esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Experimental Results  
### Experimental Conditions  
In order to prove the feasibility of WPD to identify potential damage in an orthotropic steel bridge girder, the single U rib model of an orthotropic steel bridge panel is used [10]. The test setup, experiments, and observation from the earlier study [10] are presented here to aid in better understanding. This specimen size is 1500 mm \(\times\) 900 mm \(\times\) 780 mm. The specimen has a U-shaped longitudinal stiffener. This model adopts the constraint mode of two-end anchorage, and each anchorage point area is arranged with a diaphragm. The material of the whole specimen is Q345D, and the thickness of the top plate and U rib are 4 mm and 2 mm, respectively. The test model is shown in Figure 2a,b.  
Static displacement and dynamic response signals of orthotropic steel bridge panels were collected by TZT3828E (dynamic and static signal acquisition instrument). The displacement sensor layout is shown in Figure 3a. The layout of acceleration sensors is shown in Figure 3b. It should be noted that in order to effectively collect acceleration response signals, the sampling frequency of acceleration sensors is set at 1000 Hz.  
In the test, a harmonic force of 120 N, 10 Hz is applied to the center of the top plate of the orthotropic steel bridge panel by the shaker, and the acceleration response signal of the orthotropic steel bridge panel is collected under nondestructive conditions. Then, an area of rectangular damage of size 1 cm (width) \(\times\) \(<\)5 mm (depth) \(\times\) 1 mm (height along thickness) is manufactured between sensor 2-4 and sensor 2-5, which is denoted as working Condition 1, as shown in Figure 4. And the same excitation is applied to the center of the  
Figure 2: Test setup (photographs and schematic diagrams). (**a**) Front view. (**b**) Lateral view (dimension in mm).  
panel with the shaker to collect the acceleration response signal. After the signal collection is completed, the human-made damage width is extended to 3 cm, which is denoted as working Condition 3. The same excitation is then applied to the center of the roof, and the acceleration response signal is also collected. The test conditions are shown in Table 1.
## 5 Conclusions  
An early and accurate diagnosis supported by clinical and radiological examinations, such as OPG X-ray and CBCT, is essential.  
It is crucial to evaluate the predictive eruption factors that influence the treatment plan, such as: age of the patient, history, compliance, distance from the occlusal plane, vertical position of unerupted incisors and inclination in relation to the midline.  
A complication during the tooth eruption could adversely affect the occlusion development and potentially burden the child's psychological evolution.  
The early orthodontic interceptive treatment with obstacle removal and an orthopedic expansion with RME is fundamental.  
Elastic tractions with the closed eruption technique for occlusal repositioning is preferred. This approach improves the intraosseous position and the mucogingival condition of the retained tooth.  
In general, surgical-orthodontics treatment of impacted incisors has a good chance of success, but it is relatively time-consuming.  
It is necessary to inform the patients and their parents of the failure risk and the increased treatment time, especially in the presence of impacted incisors in a very high alveolar position.  
Conceptualization, F.I., A.D.I., A.M.I., D.D.V., G.D., A.S., S.C., G.C., F.L. and A.P.; methodology, A.D.I., M.G., F.C., L.N., A.M., A.C., G.C., F.P., S.C. and M.C.; software, I.R.B., A.P., F.C., S.C., D.G., A.M., F.C. and G.D.; validation, F.I., F.C., V.S., L.N., G.D., A.D.I., A.M.I. and A.S.; formal analysis, A.M.I., F.L., V.M.P., D.D.V., A.D.I., B.R. and G.M.; investigation, G.M., G.D., A.D.I., F.L., A.M.I., A.P., S.C., A.S. and F.I.; resources, A.M.I., S.C., A.P., G.D., A.D.I., F.I., I.R.B. and G.M.; data curation, G.D., F.C., F.L., M.G., A.M., G.C., M.G., F.I., D.D.V. and G.M.; writing--original draft preparation, A.D.I., A.M.I, G.D., M.G., A.S., F.C., F.L. and F.I.; writing--review and editing, F.I., F.L., D.D.V., G.M., M.G., A.S., V.S. and G.D.; visualization, F.L., A.S. and I.R.B.; supervision, M.G., D.D.V., F.I., A.D.I. and F.L.; project administration, F.I., G.D., G.M., A.P., G.C., S.C. and V.M.P. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The present clinical study was based in the University of Bari (Italy), in full accordance with ethical principles, including the World Medical Association Declaration of Helsinki and the additional requirements of Italian law. Furthermore, the University of Bari, Italy, classified the study to be exempt from ethical review as it carries only negligible risk and involves the use of existing data that contain only non-identifiable data about human beings. The patient signed a written informed consent form.  
Informed Consent Statement:Informed consent was obtained from the subjects involved in the study. Written informed consent has been obtained from the patient and his parents to publish this paper.  
Data Availability Statement: All experimental data to support the findings of this study are available contacting the corresponding author upon request.
# Remote Low-Cost Differential Isolated Probe for Voltage Measurements
## 2 Hardware Description
### Output Conditioning and Filtering Module in Oscilloscope Probe Configuration  
The configuration of the proposed voltage probe for its application as an oscilloscope probe (Figure 1, bottom right, brown box), includes three consecutive stages at the output of the IA (Figure 6). Firstly, an offset compensation circuit cancels DC offsets in the IA output signal by means of a summing stage with a settable DC voltage supplied by a potentiometer, which provides a voltage in the range of \(\pm\)15 V. Next, a configurable \(\times\)1-\(\times\)10 inverting amplifier circuit allows setting the probe gain, thus allowing the measurement of low-value  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Remote Probe Input** & **Attenuation Factor** & **IA Input** & **IA Output** \\ \hline
600 V & \(\times\)100 & 6 V & 6 V \\
60 V & \(\times\)10 & 6 V & 6 V \\ \hline \hline \end{tabular}
\end{table}
Table 1: Selectable input ranges.  
Figure 4: Attenuation and input protection block diagram.  
Figure 5: Attenuation and input protection circuit scheme.  
voltages with electrical isolation. Finally, a second order Sallen-Key filter with a 50 kHz cut-off frequency, in the frequency range of the ISO122P IA, filters frequencies above the range of interest.  
The three stages described above use TLV9352, a dual low-power Operational Amplifier (OA). This operational amplifier in a SOIC 8 package is pin compatible with the TL082 OA, so it can be easily replaced in case of lack of availability, price increase, etc. without the need of printed circuit board redesign.  
The different circuit stage schemes that correspond with the block diagram shown in Figure 6 are shown in Figure 7.  
Figure 6: Conditioning stage block diagram for oscilloscope connection.  
Figure 7: Circuit schemes of conditioning circuit stages: (**a**) offset compensation, (**b**) amplification stage, and (**c**) Sallen-Key filter.
## 2 Mathematical Model  
### Basic Equations  
The proposed simulation method is based on a homogeneous assumption, where the mixture of water and vapor is a flowing fluid. With the conventional simulation method, the acting force between the interfaces is usually ignored. However, in cavitating flow, surface tension was proved to play an important role during the cavitation evolution [11]. Thus, the level set method was adopted in this study. The basic governing equations for homogeneous flow are listed as follows:  
\[\frac{\partial\rho_{\text{m}}}{\partial t}+\
abla\bullet(\rho_{\text{m}}\mathbf{U} )=0 \tag{1}\]\[\frac{\partial\rho_{\rm m}u_{\rm i}}{\partial t}+\frac{\partial\rho_{\rm m}u_{\rm i }u_{\rm j}}{\partial x_{\rm j}}=-\frac{\partial p}{\partial x_{\rm i}}+\frac{ \partial}{\partial x_{\rm j}}\left[(\mu_{\rm t}+\mu_{\rm m})\left(\frac{\partial u _{\rm i}}{\partial x_{\rm j}}+\frac{\partial u_{\rm j}}{\partial x_{\rm j}} \right)\right]+\sigma_{\rm s}\kappa\delta(\phi)n \tag{2}\]  
where \(\rho\), \(u\), and \(p\) represent the fluid density, velocity, and pressure, respectively. The subscripts m and v mean the mixture and vapor, respectively. \(\mu_{\rm m}\) and \(\mu_{\rm t}\) are the molecular and turbulent viscosity.  
The last term of Equation 2 is the surface tension force acting on the interface, with \(\sigma_{\rm s}\) representing the surface tension coefficient, \(\kappa\) representing the surface curvature, and \(n\) representing the interface normal vector pointing from the primary fluid to the second fluid (calculated using the volume fraction gradient). In order to solve the surface tension term, a level set function [11] i.e. \(\delta\) is adopted.  
Cavitating flow is a multi-scale turbulent flow. So, in order to simulate different turbulent scales accurately, the filter-based model [19] (FBM) was adopted. The FBM uses different methods to define the turbulent viscosity \(\mu_{t}\) in different turbulent scales, so the FBM is more superior than the \(k\)-\(\varepsilon\) model, and the results that conclude by using FBM are more precise. The turbulent viscosity \(\mu_{t}\) in FBM is defined as follows:  
\[\mu_{\rm t}=\frac{C_{\rm\mu}\rho_{\rm m}k^{2}}{\varepsilon}F_{\rm FBM} \tag{3}\]  
\[F_{\rm FBM}=min\left(1,C_{3}\frac{\lambda\cdot\varepsilon}{k^{3/2}}\right) \tag{4}\]  
In the equation, \(\lambda\) is the filter scales, \(F_{\rm FBM}\) is the filter function, and \(C_{\rm\mu}\) = 0.09, \(C_{3}\) = 1.0.
## 4 Composite Formation Techniques
### Ex situ _processes_  
_Ex situ_ processes are generally spoken methods, where nanoparticles, synthesized in an external synthesis step, are added or mixed to a monomer or resin (organic solution), usually followed by a polymerization. This is shown schematically in Figure 6. In the simplest case the nanoparticles are used as produced or delivered, posing the most problems concerning agglomeration. Such an approach was used by [PERSON] _et al._[66] to generate luminescent polymer-dielectric nanocrystal composites using commercial Al\({}_{2}\)O\({}_{3}\), Y\({}_{2}\)O\({}_{3}\), ZnO and SnO\({}_{2}\)/Sb\({}_{2}\)O\({}_{3}\)/Sb\({}_{2}\)O\({}_{5}\) nanoparticles, respectively. In more elaborated setups the nanoparticles were first surface functionalized and then added to the organic solution [67]. This principal method is also used by [PERSON] and [PERSON] [68] for the synthesis of styrene polymer/ZnO nanocomposite latex. [PERSON] _et al._[69] encapsulate commercial Al\({}_{2}\)O\({}_{3}\) nanoparticles by coeval use of an emulsifier with styrene/MMA using sonification and subsequent miniemulsion polymerization. Nanocomposites, consisting of epoxy thermosets and Al\({}_{2}\)O\({}_{3}\), have been prepared by simple mixing at elevated temperatures [70; 71].  
[PERSON] _et al._[72] attached spherical SiO\({}_{2}\) nanoparticles (100-200 nm) chemically to polycaprolactone via grafting with a solid load of 1.0 and 2.5 wt %. [PERSON] _et al._[44] applied a surface functionalization to commercial TiO\({}_{2}\), and then performed a free radical polymerization of styrene to generate a nanocomposite. Alternative approaches used commercial nanoparticles, applied coupling agents and finally blended the particles with polymer powder [73]. These methods lead to \"bulk\" composite materials. [PERSON] _et al._[47] combined the mixing of commercial nanoparticles in a monomer with the polymerization using electron irradiation to obtain polymer/TiO\({}_{2}\) and Al\({}_{2}\)O\({}_{3}\) nanoparticle composites. Another _ex situ_ method is the coating of nanoparticles with a polymer by a subsequent polymerization treatment. An example is the coating of commercial Al\({}_{2}\)O\({}_{3}\) nanoparticles with PAA [42] by controlled polymer bridging. Very frequently, plasma polymerization processes are used to generate core/shell type nanoparticles as shown in Table 1. Here also, externally produced nanoparticles are used. [PERSON] _et al._[45; 49] combined a fluidized bed reactor with the classical plasma polymerization to generate polymer coated ZnO and Al\({}_{2}\)O\({}_{3}\), respectively. [PERSON] _et al._[51] deposited a thin polymer film on ZrO\({}_{2}\) nanoparticles by inductively coupled C\({}_{2}\)H\({}_{2}\)/N\({}_{2}\) plasma.
## 2 Experimental
### Hs/di-spme-gc-ms Analysis  
Headspace (HS) and direct immersion (DI)-SPME parameters, and GC-MS conditions used for the analysis of the SPME test mixes are described in Tables 2 and 3, respectively.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Compounds** & **Structure** & **Functional Groups** & **Properties** \\ \hline \hline Discyclohexylamine & & Cycloalkane, Amine & Irreversible adsorption \\ \hline
4-Methyl-2- & & CH\({}_{3}\) & \\ pentanone & & & Alkane, Ketone & Proton acceptor \\ (MIBK) & & & \\ \hline
2-Picoline & & & Arene, Amine & Acid-base interactions \\ \hline n-Pentane (C5) & H\({}_{3}\)C & CH\({}_{3}\) & Alkane & Nonpolar, short chain, volatile alkane \\ \hline
1,_A_-Butanediol & HO & OH & Alkane, Alcohol & Short chain, volatile alkane, hydrogen bonding \\ \hline
1-Octanol & H\({}_{3}\)C & OH & Alkane, Alcohol & Fatty alcohol, hydrogen bonding \\ \hline \(N\),\(N\)-Dimethylaniline & & & Arenate pi-pi interactions, irreversible adsorption \\ \hline \hline Sulfolane & & Sulfonyl & Polar aprotic solvent \\ \hline
2,6–Di-tert-butyl-4- & & & Aromatic pi-pi interactions, hydrogen bonding \\ methylphenol & & & Arene, Alcohol & Aromatic pi-pi interactions, hydrogen bonding \\ \hline \hline Acenapthhylene & & Arene & PAH of interest, aromatic pi-pi interactions \\ \hline
2,6-Dimethylphenol & & & Aromatic pi-pi interactions, acid-base interactions \\ \hline n-Docosane (C22) & H\({}_{3}\)C & & Alkane & Nonpolar, long chain, semi volatile alkane \\ \hline Chloroform & & & Altoalkane & Very volatile alkyl chloride \\ \hline \hline Linalool & & & Monoterpene alcohol of interest, hydrogen bonding \\ \hline Hexachlorobutadiene & & & Haloalkane & Highly halogenated, unsaturated alkane \\ \hline \end{tabular}
\end{table}
Table 1: Custom test mix used to evaluate SPME fiber performance across a range of functional groups.
# Energy-Aware Online Non-Clairvoyant Scheduling Using Speed Scaling with Arbitrary Power Function
###### Abstract  
Efficient job scheduling reduces energy consumption and enhances the performance of machines in data centers and battery-based computing devices. Practically important online non-clairvoyant job scheduling is studied less extensively than other algorithms. In this paper, an online non-clairvoyant scheduling algorithm Highest Scaled Importance First (HSIF) is proposed, where HSIF selects an active job with the highest scaled importance. The objective considered is to minimize the scaled importance based flow time plus energy. The processor's speed is proportional to the total scaled importance of all active jobs. The performance of HSIF is evaluated by using the potential analysis against an optimal offline adversary and simulating the execution of a set of jobs by using traditional power function. HSIF is 2-competitive under the arbitrary power function and dynamic speed scaling. The competitive ratio obtained by HSIF is the least to date among non-clairvoyant scheduling. The simulation analysis reflects that the performance of HSIF is best among the online non-clairvoyant job scheduling algorithms.  
Keywords:non-clairvoyant scheduling; online scheduling; traditional power function; speed scaling +
Footnote †: journal: Applied Sciences
## 3 Results
### Berlin Questionnaire Score and Metrics
\begin{table}
\begin{tabular}{l l l l} \hline  & **BQ** & **ML-10** & **ML-2** \\ \hline AUC & (not applicable) & 86\% & 78\% \\ Sensitivity & 82\% & 93\% (Figure 1, point B10) & 88\% (Figure 1, point B2) \\ Specificity & 53\% & 73\% (Figure 1, point A10) & 54\% (Figure 1, point A2) \\ \hline \end{tabular} AUC = Area Under the (ROC) Curve.  
\end{table} 
Table 3: Comparing the performance of the standard BQ, the BQ enhanced through Machine Learning (ML-10) and the simplified BQ (i.e., BQ-2) enhanced through ML (ML-2), using metrics such as the AUC, Sensitivity, and Specificity. Note that the Sensitivity and Specificity for ML-10 and ML-2 were obtained with the procedure described in the text (i.e., by preserving BQ Specificity or Sensitivity, respectively), at specific points A10/A2 and B10/B2 (see Figure 1).
## 4 The Third-Order Beam Theory
### Kinematics  
The displacement field of the Reddy-Bickford third-order beam theory (RBT) is  
\[\mathbf{u}(x,z)=\left[u(x)+z\phi_{x}(x)-\alpha\,z^{3}\Big{(}\phi_{x}+\frac{dw} {dx}\Big{)}\right]\hat{\mathbf{e}}_{x}+w(x)\hat{\mathbf{e}}_{z}, \tag{73}\]  
where \(\alpha=4/3\hbar^{2}\). The nonzero strain and curvature components are  
\[\varepsilon_{xx}\varepsilon_{xx}^{(0)}+z\varepsilon_{xx}^{(1)}+z ^{3}\varepsilon_{xx}^{(3)},\quad\gamma_{xz}=\gamma_{xz}^{(0)}+z^{2}\gamma_{xz }^{(2)}, \tag{74a}\] \[\chi_{xy}=\chi_{xy}^{(0)}+z^{2}\chi_{xy}^{(2)},\quad\quad\chi_{ yz}=z\,\chi_{yz}^{(1)} \tag{74b}\]  
where (omitting the higher-order terms in the thickness strain)  
\[\varepsilon_{xx}^{(0)}=\frac{du}{dx}+\tfrac{1}{2}\left(\frac{dw}{ dx}\right)^{2},\ \varepsilon_{xx}^{(1)}=\frac{d\phi_{x}}{dx},\ \varepsilon_{xx}^{(3)}=-\alpha \left(\frac{d\phi_{x}}{dx}+\frac{d^{2}w}{dx^{2}}\right),\] \[\gamma_{xz}^{(0)}=\phi_{x}+\frac{dw}{dx},\ \gamma_{xz}^{(2)}=- \beta\Big{(}\phi_{x}+\frac{dw}{dx}\Big{)},\ \beta=3\alpha=\frac{4}{\hbar^{2}} \tag{74c}\] \[\chi_{xy}^{(0)}=\tfrac{1}{4}\left(\frac{d\phi_{x}}{dx}-\frac{d^{2}w}{dx^{2}} \right),\ \chi_{xy}^{(2)}=-\tfrac{1}{4}\beta\left(\frac{d\phi_{x}}{dx}+\frac{d^{2}w}{dx^ {2}}\right),\] \[\chi_{yz}^{(1)}=-\tfrac{1}{2}\beta\left(\phi_{x}+\frac{dw}{dx}\right)\]  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & \multicolumn{2}{c}{**L/\(h=50\)**} & \multicolumn{2}{c}{**L/\(h=20\)**} & \multicolumn{2}{c}{**L/\(h=10\)**} \\ \hline \(n\) & \(w\)-CBT & \(w\)-TBT & \(\widehat{w}\)-CBT & \(\widehat{w}\)-TBT & \(\widehat{w}\)-CBT & \(\widehat{w}\)-TBT \\ \hline
0.0 & 0.06510 & 0.06517 & 0.04167 & 0.04193 & 0.05208 & 0.05338 \\
1.0 & 0.12517 & 0.12529 & 0.08011 & 0.08058 & 0.10014 & 0.10250 \\
2.0 & 0.15793 & 0.15809 & 0.10108 & 0.10173 & 0.12635 & 0.12960 \\
3.0 & 0.17827 & 0.17847 & 0.11409 & 0.11409 & 0.14261 & 0.14661 \\
4.0 & 0.19300 & 0.19324 & 0.12352 & 0.12445 & 0.15440 & 0.15905 \\
5.0 & 0.20518 & 0.20544 & 0.13132 & 0.13236 & 0.16415 & 0.16935 \\
6.0 & 0.21608 & 0.21636 & 0.13829 & 0.13943 & 0.17286 & 0.17855 \\
10.0 & 0.25382 & 0.25417 & 0.16244 & 0.16387 & 0.20305 & 0.21020 \\
20.0 & 0.32559 & 0.32605 & 0.20838 & 0.21020 & 0.26047 & 0.26957 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Numerical results obtained with the classical (CBT) and the Timoshenko (TBT) beam theories for the transverse deflections of a _pinned–pinned_ FGM beams under a uniformly distributed load (the results are normalized with the load, \(q_{0}\)); \(\widehat{w}=w(0.5L)\,10\) and \(\widehat{w}=w(0.5L)\,\times 10^{2}\).
# Intelligent Interference Management in UAV-Based HetNets +
## 3 System Model
### Greedy Algorithm  
In order to reduce the time complexity, we utilized a heuristic algorithm that initially assumes that there is only one UABS in the system and finds the best location, eICIC, and FeICIC parameters for this UABS. It then considers that there are two UABSs in the system, with the parameters of the first UABS set to those found earlier, and finds the best parameters for this second UABS. Similarly, it then finds the best parameters for the third UABS considering the first two UABSs to be at their earlier determined states. The algorithm continues this procedure for the given number of UABSs.  
A similar approach is used to optimize the parameters of MBSs. This algorithm is summarized in Algorithm 2. As we will see in the simulation results, this algorithm, somewhat surprisingly, performs close to the brute force search, and outperforms the DDQN algorithm, to be discussed in the next section. A main reason for this is that the large number of parameters in Table 1 allows to _compensate_ for a non ideal selection of parameters in earlier stages, e.g., by tuning the scheduling thresholds and CRE, non-ideal location of a UABS can still result in good SE.  
```
1:for all\(UABS\)do
2: Assume all previous \(UABS\) to be positioned at their best location and operating at their best ICIC parameters.
3: Find best location and FeICIC parameters for current \(UABS\).
4:endfor
5:for all\(MBS\)do
6: Assume all previous \(MBS\) to be operating at their best ICIC parameters.
7: Find best ICIC parameters for current \(MBS\).
8:endfor
```  
**Algorithm 2** Greedy algorithm.
# Forward-Looking Element Recognition Based on the LSTM-CRF Model with the Integrity Algorithm
## 3 LSTM-CRF Model with the Integrity Algorithm
### LSTM-CRF Model
The labeling of each current word is related to the labeling result at the previous moment. The LSTM-CRF model consists of a word embedding layer, a bidirectional LSTM layer, and a CRF layer. The first word embedding layer uses pretraining to map each word \(\mathrm{w}_{i}\) of a sentence into a \(d\)-dimensional word vector. The LSTM-CRF model architecture is shown in Figure 2.  
\[\dot{\mathbf{f}}_{t}=\sigma\left(\mathbf{W}_{xf}\,\mathbf{x}_{t}+\mathbf{W}_{bf}\,\mathbf{h}_{t-1}+ \mathbf{W}_{ci}\,\mathbf{c}_{t-1}+\mathbf{b}_{j}\right) \tag{2}\]0 LSTM-CRF model architecture. The word vector is input into the bidirectional LSTM layer, and the hidden state of the forward LSTM output and the hidden state of the backward LSTM output are obtained. The hidden state sequence output by each position is spliced by position to obtain a complete hidden state sequence \(h_{t}= \begin{bmatrix}\vartriangleleft\\ \vartriangleleft\\ h_{t};h_{t}\end{bmatrix} \). Next, P is regarded as the matrix of scores outputted by the LSTM network of size \(n\times k\), where \(k\) indicates the category of the tags. P\({}_{i,j}\) corresponds to the score of the j-th tag of the i-th word in a sentence. Given an input sentence \(X=(x_{1},x_{2},\ldots,x_{n})\) and a sequence of predictions, \(y=(y_{1},y_{2},\ldots,\)\(y_{n})\), the associated score is defined as follows:  
\[score(X,y)=\sum_{i=1}^{n}P_{i,yi}+\sum_{i=1}^{n}A_{yi-1,yi}\qquad s.t.P\in R^{ n\times k},A\in R^{(k+2)\times(k+2)} \tag{9}\]  
where \(A_{i,j}\) is the transfer score from the \(i\)th tag to the \(j\)th tag. The start and end tags are added to the set of possible tags, and these tags, namely, \(y_{0}\) and \(y_{n}\), denote the start and end of a sentence. Thus, \(A\) is a square matrix of size \(k+2\). After applying a softmax function to all possible tag sequences, the probability of the sequence \(y\) is as follows:  
\[P(y|X)=\frac{\exp(score(X,y))}{\sum_{y^{\prime}}\exp(score(X,y^{\prime}))} \tag{10}\]  
The model is trained by maximizing the log likelihood function:  
\[\log P(y^{x}|X)=score(X,y^{x})-\log(\sum_{y^{\prime}}score(X,y^{\prime})) \tag{11}\]  
Finally, the Viterbi algorithm is used to solve the optimal path:  
\[y^{*}=\arg\max_{y^{\prime}}score(X,y^{\prime}) \tag{12}\]