esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Principle  
Due to the limitations of material property and fabrication technology, the vertical natural frequency of an optical platform supported by pneumatic springs, which is shown in Figure 1, is usually higher than 2 Hz. To generate low and ultra-low frequency isolation characteristics, EANSG was used to counteract the partial positive stiffness of each pneumatic spring. It mainly involves feedback sensors, a controller, an amplifier, and an actuator. A nano-resolution laser interferometry sensor was developed to monitor the micro-vibration of the optical platform relative to the ground, i.e., x\({}_{1}\)(t)-x\({}_{2}\)(t), and serve as a feedback sensor. The controller and the amplifier were used to output a driving current into the electromagnetic actuator according to the feedback signal of the laser interferometry sensor and the control strategy. The electromagnetic actuator with high linearity was used to counteract the positive stiffness of the pneumatic spring by actively producing negative stiffness within a micro-vibration stroke. The pneumatic spring together with the paralleled EANSG form a low frequency performance enhanced isolator (LFPEI).  
The displacement response of an optical platform to environmental random excitations is generally as small as \(\pm 10\)\(\upmu\)m, and the force-displacement characteristics of a pneumatic spring within this range can be considered as linear. The principle of EANSG was illustrated in Figure 2. Solid lines \(OB\), \(CLMD\), and dotted-line \(CEFG\) are force-displacement curves of the pneumatic spring, EANSG, and LFPEI. Slopes of the above three curves \(K_{\text{p}}\), \(K_{\text{n}}\), and \(K\) represent their stiffness, respectively. \(x_{0}\) is the static equilibrium position of the pneumatic spring and \(LM\) is the effective stroke of the electromagnetic actuator. At point \(x_{0}\), the force exerted by the EANSG is zero, i.e., the optical platform and payload are supported by the pneumatic spring. In the range of \(LM\), the optical platform and payload are supported by the pneumatic spring and EANSG, and the stiffness of LFPEI equals to the sum of \(K_{\text{p}}\) and \(K_{\text{n}}\). Beyond that range of \(LM\), the force exerted by EANSG is constant, and \(K\) is equal to \(K_{\text{p}}\). Adjusting \(K_{\text{n}}\) can make \(K\) close to but a little greater than zero in the range of \(LM\), i.e., the adoption of EANSG makes the pneumatic spring have lower local dynamic stiffness to isolate low and ultra-low frequency micro-vibrations without sacrificing its payload capability. Therefore, it can be concluded that the proposed method can produce high-static-low-dynamic stiffness and resolve the conflict between the high payload and low stiffness of an optical platform.  
Figure 1: Scheme of electromagnetic active-negative stiffness generator (EANSG).  
Figure 2: Force–displacement curves indicating the principle of EANSG.
# The Use of Augmented Reality for the Management of Equipment Ageing with a Virtual Sensor
## 2 Architecture of the Virtual Sensor  
A virtual sensor for ageing management is a tool supporting inspectors in major accident hazard establishments. Inspectors usually need to understand the actual deterioration level of critical equipment, acquire information that cannot be found with a visual inspection, and finally, elaborate the metrics related to the ageing status and about the adequacy of the ageing management.  
The system has been designed to collect various information, process the acquired data, produce prognostic estimates regarding the corrosion rate, the critical pit probability, the evolution of the corrosion surface, and the RUL of the equipment, and finally, it allows visualising the results by using AR. Therefore, the sensor is composed of four elements: the dataset, which is fed through the collection of information about the equipment to be analysed; the set of the models; the software for the management of the data and the elaboration of ageing-related metrics; the tool for the visualisation of the results in AR.  
The models used by the virtual sensor are:  
* the ageing fishbone model for the estimation of the overall adequacy index (also simply named ageing index) [43];the failure frequency model for the quantification of the failure frequency due to the equipment deterioration by taking into account the ageing management;
* the model for the identification of the probability of the critical pit, based on the extreme values theory (Gumbel distribution model) [44];
* the model for the calculation of the residual useful lifetime based on a combination of the Gumbel distribution and the Bayes theorem [45];
* an advanced spatial interpolation technique of the thickness data to produce corrosion maps (the kriging interpolation model) [46]. More details about these models are given by [PERSON] et al. [42]. The virtual sensor is made up of an \"App Desktop\" that acquires and processes inputs (the equipment information) and an \"App Mobile\" for the AR visualisation of the acquired and processed data.
# Application of Graph Theory for Blockchain Technologies
## 5 Graph Theory Application in Blockchain Systems
### Simulating Blockchain Networks
#### 5.4.4 Forecasting Trends  
Evolving synthetic graphs by adding projected nodes and edges predicts emerging usage patterns and helps plan node additions and infrastructure upgrades [90]. Figure 22 represents an evolved synthetic blockchain network, developed for forecasting future trends in network growth and usage patterns. This network has been expanded based on projected increases in nodes and edges, simulating expected expansion and enabling predictions for emerging usage patterns and infrastructure requirements. The network starts with a historical state and evolves by adding a projected number of new nodes and edges, reflecting the anticipated growth. The orange nodes represent both historical and newly added nodes in the synthetic graph, showcasing the network's expansion. Edges indicate transaction links, increased according to growth predictions.  
**Assumption 21**.:
* _The historical blockchain network is modeled as transaction graph_ \(G(V,E)\)_._
* _Future growth and usage patterns need estimation._  
**Application Statement 21**.:
* _Extrapolating synthetic blockchain network graphs based on adding projected nodes and edges to model expected expansion enables predicting emerging usage patterns and required infrastructure upgrades._  
Proof.:
1. Analyze historical transaction graph \(G(V,E)\) to develop blockchain adoption forecast models.
2. Initialize synthetic graph \(G^{\prime}\) matching the latest state of \(G\).  
Figure 22: Forecasting trends.  
3. Evolve \(G^{\prime}\) by adding nodes/edges based on growth predictions. 4. Analyze properties of the simulated expanded graph \(G^{\prime}\) across multiple periods. 5. This forecasts transaction volumes and infrastructure demands to plan upgrades.  
Generating synthetic blockchain graphs helps estimate future adoption trends for capacity planning.  
All the above theorems and proofs using the graph theory model can enable modeling attack scenarios, simulations, forecasting and vetting decisions before modifying production systems. Graph theory can be used as a tool for blockchain simulation models and facilitate safer innovation.
# XAI-Based Framework for Protocol Anomaly Classification and Identification to 6G NTNs with Drones
## 5 Self-Evolving Classification Method
### Rule Detection with an Explainable Process  
In this section, the rule detection process is made transparent, allowing the focused features and their weights to be adaptively adjusted to classify the uncovered protocol attacks in 6G NTNs.  
The DL model for rule detection trains feature weights, assigning larger weights to fingerprint features of the covered attacks, a process referred to as the attention mechanism; features with larger weights receive more attention. To classify the uncovered protocol attacks, their fingerprints must also receive more attention. Thus, an explanation of the attention mechanism is required to support the adjustment of the weights. To make the attention mechanism understandable and thus adjustable, i.e., input the feature weights of the uncovered features, the self-attention model is introduced, which is applied before the deep learning models in rule detection.  
This method is designed to consist of an XAI mechanism in the detection process, which involves adjusting the rule detection feature patterns, and a rule detection model, which involves matching the detected protocol features with the feature patterns of the covered attacks, as illustrated in Figure 7. During training, a wide range of fingerprint features of covered attacks can be obtained from extensive open-source datasets and used to predefine the rule detection patterns. In the rule detection model, a one-dimensional CNN and a bidirectional LSTM (BiLSTM) network are integrated; this approach enables efficient matching of the protocol features with the covered attack patterns.  
```
1:Input: Normal, covered attack, undetected protocol data.
2: Extract protocol features [21].
3: Train the AE-based baseline detection model described in Section 5.1 with normal features.
4: Train the CNN and BiLSTM rule detection models described in Section 5.2 with the features of covered attacks.
5: Input the undetected protocol features of 6G NTNs.
6:if matches the covered rules then
7: Output: CNN and BiLSTM models output the matched protocol attack.
8: Break.
9:if matches the baseline then
10: Output: AE model outputs normal traffic.
11: Break.
12:else
13: Self-attention model described in Section 5.2 self-evolves based on Equation (5).
14: Rule detection method described in Section 5.2 classifies uncovered protocol attacks of 6G NTNs.
15:endif
16:endif
17:Output: Classification results.
```  
**Algorithm 1** Self-evolving classification algorithm.
## 3 Results
### Tomato Organic Fraction
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Compound** & **Assignment\({}^{\text{a}}\)** & \({}^{\text{1}}\)**H (ppm)** & **Multiplicity: J [Hz]** & \({}^{\text{13}}\)**C (ppm)** \\ \hline Di-unsaturated fatty & & & & 174.4 \\ acids (DUFA) & COO & & & \\ Linoleic fatty chain & & & & \\ (C18:2 A\({}^{\beta,12}\)) & CH\({}_{2}\)-2 & 2.30 & & 34.6 \\  & CH\({}_{2}\)-3 & 1.58 & m & 25.3 \\  & CH\({}_{2}\)-4,7 & 1.32-1.28 & m & 29.5 \\  & CH\({}_{2}\)-8 & 2.02 & m & 27.6 \\  & CH-9 & 5.33 & m & 130.4 \\  & CH-10 & 5.30 & m & 128.6 \\  & CH\({}_{2}\)-11 & 2.73 & t [6.8] & 26.0 \\  & CH-12 & 5.30 & m & 128.6 \\  & CH-13 & 5.33 & m & 130.4 \\  & CH\({}_{2}\)-14 & 2.02 & m & 27.6 \\  & CH\({}_{2}\)-15 & 1.27 & m & 29.4 \\  & CH\({}_{2}\)-16 & 1.27 & m & 31.6 \\  & CH\({}_{2}\)-17 & 1.23 & m & 22.9 \\  & CH\({}_{3}\)-18 & 0.85 & t & 14.3 \\ Tri-unsaturated fatty & & & & 174.4 \\ acids (TUFA) & COO & & & 174.4 \\ Linoleic fatty chain & & & & \\ (C18:3 A\({}^{\beta,12,15}\)) & CH\({}_{2}\)-2 & 2.30 & & 34.6 \\  & CH\({}_{2}\)-3 & 1.58 & m & 25.3 \\  & CH\({}_{2}\)-4,7 & 1.30 & m & 29.5 \\  & CH\({}_{2}\)-8 & 2.03 & m & 27.6 \\  & CH-9 & 5.33 & m & 130.4 \\  & CH-10 & 5.30 & m & 128.6 \\  & CH\({}_{2}\) 11 & 2.77 & t [6.2] & 26.0 \\  & CH-CH\({}_{2}\)-13 & 5.30 & m & 128.6 \\  & CH\({}_{2}\)-14 & 2.77 & t [6.2] & 26.0 \\  & CH-15 & 5.27 & m & 127.4 \\  & CH-16 & 5.35 & m & 132.2 \\  & CH\({}_{2}\)-17 & 2.04 & m & 20.9 \\  & CH\({}_{3}\)-18 & 0.94 & t [7.6] & 14.4 \\ Diacylglycerolglycerol & CH\({}_{2}\)-sn 1 & 4.34.16 & & 62.6 \\ moiety & CH\({}_{2}\)-sn 2 & 5.20 & m & 70.2 \\  & CH\({}_{2}\)-sn 3 & 4.07 & & 64.7 \\  & COO & & & 174.4 \\  & CH\({}_{2}\)-2 & 2.28 & & 34.6 \\  & CH\({}_{2}\)-3 & 1.58 & m & 25.3 \\  & CH\({}_{2}\) & 1.28-1.22 & m & 29.6-32.0 \\  & CH\({}_{2}\)-n-1 & 1.26 & & 22.9 \\  & CH\({}_{3}\) n & 0.84 & t & 14.2 \\ \(\beta\)-Sitosterol & CH\({}_{3}\)-18 & 0.66 & s & 12.2 \\ Stigmasterol & CH\({}_{3}\)-18 & 0.68 & s & 12.2 \\  & CH=CH\({}_{2}\)-22,3 & 5.12.49 & & \\  & CH(OH)-3 & 3.50 & & 71.7 \\ Squalene & CH\({}_{3}\)-a & 1.56 & & 16.2 \\  & CH\({}_{3}\)-b & 1.64 & & 25.8 \\  & CH-c & 5.07 & m & 124.7 \\  & CH\({}_{2}\)-d & 2.03 & & 27.4 \\  & CH\({}_{2}\)-e & 1.94 & & 40.1 \\ Phosphatidylcholine & N(CH\({}_{3}\))\({}_{3}\) & 3.21 & s & 54.5 \\ \hline \hline \end{tabular} \({}^{\text{a}}\) For structure fragment numbering see [33].  
\end{table} 
Table 3: Cont. and Bamano (15.9 and 16.5%, respectively) were characterized by the lowest contents. Di-unsaturated fatty acids (DUFA) level (linoleic acid) was comparable in the five cultivars ranging from 24.7% in King Creole to 30.7% in DulceMiel, whereas tri-unsaturated fatty acid content (TUFA, linolenic acid) was found to be nearly doubled in King Creole (15.96%) compared to Bamano (8.9%) which was characterized by the lowest content.
## 2 Security Requirement and S-Box Design Methods
### S-Box Properties
#### 2.1.1 Nonlinearity (NL)  
Let \(c=(c_{1},c_{2},\ldots,c_{n})\) be a nonzero element in \(\mathbb{F}_{2^{n}}\) and \(c\cdot F=c_{1}f_{1}+c_{2}f_{2}+\ldots+c_{n}f_{n}\) be a linear combination of the coordinate Boolean functions \((f_{1},f_{2},\ldots,f_{n})\) of \(F\). The NL of an S-box, \(F\), is the Hamming distance between the set of all affine functions over \(\mathbb{F}_{2^{n}}\) and the set of all non-constant linear combinations of component functions of \(F\), as defined below:  
\[\mathrm{NL}(F)=\min_{c\in\mathbb{F}_{2^{n}},c\
eq 0}\mathrm{NL}(c\cdot F)\]  
[PERSON] [14] suggested that the value of NL should be as close as possible to the best-known NL (i.e., \(\mathrm{NL}\approx 112\)) to thwart linear cryptanalysis [3]. In our study, we set the minimum threshold for NL as 100 (i.e., \(\mathrm{NL}>100\)).
## 3 Results and Discussion
### Microstructural Observations and Fracture Analysis  
Figure 3a-c present OM micrographs of the as-cast NiAl alloys with different levels of Cu addition. It is seen that the matrix contains a random distribution of annealing twins and precipitates in every case. Moreover, the number of precipitates increases with an increasing Cu content. (Figure 4a-c present the X-ray diffraction (XRD) analysis results for the NiAl alloys with different levels of Cu addition. Moreover, it is seen that for each specimen, the peak value of the \(\beta\)-phase (Ni,Cu)Al is greater than that of the \(\gamma\)'-phase (Ni,Cu)\({}_{3}\)Al. In general, the results presented in Figures 3 and 4 suggest that the enhanced flow stress and strain rate sensitivity of the NiAlCu alloy observed at higher strain rates and levels of Cu addition are a result of the increased precipitation of \(\beta\)-phase (Ni,Cu)Al and \(\gamma\)'-phase (Ni,Cu)\({}_{3}\)Al.  
Figure 5a-c present SEM micrographs of the fracture surfaces of the NiAl alloy containing 5% Cu following impact testing at strain rates of 3 \(\times\) 10\({}^{3}\) s\({}^{-1}\), 4 \(\times\) 10\({}^{3}\) s\({}^{-1}\) and 5 \(\times\) 10\({}^{3}\) s\({}^{-1}\), respectively. The images show that the specimens fracture in a brittle failure mode. Furthermore, the number of cleavage surfaces increases with an increasing strain rate. However, for the specimen with a higher Cu content of 6%, the number of cleavage surfaces is reduced and melted knobby structures are observed (Figure 5d,e). The presence of the knobby features suggests that the local temperature exceeded the melting point of NiAl alloy during deformation. Furthermore, only the specimens tested under strain rates of 4 \(\times\) 10\({}^{3}\) s\({}^{-1}\) and 5 \(\times\) 10\({}^{3}\) s\({}^{-1}\) failed, which suggests that a higher Cu content increases the ductility of NiAl alloy. For the highest considered Cu content of 7 at%, the fracture surface contains a greater number of knobby features (Figure 5f). Moreover, only the specimen tested at the maximum strain rate of 5 \(\times\) 10\({}^{3}\) s\({}^{-1}\) failed. Consequently, the effect of Cu addition in improving the ductility of NiAl alloy is further confirmed.  
Figure 2: Variation of strain rate sensitivity with true strain as function of strain rate for different NiAl intermetallic alloys: (**a**) Ni\({}_{63}\)Al\({}_{32}\)Cu\({}_{5}\); (**b**) Ni\({}_{63}\)Al\({}_{32}\)Cu\({}_{6}\) and (**c**) Ni\({}_{63}\)Al\({}_{32}\)Cu\({}_{7}\).  
Figure 4: X-ray diffraction (XRD) analysis results for as-cast NiAl intermetallic alloys: (**a**) Ni\({}_{63}\)Al\({}_{32}\)Cu\({}_{5}\); (**b**) Ni\({}_{63}\)Al\({}_{32}\)Cu\({}_{6}\); and (**c**) Ni\({}_{63}\)Al\({}_{32}\)Cu\({}_{7}\).  
Figure 3: Optical micrographs of as-cast NiAl intermetallic alloys: (**a**) Ni\({}_{63}\)Al\({}_{32}\)Cu\({}_{5}\); (**b**) Ni\({}_{63}\)Al\({}_{32}\)Cu\({}_{6}\); and (**c**) Ni\({}_{63}\)Al\({}_{32}\)Cu\({}_{7}\).
## 3 Problem Definitions and Formulation
### The Definitions of BAP, QCAP, and QCSP
The set \(C_{2}\) includes constraints such as sequential assignments of QCs to berths and the constraint ensuring that the total number of QCs assigned to ships at the same time period is equal to or less than the total number of QCs available. **Definition 3**. : _The problem \(P3\) is defined as the quay crane scheduling problem (QCSP) that includes 8-tuple:_  
\[P3=(S,B,C_{3},Q,\varphi,f_{3},T1_{i\eta k},\ T2_{i\eta k})\ \forall\ i\in S,\ q\in Q,\ k\in K_{i}\]  
_where_ \begin{tabular}{l l} \(i\) & a ship number (\(i\in S\)) \\ \(k\) & a task number (\(k\in K_{i}\)) \\ \(q\) & a quay crane number (\(q\in Q\)) \\ \(m\) & the number of ships \\ \(l\) & the total number of quay cranes \\ \(l_{i}\) & the total number of quay cranes assigned to the ship \(i\) (\(1\leq i\leq m\)) \\ \(K_{i}\) & the total number of tasks of ship \(i\) \\ \(S\) & a set of ships; \(S=\{1,\ldots,m\}\) \\ \(B\) & a set of berths; \(B=\{1,\ldots,n\}\) \\ \(C_{3}\) & a set of constraints \\ \(Q\) & a set of quay cranes \(Q=\{1,\ldots,l\}\) \\ \(T1_{i\eta k}\) & a decision variable; the beginning time of QC \(q\) to process the task \(k\) of ship \(i\) \\ \(T2_{i\eta k}\) & a decision variable; the end time of the QC \(q\) to process the task \(k\) of ship \(i\) \\ \(T\) & the planning horizon in units of hours \(T=\{1,\ldots,H\}\); \(H=168\) h (10,080 min) for 1 week. \\ \(\varphi\) & a collection of sets of QC schedules for all ships; \\ \(\forall\ \varphi_{g}\in\varphi,\ \exists\ \varphi_{g}=\{U^{t}_{i=1}\Big{(}T1_{i\eta k},T2_{i \eta k}\Big{)}:X^{t}_{ij}=1,Y_{i\eta k}=1,q\in Q,k\in K_{i},\ t\in T\}\) \\ \(f_{3}\) & a function that maps \(\varphi_{g}\) to a time/cost value \\ \end{tabular}   
The objective of \(P3\) is to find a \(\varphi_{g}\) or \(\varphi^{*}\) (\(\varphi_{g},\varphi^{*}\in\rho\)), where \(\varphi_{g}\) is a feasible solution and \(\varphi^{*}\) is an optimal solution. Both \(\varphi_{g}\) and \(\varphi^{*}\) are subject to \(C_{3}\). In \(\varphi_{g}\) and \(\varphi^{*}\) a time interval \(\Big{(}T1_{i\eta k},T2_{i\eta k}\Big{)}\)indicates that a quay crane \(q\) is assigned to work for the task \(k\) of ship \(i\). The set \(C_{3}\) includes constraints stipulating the reasonable ranges of value for \(T1_{i\text{\emph{i}}k}\) and \(T2_{i\text{\emph{i}}k}\) and their relationships. **Definition 4**. : _The integrated problem \(P\) consisting of \(P1\), \(P2\), and \(P3\) is represented as 8-tuple._  
\[P(P1,P2,P3)=\{S,B,C,Q,f,\{X_{ij}^{t}\},\{Y_{i\text{\emph{i}}k}^{t}\},\{\left(T 1_{i\text{\emph{i}}k},T2_{i\text{\emph{i}}k}\right)\}\}\ \forall\ i\in S,\ j\in B,\ k\in K_{i},\ q\in Q,\ t\in T\]  
_where \(f\) is a function that maps \(\varphi_{g}\) to a makespan._  
The objective of the integrated problem \(P\) is to find a solution with the minimum makespan, subjecting to the constraints defined in \(C_{3}\cup C_{3}\cup C_{3}\).
## 3 Genetic and Molecular Regulation Mechanisms of Vegetable Fruit Shape
### Carpel Number (CN)  
The CN is one of the most important fruit traits among vegetables, it can affect the fruit shape and size. In nature, fruits generally have two or more carpels. These differences are related to domestication and mutation. In addition, further research shows that common regulatory factors can play a role in the CN of fruits. In _Arabidopsis_, _CLAVATA_ (_CLV_) and _WUSCHEL_ (_WUIS_) can generate negative feedback in regulating the size of the meristem and the number of floral organs [40; 41]. Mutations in the _CLV_ family genes lead to an increased number of undifferentiated cells in the central region, causing the expansion of the meristem [42]. Large floral meristems result in increased CN and fruit width [43; 44; 45]. Moreover, the function of the CLV-WUS pathway is conserved in higher plants [46] and regulates the number of fruit carpels in cucurbitaceous, solanaceous, and cruciferous plants [47; 48; 49; 50]. In cucumbers, two transcription factors (TFs), namely, _FRUITFULL-like MADS-box gene_ (_CsFULIA_), and _CsARF14_, can regulate the CsWUS-CsCLV3 pathway and work together to participate in the regulation mechanism of the cucumber CN [47]. In tomato, the loss-of-function mutation _SICLV3_ leads to a large fruit with an increased number of locules [48; 49], and the up-regulation _WOX1_ TF family members of _SINUIS_ can increase the CN and affect fruit shape [51; 52]. In tomato, _LC_ is encoded by _WUIS_, whereas _FAS_ is encoded by _CLV3_; _lc_ and _fis_ can lead to a high locule number [53]. In addition, the transcriptional regulation of small and long non-coding RNAs can regulate fruit shape. MicroRNA 156 (MIR156) overexpression alters the locule number of the tomato fruit [54]. In rapeseed, the interruption of _CLV1_ results in a trilocular phenotype [50] (Table 1). In addition, the _YABBY_ family is also a plant-specific TF, and several of its members can increase the number of locules and flat fruit shape in tomatoes [38; 55].
# Wireless and Fiber-Based Post-Quantum-Cryptography-Secured IPsec Tunnel
## 7 Discussion  
Kyber [16], being the only remaining KEM in the NIST competition chosen for standardization, is integral to every version of the encryption stack presented in this work. The choice of security level for Kyber (NIST levels I, III, or V) can vary based on numerous factors, including security requirements and the processing power of the devices involved. This decision is typically made by the application or, ultimately, by the software developer.  
Dilithium [15], developed by the same group ([[https://pq-crystals.org/](https://pq-crystals.org/)]([https://pq-crystals.org/](https://pq-crystals.org/)) accessed 19 March 2024) that submitted Kyber, offers excellent performance in terms of execution speed  
Figure 17: AES-256 GCM encrypted IPsec throughput between DPU and DPU depending on the set MTU. We achieve 100 Gbit/s from 1024 B MTU on.  
Figure 18: Throughput of the IPsec tunnel with different MTU sizes. The traffic is generated by VIAVI and passed through the IPsec tunnel that we present in this work. For all MTU sizes equal to or bigger than 1024 B, we achieve the maximum supported line rate of 100 Gbit/s. (**a**) 64 B MTU; (**b**) 128 B MTU; (**c**) 256 B MTU; (**d**) 512 B MTU; (**e**) 1024 B MTU; (**f**) 1518 B MTU.  
when combined with Kyber [16]. However, Dilithium's signatures are larger compared to Falcon's, resulting in larger certificates and more data that need to be transmitted over networks. This might not be an issue in high-performance environments, such as data centers, where network bandwidth is abundant, making signature sizes irrelevant. However, in mobile applications with limited and potentially unstable network connections, the larger signature size could negatively impact performance.  
Falcon's performance is inferior to Dilithium's in terms of computation. Falcon requires more CPU clock cycles per execution, and especially its key generation process is significantly more demanding. Despite this, in scenarios where keys are generated infrequently, the impact of this disadvantage is minimal. However, in high-performance environments with numerous sessions, each requiring its own key, this becomes a significant drawback of Falcon. The advantage Falcon offers is its smaller signature size, which may be more suitable for mobile, low-power, and low-performance environments.