esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Method Development
### Modal Amplitudes in Space State  
Once the modal shapes are computed, the next step is to obtain a representation of the dynamics of the modal amplitudes \(T^{k}(t)\), for each \(\omega^{k}\), as function of applied loads. Let us consider the displacement model for the \(i\)-th beam element, with an uniform damping \(\gamma\) and load \(f(i,x_{i},t)\), where \(f(i,x_{i},t)\) denotes the force applied on element \(e_{i}\) at coordinate \(x_{i}\in[0,l_{i}]\) at time \(t\):  
\[E_{i}I_{i}\frac{\partial^{4}w_{i}(x_{i},t)}{\partial x_{i}^{4}}+\gamma\rho_{i} A_{i}\frac{\partial w_{i}(x_{i},t)}{\partial t}+\rho_{i}A_{i}\frac{\partial^{2}w_{i}(x,t)}{\partial t^{2}}=f(i,x_{i},t) \tag{23}\]  
Considering (4) and (10), it is obtained:  
\[\sum_{k=1}^{\infty}W_{i}^{k}(x)\left[E_{i}I_{i}(\beta_{i}^{k})^{4}\,T^{k}(t)+ \gamma\rho_{i}A_{i}\frac{dT^{k}(t)}{dt}+\rho_{i}A_{i}\frac{d^{2}T^{k}(t)}{dt^{ 2}}\right]=f(i,x_{i},t)\]  
Notice that modal amplitudes \(T^{k}(t)\) do not have subindex, since each \(k\)-th modal amplitude is shared for all the beam elements. Multiplying the previous equation by the \(j\)-th mode \(W_{i}^{j}(x)\) and considering the orthogonality property \(W_{i}^{k}(x_{i})W_{i}^{j}(x_{i})=0\) if \(k\
eq j\), the following is obtained:\[W_{i}^{j}(x_{i})^{2}\Big{[}E_{i}l_{i}(\beta_{i}^{j})^{4}\,T^{j}(t)+\gamma\rho_{i}A _{i}\frac{dT^{j}(t)}{dt}+\rho_{i}A_{i}\frac{d^{2}T^{j}(t)}{dt^{2}}\Big{]}=W_{i}^ {j}(x)f(i,x_{i},t)\]  
The previous expression is valid for any beam element \(e_{i}\in\{e_{1},e_{2},...,e_{n}\}\) at any local coordinate \(x_{i}\). Now, integrating over all the spatial domain (i.e., over \(x_{i}\in[0,l_{i}]\) for each \(e_{i}\)), it is obtained:  
\[\sum\limits_{i=1}^{n}\int\limits_{0}^{l_{i}}W_{i}^{j}(x)^{2}dx \bigg{[}E_{i}l_{i}(\beta_{i}^{j})^{4}\,T^{j}(t)+\gamma\rho_{i}A_{i}\frac{dT^{j }(t)}{dt}+\rho_{i}A_{i}\frac{d^{2}T^{j}(t)}{dt^{2}}\bigg{]}\] \[=\sum\limits_{i=1}^{n}\int\limits_{0}^{l_{i}}W_{i}^{j}(x)f(i,x_{i },t)dx\]  
Finally, using (6) and rearranging the terms, the following is obtained:  
\[(\omega^{j})^{2}\,T^{j}(t)+\gamma\frac{dT^{j}(t)}{dt}+\frac{d^{2}T^{j}(t)}{dt^ {2}}=\frac{\sum\limits_{i=1}^{n}\int\limits_{0}^{l_{i}}W_{i}^{j}(x)f(i,x_{i}, t)dx}{\sum\limits_{i=1}^{n}\rho_{i}A_{i}\int\limits_{0}^{l_{i}}W_{i}^{j}(x_{i})^{2}dx} \tag{24}\]  
Equation (24) is a second-order ordinary differential equation that describes the dynamics of the \(j\)-th modal amplitude. The right-hand side is a function of time, which can be determined for different load patterns. For instance, consider that three loads are applied simultaneously, denoted as \(f(i,x_{i},t)=f_{1}(i,x_{i},t)+f_{2}(i,x_{i},t)+f_{3}(i,x_{i},t)\), a punctual load applied on the beam element \(e_{i}\), at the position \(x_{l}=x_{a}\) (i.e., \(f_{1}(i,x_{i},t)=\delta_{l}(i)\delta(x_{a})f_{1}(t)\), where \(\delta_{l}(i)=1\) if \(i=l\), otherwise \(\delta_{l}(i)=0\)), an uniform load with time-varying magnitude on the beam \(e_{r}\) (i.e., \(f_{2}(i,x_{i},t)=\delta_{r}(i)f_{2}(t)\)), and an uniform constant load applied on all the beams, such as gravity (i.e., \(f_{3}(i,x_{i},t)=-gA_{i}\rho_{i}\)).
# Polynomial Cancellation Coded DFT-s-OFDM for Low-PAPR Uplink Signaling
## 4 Simulation and Discussion
### Peak-to-Average Power Ratio  
Figure 4 shows the PAPR CCDFs of PCC-DFT-s-OFDM at \(d=0\), \(1\), \(2\), \(3\) for PSK and QAM signals. The PAPR performance of both signals improves significantly by changing \(d=0\) to \(d=1\). In Figure 4a, the PAPR performances of all regular PSK signals appear similar for each given \(d\) and can be improved further as \(d\) increases. The PAPR performance curve of \(\pi/2\)-BPSK at \(d=1\) almost overlaps that of the regular PSKs at \(d=2\). This indicates that the PAPR performance for \(\pi/2\)-BPSK is greatly superior to that of regular PSK.  
However, Figure 4b shows that the improvements in the PAPR of QAM signals when \(d=3\) are lower than when \(d=2\). This indicates that the PAPR performance is not always improved as \(d\) increases. This result supports the inferences made in Section 3.1 that PCC-DFT-s-OFDM filters provide a minor reduction in PAPR performance for dynamic-envelope symbols because they are moving average-like.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Carrier Bandwidth & 10 MHz \\ Subcarrier Spacing & 15 kHz \\ Fast Fourier Transform (FFT) Size (\(N\)) & 1024 \\ Number of allocated subcarriers for User 1 (medium bandwidth) & 144 (12 PRBs) \\ Number of allocated subcarriers for User 2 (narrow bandwidth) & 48 (4 PRBs) \\ Cyclic prefix (CP) length 1 & 72 \\ Modulation & \(\pi/2\)-BPSK, QPSK, 16-QAM \\ \hline \hline \end{tabular}  
* Length of channel impulse response (\(L\)) is assumed to equal the CP length in the simulation.  
\end{table}
Table 2: System parameterization.  
Figure 4: \(Cont.\)
## 3 Epidemiology and Diagnosis
### Incidence Associated with Medication  
Antiresorptive and antiangiogenic medications, primarily used in the treatment of osteometabolic diseases and cancer, have been associated with the onset of MRONJ, a condition notably characterized by its unique localization to the maxillofacial region [1; 2]. A comprehensive review of the existing in vitro literature has shed light on the extensive research conducted on these medications, particularly nitrogen-containing BPs (N-BPs) like zoledronate (ZA) [18]. ZA, owing to its high potency, prolonged duration of action, and role as a first-line therapy for osteoporosis and adjunct therapy in cancer treatment, has been at the forefront of these investigations [42]. The review emphasizes the need for a nuanced understanding of these drugs' cellular impact, especially given their potent antiresorptive properties compared to non-nitrogen BPs, and the variations in potency among different N-BPs due to structural differences in their R2 side chains [18].  
The cytotoxic effects of these medications are multifaceted, affecting cellular functions such as proliferation, viability, migration, and inducing apoptosis in oral tissues in a dose- and time-dependent manner. Drugs like ZA not only impede cell proliferation and viability starting at 5 \(\mu\)M [43] but also interfere with key cellular pathways such as the mevalonate pathway, thereby affecting cell signaling and function [44]. Interestingly, the review reveals that antiresorptive and antiangiogenic drugs do not solely impact the bone tissue; they also exhibit genotoxic and cytotoxic effects on oral soft tissues, impairing cell proliferation, metabolism, and migration, thereby altering cell morphology and inducing apoptosis and inflammation [18]. This complex interplay of drug effects underscores the need for clinicians to approach treatment with these medications cautiously, especially considering the significant role of factors like transforming growth factor-\(\beta\) in wound healing and the implications of drug-induced reactive oxygen species production on cell growth and signaling pathways [45].  
Aside from antiresorptive (AR) therapy, various other medications have been identified as potential inducers of osteonecrosis of the jaw. These include angiogenesis inhibitors, immunosuppressive, anti-cancer drugs, and inhibitors of the mammalian target of rapamycin [19]. Notably, patients undergoing treatment with anti-cancer drugs or steroids have been found to exhibit a higher association with MRONJ [19]. Specifically, anti-cancer drugs like gemcitabine can contribute to the development of MRONJ due to their anti-angiogenic effects, which involve the inhibition of vascular endothelial growth factor [46]. Similarly, long-term use of corticosteroids may lead to MRONJ through a mechanism akin to that of gemcitabine, highlighting the complex interplay between various drug therapies and the risk of MRONJ [47].
## 4 Numerical Models for Phase Change Processes
### Velocity Transition Modeling
#### 4.2.2 Source Term Methods  
In the source term methods, a source term (S) is added to the conventional momentum equation (Equation (8)), assuming a high value when the material is solid ([PERSON] et al., 2018). Thus, to solve the momentum equation, the velocity is suppressed in the solid region to reach equilibrium with the high value of the source term. It is worth mentioning that discontinuities can be produced in the velocity field, similarly to SOM methods. Ramped source term methods have been developed in order to reduce problems with discontinuities, similarly to RSOM ([PERSON] et al., 2018). Thus, ramped methods are more suitable to be applied with E-TTM than conventional STM and SOM due to the smoother transition provided within the phase change interval ([PERSON] et al., 2018). Darcy STM proposed by [PERSON] and [PERSON] in work ([PERSON] and [PERSON], 2018) represents a variant of RSTM that is generally considered as a separated method, since it is largely used in studiesof phase change processes. In such a method, the source term is based on the Darcy law for the flow in porous media, according to the equation  
\[S=\frac{(1-\beta)^{2}}{(\beta^{3}-\varepsilon)}C\overrightarrow{V} \tag{9}\]  
where \(\varepsilon\) is a small value (\(\varepsilon=0.001\)) used to avoid dividing by zero and \(C\) is the mushy zone constant, which is adjusted according to the case analyzed. The value of \(C\) must be large enough to allow significant flow in the mushy region and to suppress the velocity in the solid phase [51].
## 3 Problem Description and Modeling
### Communication Model  
The communication latency is composed of two parts: propagation delay and transmission delay.  
In this paper, we use Ka-band for the links between the observation satellites and SEC satellites. Therefore, for task \(t_{i}\in T\), let \(r_{i,a}^{RISL}\) be the rate of radio intersatellite links (RISLs) from observation satellite \(i\) to access satellite \(a\), which can be obtained by [22]. Then, the latency for uploading \(t_{i}\) is  
\[\tau_{i,a}^{RISL}=\frac{l_{i,a}}{c}+\frac{\lambda_{i}}{r_{i,a}^{RISL}} \tag{1}\]  
where \(l_{i,a}\) is the distance of RISL, and \(c\) is the speed of light. Similarly, let \(r^{LISL}\) be the rate of LISLs among SEC satellites, which is a constant. The latency for transmitting \(t_{i}\) from \(a\) to another satellite \(s\) is  
\[\tau_{i,a,s}^{LISL}=\frac{\ell_{a,s}}{c}+\frac{\lambda_{i}}{r^{LISL}} \tag{2}\]  
where \(\ell_{a,s}\) represents the length of the shortest route from satellite \(a\) to \(s\).  
Thus, when task \(t_{i}\) is offloaded to satellite \(s\in S\), the communication latency of task \(t_{i}\) is given by  
\[\tau_{i,s}^{comm}=\tau_{i,a}^{RISL}+\tau_{i,a,s}^{LISL} \tag{3}\]  
Specially, if \(t_{i}\) is offloaded to access satellite \(a\), there is no LISL transmission, and we have \(\tau_{i,a}^{comm}=\tau_{i,a}^{RISL}\).
# Mdpj _sciences_
###### Abstract
Given the potential influence of the DMRN Protocol on future mobile network security standards, a comprehensive security analysis is crucial. Therefore, this paper aims to provide an in-depth and thorough examination of the DMRN Protocol's security properties using two rigorous formal verification techniques. By conducting a rigorous, multi-faceted, and systematic formal security analysis, we evaluate the protocol's resistance to known attacks, identify potential vulnerabilities, and consider possible attack scenarios. Through this analysis, we aim to contribute valuable insights that will guide future research directions in mobile network security protocols. Our work not only serves to validate the security claims of the DMRN Protocol but also provides a foundation for further improvements and adaptations as we progress toward 6G and beyond. Furthermore, as 6G networks are expected to integrate optical communication technologies for ultra-high-speed and low-latency data transmission, the security of optical networks becomes a critical concern [6]. Optical fiber communication systems, which form the backbone of modern telecommunications, offer immense bandwidth, energy efficiency, and immunity to electromagnetic interference. However, they are susceptible to unique security threats such as optical tapping, signal jamming, and side-channel attacks [7]. Given that quantum computing is expected to operate within such fiber-optic communication infrastructures, preparing for attacks leveraging quantum computing is of utmost importance. In this context, the integration of quantum-safe cryptographic techniques in security protocols is particularly relevant for securing optical networks, as quantum computers pose a significant threat to traditional encryption methods used in optical communications [4]. Consequently, the development of robust authentication and key agreement protocols that can protect both radio frequency and optical segments of 6G networks is crucial for ensuring end-to-end security in next-generation mobile communications, especially considering the increasing reliance on fiber-optic infrastructure for backhaul and fronthaul connections in 6G architectures [8].
## 4 Results and Discussion
### Incoming Velocity Considering Atmospheric Boundary Layer
Since the external air flow at the outlet of Model 1 mainly obstructs the internal air flow, the larger the wind profile index is, the lower the velocity of the external air flow at the outlet will be, the smaller the obstruction effect will be and the speed ratio will be improved. For Model 2, the external airflow at the system exit has a good gain effect on the overall performance after installing the windshield. Therefore, when the external velocity at the exit changes, the overall performance of the system degrades significantly. The average speed ratio decreases by 13.48, 18.13 and 21.71% compared with the uniform inflow. Even so, Model 2 performs better than Model 0 and Model 1. When the wind profile index is equal to 0.3, the improvement of Model 2 is about 4.57% and 17.08% compared with Model 0 and Model 1. By changing the outlet direction of the Invelox system and optimizing the flow field near the outlet, the aerodynamic performance of the machine has been greatly improved. Furthermore, when the Venturi tube is placed vertically, the wind turbine rotates in the direction of gravity, which will relieve the alternating stress caused by gravity during the rotation of the blade. Therefore, the improved Invelox wind turbine system has a certain application value.
# Reinforcement Learning for Mean-Field Game
## 4 Convergence Result
### Conditions for a Strategy to Be a MFE  
In this section, we will describe the conditions for an oblivious strategy \(\pi\) to be a MFE. Recall that, in Section 2.2, we defined two maps \(\mathcal{P}(\alpha)\) and \(\mathcal{D}(\pi,\alpha)\). For a given action coupled stochastic game, the map \(\mathcal{P}(\alpha)\) for a given population action distribution \(\alpha\) gives the set of the optimal oblivious strategies. Further, the map \(\mathcal{D}(\pi,\alpha)\) for a given population action distribution \(\alpha\) and oblivious strategy \(\pi\) gives the set of invariant population state distribution \(f\).  
We define the map \(\hat{\mathcal{D}}(\pi,f)\) which gives the induced population action distribution \(\alpha\) induced from the oblivious strategy \(\pi\) and the population state distribution \(f\). The following lemma gives the conditions that the stochastic game constitutes a mean-field equilibrium. These conditions have been provided in [11], and the reader is referred to [11] for further details and proof of this result.  
**Lemma 1** (Definition 7 [11]).: _An action coupled stochastic game with the strategy \(\pi\), population state distribution \(f\) and population action distribution \(\alpha\) constitute a mean-field equilibrium if \(\pi\in\mathcal{P}(\alpha),f\in\mathcal{D}(\pi,\alpha)\) and \(\alpha\in\hat{\mathcal{D}}(\pi,f)\)._
# Heterodyne Angle Deviation Interferometry in Vibration and Bubble Measurements
###### Abstract  
We proposed heterodyne angle deviation interferometry (HADI) for angle deviation measurements. The phase shift of an angular sensor (which can be a metal film or a surface plasmon resonance (SPR) prism) is proportional to the deviation angle of the test beam. The method has been demonstrated in bubble and speaker's vibration measurements in this paper. In the speaker's vibration measurement, the voltage from the phase channel of a lock-in amplifier includes the vibration level and frequency. In bubble measurement, we can count the number of bubbles passing through the cross section of the laser beam and measure the bubble size from the phase pulse signal.  
heterodyne interferometry; phase shift; vibration; bubble; deviation angle; spectrum Article
## 3 Proposed MISO Converter
### Basic Operating Principles
#### 3.2.11. State 11 [\(t_{10}\leq t\leq t_{11}\)]  
As shown in Figure 16, the switch \(S_{2a}\) is on, the switches \(S_{1a}\), \(S_{1b}\), and \(S_{2b}\) are off, the diodes \(D_{1}\) and \(D_{3}\) are on, and the diodes \(D_{2}\) and \(D_{4}\) are off. At the same time, the input voltage \(V_{d2}\) continues to excite the magnetizing inductance \(L_{m2}\) and the leakage inductance \(L_{lRp2}\); the magnetizing inductance \(L_{m1}\) and the leakage inductance \(L_{lRp1}\) continue to be demagnetized. As soon as \(S_{1a}\) is turned on, state 11 comes to an end.  
Figure 14. Circuit operation for state 9.  
Figure 15. Circuit operation of state 10.  
3.2.12. State 12 [\(t_{11}\leq t\leq t_{12}\)]  
As shown in Figure 17, the switches \(S_{1a}\) and \(S_{2a}\) are on, the switches \(S_{1b}\) and \(S_{2b}\) are off, the diode \(D_{1}\) is on, and the diodes \(D_{2}\), \(D_{3}\), and \(D_{4}\) are off. At the same time, the input voltages \(V_{d1}\) and \(V_{d2}\) excite the magnetizing inductances \(L_{m1}\) and \(L_{m2}\), respectively. The leakage inductances \(L_{lbs1}\) and \(L_{lbs2}\) charge the energy-transferring capacitor \(C_{2}\) to achieve leakage inductance energy recovery.
## 3 Preliminaries
### Problem Formulation  
**Definition 1** (City as Grid Zones).: _From the previous study, we divided the whole city into \(H\times W\) where the grid represents the region of the city. We can define the regions of the city as pairs \((h,w)\), where \(h^{th}\) denotes the rows for the region in the city and \(w^{th}\) the columns of the whole grid map._  
**Definition 2** (Historical Traffic, Trajectories).: _The historical traffic zones in the entire period \(t\), we split the traffic zones into \(N\) grid-based regions \(\{R_{1},R_{2},...,R_{N}\}\)._  
**Definition 3** (Inflow and Outflow Citywide Traffic).: _According to the previous study of research, we can determine the inflow and outflow of a region of the city, the total traffic of crowds that have entered the region of the city, and the total traffic of the crowd that left the region of the city. Let \(\Phi\) be the collection of the given crowd flow trajectories formally defined in the Equations (1) and (2) as:_  
\[\mathbb{R}^{t}_{in,h,w}=\sum_{T_{p}\in\phi}|\{n>1|kn-1\
otin R_{M}\text{and}|kn \in R_{M}| \tag{1}\]  
\[\mathbb{R}^{t}_{out,h,w}=\sum_{T_{p}\in\phi}|n\geq 1|kn\in R_{M}\text{and}|kn+1 \
otin R_{M}| \tag{2}\]  
In the above equations, \(T_{p}\colon k_{1}\to k_{2}\rightarrow\cdots k_{|T_{p}|}\) is the set of trajectories in \(\phi\), the geospatial coordinates are \(kn,kn\in R_{M}\) means the location \(kn\) is occupied within the region \(\mathbb{R}_{M}\) and vice versa \(|\cdot|\). According to the previous study, the inflow in the region of the cell and the outflow of the region of the cell in the time interval \(t\) of the traffic flow is \(\widehat{\mathbb{N}}^{t}\in\mathbb{R}^{h\times w\times k}\).  
**Problem 1**.: _The traffic flow is dynamic; traffic flow always considers the time-dependent data. The higher accuracy is achieved when we consider spatio-temporal data. The traffic flow tensors are \(\{\widehat{\mathbb{N}}^{i}|t=0,1,...,n-1\}\) in the grid region \(R\) and the previous time slot \(n-1\). The main objective in our problem statement is to predict the citywide traffic flow tensor \(\widehat{\mathbb{N}}^{n+1}\), where \(n+1\) is the next time slot. In Figure 1, we illustrate the problem statement._
## 4 Properties
### Biodegradation Properties
#### 4.2.1. Hydrolysis  
Esters, orthoesters, ethers, anhydrides, amides, carbamides (ureas), and ester amides (urethanes) are among the chemical bonds that can be cleaved by the action of water [87]. The bond kind determines also the hydrolysis rate. Anhydrides and orthoesters are the most susceptible to water degradation, followed by ester and amide linkages. It must be noted that hydrolysis rate can significantly vary depending on the conditions (e.g., temperature, pH, etc.), the presence of catalysts, and on the chemical neighborhood, since different functional groups may have an electronic and/or steric influence [88].  
Two main degradation routes can be highlighted: bulk and surface erosion, depending of the water diffusion rate. If water diffusion is faster than bond cleavage, the material will undergo bulk erosion, vice versa when the bond scission is faster than water diffusion, the polymer will be degraded by surface erosion.  
APs hydrolysis occurs in bulk and involves various steps, i.e., water absorption, ester bond scission, neutralization of carboxyl end groups at the surface, autocatalysis, and diffusion and solubilization of soluble oligomers [89] (Figure 3). In other words, water penetrates the polymer matrix (with or without swelling) and activates the polymer degradation, leading to the formation of oligomers and monomers [88] through the following reaction:  
\[\mathrm{RCOOR}^{1}+\mathrm{H_{2}O}\leftrightarrow\mathrm{RCOOH}+\mathrm{R^{1}OH} \tag{2}\]  
Hydrolysis is catalyzed by acid or basic compounds. Thus, RCOOH byproducts are capable of accelerating the hydrolysis by an autocatalytic process. Macroscopically, two steps can be highlighted. The first one results in random cleavage of the macromolecular chains together with molecular weight reduction, which leads to a worsening of the mechanical properties, while weight losses are negligible [53; 90]. In the second step, the molecular fragments are solubilized with concomitant mass loss [91].
## 4 Discussion  
### Study Results and Model Accuracy  
The RMSE was 3.820 degrees and the correlation coefficient r was 0.981. The RMSE was used as an index to evaluate the error between the actual angle of the lumbar oblique image and the estimated angle output by the angle estimation model created in this study. The smaller the RMSE, the better the accuracy of the created model. On the other hand, the correlation coefficient is a statistical index that numerically indicated the strength and direction of the relationship between two variables, with a value closer to 1 indicating a stronger correlation. However, we compared the accuracy with that of other studies in similar fields as a reference.