esa-sceva/satcom-chunk-collection huggingface dataset:
# A Redactable Blockchain Scheme Supporting Quantum-Resistance and Trapdoor Updates
## 2 Preliminaries
### Concepts of Lattices
\begin{table}
\begin{tabular}{c c} \hline \hline
**Symbols** & **Description** \\ \hline \(\leftarrow_{\mathbb{R}}\) & A random variable from a certain distribution \\ \hline \(\lambda\) & Security parameter \\ \(\mathbf{A}\) & The matrix is denoted in bold and capitals \\ \(\mathbf{a}\) & The vector is denoted in bold and lowercase \\ \(\mathbf{A}^{T},\mathbf{a}^{T}\) & The transpose of the matrix or vector \\ \(n,q\) & Positive integer \\ \(\mathbb{Z}_{q}\) & The set of integers \(\{0,\cdots,q-1\}\) of modulus \(q\) \\ \(\beta\) & The upper limit \\ LWE & Learning with errors \\ ISIS & Inhomogeneous small integer solution \\ \(\mathbf{id}_{\mathbf{\ell}}\) & The identity of level \(\ell\) \\ \(\mathbf{id}_{\ell-1},\mathbf{id}_{\mathbf{\ell}}^{\star}\) & The parent of identity at level \(\ell\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Description of symbols. This paper combines the trapdoor generation algorithm \(TrapGen\), Gaussian sampling algorithm \(SampleD\), and trapdoor delegation algorithm \(Deltrap\) in [36], and the \(FRD\) encoding in [37]. **Definition 4**. : \(TrapGen\)_: For \(n\geq 1,q>2\), there is an efficient randomized algorithm that generates matrix \(\mathbf{A}\in\mathbb{Z}_{q}^{n\times\mathbb{H}}\) and \(G\)-trapdoor \(\mathbf{R}\in\mathbb{Z}^{nk\times w}\) from distribution \(\mathcal{D}_{\mathbb{Z},\omega(\sqrt{\log n})}\) with invertible tag \(\mathbf{H}\in\mathbb{Z}_{q}^{n\times n}\) satisfying \(\mathbf{A} \begin{bmatrix}\mathbf{R}\\ \mathbf{I_{w}}\end{bmatrix} =\mathbf{H}\mathbf{G}\) mod \(q\)._  
**Definition 5**. : \(SampleD\)_: There is a \(\mathbf{E}\in\mathbb{Z}^{\mathbb{H}\times\mathbb{H}}\) that samples from a probabilistic polynomial time (PPT) algorithm \(SampleD(\mathbf{R},\mathbf{A},\mathbf{H},\mathbf{U},\sigma)\) satisfying \(\mathbf{AE}=\mathbf{U}\) mod \(q\) with Gaussian parameter \(\sigma\), and \(\|\mathbf{E}\|\leq\sigma\sqrt{m}\) with an overwhelming probability._  
**Definition 6**. : \(DelTrap\)_: A PPT algorithm \(DelTrap(\mathbf{A},\mathbf{H},\mathbf{R},\sigma_{d})\) delegates its trapdoor key for sub-members and generates a new trapdoor key \(\mathbf{R}^{\prime}\) satisfying \(\mathbf{A} \begin{bmatrix}\mathbf{R}^{\prime}\\ \mathbf{I_{w}}\end{bmatrix} =\mathbf{H}\mathbf{G}\)._  
**Definition 7**. : \(FRD\) _encoding: Let the node ID of hierarchy \(k(k\geq 0)\) be a \(k\)-dimensional vector, which we denote by \(\mathbf{id_{\ell}}=(d_{1},d_{2},\ldots,d_{\ell})\). When \(\ell=0\), ID is the primary node. An efficient FRD coding algorithm exists to map the identity ID to a matrix, i.e., \(H_{fnd}:ID\in\mathbb{Z}^{k}\rightarrow\mathbb{Z}_{q}^{n\times n}\)._
## 2 Prediction Algorithm
### Online Sequential ELM (OS-ELM)  
The classical ELM assumes that all the data (samples) are used for training, but in the prediction model, the data is coming chunk-by-chunk (a block of data) or one-by-one (the latter can be seen as a special condition of the former). Therefore, the classical ELM should be adjusted to such conditions [19]. In the PV power prediction model, historical weather and PV power data are collected from the Supervisory Control And Data Acquisition (SCADA) system periodically. As OS-ELM updates the training data on time, it is more suitable for the PV power prediction. The algorithm is shown as follows.  
Step 1: Initialization--use a chunk of training data \(\{(x_{i},y_{i})\}_{i=1}^{N_{0}}\) as initial data.  
1. Randomly generate \(\mathbf{a}_{j}\) and \(b_{j}\) where \(j=1,2\
# Guaranteeing QoS for NOMA-Enabled URLLC Based on \(\kappa\)-\(\mu\) Shadowed Fading Model
## 3 Analysis of the Delay Performance
### Service Transmission in FBL Regime  
Based on FBL information theory, the maximum achievable data rate (bit/CU) with an instantaneous SNR and a decoding error probability for the \(k\)th user can be obtained as follows.[22; 33]  
\[\begin{split} r_{k}\Big{(}\hat{\gamma}_{k},\varepsilon_{k}^{d} \Big{)}&=C(\hat{\gamma}_{k})-\sqrt{\frac{V(\hat{\gamma}_{k})}{ \hat{n}}}Q^{-1}\Big{(}\varepsilon_{k}^{d}\Big{)}\\ &=\log_{2}^{(1+\hat{\gamma}_{k})}-\log_{2}^{\infty}\sqrt{\frac{ \left(1-\frac{1}{(1+\hat{\gamma}_{k})^{2}}\right)}{\hat{n}}}Q^{-1}\Big{(} \varepsilon_{k}^{d}\Big{)}^{\prime}\\ &=\log_{2}^{\left(f_{k}\left(\hat{\gamma}_{k},\varepsilon_{k}^{d} \right)\right)}\end{split} \tag{17}\]  
where \(f_{\hat{\gamma}_{k}}\Big{(}\hat{\gamma}_{k},\varepsilon_{k}^{d}\Big{)}=\frac{ 1+\hat{\gamma}_{k}}{\exp\left(\sqrt{\frac{\hat{\gamma}_{k}^{2}+2\hat{\gamma}_ {k}}{(1+\hat{\gamma}_{k})^{2}}\varepsilon^{-1}\left(\varepsilon_{k}^{d} \right)}\right)}\), \(\hat{n}\) is the number of CUs occupied by data transmission and \(\varepsilon_{d}\) is the decoding error probability. \(Q(x)=\frac{1}{\sqrt{2\pi}}\int_{x}^{\infty}e^{-y^{2}/2}dy\) is the tail distribution function of the standard normal distribution. \(C(\hat{\gamma}_{k})=\log_{2}^{(1+\hat{\gamma}_{k})}\) and \(V(\hat{\gamma}_{k})=\left(1-\frac{1}{(1+\hat{\gamma}_{k})^{2}}\right)\left( \log_{2}^{\epsilon}\right)^{2}\) are the Shannon capacity and channel dispersion, respectively. Given a decoding error probability of \(\varepsilon_{k}^{d}\), the achievable data rate \(r_{k}\Big{(}\hat{\gamma}_{k},\varepsilon_{k}^{d}\Big{)}\) is less than zero when the PPSNR \(\hat{\gamma}_{k}\) is below a threshold \(\gamma_{0}\). As a consequence, we redefine \(f_{\hat{\gamma}_{k}}\Big{(}\hat{\gamma}_{k},\varepsilon_{k}^{d}\Big{)}\) as \(g_{\hat{\gamma}_{k}}\Big{(}\hat{\gamma}_{k},\varepsilon_{k}^{d}\Big{)}\)  
\[g_{\hat{\gamma}_{k}}\Big{(}\hat{\gamma}_{k},\varepsilon_{k}^{d}\Big{)}=\left\{ \begin{array}{l}f_{\hat{\gamma}_{k}}\Big{(}\hat{\gamma}_{k},\varepsilon_{k} ^{d}\Big{)},\hat{\gamma}_{k}>\gamma_{0}\\ 1,\hat{\gamma}_{k}\leq\gamma_{0}\end{array}\right.. \tag{18}\]  
Furthermore, the maximum achievable data rate can be simplified as follows:  
\[r_{k}\Big{(}\hat{\gamma}_{k},\varepsilon_{k}^{d}\Big{)}=\left\{\begin{array}[ ]{l}\log_{2}^{f_{\hat{\gamma}_{k}}\big{(}\hat{\gamma}_{k},\varepsilon_{k}^{d }\big{)}},\hat{\gamma}_{k}>\gamma_{0}\\ 0,\hat{\gamma}_{k}\leq\gamma_{0}\end{array}\right.. \tag{19}\]
## 4 Agro-Food Substrates for Anaerobic Digestion  
### Livestock Manure  
Manure from farming animals has been traditionally reused as fertilizer, providing a nitrogen and phosphorous source for plants and crops. However, accumulation of carbon and leaching of nitrogen and phosphorous may produce negative environmental impacts. After enteric methane (CH\({}_{4}\)), manure represents the second largest source of GHG emissions in intensive dairy cattle [36] and buffalo farms [37]. The total amount of methane released from animal manure is 18 million tons CH\({}_{4}\) per year [38] with a breakdown of 2200 to 12,000 g CO\({}_{2}\)-eq for collection, 200 to 2400 g CO\({}_{2}\)-eq for transportation, 16,000 to 84,000 g CO\({}_{2}\)-eq for storage, and 16,400 to 33,500 g CO\({}_{2}\)-eq for land application, depending on the practice and farm size [36]. In addition, volatilized ammonia (NH\({}_{3}\)) from manure (up to 70% of excreted nitrogen) can remain as residual in water and terrestrial ecosystems or be converted into N\({}_{2}\)O emissions, contributing to both eutrophication and climate change [39]. Anaerobic digestion of animal wastes for biogas production, offers environmental benefits as it can reduce GHG emissions related to manure management by more than 50% [40] and by replacing on-farm fossil fuel-based processes with electricity produced through AD [41]. In addition, AD may represent a supplementary source of income for farmers as renewable energy is produced and the residual digestate has high fertilizing properties. One aspect to be considered is that AD has only minor effects on substrate nitrogen content. Therefore, this process gives no advantages in terms of compliance with the nitrates directive (91/676/EEC) [42]. Animal manure is a mixture of exceta (feces and urine) and materials added during management, such as sand, water from cleaning, straw and other bedding materials and, as other material used as biogas substrate, should satisfy different requirements in terms of suitability, digestibility and absence of inhibitors and impurities [43]. Suitability of a substrate for AD depends on the levels of total solids (TS) and volatile solids (VS), the carbon to nitrogen ratio (C/N) and pH. Livestock manure is usually in a liquid form with a dry matter content (DM) of 1-10%. Dry matter content is a key parameter to design the biogas reactor size and capacity [44]. Too diluted animal manure reduces economic feasibility, whereas too high DM (e.g., higher than 15%) may cause operating problems. An optimal DM content is about 10% and it may be corrected by co-digestion with other solid organic substrate such as energy crops with the aim to enhance biogas yield [45].
# Influence of Stress Anisotropy on Petrophysical Parameters of Deep and Ultradeep Tight Sandstone
## 4 Results and Discussion
### Influence of Axial Compression on Sonic Velocity and Resistivity  
Four groups of rock physical parameters were tested for rock sample No. 3-10-5-1, and the results show that (1) the S-wave and P-wave ratios varied with axial compression in two stages. When the axial pressure was less than 80 MPa, the P-S wave velocity ratio decreased with increasing axial pressure. When the axial pressure was greater than 80 MPa, the P-S wave velocity ratio increased with increasing axial pressure (Figure (a)a). (2) The resistivity increased with increasing axial pressure (Figure (b)b).
# Teleportation-Based Error Correction Protocol of Time-Frequency Qubit States
## 3 Spatial Separation of the Two Logical Time-Frequency Qubit States
### Spatial Separation of the Two Logical Time-Frequency Cat States  
In this section, we explicitly show how to separate spatially the two Gaussian wave packets with linear optics, using a Mach-Zehnder interferometer. The frequency cat state as described by Equation (1) is introduced into a balanced beam splitter and the associated wave function is  
\[|\psi\rangle=\frac{1}{2}(|\omega_{1}\rangle_{a}+|\omega_{2}\rangle_{a}+|\omega _{1}\rangle_{b}+|\omega_{2}\rangle_{b}). \tag{17}\]  
We assume for simplicity that the two frequency states are well separated \(\omega_{1}-\omega_{2}\gg\sigma\). Then, a pulse shaper is placed at the spatial port \(b\), described by the following unitary operation:  
\[\hat{U}|\omega_{1}\rangle_{b}=|\omega_{1}\rangle_{b},\ \hat{U}|\omega_{2} \rangle_{b}=e^{i\phi}|\omega_{2}\rangle_{b}. \tag{18}\]  
Such an operation can be implemented, for instance, by mapping the spectral to the spatial degree of freedom with a grating, a spatial light modulator at the focal length of two lenses, and then performing back the mapping from the spatial to the spectral degree of freedom [2; 55]. We assume that the frequency peaks are spaced enough so that the pulse shaper acts on each logical state independently. The two spatial paths are then recombined into another balanced beam splitter. The output state has the final form:  
\[|\psi\rangle=\frac{1}{\sqrt{2}}|\omega_{1}\rangle_{a}|\Omega\rangle_{b}+\frac {1}{2\sqrt{2}}((1+e^{i\phi})|\omega_{2}\rangle_{a}|\Omega\rangle_{b}+(1-e^{i \phi})|\Omega\rangle_{a}|\omega_{2}\rangle_{b}). \tag{19}\]  
If \(\phi=\pi\), the two logical states are spatially separated \(|\psi\rangle=\frac{1}{\sqrt{2}}(|\omega_{1}\rangle_{a}|\Omega\rangle_{b}+| \Omega\rangle_{a}|\omega_{2}\rangle_{b})\). This optical interferometer is the equivalent of the polarizing beam splitter that separates the vertical and horizontal polarization of optical fields into two distinct spatial paths.
# Traffic Signal Control with State-Optimizing Deep Reinforcement Learning and Fuzzy Logic
## 2 Fundamental Principles
### Fuzzy Logic  
Fuzzy logic [44; 45] is an alternative way of thinking to standard logic. Typically, it only considers right or wrong, yes or no. In digital thinking or Boolean logic, binary values of 0 and 1 are used. It is a method for analyzing situations that can be confusing or unclear. For instance, when discussing light or dark pink shades to determine whether they are considered red, fuzzy logic may evaluate the probability of red and white being present in combination. However, there are differing perspectives on this topic. Fuzzy logic is used in multiple fields to help decision-making in confusing or unclear situations and is beneficial in situations where there is considerable uncertainty.
# Smart Grid Data Management in a Heterogeneous Environment with a Hybrid Load Forecasting Model
## 4 The Proposed System
### Application Tier Structure  
The application tier is the third tier of the proposed application, and it is the logic tier that contains the business logic. This tier controls the application's functionality by performing detailed processing while interacting with the data tier to process the customer's information [52]. It ensures that the customer's queries are effectively transmitted to the analytics and database tier, hence enabling them to retrieve the desired information. Moreover, the application tier is a core part of the application, where logical decisions are made, and problems are solved [53]. The business rules and algorithms are built into this tier by writing the application tier in programming languages such as C# and ASP.net.  
Figure 2: PIAS Data Acquisition. (**a**) Acquisition Block Diagram. (**b**) Process Diagram.  
This activity's main objective is to provide the user with the desired results [54]. This tier is also known as server back-end development. A part of the application works at the back of the application without letting the user know about the processes being performed. The proposed application's portal system is the application tier that forms the basis of all the operations being performed by the application. All the user's information input into the application must pass the logic gateway, i.e., application tier, to display the correct information to the user. For example, when the user logins to the portal using their User ID and password, the information is sent to the application tier, where it is processed to check if the user has entered both fields correctly. If the fields match, the user is granted access to his account, and if the fields do not match, the user is denied access. Similarly, several other logical operations are carried out by the application tier. Therefore, it can be regarded as the application's brain. The application tier also sends commands to the database tier and analytics tier to retrieve the right data from the information and analytics presentation [55].
# The Impact of Eclipsing GNSS Satellites on the Precise Point Positioning
## 3 Results and Discussion
### The Impact of Eclipsing Satellites on GNSS PPP  
To analyze the impact of the eclipsing satellites on GNSS PPP, as shown in Figure 10, the observation data of 65 MGEX stations for 31-day period in July 2017 are selected. All these stations can track GPS/GLONASS/GALILEO/BDS signals. Then, three eclipsing strategies are designed:  
1. Strategy 1 (S1): delete all the eclipsing satellites;
2. Strategy 2 (S2): always use nominal attitude, even when this satellite is in eclipsing season; and
3. Strategy 3 (S3): use the modeled attitude when this satellite is in eclipsing season; otherwise, the nominal attitude is used.  
Figure 8: The yaw angle differences of E01 (FOC) during noon maneuver for different sun angles (\(-4.00^{\circ}\) to \(0.02^{\circ}\)).  
Figure 9: The attitude switch of BDS C10.  
In the subsequent subsection, the positioning accuracy, the observation residuals and the convergence time of these three eclipsing strategies are compared for the single-system PPP and GNSS PPP. All stations are used to conduct GPS-only PPP, GLONASS-only PPP and GNSS PPP in both static and kinematic mode. Because the number of GALILEO satellites is still small, only the static mode is performed for GALILEO-only PPP. Considered that the BDS satellites are mainly concentrated in the Asia Pacific Region, 10 stations marked as triangles are used to perform BDS-only PPP in both static and kinematic mode. The reference coordinates of these stations were given by IGS SINEX weekly solutions with an accuracy of a few millimeters. To ensure the positioning reliability, the convergence time is defined as the time required to achieve the 3D positioning error less than 10 cm for consecutive 20 epochs.
## 3 Results
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Stage** & _d/\(\Lambda\)_ & **Elements** & \multicolumn{2}{c}{**Original**} & \multicolumn{2}{c}{**Elements**} & \multicolumn{2}{c}{**Design A**} & \multicolumn{2}{c}{**Design B**} \\  & & & **SLL (dB)** & **HPBW (*)** & & **SLL (dB)** & **HPBW (*)** & **SLL (dB)** & **HPBW (*)** \\ \hline \multirow{4}{*}{2} & 0.5 & ON & \(-\infty\) & 63.33 & ON & \(-\)40.77 & 55.82 & \(-\)26.87 & 59.83 \\  & 1 & 16 & \(-\)22.60 & 30.29 & 10 & \(-\)15.69 & 26.78 & \(-\)23.24 & 28.79 \\  & 1.5 & OFF & \(-\)22.60 & 19.77 & OFF & \(-\)15.69 & 17.27 & \(-\)23.24 & 18.77 \\  & 2 & 0 & \(-\)8.64 & 14.77 & 6 & \(-\)13.35 & 13.26 & \(-\)9.94 & 14.26 \\ \hline \multirow{4}{*}{3} & 0.5 & ON & \(-\)25.59 & 29.79 & ON & \(-\)38.72 & 28.79 & \(-\)27.11 & 27.28 \\  & 1 & 64 & \(-\)25.59 & 14.77 & 40 & \(-\)21.29 & 14.26 & \(-\)27.12 & 13.26 \\  & 1.5 & OFF & \(-\)25.59 & 9.76 & OFF & \(-\)19.25 & 9.26 & \(-\)27.11 & 8.76 \\  & 2 & 0 & \(-\)25.58 & 7.26 & 24 & \(-\)19.25 & 6.75 & \(-\)27.14 & 6.75 \\ \hline \multirow{4}{*}{4} & 0.5 & ON & \(-\)26.29 & 14.26 & ON & \(-\)38.74 & 14.26 & \(-\)29.86 & 13.26 \\  & 1 & 256 & \(-\)26.28 & 7.26 & 160 & \(-\)34.96 & 7.26 & \(-\)29.85 & 6.25 \\  & 1.5 & OFF & \(-\)26.28 & 4.75 & OFF & \(-\)34.54 & 4.75 & \(-\)29.83 & 4.25 \\  & 2 & 0 & \(-\)26.27 & 3.25 & 96 & \(-\)34.55 & 3.25 & \(-\)29.85 & 3.25 \\ \hline \multirow{4}{*}{5} & 0.5 & ON & \(-\)26.46 & 7.26 & ON & \(-\)39.01 & 7.26 & \(-\)30.30 & 6.25 \\  & 1 & 1024 & \(-\)26.44 & 3.25 & 640 & \(-\)35.42 & 3.25 & \(-\)30.26 & 3.25 \\ \cline{1-1}  & 1.5 & OFF & \(-\)26.45 & 2.25 & OFF & \(-\)34.85 & 2.25 & \(-\)30.39 & 2.25 \\ \cline{1-1}  & 2 & 0 & \(-\)26.49 & 1.75 & 384 & \(-\)34.82 & 1.75 & \(-\)30.34 & 1.25 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparative performance of proposed wideband optimized designs with original base Eisenstein fractile with complete structure and uniform amplitudes. Figure 12: Array factor patterns comparing different stages for (**a**) Original design, (**b**) Design A, and (**c**) Design B at initial operation frequency \(f_{l}\).
## 2 Materials and Methods
### Discretisation through Voxelisation  
Once the CT pore data and the part processing data were aligned, the dataset volume was discretised by voxelisation. Cubic voxels with sizes of 0.5 mm, 1.0 mm, and 2.0 mm were used. Three sizes were used to investigate the effect of voxel size on the accuracy of porosity prediction and to investigate the trade-off between computational processing time and spatial resolution. Smaller voxel sizes require more computational processing but provide a higher spatial resolution. Pores were included in a voxel if their centre of volume fell within the region, while a single value for each process parameter was calculated for each voxel as the arithmetic mean of all data points falling within the voxel.  
Two variants of discretisation by voxelisation were applied. One approach carried out the discretisation centred around the pore centres and this approach is termed the defect-centric approach (DCA). In the other approach, discretisation was carried out uniformly on the part and this approach was termed the uniform-discretisation approach (UDA).
## 4 Application Example, Results and Discussion
### Features and Raking  
After the measurements are validated, the scenarios question needs the following features from the set introduced in Section 3.2 to find the most power-efficient sensor: _Power_, _Sensitivity_, _Reaction Speed I_, _Reaction Speed II_ and _Repeatability_. The priorities were set as listed in Table 4.  
The resulting list in Table 5 shows the most power-efficient sensor for the task of measuring Acetone and is depicted in Figure 6. The second and third best sensors are  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Feature** & & **Priority** & **Comment** \\ \hline Power & (\(f_{8}\)) & Highest & (\(\phi_{8}=0.9\)) & Cooler sensors need less power. \\ Sensitivity & (\(f_{1}\)) & High & (\(\phi_{1}=0.7\)) & Better for small amounts of the gas. \\ Reaction Speed I & (\(f_{2}\)) & Normal & (\(\phi_{2}=0.5\)) & Hot sensors have higher speeds. \\ Reaction Speed II & (\(f_{3}\)) & Normal & (\(\phi_{3}=0.5\)) & \(\phi_{3},\phi_{2}=0.5\) are a good trade of. \\ Repeatability & (\(f_{5}\)) & Normal & (\(\phi_{5}=0.5\)) & Consider sensor stability ov. time. \\ \hline \hline \end{tabular}
\end{table}
Table 4: Priorities of the features used for the exemplary ranking.  
Figure 5: Curve similarity of a subset of test curves with respect to the reference run 270 (blue). The curve of run 54 (red) yields a different signature (**–+)** to the other curves (green) (**+**) which is therefore filtered out although it has very similar distances (see Table 3) to the remaining curves.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Run** & **Method** & **Distance to 270** & **Distance of 52 to 270** \\ \hline
261 & PCM & 68.82963 & 68.62570 \\
267 & Area & 268.05069 & 264.02023 \\
343 & Fréchet & 0.62149 & 0.62126 \\
374 & Point & 0.23268 & 0.22901 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Distance values for the four implemented distance metrics for the runs in the selected test set, compared to the reference run 270.
# Ontology Modeling Using Fractal and Fuzzy Concepts to Optimize Metadata Management
## 2 Literature Review
### Ontology Modeling Methodologies
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Methodology** & **Pros** & **Cons** \\ \hline \multirow{4}{*}{VOWL} & - & Provides an intuitive, graphical notation, making it & - & Can become crowded or less clear for \\  & & relatively easy for users to grasp & - & large-scale ontologies \\  & - & Good tool support (e.g., WebVOWL, & - & Does not fully support all advanced OWL 2 \\  & & ProtegeVOWL) for quick ontology visualization & & features (e.g., complex property \\ \hline \multirow{4}{*}{Gaffoo} & - & Employs UML-style diagrams, familiar to those & - & Lacks robust features for complex or \\  & - & with a software engineering background & - & large-scale ontologies \\  & - & Useful for relatively small or mid-sized ontologies, & - & Does not inherently address uncertainty \\  & - & Offers a richer set of UML-like constructs than & - & Requires users to be comfortable with UML \\  & & Graffoo, enabling more advanced modeling & - & conventions \\  & - & Supports direct mappings between UML class & - & Complex ontologies visualization still \\  & - & diagrams and OWL & becomes complex and there is no built-in \\  & - & Embraces fractal structures to ensure scalability & \\  & - & and hierarchical consistency & \\  & - & Incorporates fuzzy logic to effectively manage & - & Relatively new approach, which may \\  & - & uncertain or ambiguous data & - & require additional learning by practitioners \\  & - & Enables real-time adaptability, handles evolving & - & Tool support may not be as widespread as \\  & - & data without major structural changes & - & established visualization techniques \\  & - & Seamlessly transforms into OWL for & \\  & - & standardization and interoperability purposes & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of ontology visualization methodologies.