esa-sceva/satcom-chunk-collection huggingface dataset:
# Motion Planning in UAV-Aided Data Collection with Dynamic Jamming
## 3 Global Replanning Based on CFC
### Convergence and Complexity Analysis  
Motion planning of a UAV in a data collection mission with dynamic jamming consists of five main parts: CFC construction, generation of the initial CFC path, generation of a safe path, SCA-based path optimization, and B-spline-based trajectory optimization. The convergence of the algorithm depends mainly on solving the P1 problem, which uses a method based on SCA. Section 2.1.2 in [30] presents an analysis of the convergence of SCA. We set \(\bar{x}\) as the limit point of the iterative result produced via Algorithm 4, which met and slater condition holds at the point \(\bar{x}\). Subsequently, \(\bar{x}\) becomes a KKT point of P1. First of all, problem P1 indicates that there exist \(5 MN\) obstacle avoidance constraints of the UAV, \(3N\) speed constraints, \(3N\) initial position constraints, and \(3N\) end position constraints, \(6N\) equation of state constraints, and a \(4 NK\) quality of communication link or the amount of collected data. Hence, the computational complexity is approximately \(O(R(5 MN+12N+4 NK))\), where \(R\) represents the number of iterations, \(M\) is the obstacle number, \(N\) is the number of time slots, and \(K\) is the SN number. In the construction process of the CFC, the goal is to acquire an effective communication area by applying geometric approaches. The complexity is only associated with the number of sensors and jammers. Thus, its complexity is \(O(KJ)\). In the generation of the CFC initial path and safe path, the calculation volume is also related to the number of obstacles and number of sensors. Thus, the assistance is also \(O(2 KM)\). Finally, the B-spline trajectory only computes a local number of control points. Because we can ignore the number of operations, the total complexity is \(O(R(5 MN+12N+4 NK)+2 KM+KJ+N)\). It is worth mentioning that motion planning in this paper is divided into global path planning and local trajectory optimization.The replanning time of global path planning is \(1\)Hz; that is, it is updated once every second.In the hardware environment mentioned in reference [12], when the main frequency is 3 GHz, for a sensor, when the number of obstacles is 5, the number of interference sources is 2, the number of discrete points is 100, and the calculation time of the algorithm is about 3 ms. Therefore, it can fully support 1 s update frequency of path planning.At the same time, the local trajectory optimization directly selects the path points and adopts the B-spline method for fitting, which takes almost no time and is consistent with the literature [27]. The planning time is about 0.8 ms, which can support the update frequency of 1000 Hz.
# Downlink Training Design for FDD Massive MIMO Systems in the Presence of Colored Noise
## 3 Problem Formulation of Channel Estimation with Colored Noise  
Since the performance of precoding scheme in the DL transmission depends on the accuracy of the CSI estimation, designing a feasible DTS for the channel estimation problem is crucial. This section presents the DL channel estimation process using DTS in an FDD MaMi system with a colored noise environment. In particular, the CSI estimation process is conditioned on the received training signal from a known DTS, which can be potentially designed based on the long-term statistical information, i.e., the channel and noise statistics. To obtain the CSI knowledge, the BS first sends a known DTS of length \(T_{\mathrm{s}}\) in symbol in a coherent process to all users across the cell during the training transmission. As such, the \(k\)-th user received training signal, \(\mathbf{y}_{k}\in\mathbb{C}^{T_{\mathrm{s}}}\) is expressed as  
\[\mathbf{y}_{k}=\mathbf{S}^{\mathrm{H}}\mathbf{h}_{k}+\mathbf{n}_{k}, \tag{8}\]  
where \(\mathbf{n}_{k}\) denotes the receiver colored noise, which exhibits a CSCG distribution with zero mean and covariance \(\mathbf{R}_{\mathrm{n}}\). The noise statistic is considered to be stationary i.e., varying slowly over time. The term \(\mathbf{S}\in\mathbb{C}^{N\times T_{\mathrm{s}}}\) is the common training matrix, which satisfies the energy constraint i.e., \(\mathrm{tr}\big{(}\mathbf{S}^{\mathrm{H}}\mathbf{S}\big{)}=\rho_{\mathrm{s}}T _{\mathrm{s}}\), where \(\rho_{\mathrm{s}}\) is the average transmitted power during the training-phase. This paper considers \(\rho_{\mathrm{s}}=\rho_{\mathrm{d}}\). However, non-uniform power allocations across the users and optimization with respect to different choices of \(\rho_{\mathrm{s}}\) and \(\rho_{\mathrm{d}}\) could be considered in future work. Furthermore, CSI feedback compression schemes [42; 43; 44; 45] or using signal compressing methods [46; 47] can also be considered in future work. To optimize the DL channel estimation performance, a Bayesian linear estimation based on MMSE filter is used [43; 48].
## 2 Materials and Methods
### Design of Tracking Differentiators  
#### 2.3.1 Problem Definition  
Let \(\chi_{1}(t)=\left(\chi_{11}(t),\chi_{12}(t)\right)^{\mathrm{T}}\) be a vector of reference influences for the output variables of System (2) \(y_{1}(t)=\left(y_{11}=x,y_{12}=y\right)^{\mathrm{T}}\), which determines the reference trajectory of the wheeled robot at a time interval \(t\in[t_{1};t_{2}]\); namely, it specifies in the stationary Cartesian coordinate system \(Oxy\) the track path \(\left(\chi_{11},\chi_{12}\right)\in R^{2}\), as well as the motion velocity \(\dot{\chi}_{1}(t)=\left(\dot{\chi}_{11}(t),\dot{\chi}_{12}(t)\right)^{ \mathrm{T}}\), acceleration \(\ddot{\chi}_{1}(t)=\left(\ddot{\chi}_{11}(t),\ddot{\chi}_{12}(t)\right)^{ \mathrm{T}}\), etc. The problems of starting, stopping the vehicle, and reaching a reference point of a reference trajectory with a reference orientation are not considered in this paper. It is assumed that the interval \([t_{1};t_{2}]\) corresponds to a continuous motion of the robot without stops, and the time of staying on the route \(t_{2}-t_{1}\) is acceptable. Under the made assumptions, we can introduce the notation \(t_{1}:=0,t_{2}:=T\), with the velocity vector \(v\), which coincides with the center line of the platform, directed tangentially to the reference trajectory. Under the assumptions made, we can introduce the notations \(t_{1}:=0,t_{2}:=T\), with \(y_{1}(0)\approx\chi_{1}(0)\), \(v(0)=\left(\dot{y}_{11}^{2}(0)+\dot{y}_{12}^{2}(0)\right)^{1/2}\
eq 0\), and the velocity vector \(\overrightarrow{v}(0)\), which coincides with the center line of the platform, directed tangentially to the reference trajectory.  
Let us highlight the main problems that need to be comprehensively considered when defining a trajectory for a single-wheeled robot:  
1. The path must be implementable by a mechanical plant, i.e., it must be sufficiently smooth and have continuous curvature, minimum requirements \[\chi_{1j}(t)\in C^{3},j=1,2.\] (15) In addition, the reference motion velocity and the acceleration and jerk must not exceed the robot's constraint values (4), i.e., \[\left\|\chi_{1}^{(i)}(t)\right\|\leq X_{i}<Y_{i},t\in[0;T],i=1,2,3.\] (16)
2. The path must be safe and not lead to collisions with fixed and dynamic obstacles. It is therefore necessary to consider the dimensions of the vehicle, the configuration of the polygon, etc.
3. A reference trajectory must satisfy various criteria, which, depending on the robot's mission and work scenario, are formulated as various terminal and optimization problems. For example, to reach the end point of the route in minimum time, to create the shortest route by avoiding reference points, to perform a task with minimum energy consumption, to solve pursuit or evasion problems, etc.  
In the following subsubsections of this section, the first problem is discussed in various formulations, and the second problem in terms of vehicle dimensions in planning a polygon with stationary obstacles. The third problem is beyond the framework of this research and is not considered here.
## 4 Experimental Analysis  
In this section, we describe results from running the progeny generation and haplotype computation methods on various simulated scenarios, as detailed below. We created a C++ code for the progeny generation and phenotype computation, using the haplotype segment representation described in the previous sections. As a comparison, we created a modified code to store each progeny as a vector of haplotype marker values. We performed a comparison of segments with standard simulation software and the vector based representation approach for progeny generation, as detailed in Section 4.1. From this analysis, it is clear that the segment and vector representations provide the best timing performance. Therefore, we perform an extensive comparison between them in terms of time and memory requirements for progeny generation and phenotype computation, as detailed in Section 4.2, to demonstrate that the segment representation is much more efficient than the vector representation. Furthermore, given the comparison in Table 1, the segment representation scales better than existing software for progeny generation with a large number of markers.  
\begin{table}
\begin{tabular}{l c c c c} \hline  & 1,000 markers & 10,000 markers & 100,000 markers & 1,000,000 markers \\ QGene & 1 & 3 & 14 & 174 \\ hypred & 0.031 & 0.331 & 4.139 & 40.388 \\ vector & 0.008 & 0.019 & 0.253 & 2.758 \\ segment & 0.017 & 0.011 & 0.006 & 0.010 \\ \hline \end{tabular}
\end{table}
Table 1: Comparison of timing on generating \(100\) backcrossed progeny (\((A\times B)\times B\)). Each entry corresponds to the execution time in seconds. Compared to existing methods QGene and hypred, a greater than ten-fold decrease by segments is shown in blue and a greater than hundred-fold decrease in green.
###### Abstract  
Land surface albedo is a key parameter in regulating surface radiation budgets. The gridded remote sensing albedo product often represents information concerning an area larger than the nominal spatial resolution because of the large viewing angles of the observations. It is essential to quantify the spatial representativeness of remote sensing products to better guide the sampling strategy in field experiments and match products from different sources. This study quantifies the spatial representativeness of the MODerate Resolution Image Spectroradiometer (MODIS) (collection V006) 500 m daily albedo product (MCD43A3) using the high-resolution product as intermediate data for different land cover types. A total of 1820 paired high-resolution Landsat Thematic Mapper (TM) and coarse-resolution (MODIS) albedo data from five land cover types were used. The TM albedo data was used as the spatial-complete high resolution data to evaluate the spatial representativeness of the MODIS albedo product. Semivarioograms were estimated from 30 m Landsat data at different spatial scales. Surface heterogeneity was evaluated with sill value and relative coefficient of variation. The 30 m Landsat albedo data was aggregated to 450 m-1800 m using two different methods and compared with MODIS albedo product. The spatial representativeness of MODIS albedo product was determined according to the surface heterogeneity and the consistency of MODIS data and the aggregated TM value. Results indicated that for evergreen broadleaf forests, deciduous broadleaf forests, open shrub lands, woody savannas and grasslands, the MODIS 500 m daily albedo product represents a spatial scale of approximately 630 m. For mixed forests and croplands, the representative spatial scale was approximately 690 m. The difference obtained was primarily because of the complexity of the landscape structure. For mixed forests and croplands, the structure of the landscape was relatively complex due to the presence of different forest and plant types in the pixel area, whereas the other landscape structures were considerably simpler.  
albedo; spatial representativeness; semivariogram; MODIS; Landsat 11 February 2019; Accepted: 28 February 2019; Published: 6 March 2019
## 3 Results and Discussion
### Pitch Spacing  
The SEY results and surface topography images of the laser processed Mo samples #3 (crimson curve) and #4 (pink curve) with the line hatched pattern are given in Figure 2, respectively. Samples #3 and #4 were processed by laser with the same laser parameters except for pitch spacing. The \(\delta_{\rm max}\) of samples #3 and #4 decreased from 1.46 to 0.96 and 0.95, comparing to the one of non-treated Mo sample. The values and shapes of the SEY curves for sample #3 with the pitch spacing of 15 \(\upmu\)m and #4 of 20 \(\upmu\)m were very similar. For samples #3 and #4, the SEYs of these two curves increased linearly at \(E_{\rm P}\leq 50\) eV and then flattened off at \(500\) eV \(\leq E_{\rm P}\leq 3000\) eV. It can be conjectured that the SEYs of samples #3 and #4 decreased slowly at \(E_{\rm P}\geq 3000\) eV.  
The surface topography images of samples #3 and #4 are shown in Figure 3(c1,c2,d1,d2), respectively. It was suggested that the surface topographies of samples #3 and #4 were very similar, all covered by sphere/columnar-like structures. More specifically, the surface topographies of these two samples at a view field of 5.54 \(\upmu\)m all looked like the flower of allium giganteum regel.
## 2 Methods
### Task Scheduling Model
#### 2.1.3 Multi-Objective Task Scheduling Based on Task Publisher
It is known that the power of hardware such as motherboards, processors, graphics cards, hard drives, memory, and monitors is the main factor affecting the energy consumption of the machine. The total power is the sum of the power of the above hardware. Therefore, when the task scheduling of energy consumption constraints is carried out in this paper, each node is used for a period of time. The energy consumption of running tasks is used as an index to evaluate the energy consumption of each execution node. The total energy consumption of node set \(P\) to complete task set \(T\) can be expressed as:  
\[SumEnergy=\sum_{j=1}^{m}\sum_{i=1}^{n}B[i][j]\times Energy[i][j] \tag{7}\]  
in which \(Energy[i][j]=Energy_{j}\times Time[i][j]\), and it represents energy consumption for the total execution time of task set \(T_{j}\) on node set \(P_{j}\). \(Energy_{j}\) represents the energy consumption on node \(P_{j}\) in unit time, that is, the total power of the node. \(Time[i][j]\) represents the task execution time of \(T_{j}\) on node \(P_{j}\). The task scheduling of energy consumption constraints aims to find a set of optimal task allocation schemes to minimize \(SumEnergy\). Since each node participating in the collection of public remote sensing data is obtained through crowdsourcing, the task initiator needs to pay remuneration to crowdsourcing users. According to the different abilities of each node to perform tasks, the unit task cost obtained is different. The total cost of the task publisher using node resource set \(P\) to complete a batch of tasks \(T\) can be expressed as:  
\[SumCost=\sum_{j=1}^{m}\sum_{i=1}^{n}B[i][j]\times Cost[i][j] \tag{8}\]  
In the equation above, \(Cost[i][j]=Cost_{j}\times count\) represents the total cost of executing task set \(T_{j}\) on node set \(P_{j}\), where \(Cost_{j}\) represents the unit task cost of node \(P_{j}\), and \(count\) represents the number of tasks allocated to node \(P_{j}\). The task scheduling of bundles aims to find a set of optimal task assignments that minimize \(SumCost\). From the task issuer's perspective, in this work, when carrying out multi-objective task scheduling of the time limit, energy consumption, and cost, the goal of task scheduling is to map the task set to the appropriate collection node so as to achieve the purpose of realizing the lowest energy consumption and lowest cost. Therefore, the task scheduling objective function can be expressed as:  
\[Min(SumTime,\ SumEnergy,\ SumCost) \tag{9}\]  
\(SumTime\) represents the total task execution time, \(SumEnergy\) represents the total energy consumption of the task, and \(SumCost\) indicates the total cost of the task.
# A Survey on Machine Learning Approaches for Personalized Coaching with Human Digital Twins
## 5 Principal Results
### Findings on Machine Learning
#### 5.1.2 Evaluation and Improvement of Performance  
Once implemented, the evaluation of algorithm performance can be divided into operational performance, measured in speed and training time, and analytical performance, whose metrics depend on the type of prediction. When the prediction can be classified as true or false, accuracy, precision, recall, specificity, F1-score, and Area Under the Curve are used. These metrics are calculated using the number of true and false positives and negatives [51,56]. When considering regression problems, metrics such as the fitting error, model accuracy error, root mean square error, variance interpretation rate, coefficient of determination, and Pearson correlation coefficient can be used.  
Although operational performance can be important, most evaluation efforts focus on analytical performance. There are several approaches to improving the performance of algorithms. The most common is to use training data or data acquired during an evaluation period to compare the performance of several algorithms. Generally, this requires a significant amount of processing time, research time, and effort. Therefore, these evaluations are conducted at a single point in time, typically at the application's conception. This approach is particularly useful when examining systems where behavior remains constant over time, meaning the correlation between data features and observed results remains unchanged. This approach can be used, for example, in developing models to predict the prevalence of influenza-like diseases [52], or in industrial situations when developing smart control applications.  
Another approach to improving analytical performance is to divide the problem to be solved horizontally or vertically. With horizontal division, we refer to the implementation of several layers of algorithms or parts thereof. Vertical division, similarly, refers to the parallel implementation of components. Deep learning, Ensemble learning, and Multi-Task learning are examples of this approach. The idea behind this approach is to simulate the human thinking process, which operates at multiple levels, rather than a simple one-layer algorithm. The aim is to be able to understand more complex problems, such as facial recognition or automated text generation [54]. This approach is also used in the analysis of time series for anomaly detection or forecasting of regression results [52,55].  
Hybrid learning is a similar approach to improving the performance of an ML solution. The main advantage of hybrid learning is that it combines the strengths of SL and USL. This allows for more accurate predictions and better generalization of the model; An example focused on mortality prediction in COVID-19 cases can be found in [59]. Additionally, hybrid learning can be utilized to reduce the amount of labeled data required for training, which is particularly beneficial when labeled data is scarce or expensive to obtain.
# Transformation of Trigonometric Functions into Hyperbolic Functions Based on Cable Statics
## 4 Application of Hyperbolic Function Transformation
### Trigonometry
#### 4.4.2 Law of Hyperbolic Cosines and Tangents  
The relationship between the sides of the triangle and the hyperbolic angles can be verified for a triangle with the following sides: \(a=9\), \(b=5\), and \(c=12\). In this section, the solution is obtained using the law of hyperbolic cosines and tangents. The angles are represented by \(\theta\), where the subscript \(h\) indicates that they are hyperbolic angles. The subscripts \(A\), \(B\), and \(C\) are added, corresponding to the vertices of the triangle. Therefore, the three hyperbolic angles are denoted as \(\theta_{hA}\), \(\theta_{hB}\), and \(\theta_{hC}\). The convention for the hyperbolic angles is as follows: \(\theta_{hA}=\angle CAB\), \(\theta_{hB}=\angle ABC\), and \(\theta_{hC}=\angle BCA\). The triangle is shown in Figure 13.  
The calculation of the hyperbolic angle \(A\) is performed:  
\[\theta_{hA}=\cosh^{-1}\frac{2 bc}{b^{2}+c^{2}-a^{2}}. \tag{81}\]  
The values are replaced, and the result is obtained:  
\[\theta_{hA}=\cosh^{-1}\frac{2\times 5\times 12}{5^{2}+12^{2}-9^{2}}=0.8289. \tag{82}\]  
The hyperbolic angle \(B\) is calculated:  
\[\theta_{hB}=\cosh^{-1}\frac{2 ac}{a^{2}+c^{2}-b^{2}}. \tag{83}\]  
The values are substituted, yielding the result:  
\[\theta_{hB}=\cosh^{-1}\frac{2\times 9\times 12}{9^{2}+12^{2}-5^{2}}=0.3974. \tag{84}\]  
The hyperbolic angle of vertex \(C\) is determined:  
\[\theta_{hC}=\cosh^{-1}\biggl{|}\frac{2 ab}{a^{2}+b^{2}-c^{2}}\biggr{|}. \tag{85}\]  
The values are inserted, and the result is obtained:  
\[\theta_{hC}=\cosh^{-1}\biggl{|}\frac{2\times 9\times 5}{9^{2}+5^{2}-12^{2}} \biggr{|}=1.508. \tag{86}\]  
Proportionalities are proven with the law of hyperbolic tangents. By calculating the sides with the value of the hyperbolic tangents, it can be verified that the proportionalities are maintained; therefore, the law of hyperbolic tangents can be used to determine the relationships between the sides of a triangle with its hyperbolic angles:  
\[\frac{a}{\tanh\theta_{hA}}=\frac{b}{\tanh\theta_{hB}}=\frac{c}{\tanh\theta_{hC }}. \tag{87}\]  
Figure 13: A triangle with the representation of hyperbolic angles.  
By substituting the values of the angles, the result is obtained:  
\[\frac{9}{\tanh 0.8289}=\frac{5}{\tanh 0.3974}=\frac{12}{\tanh 1.508}. \tag{88}\]  
The values allow the equality to be verified:  
\[13.238=13.238=13.238.\]
## 4 Experiments
### Training Details  
Following the settings in [PERSON] et al. [4], we conducted our experiments with transformer architecture using the fairseq toolkit [50], while our methods are model-agnostic and can be applied to other machine translation frameworks. Considering the diversity of the dataset volume, we used the transformer-small settings (512/1024, 4 heads, 6 layers) for IWSLT-8 experiments and the transformer-base settings (512/2048, 8 heads, 6 layers) for OPUS-100 experiments by default. To verify the effectiveness of our approaches with stronger modelling capacity, we further validated with the transformer-big (1024/4096, 16 heads, 6 layers) and some other hyperparameters. In the training process, we used the Adam optimizer with \(\beta_{1}=0.9\), \(\beta_{2}=0.98\), learning rate = \(7\times 10^{-4}\) and warm-up steps = 4000. Dropout was 0.1 in the transformer-small/base settings, and 0.3 in the transformer-big settings. Experiments were conducted using eight NVIDIA A100 GPUs for the OPUS-100 dataset and one GPU for the IWSLT-8 dataset, where the batch size of each GPU was set to 4096 tokens. We accumulate the gradient of parameters and update every two steps, with half-precision floating point (FP16) training.