1\)) \\ NB-IoT deployment & standalone \\ Center frequency & 1810 MHz \\ Channel width & 180 kHz \\ Investigated NB-IoT channels & NPUSCH, NPRACH \\ NPUSCH settings & Format 1, single-tone, \\ NPUSCH MCS index & \(\left\{0,5,10\right\}\) \\ NPUSCH Repetitions number (N\({}_{\text{rep}}\)) & \(\left\{1,4,16,64,128\right\}\) \\ Resource assignment (\(I_{\text{R}U}\)) & 3 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The key narrowband Internet of Things (NB-IoT) measurement settings.  
Figure 3: The narrowband physical uplink shared channel (NPUSCH) detection success ratio profiles for 15 combinations of {MCS;Nrep} parameters.
# Detection of Electromagnetic Seismic Precursors from Swarm Data by Enhanced Martingale Analytics
## 4 Quantitative Experiment
### Mexico 2017  
The seismic activity of Mexico is deeply rooted in its geographical composition, being located atop several intersecting tectonic plates. The convergence of the Cocos Plate and North American Plate along the Pacific Coast, alongside activity along the edges of the Rivera and Caribbean plates, generates approximately 40 earthquakes daily in the country. The susceptibility of Mexico City to seismic events is exacerbated by its foundation on a dry lake bed characterized by soft soil comprising sand and clay. This geological makeup amplifies the destructive impact of major earthquakes, as loose sediments near the surface slow down shock waves, increasing both their amplitude and duration.  
On 19 September 2017, at approximately 6:15 p.m. local time, the Ayutla region in Mexico, situated southeast of Mexico City, experienced a seismic event of considerable magnitude. The impact of the earthquake was profound, resulting in widespread damage categorized with a severity rating of VII (severe) intensity. The aftermath of the earthquake left a lasting imprint on the region, with buildings damaged, infrastructure disrupted, and communities in disarray. To visually contextualize the epicenter of the Mexico 2017 earthquake, a detailed plot of the 500 \(\times\) 300 km area of interest is provided in Figure 3.  
Figure 3: A tilted plot of our 500 \(\times\) 300 km area of interest with the epicenter of the Mexico 2017 earthquake indicated with a pin.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Case Study**} & **Mexico** & **Mexico** & **Greece** & **Greece** & **Croatia** & **Croatia** \\  & **(500 \(\times\) 300)** & **(1000 \(\times\) 800)** & **(500 \(\times\) 300)** & **(1000 \(\times\) 800)** & **(500 \(\times\) 300)** & **(1000 \(\times\) 800)** \\ \hline Martingale & 3 & 5 & 21 & 21 & 17 & 20 \\ \hline \(Z\)-Martingale & 4 & 5 & 10 & 9 & 6 & 10 \\ \hline \end{tabular}
\end{table}
Table 3: Anomaly detection numbers for Martingale and \(Z\)-Martingale methods.