esa-sceva/satcom-chunk-collection huggingface dataset:
# SPEEDY Quantum Circuit for Grover's Algorithm
## 3 Quantum Circuit for SPEEDY
### S-Box (Sb)  
The SPEEDY S-box uses NAND and OAI gates best suited for ultra-low latency. Therefore, the operation of the S-box follows Equation (1), expressed in disjunctive normal form (DNF). However, DNF is inefficient in terms of resources in the quantum circuit. In quantum circuits, NAND and OAI operations must allocate as many qubits as the number of operations to store intermediate values. To solve this problem, we reduced the quantum resources by using Algebraic Normal Form (ANF), which is performed as XOR gates. ANF is expressed using a combination of XOR and AND. The equation of the S-box expressed as ANF can be found in detail in [21]. Algorithm 1 shows our S-box quantum circuit implemented using CNOT and multi-controlled X gates. Furthermore, we have schematically shown the operation of Algorithm 1 as a quantum circuit in Figure 6. Here, we reduce the quantum resource by omitting the extra qubits for intermediate values. Since the SPEEDY S-box uses a lot of multi-controlled X gates, the gate cost is the highest part of the overall operation. In the S-box, the results of inputs \(x_{0}\) to \(x_{5}\) are output in ancilla \(y_{0}\) to \(y_{5}\). At the input ancilla, qubit \(y\) should initially be set to zero, and at the end of the circuit, it stores the 6-bit result of the S-box. Input \(x\) is the result of ShiftColumn and is the target of the S-box operation. That is, the S-box execution result of x is stored in \(y\). Figure 6: Quantum circuit for S-box.
## 3 The Christoffel Equation and the Use of Slowness Curves
### Deriving the Expression for the Slowness Curves of an Isotropic Solid  
For an isotropic linear elastic solid, Equation (2) can be replaced with:  
\[\sigma_{ij}=\lambda\epsilon_{kk}\delta_{ij}+2\mu\epsilon_{ij} \tag{6}\]  
where \(\lambda\) and \(\mu\) are the Lame parameters and \(\delta\) is the Kronecker delta. As a side note, in addition to replacing Equation (2) with Equation (6), if Equation (4) is replaced with:  
\[u_{i}^{L}(x,t)=U_{o}xe^{i(-k_{x}x+\omega t)} \tag{7}\]  
or:  
\[u_{i}^{S}(x,t)=U_{o}ze^{i(-k_{x}x+\omega t)} \tag{8}\]  
then, the Christoffel equation can be used to derive the relationship between the Lame parameters, the longitudinal wave speed, \(c_{L}\), and the shear wave speed, \(c_{S}\):  
\[\lambda+2\mu=\rho c_{L}^{2} \tag{9}\]  
\[\mu=\rho c_{S}^{2} \tag{10}\]  
where \(\hat{x}\) and \(\hat{z}\) are the unit vectors along the \(x\)-axis and the \(z\)-axis. Using Equation (6), assuming \(k_{y}=k_{z}=0\) (i.e., wave propagation in the \(x\)-\(z\) plane), and dividing through by \(\omega^{2}\), Equation (5) can be rearranged into matrix form:  
\[Au_{i}=0 \tag{11}\]  
where:  
\[A=\left[\begin{array}{ccc}(\lambda+2\mu)c_{x}^{-2}+\mu c_{z}^{-2}-\rho&0&c_ {x}^{-1}c_{z}^{-1}(\lambda+\mu)\\ 0&\mu\left(c_{x}^{-2}+c_{z}^{-2}\right)-\rho&0\\ c_{x}^{-1}c_{z}^{-1}(\lambda+\mu)&0&\mu c_{x}^{-2}+(\lambda+2\mu)c_{z}^{-2}- \rho\end{array}\right] \tag{12}\]  
Equations (11) and (12) represent a system of linear homogeneous equations, where \(c_{x}^{-1}=k_{x}/\omega\) and \(c_{z}^{-1}=k_{z}/\omega\). The non-trivial solution to Equation (11) only exists if:  
\[\det(A)=0 \tag{13}\]  
Expanding Equation (13) based on Equation (12) results in:  
\[\left(\rho-(\lambda+2\mu)\left(c_{x}^{-2}+c_{z}^{-2}\right)\right)\left(\rho- \mu\left(c_{z}^{-2}+c_{x}^{-2}\right)\right)^{2}=0 \tag{14}\]  
The solutions to the characteristic equation (Equation (14)) are:  
\[c_{x}^{-2}+c_{z}^{-2}=\frac{\rho}{(\lambda+2\mu)} \tag{15}\]\[c_{x}^{-2}+c_{z}^{-2}=\frac{\rho}{\mu} \tag{16}\]  
If Equations (9) and (10) are considered, the right-hand side of Equations (15) and (16) become \(c_{L}^{-2}\) and \(c_{S}^{-2}\), respectively. These represent the slowness curve solutions to the Christoffel equation of an isotropic material. It should be noted that in Equation (14), the squared term represents the multiplicity in the shear wave's slowness curve solutions.
# Enhancing Reliability in Wind Turbine Power Curve Estimation
## 2 Materials and Methods
### Fultlander FL 2500/100 Power Curve Provided by the Manufacturer  
The Fuhrlander FL 2500/100 manufacturer characterizes the power generated with the wind speed of its WT model at increments of 0.5 m/s. One can find such data at [[https://www.thewindpower.net/turbine_en_154_fuhlander_fl-2500-100.php](https://www.thewindpower.net/turbine_en_154_fuhlander_fl-2500-100.php)]([https://www.thewindpower.net/turbine_en_154_fuhlander_fl-2500-100.php](https://www.thewindpower.net/turbine_en_154_fuhlander_fl-2500-100.php)) (accessed on 15 February 2024). Notice that the manufacturer provides a set of 50 pairs of wind-power points measured precisely following the recommendations of the measurement protocol, but does not provide the intermediate values. Indeed, carrying out these measurements is expensive. In the left graph of Figure 4, one can see those points represented by small black squares. So, the function on the left of Figure 4, shown in green, is made by connecting the points provided by the manufacturer with straight lines. The green function is, therefore, a function defined by parts. To carry out the filtering we propose, we need a continuous function defined for any wind value, not only for the values provided by the manufacturer. If the interest was a continuous function defined by parts, a better alternative solution could be to use the third-order splines which, in addition to providing continuity at the points, would give continuity for the derivatives in such points. In this case, to manipulate functions defined by such a large number of parts makes them few operational. In the representation on the right of Figure 4, in blue, we show the continuous function used to have a power value for the wind speeds between the points provided by the manufacturer from the sum of only seven sinusoidal functions, so it is very compact. Previously, to decide the used curve, we compared techniques such as polynomial approximations of different orders, developments in the Fourier series, and even third-order splines to make this approximation. We discarded the third-order splines because we did not want to handle a piecewise function with such many parts. Of the contrasted approximations, the decomposition into sinusoidal functions is the one that provides better results in terms of RMSE, better even than the Fourier series for the same number of terms. Using sinusoidal functions, we have verified that seven sinusoidal terms obtain a better approximation than nine. For the approximation of the curve, we use the following expression:  
\[P_{N}(w)=\sum_{i=1}^{N}A_{i}sin(a_{i}w+\phi_{i}). \tag{1}\]  
where \(P_{N}(w)\) provides the power at the wind speed \(w\). So, we particularize \(P_{N}(w)\) for \(N=7\). We represent the values of amplitudes \(A_{i}\), frequencies \(a_{i}\), and phases \(\phi_{i}\) in Table 1.  
Figure 3: Active power of each WT (wgdc_avg_TriGri_PwrAt) in different colors and a scaled version of their main axes rotation speed (wgen_avg_RtrSpd_IGR) in black, to verify the consistency o the SCADA data.
## 3 Observer Design  
The structure of the proposed interconnected observer is shown in Figure 2. It is a two-stage interconnected observer system, consisting of an actuator and a process state estimator. The actuator state estimator deals with estimating the states of the actuator subsystem, where the major challenge is that the output is inaccessible. Aiding the actuator, the process state estimator is a coordinator that extends the interconnection as an additional state of the process subsystem. This process state estimator generates an input sequence which is applied to the actuator subsystem. Then, the overall observer estimates the states and interconnections of the interconnected system by using the estimates of the two estimators.  
The main idea of the interconnected observer design is as follows. In the first aspect, the unknown interconnection is extended as new states of the process subsystem, where the expression can be achieved via derivatives of the output expression of the actuator subsystem, thus forming a new process subsystem. Then, for the state estimation of each subsystem of the interconnected system, the state estimation of one subsystem is realized by the state estimation of the other subsystem, and the global estimator is formed by the set of both observers. Specifically, it is assumed that an existing observer is already available for the actuator subsystem \(\sum_{\mathrm{a}}\), where the measured output is \(\mathrm{u}_{\mathrm{a}}\), while the observer is implemented using an estimate of \(\mathrm{u}_{\mathrm{a}}\), denoted by \(\mathrm{\widetilde{u}}_{\mathrm{a}}\). In order to obtain this estimate, the state space of the process subsystem \(\sum_{\mathrm{p}}\) is extended to include \(\mathrm{u}_{\mathrm{a}}\) as an additional state. By calculating the derivatives of the value \(\mathrm{u}_{\mathrm{a}}\) of the actuator subsystem, the expression of the time derivatives of \(\mathrm{u}_{\mathrm{a}}\) is obtained; it is a function of \(\mathrm{u}\), with derivatives of \(\mathrm{u}\) and \(\mathrm{x}_{\mathrm{a}}\). In summation, for the studied interconnected nonlinear systems, an interconnected observer design method is proposed by combining both actuator and process subsystem state estimators.  
Figure 2: Structure of the proposed interconnected observer.
_Energies_**2014**, \(7\), 2535-2557; doi:10.3390/en7042535  
_Article_  
**Energy-Efficient Power Allocation Using Probabilistic Interference Model for OFDM-Based Green Cognitive Radio Networks**  
**[PERSON] \({}^{1}\), [PERSON] \({}^{1,2}\), [PERSON] \({}^{1,*}\) and [PERSON] \({}^{1}\)**  
\({}^{1}\) Department of Electrical and Computer Engineering, Ryerson University, 350 Victoria Street,  
M5B 2K3, Toronto, Canada; E-Mails: [EMAIL_ADDRESS] (A.K.);  
[EMAIL_ADDRESS] (M.N.); [EMAIL_ADDRESS] (M.J.)  
\({}^{2}\) Department of Electrical Engineering, COMSATS Institute of IT, Wah Campus, Wah, Pakistan  
* Author to whom correspondence should be addressed; E-Mail: [EMAIL_ADDRESS];  
Tel.: +1-416-979-5000 (ext. 6079); Fax: +1-416-979-5280.  
_Received: 20 January 2014; in revised form: 8 April 2014 / Accepted: 9 April 2014 / Published: 22 April 2014_  
**Abstract:** We study the energy-efficient power allocation techniques for OFDM-based cognitive radio (CR) networks, where a CR transmitter is communicating with CR receivers on a channel borrowed from licensed primary users (PUs). Due to non-orthogonality of the transmitted signals in the adjacent bands, both the PU and the cognitive secondary user (SU) cause mutual-interference. We assume that the statistical channel state information between the cognitive transmitter and the primary receiver is known. The secondary transmitter maintains a specified statistical mutual-interference limits for all the PUs communicating in the adjacent channels. Our goal is to allocate subcarrier power for the SU so that the energy efficiency metric is optimized as well as the mutual-interference on all the active PU bands are below specified bounds. We show that the green power loading problem is a fractional programming problem. We use Charnes-Cooper transformation technique to obtain an equivalent concave optimization problem for what the solution can be readily obtained. We also propose iterative Dinkelbach method using parametric objective function for the fractional program. Numerical results are given to show the effect of different interference parameters, rate and power thresholds, and number of PUs.  
**Keywords:** green energy allocation; energy efficiency; cognitive radio
# A Blockchain Copyright Protection Model Based on Vector Map Unique Identification
## 2 Related Work
### Research on Methods for Constructing Vector Map Unique Identifiers  
Currently, methods for constructing unique feature identifiers in vector maps can be broadly categorized into approaches based on fragile hashing, approaches based on frequency domain coefficient analysis, approaches based on geometric feature extraction, and approaches based on topological feature extraction. The fragile hashing approach generates unique and irreversible identifiers for map features by utilizing hash functions, effectively verifying the integrity and authenticity of map data while preventing unauthorized modifications or tampering [14; 22]. This method is versatile as it does not rely on specific geometric or semantic features [15]. However, its robustness is limited, as even minor edits or geometric transformations in the data can invalidate the hash. In contrast, methods based on frequency domain coefficient analysis involve transforming vector maps into the frequency domain to extract features using techniques such as Fouriertransform and wavelet transform [23]. These methods excel at capturing periodicity and frequency-related characteristics in map data, making them particularly effective for handling periodic changes [24]. However, they exhibit limitations in sensitivity to non-periodic features and face high computational complexity when applied to large-scale or intricate vector maps [25].  
Geometric feature extraction, a fundamental technique, focuses on identifying and leveraging essential geometric attributes from spatial data, such as vertex counts [26], angles [27], and distances [28; 29]. This approach provides an intuitive representation of spatial information, effectively capturing the shape and directional characteristics of geographic entities. Geometric features exhibit strong robustness against transformations, such as scaling, rotation, and translation. Nevertheless, methods that rely solely on individual geometric features may be susceptible to specific attacks, such as feature distortion, which can compromise their robustness. Therefore, combining geometric features with other attributes could enhance the robustness of unique identifier construction. Topological feature extraction, on the other hand, emphasizes the relational properties between geographic entities, such as adjacency, intersection, and containment [30]. By constructing unique identifiers based on these topological relationships, this approach effectively captures the connectivity and relational structure of vector data [31]. Such methods are particularly resilient to data cropping and merging attacks and remain unaffected by format conversions [32].  
From the existing research, it is evident that geometric feature extraction and topological feature extraction possess distinct advantages in robustness, effectively addressing various attack patterns. Future research will likely focus on integrating these two approaches to construct unique identifiers for vector maps, aiming to achieve enhanced robustness and applicability in diverse scenarios.
# A Truly Second-Order and Unconditionally Stable Thermal Lattice Boltzmann Method
## 3 Unconditionally Stable Thermal Lattice Boltzmann Method (USTLBM)
### Computational Procedure  
The computational sequence of the present unconditionally stable thermal lattice Boltzmann method (USTLBM) can be summarized as follows:  
1. Specify the streaming distance \(\delta_{x}\) (\(\delta_{x}=\delta_{t}\)). Determine the single relaxation parameters \(\tau_{v}\) and \(\tau_{c}\) according to Equations (15) and (16).
2. Predictor step: Use Equations (39)-(41) to calculate the intermediate macroscopic properties \(\rho^{*}\), \(\mathbf{u}^{*}\) and \(e^{*}\).
3. Approximate the non-equilibrium distribution functions (\(f_{a}\,^{\mathit{n}\mathit{q}}\) and \(g_{a}\,^{\mathit{n}\mathit{q}}\)) by applying Equations (45) and (46).
4. Implement non-equilibrium extrapolation scheme to determine boundary values of the non-equilibrium distribution functions.
5. Corrector step: Evaluate density, velocity, and internal energy at the new time step from Equations (42)-(44). The external force term \(\mathbf{F}_{E}\) is calculated by Equation (47).
6. Implement physical boundary conditions for the macroscopic variables.  
Repeat Steps (2)-(6) until the computation converges or the prescribed maximum time step is reached.
## Abbreviations  
The following abbreviations are used in this manuscript:  
AERONET  Aerosol Robotic Network  
CLRM  Classical linear ratio model  
CRESDA  China Center for Resources Satellite Data and Application  
DBMA  Downscaling bathymetric mapping approach  
DBSCAN  Density-based spatial clustering of applications with noise  
DN  Digital number  
GEE  Google Earth Engine  
ICESat-2  Ice, Cloud, and Land Elevation Satellite-2  
LiDAR  Light detection and ranging  
NNDiffuse  Nearest-neighbor diffusion-based pan-sharpening  
QPRM  Quadratic polynomial ratio model  
RGB  Red-green-blue  
WDI  Water depth index
# Stereo-DIC Measurements of a Vibrating Bladed Disk: In-Depth Analysis of Full-Field Deformed Shapes
## 3 Digital Image Correlation Strategy  
Since low frame-rate cameras are adopted, the downsampling approach was implemented, and the displacement signal was required to be composed by only one harmonic. In this scenario, it was possible to set the camera sampling frequency \(f_{\rm s}\) to describe the chosen number of displacement periods (namely, \(n_{\rm p}\) ). This frequency was obtained with the following relation:  
\[f_{\rm s}=f_{\rm v}(n_{\rm s}/n_{\rm p})/(1+(n_{\rm s}/n_{\rm p})k) \tag{1}\]  
where \(f_{\rm v}\) is the actual signal frequency, \(n_{\rm s}\) is the number of frames to be acquired, and \(k\) is any integer number. In this work, \(n_{\rm p}=1\) was considered. The value of the integer \(k\) can be set arbitrarily high, knowing that higher values of \(k\) correspond to lower values of \(f_{\rm s}\). According to Equation (1), the downsampled acquired signal shows only one complete period of the vibration, thus allowing for the proper description of its amplitude. In order to achieve 3D measurements, the information from the two cameras was combined trough the stereo-triangulation method. To find the correspondence between left and right pixels (i.e., solving the stereo matching problem) a structured light approach was adopted exploiting the multimedia projector, to obtain an automate, robust and accurate solution. Once the correspondence between left and right pixels is known, as well as the stereo camera calibration parameters, it is possible to obtain 3D displacement maps starting from the 2D displacements measured by each camera. To speed up the process, the stereo matching problem was solved only once with the first couple of frames. The displacements were then tracked through Digital Image Correlation along the frame series on left and right cameras, without the need to repeat the stereo matching task. Additionally, a time domain filtering was applied to the raw camera frames to enhance the information related to the first harmonic of the time series (since \(n_{\rm p}=1\) was used). This approach proved to be effective in previous research, saving elaboration time without losing reconstruction accuracy and obtaining smooth displacement maps. A full description of the image processing was recently presented by the authors in [32], along with the method validation. Both data acquisition and elaboration were performed with MATLAB software. The open source 2D DIC script was downloaded from the Mathworks website [33] and used to compute the left and right camera displacements. Custom scripts were developed for the further tasks: solve the stereo matching problem through fringe projection, then implement the time domain filtering, and eventually triangulate the 2D displacements to obtain the 3D maps.  
Figure 1: Optical setup of the stereo-DIC measurement system.
## 4 Discussion
### Comparative Analysis of Forest NEE Flux Across Different Sites  
There was considerable variation in the forest CO\({}_{2}\) flux between years and sites [19]. Annual total carbon fluxes of pine forests were \(-756.84\), \(-834.73\), and \(-629.37\) g C m\({}^{-2}\) based on the eddy covariance system in 2015, 2016, and 2017 in Northeast China [8], indicating that boreal forests were robust carbon sinks in relative high latitude regions. A strong carbon sink of \(-660\) g C m\({}^{-2}\) was indicated with small interannual variability in Western Germany spruce forests from 2011 to 2017 [20]. Furthermore, net exchanges of taiga CO\({}_{2}\) between spruce and the atmosphere were \(-327\) and \(-174\) g C m\({}^{-2}\) in 2013 and 2016 in Russian [21]; spruce and pine forests NEE were reported as \(-262\) and \(-246\) g C m\({}^{-2}\) in Sweden [16]. However, arctic treelined forest was a weak sink of \(-37.73\), \(-85.36\), and \(-130.36\) g C m\({}^{-2}\) from 1997 to 1999 in Canada [19].  
In this study, we discovered that Qilian Mountain spruce forests were a robust carbon sink of approximately \(591.51\) (\(-617.96\) and \(-565.06\) in 2021 and 2022) g C m\({}^{-2}\) on the northwest Tibetan Plateau. This carbon sink capacity was higher than \(545.99\) g C m\({}^{-2}\) in an  
Figure 4: Driving factors on NEE and VPD and latent heat flux through structural equation model. Note: VPD, TEM, NEE, PRE, and LE are vapor pressure deficit, air temperature, net ecosystem exchange, precipitation, and latent heat flux. Solid arrow and dotted arrow stand for positive and negative direct effect coefficients. Effects coefficients of “nees”, “nees”, and “nees” were significant at \(p<0.001\), \(p<0.01\), and \(p<0.05\), respectively.  
annual study [10]. The carbon sink was a little lower than those in Northeast China and Western Germany, but it was significantly more robust than these in Russian, Sweden, and Canadian forests [6; 8]. In addition, the annual net ecosystem exchanges of alpine meadows and shrubs were \(-\)79.3 and \(-\)77.8 g C m\({}^{-2}\) in the same region of Qilian Mountain [22]. In conclusion, spruce forests were vital carbon sinks across the different ecosystems.  
Furthermore, data gaps were caused by equipment failures or environmental conditions, along with low-quality data spikes exceeding 1% of raw data in each 30 min period in Swedish forests [16]. Half-hour average CO\({}_{2}\) fluxes were computed after spike removal, two-dimensional coordinate rotation, time lag compensation, and Webb-Pearman-Leuning corrections for density fluctuations, with minimal data gaps contributing less than 3% to the net ecosystem exchange (NEE), making them negligible [22]. EddyPro software (version 7.0) was used to screen the 30 min flux data, eliminating values associated with instrumental errors, resulting in an average retention of 68% of the original data [8]. Similarly, our study also demonstrates high reliability, as data gaps were limited to a few winter days (less than 5%), a period when high-latitude northern forests act as minor carbon sources, having minimal impact on the annual carbon flux calculations.