esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Data and Methodology
### Methodology
#### 3.3.3 Local Models  
Global models provide a uniform estimate across the study area, ignoring potential local variations. However, cities typically have different functional features across regions, and the relationship between dependent and independent variables may change depending on spatial location. This phenomenon, known as spatial heterogeneity, contradicts the assumptions of global models. To more accurately capture these local features, we employ local regression models that allow parameters to vary spatially, thereby identifying spatial differences.  
To overcome the limitation of global models, where regression coefficients only represent the global average, the Geographic Weighted Regression (GWR) model assigns geographic weights (typically distance-based) to each observation [72]. This allows GWR to estimate local regression coefficients that reflect the characteristics of the specific observation and its neighboring areas, thus more precisely capturing the local distribution of variables [88]. The GWR takes the following form as in Equation (8):  
\[y(u,v)=\beta_{0}(u,v)+\sum_{k}\beta_{k}(u,v)x_{k}(u,v)+\varepsilon(u,v) \tag{8}\]  
where \(y(u,v)\) represents the dependent variable at the spherical coordinates \((u,v)\), \(\beta_{0}(u,v)\) serves as the constant term, \(x_{k}(u,v)\) denotes the explanatory variable \(k\) with \(\beta_{k}(u,v)\) as the corresponding local regression coefficient for each variable, and \(\varepsilon(u,v)\) the error terms at the point. The local coefficients \(\beta(u,v)\) are estimated by applying a weighted-least-squares procedure at each location as in Equation (9):  
\[\hat{\beta}(u,v)=\left[X(u,v)^{T}W(u,v)X(u,v)\right]^{-1}\!X(u,v)^{T}W(u,v)y \tag{9}\]  
where \(X(u,v)\) is the local design matrix with each row corresponding to an observation's explanatory variables, \(W(u,v)\) is a diagonal matrix containing spatial weights \(w^{h}(u,v)\) for each observation, and \(y\) is the vector of observed dependent variable values. This weighted-least-squares solution ensures that observations closer to the location \((u,v)\) have a higher influence on the parameter estimates, and the estimation begins with the minimization of the local weighted sum of squared residuals. The weights \(w^{h}(u,v)\) determine the influence of each observation on the local regression. Using an adaptive bisquare kernel, the weight for the \(h\)th observation is defined as in Equation (10):  
\[w^{h}(u,v)=\begin{cases}\left[1-\left(\frac{d((u,v),(u^{h},v^{h}))}{bw^{*}} \right)^{2}\right]^{2},&d((u,v),(u^{h},v^{h}))\leq bw^{*},\\ 0,&\text{otherwise}.\end{cases} \tag{10}\]  
where \(d((u,v),(u_{h},v_{h}))\) represents the distance between the target location \((u,v)\) and the \(h\)th observation's location \((u^{h},v^{h})\), and \(bw^{*}\) is the optimal bandwidth that controls the spatial extent over which data are used to estimate local parameters. The optimal bandwidth \(bw^{*}\) is typically determined by minimizing the corrected Akaike Information Criterion (AICc) using the Golden Section Search.
## 1 Introduction
On the other hand, for diffractive lenses of low f-number, the facets become denser at the boundary of the lens aperture so the resolution needed to encode them may exceed the Nyquist frequency of the pixels on the LC-SLM [7]. To avoid aliasing of the lens function at the periphery, the design focal length \(f\) of the diffractive lens must meet the condition \(f_{N}<f<50f_{N}\), where the inferior limit \(f_{N}\) is the Nyquist focal length defined in [7; 11]. In this paper, we present experimental results for multiorder diffractive lenses implemented in a parallel-aligned LCoS from Holoeye that reaches up to an \(8\pi\) phase modulation range in the green region of the visible spectrum. To this end, we thoroughly characterize the device to optimize the setting parameter selection so as to obtain various linear operating phase modulation ranges (\(\pi\), \(2\pi\), \(3\pi\), \(4\pi\), \(6\pi\), and \(8\pi\)) for an intermediate wavelength of the visible spectrum (\(\lambda_{\text{G}}=530\) nm). Multiorder diffractive lenses with multiwavelength jumps at the edge of their facets permit to implement, on the LCoS device, higher optical power lenses with their focal length below the Nyquist focal length. These multiorder diffractive lenses overcome the aliasing effects that encoding of common first-order diffractive lenses have. An extended characterization of the LCoS display is carried out by determining the experimental phase modulation not only for the design wavelength, \(\lambda_{\text{G}}=530\) nm, but also for two additional wavelengths at the extremes of the visible spectrum (\(\lambda_{\text{B}}=476\) nm and \(\lambda_{\text{R}}=647\) nm). Based on the measured chromatic performance of the LCoS screen, we design an achromatic diffractive lens that operates with higher diffraction orders. We take advantage of the larger phase depth modulation of recently available parallel-aligned LCoS modulators to implement these DOEs in such a device with the additional benefits of real-time reprogramming and no shadowing effects. Moreover, further studies of the optical properties of multiorder diffractive lenses can be conducted without the need for physically manufacturing them. We provide the experimental results for two multiorder lenses that overcome the issue of displaying a diffractive lens of optical power beyond the Nyquist interval and an achromatic diffractive lens. We compare their performances with that of a conventional, first-order diffractive lens.
## 6 Sine-Cosine Algorithm (SCA)  
The SCA initially creates a set of random population and allows them to move towards the best solution. In this algorithm, the optimization process contains two phases namely exploration and exploitation which lead to produce global (best) solution. The trigonometric functions namely sine sine and cosine functions are used to update the solutions in this algorithm. The position is updated as:  
\[V_{p}^{k+1} =V_{p}^{k}+\beta_{1}*sin(\beta_{2})*|\beta_{3}Q_{p}^{k}-V_{p}^{k}| \beta_{4} \geq 0.5 \tag{36}\] \[V_{p}^{k+1} =V_{p}^{k}+\beta_{1}*cos(\beta_{2})*|\beta_{3}Q_{p}^{k}-V_{p}^{k}| \beta_{4} <0.5 \tag{37}\]  
where \(V_{p}^{k+1}\) and \(V_{p}^{k}\) are old and updated positions of current solution at \(k\)-th iteration in \(p\)-th dimension. \(Q_{p}^{k}\) is the position of destination point in \(k\)-th dimension. The parameters \(\beta_{2}\), \(\beta_{3}\) and \(\beta_{4}\) are random numbers in the range of \([0,1]\). However, \(|.|\) represents the absolute value.  
The distinctive features of sine and cosine functions of (36) and (37) are shown in Figure 6. By varying the value of \(\beta_{1}\), the amplitude of sine and cosine functions can be altered which results in finding a solution outside the space between their corresponding boundaries. Figure 7 shows exploration and exploitation of search space with sine and cosine wave-forms lying between \([-2,2]\). In SCA algorithm, the balance exploration and exploitation can be achieved by changing \(\beta_{1}\) using  
\[\beta_{1}=a-k\frac{a}{T} \tag{38}\]  
where \(k\) is the current iteration, \(T\) is the total number of iterations and \(a\) is constant.
## Data Presentation  
The ionosphere responses to the geomagnetic storm were mainly analyzed by multi-GNSS data from MGEX [27] ([[ftp://cddis.gsfc.nasa.gov/pub/gps/data/campaign/mgex/daily/](ftp://cddis.gsfc.nasa.gov/pub/gps/data/campaign/mgex/daily/)]([ftp://cddis.gsfc.nasa.gov/pub/gps/data/campaign/mgex/daily/](ftp://cddis.gsfc.nasa.gov/pub/gps/data/campaign/mgex/daily/))), spanning from 22 June to 23 June at 2015. In comparison, the geomagnetic quiet days in June 2015 were also selected as a benchmark. The other supplementary data were divided by those subclasses: (1) data describing solar activities; mainly the solar wind speed measured by the Advanced Composition Explorer (ACE) in situ satellite; the interplanetary magnetic field (IMF) southward value, Bz, collected from an OMNI data website ([[https://omniweb.gsfc.nasa.gov/](https://omniweb.gsfc.nasa.gov/)]([https://omniweb.gsfc.nasa.gov/](https://omniweb.gsfc.nasa.gov/))). (2) Data describing the geomagnetic index. Kp, Dst, AE, AU, and AL were collected from the International Service of Geomagnetic Indices (ISGI: [[http://isgi.unistra.fr/](http://isgi.unistra.fr/)]([http://isgi.unistra.fr/](http://isgi.unistra.fr/))). Kp indicates the global daily geomagnetic perturbation; Dst indicates the intensity of the global geomagnetic disturbance; AE, as the initial of the auroral electrojet index, is used to measure the auroral zone magnetic activities produced by enhanced ionosphere currents though the auroral oval [28]; the AU and AL indexes serve as the upper/lower envelop of the H component disturbances observed in the auroral region; and AE represents the substitution between AU and AL (AE = AU \(-\) AL), demonstrating the eastward and westward electro-jets in the aurora region. (3) The ground geomagnetic data to measure the local geomagnetic field, provided by the geomagnetic world data center ([[http://www.wdc.bgs.ac.uk/catalog/master.html](http://www.wdc.bgs.ac.uk/catalog/master.html)]([http://www.wdc.bgs.ac.uk/catalog/master.html](http://www.wdc.bgs.ac.uk/catalog/master.html))). (4) The Global Ionosphere Maps (GIMs) as an IGS product ([[ftp://gssc.esa.int/gnss/products/ionex/](ftp://gssc.esa.int/gnss/products/ionex/)]([ftp://gssc.esa.int/gnss/products/ionex/](ftp://gssc.esa.int/gnss/products/ionex/))), to produce the global features of TEC and TEC variations. The observatories selected are demonstrated in Figure 1, where the captions GLON and GLAT indicate the geophysical longitude and geophysical latitude, the blue isoclines indicate the isoclines of geomagnetic latitudes.
# Functional Connectome Fingerprinting Through Tucker Tensor Decomposition
## 3 Results
### Between-Condition Fingerprinting
#### 3.5.1 Between-Condition Fingerprinting with Resting-State Full Scanning Length  
The between-condition matching rates when resting-state FCs are estimated using the time series of the full scanning length are shown in Figure 5. Matching rates ranged from 76% (Relational) to 91% (Language). In Figure 5, we observe a high sensitivity to brain parcellation rank, with 414 being the optimal rank. Comparatively, matching rate also benefits from a higher participant rank. However, the degree to which this occurs is task-dependent (i.e., a participant rank of 350 is nearly optimal for Emotion, but for Relational there is a clear benefit in going up to rank 426).  
In Figure 6, we observe a major increase in between-condition matching rates using Tucker decomposition when compared to original FCs. The procedure used for computing the identifiability matrix for original FCs in the between-condition setting was analogous to  
Figure 5: Parcellation rank and participant rank effects on between-condition matching rate for granularity of Schaefer parcellation 414. The fingerprinting framework was carried out by computing the ST-HOSVD of a tensor consisting of concatenated resting-state retest FCs (estimated using the entire scanning length of resting-state BOLD time series) from all participants. The obtained core tensor and brain parcellation factor matrix were then used to estimate the participants’ factor matrix of a tensor consisting of concatenated test FCs of fMRI tasks. A similar trend is observed in all plots, with parcellation ranks of 100 and 200 being insufficient to uncover fingerprints, while the small increase in parcellation rank from 400 to 414 results in a substantial improvement in matching rates.  
the one in the within-condition setting. Matching rate improvements obtained with Tucker ranged from 43% (Relational) to 72% (Language).
# Mars to Earth Data Downloading: A Directory Synchronization Approach
## 4 Comparison of Direct and DTNbox Approaches for Bulk Data Transfers  
Our aim is to demonstrate that in an interplanetary environment the DTNbox approach, based on directory synchronization, offers significant advantages in terms of flexibility with almost the same performance of direct data transfer in terms of delivery time. Let us compare the two approaches with reference to the space scenario described above.
## 2 Distribution Modeling Based on Sampling Theorem  
Digital samples are sampled from a continuous signal and can be used to characterize the original signal [27; 28; 29; 30]. This is a discretization process. When measuring pavement performance, road segment pavement performance is considered a continuous signal. The process of outputting the pavement performance index value of a unit road section after using the multi-purpose vehicle to measure the pavement performance can be regarded as sampling the pavement performance of a continuous section.  
The sampling frequency is the sampling speed, and the number of digital signal samples collected from the continuous signal per unit time, for example, 100 HZ represents 100 points sampled in 1 s. In the measurement of road performance indexes such as pavement condition index, the sampling frequency can be regarded as 1 point/km, that is, each unit road section outputs a measured value of road performance indexes.  
Through the sampling theorem, the discrete sequence can be reconstructed into the original continuous signal. Similarly, the discrete, limited, or missing measured data of road performance can be \"reconstructed\". Additionally, a continuous distribution function of road performance for the road section can be obtained by using an interpolation function.
# A Multi-Objective Approach for Optimizing Virtual Machine Placement Using ILP and Tabu Search
## 3 Proposed Methods
### Multi-Objective Tabu Search  
TS is a meta-heuristic optimization method specifically designed to address combinatorial problems. The algorithm systematically explores the solution space until it satisfies a predetermined stopping condition, such as reaching a specified number of iterations or achieving a target cost value. The process starts with an initial solution, which my be produced using another approach (e.g., randomly when no better alternative is available). This initial solution serves as the algorithm's starting point.  
At each iteration, TS generates a neighborhood of potential solutions by applying small changes to the current solution. The best candidate, evaluated using a predefined cost function, is then selected as the new current solution. To avoid revisiting solutions that have been explored, the algorithm employs a tabu list--a short-term memory structure that temporarily stores recently visited solutions. These solutions are excluded from selection for a specified number of iterations, helping the algorithm break free from cycles and local optima.  
Although TS does not guarantee convergence to a global optimum, it is widely regarded as a powerful and practical technique capable of finding high-quality solutions in many applications. For further details on TS, refer to [40, 41, 43].  
To design a TS algorithm, three problem-specific components must be defined: an initial solution, a cost function to evaluate the solutions produced by the algorithm, and a perturbation procedure to create new solutions from the current one.
# Online Control for Biped Robot with Incremental Learning Mechanism
## 2 System Description and Some Preliminaries
### Bipedal Locomotion Stability  
Zero-moment-point (ZMP) stability criterion is one of the most popular stability criteria, which is successfully applied in real biped robot platforms including ASIMO, NAO, and HRP. According to the definition of ZMP, zero-moment-point is the point on the sole, in which the horizontal component of the net moment caused by inertial and gravity forces is zero as shown in Figure 2.  
Hence, the following equation holds  
\[M_{x}=M_{y}=0 \tag{3}\]  
where \(M_{x}\) and \(M_{y}\) are the x-axis and y-axis moment of the inertial and gravity forces, respectively.  
As pointed out in [18; 19], ZMP stability criterion cannot guarantee the moment equilibrium in vertical plane, which neglects the influence caused by yaw moment on locomotion stability. Actually, the undesired yaw moment along the support leg would be generated by the motions of components of biped robot in different planes. Thus, we have  
\[M_{z}\leq M_{R} \tag{4}\]  
where \(M_{z}\) denotes yaw moment and \(M_{R}\) is the moment generated by the ground reaction force. Specially, yaw moment is defined as below  
\[M_{z}=\sum_{i=1}^{n}m_{i}(\mathbf{r}_{i}-\mathbf{r}_{zmp})\times(\tilde{ \mathbf{r}}_{i}+\mathbf{g}) \tag{5}\]  
Figure 2: Forces acting on the supporting foot.  
where \(m_{i}\) is the mass of the \(i\)th connective link; \(\mathbf{r}_{i}\) is the position vector of the center of the \(i\)th connective link; \(\mathbf{r}_{zmp}\) denotes ZMP position vector; \(\mathbf{g}=[0,0,g]\) is the gravitational acceleration vector; \(M_{z}\) is yaw moment.  
Moreover, ZMP coordinate \(\mathbf{r}_{zmp}=(x_{zmp},y_{zmp},0)\) has the following forms [27]:  
\[x_{zmp}=\frac{\sum\limits_{i=1}^{n}x_{i}(\bar{z}_{i}+g)m_{i}-\sum\limits_{i=1} ^{n}z_{i}m_{i}\bar{x}_{i}}{\sum\limits_{i=1}^{n}(\bar{z}_{i}+g)m_{i}} \tag{6}\]  
\[y_{zmp}=\frac{\sum\limits_{i=1}^{n}y_{i}(\bar{z}_{i}+g)m_{i}-\sum\limits_{i=1} ^{n}z_{i}m_{i}\bar{y}_{i}}{\sum\limits_{i=1}^{n}(\bar{z}_{i}+g)m_{i}} \tag{7}\]  
where \([x_{i},y_{i},z_{i}]\) is the position of the center of the \(i\)th link.  
To evaluate the locomotion stability in horizontal plane, ZMP stability margins introduced in [28] are adopted.  
\[J_{zmp}=\left\{\begin{array}{cl}\frac{1}{2}\frac{l_{zx}}{l_{cx}}+\frac{1}{2} \frac{l_{zy}}{d_{cy}}&\quad if\ \mathbf{r}_{zmp}\in\Omega_{zmp}\\ 0&\quad if\ \mathbf{r}_{zmp}\
otin\Omega_{zmp}\end{array}\right. \tag{8}\]  
where \(l_{zx}\) and \(l_{zy}\) denote the x-axis and y-axis distance between zero-moment-point and boundaries, respectively; \(l_{cx}\) and \(d_{cy}\) represent the x-axis and y-axis distance between the center of foot sole and boundaries, respectively; \(\Omega_{zmp}\) denotes ZMP boundaries.
# Modeling Shadow with Voxel-Based Trees for Sentinel-2 Reflectance Simulation in Tropical Rainforest
## 2 Methodology
### Forest Scene and Parameters  
Table 2 shows the parameter list of CSRS in reflectance simulation. Slope, TH, CC, CR, CL and DBH were obtained from the UAV-SfM [23]. Four patterns of virtual forests were created, along with four different canopy shapes. The Simple Model of the Atmospheric Radiative Transfer of Sunshine (SMARTS) code, version 2.9.5. [31], was employed to calculate the direct and diffuse irradiance. The spectral reflectance data of overstory and understory were selected among tree species which are found in Southeast Asia from ECOSTRESS Spectral Library (version 1.0) ([[https://speclib.jpl.nasa.gov](https://speclib.jpl.nasa.gov)]([https://speclib.jpl.nasa.gov](https://speclib.jpl.nasa.gov)), accessed on 15 May 2022). Reflectance data of _Prosopis articulata_ from tropical South Asia were used for overstory reflectance, and data from a grass species (_Avena fatua_) were used for forest floor reflectance. The wavelength interval was 1 nm. SZA was changed from 0\({}^{\circ}\) to 40\({}^{\circ}\) in a 10\({}^{\circ}\) increment, and SAA was set to 0\({}^{\circ}\).  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Slope (degree) & 0\({}^{\circ}\) \\ TH & X \(\sim\)N (16,2\({}^{2}\)) \\ Canopy shape & 4 pattern (shown in Figure 4) \\ CC (\%) & 80\% \\ CR (m) & X \(\sim\)N (7.3,1.7\({}^{2}\)) \\ CL (m) & Half of TH \\ DBH (m) & 0.3 \\ Overstory reflectance & _Prospis articulata_ \\ Understory reflectance & _Avena fatua_ \\ Sun Zenith Angle & 10\({}^{\circ}\), 20\({}^{\circ}\), 30\({}^{\circ}\), 40\({}^{\circ}\) \\ Sun Azimuth Angle & 0\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Characteristics of the forest scenes and optical parameters used in the simulation.  
Figure 5: Schematic illustration of the virtual forest scene.
# Empowering Tourism Accessibility: A Digital Revolution in Pieria, Greece
## 2 Materials and Methods  
### Study Area and Scope  
The Pieria region is a blend of natural beauty and mythological heritage. Located in Northern Greece (Figure 1), the area is renowned for its rich history, stunning landscapes, and cultural significance. Nestled between Mount Olympus and the Thermaic Gulf, it offers beautiful beaches, scenic hiking trails, and ancient archaeological sites, including the city of Dion.  
Figure 1: Study area.  
To promote the Pieria region as an \"Accessible Tourist Destination\", an online platform has been developed, aiming to enhance the accessibility of tourist destinations for individuals with special accessibility needs. The platform is specifically designed to address the needs of tourists with disabilities, elderly travelers, and others who require accessible routes and points of interest. The initiative is grounded in the fact that 71% of people with disabilities prioritize pre-trip planning based on the availability of detailed accessibility information. Given that inadequate accessibility features render tourist destinations essentially inaccessible, even if they are physically accessible, the platform plays a crucial role in communicating accessibility features effectively. The key aim of the platform is to collect, digitize, and present to public authorities and the wider public the status of accessibility infrastructure for routes and points of interest in the area. As part of the project, highly detailed on-site audits were realized in the Municipal District of Platamonas, which was selected as the testbed for validation of the service (Figure 1).