esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 System Model and Design Objectives
### Authentication Formation
#### 3.4.2 Secure Data Freshness Process  
We observed the sensor reading '\(k_{r}\)' obtained by the sensor node '\(k\)', and resultant aggregation listening capability '\(\epsilon\)' of the cluster head node '\(C_{H}\)' in the premises of any number of events \(E_{n}^{\prime}\). This is important for securing the freshness of the data. Thus, every valid sensor node '\(k\)' belongs to its respective '\(C_{H}\)' and has a total number of sensor nodes '\(k_{n}\)', which can forward the valid '\(V_{u}\)' and invalid '\(I_{u}\)' updated information to the cluster head \(C_{H}\). Hence, the current detection time '\(D_{t}\)' for the right communicating cluster head node '\(V_{CH}\)', conforms to the proposed SDAAA approach; however, it is absent in the other contending approaches like SD, EEHA, HAS, IIF, and RHC protocols. The proposed SDAAA approach secure data freshness is as shown below:  
\[D_{t}=\frac{(k_{r}*E_{n})\times k_{n}}{\epsilon} \tag{18}\]  
Nevertheless, it is a tricky process to identify a valid cluster head node. We assume the right cluster head node '\(V_{CH}\)' and non-valid cluster head node '\(NV_{CH}\)' are available in the network. However, finding the valid cluster head node increases the necessity of secure freshness to avoid compromising the aggregated data. Thus, the right cluster head node '\(V_{CH}\)' can be obtained by:  
\[V_{CH}=\begin{pmatrix}V_{CH}+1,D_{t}>\frac{V_{CH}-1}{V_{CH}}\\ V_{CH},otherwise\end{pmatrix} \tag{19}\]  
Once the valid cluster head node is determined, it is also appropriate to isolate the non-valid cluster head node '\(NV_{CH}\)' from the network; otherwise, it could damage the data integrity, which is vulnerable when securing data freshness. Thus, non-valid cluster head node '\(NV_{CH}\)' is obtained by:  
\[NV_{CH}=\begin{pmatrix}NV_{CH}+\tau(\Delta d_{r}),D_{t}>\frac{V_{CH}-1}{V_{CH}} \\ NV_{CH},otherwise\end{pmatrix} \tag{20}\]  
where \(\tau\): data-effecting process; \(\Delta d_{r}\): resultant aggregated data of cluster head node.  
Henceforth, the same process also correctly determines the valid (legitimate) and non-valid (malicious) sensor nodes when forwarding the data in the network.
# A Study on Liquid Leak Rates in Packing Seals
###### Abstract  
The accurate prediction of liquid leak rates in packing seals is an important step in the design of stuffing boxes, in order to comply with environmental protection laws and health and safety regulations regarding the release of toxic substances or fugitive emissions, such as those implemented by the Environmental Protection Agency (EPA) and the Technische Anleitung zur Reinhaltung der Luft (TA Luft). Most recent studies conducted on seals have concentrated on the prediction of gas flow, with little to no effort put toward predicting liquid flow. As a result, there is a need to simulate liquid flow through sealing materials in order to predict leakage into the outer boundary. Modelling of liquid flow through porous packing materials was addressed in this work. Characterization of their porous structure was determined to be a key parameter in the prediction of liquid flow through packing materials; the relationship between gland stress and leak rate was also acknowledged. The proposed methodology started by conducting experimental leak measurements with helium gas to characterize the number and size of capillaries. Liquid leak tests with water and kerosene were then conducted in order to validate the predictions. This study showed that liquid leak rates in packed stuffing boxes could be predicted with reasonable accuracy for low gland stresses. It was found that internal pressure and compression stress had an effect on leakage, as did the thickness change and the type of fluid. The measured leak rates were in the range of 0.062 to 5.7 mg/s for gases and 0.0013 and 5.5 mg/s for liquids.  
liquid leak rate prediction; packing seals; incompressible fluids; experimental tests; slip flow model; number and radius of capillaries +
Footnote †: journal: Applied Sci.  
**2021**, 11, 1936. [[https://doi.org/10.3390/app11041936](https://doi.org/10.3390/app11041936)]([https://doi.org/10.3390/app11041936](https://doi.org/10.3390/app11041936))
## 2 Verification of Block Decomposition
### Transformation to 2-Sat  
Let \(G=(V,E)\) be a graph with vertex set \(V=[n]\). In this subsection we show how to test if a partition of \(V\) is a block decomposition for some unipolar representation, in which case we must have \(G\in\mathcal{GS}^{+}\). Let \(\mathcal{B}\) be the partition of \(V\) we want to test. From each block of \(\mathcal{B}\), we seek to pick out some vertices to form the central clique \(V_{0}\) of a representation, with the remaining vertices in the blocks forming the side cliques. Suppose that \(|\mathcal{B}|=m\), and \(\mathcal{B}\) is represented by a surjective function \(f:V\rightarrow[m]\), so that \(\mathcal{B}=\{f^{-1}[i]:i\in[m]\}\). Let \(\{x_{v}:v\in V\}\) be Boolean variables. We use Algorithm 1 to construct a formula \(\psi(x_{1},\ldots x_{n})\), so that each satisfying assignment of \(\{x_{v}\}\) corresponds to a representation of \(G\).  
There is an exception: the first time a clause is added to \(\psi\) it should be added without the preceding sign for conjunction. The following lemma is easy to check.  
**Lemma 2.1**.: _The formula \(\psi\) is satisfiable iff \(\mathcal{B}\) is a block decomposition for some representation. Indeed an assignment \(\Phi:\{x_{v}:v\in V\}\rightarrow\{0,1\}\) satisfies \(\psi\) if and only if \(R=(V_{0},V_{1})\) is a representation of \(G\) and \(\mathcal{B}\) is a block decomposition of \(G\) with respect to \(R\), where \(V_{i}=\{v\in V:\Phi(v)=1-i\}\)._  
Proof.: Suppose \(\Phi\) is a satisfying assignment and let \(V_{0}\), \(V_{1}\) be as above. If \(u\) and \(v\) are both in \(V_{0}\), then \(uv\in E\), since otherwise \(\Phi\) contains a clause \(\
eg x_{u}\vee\
eg x_{v}\). If \(u\) and \(v\) are in \(V_{1}\), then either \(uv\in E\) and \(f(u)=f(v)\) or \(uv\
ot\in E\) and \(f(u)\
eq f(v)\), because in the other two cases \(\phi\) contains the clause \(x_{u}\lor x_{v}\). This means that the vertices in \(V_{1}\) are grouped into cliques by their value of \(f\). For the other direction, it is sufficient to verify that each generated clause is satisfied, which is a routine check.  
At most a constant number of operations are performed per pair \(\{u,v\}\), so \(O(n^{2})\) time is spent preparing \(\psi\). The formula \(\psi\) can have at most \(2\) clauses per pair \(\{u,v\}\), so the length of \(\psi\) is also \(O(n^{2})\), and since 2-SAT can be solved in linear time, the total time for this step is \(O(n^{2})\).
# Efficient User-Serving Scheme in the User-Centric Cell-Free Massive MIMO System
## 4 Proposed Scheme and Power Control
### Computational Complexity  
The proposed scheme has the following complexity. The number of unserved users existing before STEP 1 is denoted by U, and I is the count of iterative cumulative sums for the threshold value \(\xi\) in STEP 6. As a result of STEPs 1-5, if the number of APs newly connected to a specific unserved user \(k^{*}\) is A, the number of other users served by APs in a set A (excluding unserved user \(k^{*}\)) can be denoted by S. Then the complexity of the proposed scheme can be calculated as \(\mathcal{O}\)(UI(5A+2S+1)). Naturally, since the number of unserved users in the area increases in proportion to the total number of users, if the number of unserved users in the system is small, the complexity of the scheme may very low.
# Secure D2D Group Authentication Employing Smartphone Sensor Behavior Analysis
## 6 Security Analysis
### Resistance to Forgery Against Adaptive Chosen Message Attack
If the tuple \((Auth,\mathit{Tid},\mathcal{T},\eta)\) has already been stored in \(List_{H_{2}}\), \(\mathcal{B}_{1}\) outputs \(Auth=H_{2}(\mathit{Tid},\mathcal{T},\eta)\) to \(\mathcal{A}_{1}\). Otherwise, \(\mathcal{B}_{1}\) chooses random \(Auth\in\mathbb{Z}_{\mathcal{P}}\) and forwards it to \(\mathcal{A}_{1}\). The new tuple \((Auth,\mathit{Tid},\mathcal{T},\eta)\) will be subsequently added to \(List_{H_{2}}\). * \(H_{3}\) _hash Query:_ Assume that \(\mathcal{A}_{1}\) does not has the ability to calculate the hash function \(H_{3}(.)\). The response to \(H_{3}\)_hash Query_ can be simulated by maintaining a list \(List_{H_{3}}\) initialized to be empty. When the adversary \(\mathcal{A}_{1}\) invokes the \(H_{3}\)_hash Query_ with input values \((\rho,\eta)\), \(\mathcal{B}_{1}\) will then check whether the record \((\rho,\rho,\eta)\) exists in the hash list \(List_{H_{3}}\). If the tuple \((\rho,\rho,\eta)\) has
already been stored in \(List_{H_{3}}\), \(\mathcal{B}_{1}\) outputs \(\varphi=H_{3}(\rho,\eta)\) to \(\mathcal{A}_{1}\). Otherwise, \(\mathcal{B}_{1}\) chooses random \(\varphi\in\mathbb{Z}_{\mathcal{P}}\) and forwards it to \(\mathcal{A}_{1}\). The new tuple \((\varphi,\rho,\eta)\) will be subsequently added to \(List_{H_{3}}\). * _Extraction Query:_ Upon the _Extract Query_ with \(ID\) is made to \(\mathcal{B}_{1}\), \(\mathcal{B}_{1}\) conducts \(H_{1}\)_hash Query_ on the input \(ID\) and outputs the corresponding tuple \((ID,\zeta)\). Note that the tuple \((ID,\zeta)\) has already recorded in \(List_{H_{1}}\). \(\mathcal{B}_{1}\) randomly selects \(X,r\in\mathbb{Z}_{\mathbb{P}}\) and computes \(\mathcal{U}=X\zeta^{r}\) and \(\mathcal{V}=\hat{e}(\zeta,g^{-r})^{mk}\) adopting the acquired \(\zeta\) and previously stored \(mk\). The calculated tuple \((\mathcal{U},\mathcal{V})\) will be sent to \(\mathcal{A}_{1}\). Finally, adversary \(\mathcal{A}_{1}\) obtains two tuple \(\langle\mathit{Tid},\mathcal{T},Auth\rangle\) and \(\langle\mathit{Tid},\mathcal{T},Auth^{*}\rangle\) after querying \(\mathcal{B}_{1}\), where \(ID\
eq ID^{*}\). Hence, \(\zeta=\zeta^{*}\) holds. That is, \(H_{1}(ID)=H_{1}(ID^{*})\). Due to the assumption that \(H_{1}\) is a random oracle, we can get \(ID=ID^{*}\), which contradicts the aforementioned assumption. Hence the probability that adversary \(\mathcal{A}_{1}\) can win the game \(\mathcal{G}_{1}\) is \(\frac{1}{\sigma^{2}(ID^{*}+\mathcal{U}^{*}+\ell}\), where \((\ell_{ID},\ell_{X},\ell_{r})\) denote the length of \(ID\), \(X\) and \(r\) respectively. Thus, the advantage of \(\mathcal{A}_{1}\) winning the game is negligible. Our scheme is resistance to adaptive chosen message attack.
# Millimeter-Wave Multi-Channel Backscatter Communication and Ranging with an FMCW Radar
## 7 Measurement Result and Discussion  
Two measurements are demonstrated in this paper: the single tag measurement and the dual tag measurement. The single tag measurement shows the performance of the self-packaged tag with the LMF signal as a carrier. In the dual tag measurement, two tags are used to transmit two different data streams to simulate the multi-tag scenario.
# Methods for Grating Lobe Suppression in Ultrasound Plane Wave Imaging
## Materials and Methods
### GL Suppression Method with Uniformly Distributed PW Angles  
In practice, PWs are transmitted by a finite aperture (i.e., a finite-length transducer array), resulting in a finite collimated beam area. Figure 2 shows three PWs with different steering angles (black solid lines) and their collimated beam areas (gray shaded areas) with preserved LWFs. In Figure 2, the focus and the main lobe of the focused beam pattern are in the region where all the PWs preserve their LWFs (i.e., the darkest area in Figure 2). If a GL locates at this same region and the constant PW angle interval is employed (i.e., if both LWF and uniform \(d_{\alpha}\) conditions are met), the amplitude of the GL would be as high as that of the main lobe because the number of compounded PWs should be the same at both the main lobe and GL locations. Note that by reducing \(d_{\alpha}\), one can move the GL away from the main lobe towards a region where the LWF condition is satisfied by fewer PWs. In such a case, the GL level would be lower than that of the main lobe because the number of PWs coherently compounded becomes smaller at the GL location; the PWs that do not maintain LWFs at the grating lobe locations are compounded with phase errors, leading to a decrease in the corresponding GL levels. This indicates that GL levels would decrease as GLs are moved farther from the main lobe.  
One can expect that the GLs can be eliminated by locating all of the GLs in a region where none of the PWs preserve LWF (i.e., by completely violating the LWF condition). In Figure 2, for example, when the first GL position, \(x=x_{\rm GL,1}(=x_{\rm f}+\lambda/d_{\alpha})\), falls onto point A that is out of all the collimated beam areas of PWs, no GLs can be formed, even when a uniform \(d_{\alpha}\) is employed. In this case, \(x_{\rm GL,1}>D/2+z_{\rm f}\tan\theta_{\rm max}\). Consequently, the GL elimination requirement when using uniformly distributed PW angles can be defined as:  
\[d_{\alpha}<\lambda/(D/2+z_{\rm f}\tan\theta_{\rm max}-x_{\rm f}), \tag{4}\]  
Figure 2: Collimated beam areas (gray shaded areas) of PWs with steering angles of \(\theta_{max},0^{\circ}\), and \(\theta_{min}\) (from top to bottom). The points, A and B, are located at the region where none of PWs pass and the region where half of transmitted PWs propagate, respectively.  
where \((x_{\rm f},\ z_{\rm f})\) represents the focal point and \(D\) is the transducer width. One can also observe that only the PWs with \(\theta\geq 0^{\circ}\) pass through point B in Figure 2, preserving the LWF. Therefore, the GL level would be approximately halved at this point (i.e., reduced by \(-6\) dB) if the angular interval is:  
\[d_{\alpha}=\lambda/(D/2-x_{\rm f}), \tag{5}\]  
when \(\theta_{\rm max}=-\theta_{\rm min}\).
## 3 Implementation and Measurement
### Experimental Setup Testbed
It can observe the processes of collecting LTE parameters according to a LTE mode selected, generate LTE signals using the LTE system toolbox, the transmission and reception using (AD-FMCOMMS3-EBZ) RF transceiver board and the MATLAB library to pre- and post-processing of captured real-valued data. Figure 7: EVM (%) for the input and output signal, before and after applying a scale factor: (a) actual 64–QAM 10–MHz signal, and (b) receiver signal.
# Diverse Decoding for Abstractive Document Summarization
## 3 Neural Abstractive Summarization with Diverse Decoding
### Diversity-Promoting Beam Search Method
#### 3.2.2 Standard Beam Search and Its Problem  
A compromise between exact and greedy decoding is to use the beam search approach, which keeps the top \(K\) high-scoring candidates at each time; where \(K\) is known as the beam size. The beam search is the standard approach for neural decoding. At time step \(t-1\) in the decoding process, we keep record of \(K\) hypotheses based on score \(S\left(Y_{t-1}\,|\,x\right)=logP(y_{t-1},\ldots,y_{1}|x)=\Theta\left(Y_{[t-1]}\right)\). As the decoding process moves on to time step \(t\), each of the \(K\) hypotheses (denoted as \(Y_{t-1}^{k}=\{y_{1}^{k},y_{2}^{k},...,y_{t-1}^{k}\},k\in[1,K]\)) is expanded individually by selecting the top \(K\) candidates, denoted as \(Y_{t-1}^{k,k^{\prime}}\), leading to the construction of \(K\times K\) new hypotheses:  
\[S\left(Y_{t-1}^{k},y_{t}^{k,k^{\prime}}\,|\,x\right),k^{\prime}\in[1,K],k\in[ 1,K] \tag{8}\]  
The goal is to find the top \(K\) hypotheses from the newly-generated \(K\times K\) hypotheses; we rank theme with scores computed as as follows:  
\[S\left(Y_{t-1}^{k},y_{t}^{k,k^{\prime}}\,|\,x\right)=S\left(Y_{t-1}^{k}\,|\,x \right)+logP(y_{t}^{k,k^{\prime}}|x,\gamma_{t-1}^{k}) \tag{9}\]Based on the score \(S\left(Y_{t-1}^{k},y_{t}^{k,k^{\prime}}\,|\,x\right)\), the top \(K\) hypotheses are selected, and the remaining hypotheses are ignored as the decoder proceeds to next time step.  
The beam search process can be viewed as a search algorithm that explores a graph by expanding the most promising node in a limited set. However, each time step when we are expanding the top \(K\) nodes, the first node's successors can easily outcompete other nodes' successors. This is because their parental node is already the one with the highest score, and the beam search selects candidates by the sum of the words' score. This parental advantage accumulates with the increasing of decoding length, resulting in the final candidates generate mostly coming from a single beam, with minor variations in the tail.
# Energy-Saving Breakthrough in the Point-to-Point Control of a Flexible Manipulator
## 6 Conclusions  
This study addressed the PTP control problem of a single-link flexible manipulator and proposed a trajectory planning method aimed at simultaneously minimizing drive energy and residual vibration. The approach was based on the physical phenomenon where drive energy decreases with initial deflection in the manipulator. The study focused on generating a trajectory that induces significant deformation immediately after activation. In the proposed method, the trajectory of the joint angle was expressed as the sum of a cycloid curve and a cycloid function, with the input represented as a power series. To achieve both drive energy minimization and residual vibration suppression, the sum of the torques was defined as the evaluation function. The parameters of the trajectory were tuned using PSO to minimize the evaluation function, and the optimal trajectory was then generated. The efficacy and feasibility of this proposed method were verified through both simulations and model experiments. The proposed method can reduce energy consumption while also suppressing residual vibrations. Generally, energy conservation in manipulator operation is often associated with the need for smooth trajectory execution to minimize vibration. However, the proposed method produced results that differed from this concept. These findings contribute new knowledge to the field of energy conservation in the context of flexible manipulators. This study, therefore, makes a significant contribution to understanding and improving energy efficiency in robotic systems. Our future challenge is to apply the utilization of flexibility for energy saving in a multi-link flexible manipulator.  
This research received no external funding.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The raw data supporting the conclusions of this article will be made available by the authors on request.  
**Conflicts of Interest:** The author declares no conflicts of interest.
## 4 Methodology
### Graph Cross-View Contrastive Optimization  
With the heterogenous graph multi-level view encoder network we obtain the embedding representation from three views for different perspectives of the nodes, and then we obtain the final fine-grained embedding representation by cross-view contrastive learning. **Local-level Contrast Learning. ** In the local-level view, the main purpose is to contrast learning of the two embedding expressions \(e_{r}^{i}\) and \(e_{r}^{g}\) of the recipe. First, we feed the embeddings of the two views into an MLP with hidden layers so that they are mapped into a uniform space as follows:  
\[ \begin{split} z_{r-}^{i}p&=W^{(2)}\sigma\Big{(}W^{(1)}e _{r}^{i}+b^{(1)}\Big{)}+b^{(2)}\\ z_{r-}^{s}p&=W^{(2)}\sigma\Big{(}W^{(1)}e_{r}^{s}+b^{(1)} \Big{)}+b^{(2)}\end{split}  \tag{12}\]  
where \(\Big{\{}W^{(1)},W^{(2)},b^{(1)},b^{(2)}\Big{\}}\) are the parameters that can be trained and they are shared by two views. \(\sigma\) is the ELU non-linear function. After that we need to define positive and negative samples for learning, inspired by other applications of comparative learning [25; 26], we define positive and negative samples as shown in Figure 3. The same node of another view for the target node is treated as the positive sample, the other nodes of the same view are treated as the intra-view negative sample, and the nodes of another view except for the positive sample are treated as the inter-view negative sample. From the defined positive and negative samples, we have contrastive loss as follows:  
\[ \begin{split}\mathcal{L}_{local}=-log\frac{\exp\bigg{(}\frac{ sim\left(z_{r-}^{s}p,z_{r-}^{i}p\right)}{\tau}\bigg{)}}{\exp\bigg{(}\frac{ sim\left(z_{r-}^{s}p,z_{r-}^{i}p\right)}{\tau}\bigg{)}+\sum_{k\
eq i}\exp \bigg{(}\frac{sim\left(z_{r-}^{s}p,z_{k-}^{i}p\right)}{\tau}\bigg{)}+\sum_{k \
eq i}\exp\bigg{(}\frac{sim\left(z_{r-}^{s}p,z_{k-}^{i}p\right)}{\tau}\bigg{)} }\\ \end{split}  \tag{13}\]  
where \(\text{sim}(\cdot,\cdot)\) denotes the cosine similarity calculation of the two vectors and \(\tau\) denotes the temperature parameter. In Equation (13), \(\exp\big{(}\text{sim}\left(z_{r-}^{s}p,z_{r-}^{i}p\right)/\tau\big{)}\) denotes the positive sample pair, \(\sum_{k\
eq i}\exp\left(\text{sim}\left(z_{r-}^{s}p,z_{k-}^{i}p\right)/\tau\right)\) denotes the intra-view negative sample pair, and \(\sum_{k\
eq i}\exp\left(\text{sim}\left(z_{r-}^{s}p,z_{k-}^{i}p\right)/\tau\right)\) denotes the inter-view negative sample pair. We obtained the local fine-grained embedding representation by local-level cross-view comparison learning. **Global-level Contrast Learning. ** After local contrast learning, we obtain the final node representation by performing cross-view contrastive learning of the local-level view embedding with the global-level view embedding. First mapping them to the same space, we still do it by an MLP with a hidden layer:  
\[ \begin{split} z_{r-}^{g}p&=W^{(2)}\sigma\Big{(}W^{ (1)}e_{r}^{g}+b^{(1)}\Big{)}+b^{(2)}\\ z_{r-}^{l}p&=W^{(2)}\sigma\Big{(}W^{(1)}\left(e_{r}^ {i}+e_{r}^{s}\right)+b^{(1)}\Big{)}+b^{(2)}\end{split}
## 5 Experimentation
### Message Generation Distribution
#### 5.3.1 Inverted Smoothed Top Hat Distribution (Isth)  
We aim to mimic the network traffic in a working day with the ISTH distribution. The flat region (FR) of the ISTH represents the working hours where the network traffic is the heaviest, i.e., messages will be generated at a higher rate. The transient regions (TR) are shaped in two ways: (1) to logarithmically increase the rate of message generation up to reach the peak rate of the FR; and (2) to logarithmically decrease the rate of the message creation from the peak rate in the FR to a shallow rate when approaching the 24 th hour of the day.  
The ISTH function is built as a composition of a descendant logistic functions, an ascendant logistic function, and a linear function. Both logistic functions determine the message generation frequency for a time:  
* Descendant logistic function (exponential growth rate\((k)>0\)): \[f(x)=\frac{L_{2}}{1+ae^{k(x-x_{0})}}\] (12)
* Ascendant logistic function (\(k<0\)): \[g(x)=\frac{L_{2}}{1+ae^{-k(x-x_{0})}}.\] (13)  
These functions are bounded by two limits: \(L_{2}\) and \(L_{1}\). \(L_{2}\) corresponds to the lowest message generation rate (highest value) used to generate very low traffic. \(L_{1}\) corresponds to the highest message generation rate (lowest value) used to generate the highest network traffic. \(x-x_{0}\) is the flexible horizontal translation. No horizontal translation is considered: \(x_{0}=0\). \(k\) is the exponential growth rate.  
From 00:00 a.m. to 09:00 a.m., the descendant function defined in (12) needs to descend from \(L_{2}\) down to \(L_{1}\), i.e., \(f(0)=L_{2}\) and \(f(9)=L_{1}\). Both \(L_{2}\) and \(L_{1}\) limits are specified through the control configuration settings depending on the scenario. Hence, from (12), the only unknown variable (\(a\)) is isolated:  
\[a=\frac{(L_{2}-L_{1})}{L_{1}e^{\mathrm{i}9}}\.\]  
The ascendant logistic function in (13) follows the same process to ascend from \(L_{1}\) at the end of the working hours of the day (17:00 h) up to \(L_{2}\) at (00:00 h): \(g(17)=L_{1}\) and \(g(0)=L_{2}\).  
Finally, to build the ISTH function it is necessary to combine the descendant and ascendant logistic functions with a flat linear function that covers the eight working hours of the day (from 09:00 a.m. to 17:00 p.m.). During this time window, messages are generated at \(L_{1}\) rate:  
\[h(x)=\begin{cases}0\leq x<9:&f(x)\\ 9\leq x<17:&L1\\ 17\leq x<24:&g(x)\\ \end{cases}. \tag{14}\]