esa-sceva/satcom-chunk-collection huggingface dataset:
# Observations on the Computation of Eigenvalue and Eigenvector Jacobians +
## 1 Introduction
Due to these observed deficiencies, the authors of this paper proposed a new method in [39] that did not involve the left eigenvector, did not require the simultaneous solution of both the eigenvector and eigenvalue derivatives, provided the full Jacobian matrices with respect to every element of the parent matrix, and provided a solution capable of handling any matrix with real or complex elements and real or complex eigenvalues and eigenvectors. This new method found the eigenvalue Jacobian by considering the characteristic equation and solved for the eigenvector Jacobian by using the results of the eigenvalue Jacobian along with the normalization condition for the eigenvector. While the method introduced in [39] addressed the deficiencies described above, it did produce some new issues--namely that the calculation of the eigenvalue Jacobian was computationally expensive. Additionally, the eigenvector Jacobian relied on the computation of the eigenvalue Jacobian, which could lead to numerical stability issues in large matrices (\(n>30\)). This paper introduces novel improvements to [39] that address both of these shortcomings. Specifically, the present work introduces a much simpler solution that addresses all of the original deficiencies in the eigenvalue and eigenvector derivative literature and also addresses the new issues associated with the technique in [39]. The simpler solution leads to an efficient, compact, and intuitive algorithm. The compact results presented for an arbitrary real or complex matrix (with real or complex eigenvalues and eigenvectors) are found to collapse even further for special cases and to reveal new insight into the structure of this fascinating problem. Thus, the novel approach for computing eigenvalue and eigenvector Jacobians introduced in this manuscript is exceedingly general, is applicable to a wide range of problems, and represents a significant improvement to earlier methods. This paper is organized as follows. First, a brief discussion on the analyticity of eigenvector normalizations is presented. Then, a review of the solution proposed in [39] is presented. Next, these results are modified to arrive at the new technique, which is efficient to compute and is valid for general complex matrices. This general result is then shown to collapse to known relations from the literature for the special cases of real symmetric matrices and real diagonal matrices. The new derivatives are then validated numerically through comparison with forward finite differencing. Finally, the execution time on a digital computer is compared for the technique proposed in [39] and for the new technique proposed this paper.
## 2 Electro-Optic Properties of Polymers
### Inducing of the Macroscopic Electro-Optic Properties
Nevertheless, at high temperatures, there is a competition between the alignment effect of the electric field and, on the other side, the thermal motion of the molecules. For high-\(T_{g}\) copolymers, poling samples with such techniques can lead to low efficiency. The advantage of photoassisted poling [31,32] is that this procedure can be executed also at room temperature. The sample is prepared as in the electrode poling, with the polymer sandwiched between two electrodes, but in this case at least one of the electrodes must be transparent. During poling, a voltage drop is applied between the two electrodes. Meanwhile, the sample is shined, from the transparent electrode side, by a light beam which wavelength is tuned in the region of the absorption resonance of the chromophore. In conjugated molecules with a N=N bridge along the principal axis, as DR1, the light, with a suitable polarization state, is absorbed by the chromophores and produces a trans-cis-trans isomerization (Figure 3). After several _trans-cis-trans_ cycles, a net centrosymmetric orientation of the dipoles perpendicular to the pump light field can be achieved. With additionally applied dc electric poling fields, the process permits non-centrosymmetric orientation of chromophores giving rise to a macroscopic electro-optic coefficient even at room temperature. Figure 3: Photoassisted poling. In all the three cases described above, the electro-optic coefficient induced by poling will relax on a long-time scale, because the chromophores' orientational mobility is not zero, even at room temperature.
## 4 Results and Discussions
### Experimental Settings
#### 4.1.2 Evaluation Metrics  
In evaluating clothing recommendation systems, selecting appropriate metrics is essential for a comprehensive performance assessment. This study employs NDCG@5, NDCG@10, Recall@5, Recall@10, and AUC (Area Under the Curve) to evaluate the model's performance from multiple perspectives.  
NDCG (Normalized Discounted Cumulative Gain) measures ranking quality by assessing the relevance and position of recommended clothing outfits [40]. The formula is as follows:  
\[\begin{split} DCG=\sum\limits_{i=1}^{k}\frac{rel_{i}}{log_{2}(i+1 )}\\ IDCG=\sum\limits_{i=1}^{k}\frac{rel_{i}^{ideal}}{log_{2}(i+1)}\\ nDCG=\frac{DCG}{IDCG}\end{split}\]  
Recall assesses coverage by measuring the proportion of user-preferred items correctly recommended [41]. The formula is as follows:  
\[recall=\frac{TP}{TP+FN}\]  
AUC evaluates classification performance by distinguishing between preferred and non-preferred items [42]. The AUC formula is as follows:  
\[AUC=\frac{\sum_{i=1}^{N_{+}}\sum_{j=1}^{N_{-}}\mathbb{I}(p_{i}>p_{j})}{N_{+} \cdot N_{-}}\]  
By integrating these metrics, this study provides a comprehensive evaluation of ranking quality, coverage, and classification performance, supporting the development of personalized clothing recommendation systems [43].
# Intelligent Communication in Wireless Sensor Networks
## 9 Conclusions  
In an environment where the SNs are close to each other, and where there is considerable redundancy in the sensed data, the sensor nodes generate a large amount of transmissions over the wireless canal, causing not only a loss of the wireless band pass-through, but also the consumption of a great deal of battery energy. Instead of traditional mode approaches like C/S and DF, where the sensor nodes send the raw detected data to the sink, we based our approach on a paradigm of MA and agents at each sensor to process the information (useful and non-redundant).  
In this work, we have proposed a strategy that collects and processes information. As we demonstrated in our previous work, sending multiple data in multiple short messages is more than sending them in a single message. Thus, owing to the highest network density and energy consumption at the communication level, instead of each sensor sending its data to the sink, the network has been broken down into a sector.  
Our method is based on two types of agents, especially fixed agents and mobile agents. Fixed or stationary agents consist of including an agent into each sensor, so each agent processes locally sensed information from its related SN and estimates its importance. The SN has been grouped into sectors, and an MA has been proposed at each group to concatenate the data processed by the SN, to send them in a single message by a well-defined strategy. This agent will circulate in the sector sensors in a precise itinerary, to collect the processed and captured data by the agents (node). Next, each SN cooperates with its neighboring sensors of the same sector to transmit the mobile agent according to a method based on several important parameters to decide the relevance of cooperation.  
Our technique limits the communication of non-useful information, and consequently decreases the amount of traffic and energy consumed. This means a gain in the amount of information and the overhead needed to send them. First, we have proved in previous work, by successive simulations that the division of a WSN into sectors presents better performances comparing to the approaches like C/S and DF, where we used the strategy of the agent.  
In this work, we have proven through successive simulations that our approach shows better performance compared to LCF and GCF approaches, in terms of power consumption and the packet delivery rate in the dense wireless sensor network. The reason for these results is that in our approach the MA guaranteed the collection of information in its itinerary. Source nodes that do not have enough energy are able to cooperate with their neighbors to transmit the to the mobile agent in a more efficient and safer itinerary. As future work, either we attempt to minimize the loss of packets, by partitioning the network in another way, or by adding other parameters to the cooperation formula of the mobile agent with the sensor nodes.  
The authors contributed equally to this work. This research received no external funding. The authors declare no conflict of interest.
# A Novel Disturbance Rejection Control of Roll Channel for Small Air-to-Surface Missiles
## 4 Numerical Simulation
### Distance Characteristic Analysis  
The influence of disturbance factors on rolling attitude control loop is analyzed.  
1. Steerage deviation: The steering effect is the control ability of the steering gear to the course in the missile guidance process. When the missile needs to change the direction at the same angle, the shorter the time required, the smaller the angle the steering gear turns, and the better the steering effect.
2. Centroid deviation: The center of mass deviation refers to the deviation between the actual center of mass and the theoretical center of mass of the missile, including the longitudinal deviation and the transverse deviation of the center of mass. Since the center of mass does not coincide with the center of reference moment, the coupling of aerodynamic force and attitude system will inevitably affect the attitude system.
3. Stuck steering gear: In addition to the uncertainty disturbance, the complex and harsh environment is very easy to cause the aging of the structure and some components; thus, causing the failure in the flight process. The common fault of the control surface is that the steering gear is stuck. When the control surface deflects to a certain angle and cannot continue to deflect, it is stuck. After the jamming fault occurs, the control surface will no longer change according to the signal given by the controller. At this time, the rudder can only give a constant signal.
4. Wind disturbance: Describe the original quantity of wind disturbance factors for wind speed, wind speed is a random quantity, the size and direction are highly, season, climate, location, and the influence of such factors as trimming wind is pointed out that it must be the height of the horizontal wind, usually arrived at a certain height, the wind speed with height increase abruptly, then suddenly decreases, and routine as \"wind shear\". Because the time for the aircraft to pass through the shear wind area is generally very short, the effect of the shear wind is similar to the impulse moment.
5. Drifts error: Because other information of the body comes from navigation and sensor measured data, there will be drifts error and other deviations in the process of long-term storage or multiple experiments, which will also affect the control of rolling accuracy.
# A Hierarchical Mapping System for Flat Identifier to Locator Resolution Based on Active Degree
## 4 Construction Method of the Top Layer Consisting of IMS
### Model Building
#### 4.1.3 Optimization Equation  
The goal of the decision problem is to calculate a strategy that maximizes the standard value of a certain optimization. The Markov Decision Process optimization standard used in the system construction process is the total expected reward value with a limited boundary. In the process of constructing the system, the total expected reward value is the sum of the gains from physical distance and logical delay. Given a strategy \(\pi\) and an initial state \(s\), the MDP optimization problem can be formulated as  
\[V_{\pi^{*}}=\max E\left\{\sum_{k=0}^{N_{\pi^{*}}(s)}r(s_{k},a(s_{k}))\right\} \tag{6}\]  
where \(\pi^{*}\) represents the optimal strategy. According to the characteristics of MDP, the optimized value function is unique and can be defined as the solution of Formula (7).  
\[V_{\pi^{*}}(s)=\max_{a\in A(s)}\left\{r(s,a)+\gamma\underset{s^{\prime}}{\sum} p(s^{\prime}|s,a)V^{*}(s^{\prime})\right\},\forall s\in S \tag{7}\]  
Formula (7) indicates that the total reward value of a certain state is the sum of the expected immediate reward and the discount reward that is expected to be obtained from the best action. Given the optimal value function, the optimal strategy can be expressed as  
\[\pi^{*}(s)=\arg\max_{a\in A(s)}\left\{r(s,a)+\gamma\underset{s^{\prime}}{\sum} p(s^{\prime}|s,a)V^{*}(s^{\prime})\right\} \tag{8}\]  
In the process of building the system, the MDP optimal policy \(\pi^{*}\) represents which node to choose as the next node's decision. According to the optimal strategy, we can construct a mapping analysis system which is optimal or suboptimal in the overall delay performance.
## 2 Data Preprocessing Method Based on _Robust STL-BTSF_  
For the icing meteorological time series, \(Y_{t}\) can be decomposed into a trend term component \(T_{t}\), a period term component \(S_{t}\), and a residual term \(R_{t}\), as shown in Equation (1):  
\[Y_{t}=T_{t}+S_{t}+R_{t},\quad t=1,2,\ldots,N \tag{1}\]  
_Robust STL_ is used to decompose the sequence through two processes: inner loop and outer loop, as shown in Figure 1.  
The internal circulation effectively fits the temporal trend component and computes the periodic component within the time series. Simultaneously, the external circulation fine-tunes the robustness weights. This dual-layered iterative process seamlessly interweaves, yielding a coherent and harmonious alignment while effectively smoothing out the ice-covered climate data characterized by seasonal cycles. Following the application of the _Robust STL_, an innovative iterative _BTSF_ mechanism is introduced. Its role is to explicitly capture the intricate interdependencies among a profusion of time-frequency pairs. The iterative refinement of representations unfolds in a sophisticated fusion-and-squeeze fashion, facilitated by Spectrum\(-\)to\(-\)Time (\(S2T\)) and Time\(-\)to\(-\)Spectrum (\(T2S\)) aggregation modules, as illustrated in Figure 2.  
Figure 1: _Robust STL._  
Figure 2: _Robust STL\(-\)BTSF._Specifically, each augmented time series \(x_{t}\) is first transformed to the spectral domain by a Fast Fourier Transform (FFT), obtaining spectral signal \(x_{s}\). Then \(x_{t}\) and \(x_{s}\) are delivered to two encoding networks for feature extraction. The process is shown in Equation (2):  
\[\begin{cases}F_{t}=Encoder_{A}(x_{t};\theta_{t})\\ F_{s}=Encoder_{B}(x_{s};\theta_{s})\end{cases} \tag{2}\]  
where \(F_{t}\) and \(F_{s}\) are temporal and spectral features; \(\theta_{t}\) and \(\theta_{s}\) are parameters of the encoding networks \(Encoder_{A}\) and \(Encoder_{B}\), respectively. Then, the approach builds an iterative bilinear fusion channel interaction between features \(F(i,j)\) of two domains and integrates them using \(BTSF\) as shown in Equation (3):  
\[F_{bilinear}=F_{t}^{T}\times F_{s}=\sum_{i=1}^{m}\sum_{j=1}^{n}F(i,j)=\sum_{i =1}^{m}\sum_{j=1}^{n}F_{t}(i)^{T}F_{s}(j) \tag{3}\]  
Then it encodes cross-domain affinities to adaptively refine the temporal and spectral features through an iterative procedure as Equation (4):  
\[\begin{cases}S2T:&F_{t}=BiCasual\{Conv(F_{bilinear})\}\\ T2S:&F_{s}=Conv\{BiCasual\{F_{bilinear}\}\}\end{cases} \tag{4}\]  
\(S2T\), \(T2S\), and bilinear fusion jointly form a loop block in a fuse-and-squeeze manner. The bilinear fusion jointly forms a loop block in a fuse-and-squeeze manner. After several loops of Equations (3) and (4), the final bilinear feature \(F_{bilinear}\) is obtained.
## 2 System Design
### Sensors
The working domain of the proposed sensor assembly for different pipe materials and dimensions was calculated using a MATLAB script based on Equation (1). Figure 7 shows the resultant force on the sensor for different pipe dimensions at 1 bar pressure for an MDPE (medium density polyethylene) and a cast iron pipe. As is shown in Figure 7 the resultant force on the sensor is higher for the MDPE pipe (Figure 3a) than the cast iron pipe (Figure 3b). It can also be seen that the force drops rapidly with increasing pipe wall thickness for the cast iron pipe as it becomes much stiffer. Hence, the model indicates that the proposed sensor is more suitable in the pressure monitoring of plastic pipes, however it can still be  
Figure 7: Resultant force on the sensor at 1 bar for (**a**) a medium density polyethylene (MDPE) pipe and (**b**) a cast iron pipe. used for metallic pipes of certain dimensions. One way of increasing the force measured by the FSR sensor is to increase the Young's modulus of the clip and make this much stiffer than the Young's modulus of the pipe itself. As demonstrated, the sensitivity of the FSR based pressure sensor depends on various factors such as pipe wall thickness, material properties and diameter. Therefore, the sensitivity of the pressure FSR based sensor should be calculated based on the application parameters. As an example, during validation tests mentioned earlier, the pressure sensor exhibited a sensitivity of 87.6 mV/bar for a 152 mm diameter PVC pipe, with a wall thickness of 10 mm. Temperature measurements of the pipe's surroundings and the pipe wall can potentially generate useful information in leak detection and its localisation. Water leaking from a pipe into the ground can potentially change the local temperature profile in the ground compared with measurements from other nodes further away from the leak. In addition, changes in water flow through a pipe can change the temperature of the pipe wall compared to the temperature of the ambient soil around the pipe as the water has different retention times in the pipe. Therefore, temperature data in conjunction with pressure data can potentially be used to detect and localise leaks and differentiate those from other pressure changes in the system. A commercial temperature sensor (LM35) was used to detect temperature fluctuations of a pipe in this research and assess the hypothesis. The temperature sensors used in this research are analogue sensors therefore they are connected to the node via the ADC channel of the node (similar to the FSR sensor). They are non-invasively mounted on the pipe wall via a clip. Moreover, during cold periods temperature information can be used to prevent failure of pipes due to low pipe wall temperature (water companies can use temperature data to manage the water temperature in the pipe and prevent pipe failure, _i.e._, they pass warm water into the pipes).
# Replacement of Natural Sand with Expanded Vermiculite in Fly Ash-Based Geopolymer Mortars
## 3 Results and Discussion
### Water Absorption  
The water absorption test results of the different mixes are presented in Figure 8. It is shown that, for a given FA and vermiculite content, the mixes prepared with a 10 molar NaOH solution developed higher water absorption compared with those prepared with a 15 molar NaOH solution. This observation matches with those of previous research on FA-based geopolymer concrete [37, 67], FA and ground granulated blast furnace slag-based geopolymer mortar [68] and geopolymers containing marble waste and zeolitic stuff [51]. This behavior was due to the lower porosities of the mixes having larger activator concentrations in comparison with those having lower activator concentrations [51]. The 10 molar NaOH mixes with 50% and 70% FA exhibited 4-14% and 10-25% higher water absorptions than the 15 molar NaOH mixes, respectively. It is also shown that, for a given vermiculite content and NaOH concentration, the mixes with larger FA contents had higher water absorption than those with smaller FA contents. This agrees with previous studies on concrete with recycled concrete fine aggregate [52] and gypsum composite [53, 54], and this is due to the increase in the microstructure porosity of mixes with increasing FA contents, leading to increased water absorption of the mixes [69]. At a 10 molar NaOH solution, 70% FA mixes containing 0%, 10% and 30% vermiculite exhibited 31%, 23% and 42% higher water absorption, respectively, and at a 15 molar NaOH solution, they exhibited 9%, 20% and 35% larger absorption in comparison with the companion 50% FA mixes, respectively.  
According to Figure 8, adding expanded vermiculite resulted in an increase in the water absorption of the mixes for a given FA content and NaOH concentration. As is also shown, the increased content of vermiculite caused an increase in the water absorption of the mixes. These findings are consistent with previous studies on conventional mortar [12, 25, 26, 62] and gypsum composites [58], and this happens because of the porous structure of the expanded vermiculite, as discussed in Section 3.2. At 50% FA, the mixes containing 15% and 30% vermiculite exhibited approximately 8% and 16% higher water absorption, respectively, and at 70% FA, they exhibited approximately 10% and 35% higher water absorption in comparison with the companion mixes without vermiculite, respectively.  
Figure 8: Water absorption of the geopolymer mortar at 28 days.
# Integrity Analysis for GPS-Based Navigation of UAVs in Urban Environment
## 3 Simulation
### Simulation Setup
Six test constellations with different DOP values, as shown in Table 3, were defined in the Spinent GSS7000 simulator, and navigation messages were generated for each of them. Since the DOP is affected by variation in the numbers of satellites available to the receiver, test constellations were limited to four visible satellites. Other satellites were disabled for each test to cancel the effect of the number of visible satellites. Positioning outputs of the selected software receiver were collected for 30 min (approximately 1800 measurements). Probability density function (pdf) and cumulative distribution function (cdf) of the positioning error were produced from these outputs. Thirty-minute simulation provides reliable test data for each case; at the same time, it allows one to prevent dramatic DOP changes and loss of satellite visibility because of the movement of the satellites. The errors were obtained through the comparison of positioning data from the receiver with the ground truth from the simulator. From the analysis of positioning accuracy results, also utilizing the sigma inflation technique for better error representation, the upper DOP limits were specified to reflect alert limits. Then, indirect protection levels are defined as HDOP and VDOP values that are ensuring the integrity risks remain below \(1-2\times 10^{-7}\)/h. Figure 7: Flowchart of the proposed approach. At the second simulation, the distributions of DOP coefficients and the number of visible satellites were obtained under different cut-off elevations. Simulation for each cut-off elevation was covering a twelve hour period from 12 am to 12 pm on August 30, 2019. The twelve-hour period was intentionally selected for this simulation to match the orbital period of GPS satellites (\(\sim\)11.967 h); this period should give a comprehensive overview of visible satellites' configurations. Simulated cut-off elevations for this simulation start at \(5^{\circ}\) and increase by \(5^{\circ}\) up to \(30^{\circ}\). Using these results the limiting values of cut-off elevation and number of visible satellites can be derived based on predefined HDOP and VDOP, which, in turn, correspond to positioning error boundaries obtained from the first simulation. Lastly, indirect protection levels (integrity zones) mapping is produced according to the results of the first and second simulations.