esa-sceva/satcom-chunk-collection huggingface dataset:
# Fault-Tolerant Tripod Gait Planning and Verification of a Hexopod Robot
## 3 Planning Method of F-TT Gait
### Phase Sequence Planning of F-TT Gait
#### 3.2.1 F-TT Gait in Leg 1 Fault State  
During the locomotion process of a hexapod robot, the foot lifts from the ground and takes a step forward in the transfer phase, and contacts the ground to support the body in the support phase. Based on the F-TT gait phase sequence planning equation, the F-TT gait phase sequence diagram of the hexapod robot in the case of a leg 1 fault is obtained, as shown in Figure 5. The shadow parts represent the support phase, and the blank parts represent the transfer phase.  
The movement process is divided into three steps, as shown in Figure 6. The dotted line in the figure indicates that the leg is in the transfer phase, the dot-dash line indicates a broken leg, the solid line indicates a normal leg in the support phase, the red point is the COG position of the robot, and the blue triangle indicates the stable area formed by the support legs. When the COG is in the support area, the hexapod can be regarded as stabile, otherwise it will tend to topple.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Symbol** & **Definition** \\ \hline \(\overline{L}_{f}\) & The fault leg \\ \(\overline{L}_{1}\) & The ipsilateral anterior leg of the fault leg \\ \(\overline{L}_{2}\) & The ipsilateral posterior leg of the fault leg \\ \(L_{1}\) & The contralateral anterior leg of the fault leg \\ \(L_{2}\) & The contralateral middle leg of the fault leg \\ \(L_{3}\) & The contralateral posterior leg of the fault leg \\ \hline \hline \end{tabular}
\end{table}
Table 2: Symbolic representation.  
Figure 5: Phase sequence table of F-TT gait in leg 1 fault state.  
In the first process, legs 4 and 6 are lifted up to swing forward, legs 2, 3, and 5 are in the support state to push the body forward, and the robot posture is transformed from Figure 6a,b.  
In the second step, legs 4 and 6 touch down, leg 2 is lifted up to swing forward, leg 5 is raised to swing forward at a slower speed, and legs 3, 4, and 6 support the body. Meanwhile, the robot is moved forward passively, and the attitude of hexapod changes from Figure 6b,c.  
In the third process, leg 2 touches down, leg 5 continues to transfer forward while leg 3 is lifted to swing forward, legs 2, 4, and 6 are supporting legs, pushing the robot body to move forward, and the attitude of robot changes from Figure 6c,d.  
After the above three processes, the robot completes a period of the F-TT gait movement under the fault condition of leg 1. In fact, the postures in Figure 6a,d are the same, because after a period of motion, the robot returns to the initial motion posture.
## 4 Case Studies
### Three-Dimensional Point Cloud of San Nicola in Montedoro Church
#### Merging of the Datasets (Point Clouds)  
Through the survey activity and post processing of the data obtained either with IBM or RBM methods, it was possible to obtain three datasets, as shown in Table 2.  
The several point clouds were merged in a single point cloud on the base of common point. This task was carried out in 3 DF Zephyr environment, which is a commercial photogrammetry software, developed and marketed by the Italian software house 3 DFLOW. A representation of the whole structure according to point cloud is shown in Figure 7.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Dataset** & **Method** & **Point Cloud** \\ \hline
1 & Outside (exterior facade) & Terrestrial & RBM & 4,871,426 \\
2 & Inside & Terrestrial & IMB & 7,047,448 \\
3 & Outside (top of the structure) & Aerial & IMB & 3,700,522 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Point Clouds Obtained in the Several Datasets.  
Figure 6: Orthogonal projection of the inside of the structure: orthophotos (in very high resolution) of the single facade and floor of the church.
## 2 Project Overview  
A bridge with four towers and five spans part of the cable-stayed bridge, the bridge span arrangement for 122.42 m + 230 m + 230 m + 206 m + 104.42 m = 892.84 m, the bridge elevation layout in Figure 1, and the main girder section structure in Figure 2 were established. The middle two main piers using pier, tower, girder solid-rigid system, the side of the main pier set support, and tower girder solid were established according to the six-lane highway design. The cable-free zone distribution of the main girder was length of the cable-free zone next to the tower \(l_{1}\) = 67.4 m, length of the cable-free zone in the span \(l_{2}\) = 18.6 m, and length of the cable-free zone of the side support \(l_{3}\) = 22.49 m and \(l_{4}\) = 16.49 m, respectively.  
The main girder was a prestressed concrete box of variable sections, with a single box and a three-chamber section in a full-width diagonal web. The top slab of the box girder was 39.5 m wide (including sidewalks on both sides), while the cantilever length was 7 m.  
Figure 1: Bridge layout diagram (unit: cm).  
Figure 2: Cross-sectional configuration of main girder (unit: cm). (**a**) Pier top section. (**b**) Mid-span section.  
The bottom slab thickness of the 230 m main span (1,2 spans in Figure 1) changed from 0.32 m in the middle of the span to 1.1 m in the No.0 block by a 1.8-degree parabola. The bottom slab thickness of the 206 m span (3 span in Figure 1) changed from 0.32 m to 0.9 m by 1.8-degree parabola.  
The bridge had four towers, with a single column reinforced concrete structure, octagonal cross-section, 37 m (1-3# towers), 31 m (4# towers) (including 3 m decorative section above the top of the cable), and the cross-section of the main tower was 5.5 m thick in the direction of the bridge, the range of the bottom was 10 m, the width ranged from 5.5 m to 6.5 m and the main tower was 3 m wide across the bridge.  
The stayed cable adopted a \(\varphi_{\mathrm{s}}\) 15.2 mm type epoxy-coated steel strand cable system with standard strength f\({}_{\mathrm{pk}}\) = 2000 MPa; the design adopted 49-\(\varphi_{\mathrm{s}}\) 15.2 and 55-\(\varphi_{\mathrm{s}}\) 15.2 two specifications, and the tensioning end was a group anchor system of steel strands. Stayed cables, which were single-span double-row cables, were arranged at the central divider of the main girder. Nineteen pairs of cables were set on both sides of towers from 1# to 3#, numbered S1 to S19 from the near tower end to the middle of the span, and 13 pairs of cables were set on both sides of the tower from 4#, numbered S1 to S13 from the near tower end to the middle of the span. A total of 140 cables were used for the whole bridge; the space of the cable on the girder was 4.0 m, while the space of the cable on the tower was 1.0 m. The cable was passed through a fillet tube-type cable saddle.
## 2 Vitamin D\({}_{3}\)  
The term \"vitamin D\" comprises a group of fat-soluble prohormones, of which vitamin D\({}_{2}\) (ergocalciferol) and vitamin D\({}_{3}\) (cholesterol) are the major inactive precursors [24]. In the human body, vitamin D\({}_{3}\) is naturally produced in the skin upon exposure to ultraviolet B radiation (280-320 nm). Chemically, this reaction includes photolyzation of 7-dehydrocholesterol into previtamin D\({}_{3}\), which is further converted into vitamin D\({}_{3}\)[25]. Additionally, vitamin D\({}_{3}\) can be acquired from some food or nutritional supplements [26]. Vitamin D\({}_{3}\) is transported to the liver, where it is metabolized into the most abundant circulating vitamin D\({}_{3}\) form called 25-hydroxyvitamin D\({}_{3}\) (25(OH)D\({}_{3}\)). This reaction is catalyzed by the cytochrome P450 family member CYP2R1, also known as 25-hydroxylase [27]. The 25(OH)D\({}_{3}\) is further converted by CYP27B1 (1\(\alpha\)-hydroxylase) into the biologically most active metabolite, 1\(\alpha\),25-dihydroxyvitamin D\({}_{3}\) (1,25(OH)\({}_{2}\)D\({}_{3}\)), which occurs predominantly in the kidneys [28]. The 1,25(OH)\({}_{2}\)D\({}_{3}\) exerts its multiple functions via binding to the intracellular vitamin D receptor (VDR), which is expressed in the majority of cell types and is responsible for the regulation of more than 200 genes [29]. After binding of 1,25(OH)\({}_{2}\)D\({}_{3}\), VDR forms a heterodimer with the retinoid x receptor. This complex binds to vitamin D-responsive elements, inducing the transcription of VDR-regulated genes [30]. Activation of VDR by 1,25(OH)\({}_{2}\)D\({}_{3}\) moreover up-regulates the expression of cytochrome P450 member CYP24A1, which catalyzes 24-hydroxylation of 1,25(OH)\({}_{2}\)D\({}_{3}\) and leads to its inactivation in the manner of a negative feedback loop [31]. Thus, activation of vitamin D\({}_{3}\) signaling activates not only a biological response, but also the mechanisms leading to vitamin D\({}_{3}\) inactivation.  
The vitamin D\({}_{3}\) status is usually assessed by measuring serum levels of 25(OH)D\({}_{3}\), whereby concentrations of 75-125 nmol/L are considered as optimal [32; 33]. The 25(OH)D\({}_{3}\) serum concentrations \(<\)30 nmol/L indicates a risk of vitamin D\({}_{3}\) deficiency and 25(OH)D\({}_{3}\)\(>\) 50 nmol/L are indicated to be sufficient [34]. In contrast, 1,25(OH)\({}_{2}\)D\({}_{3}\) levels are much lower, ranging between 0.035 and 0.2 nmol/L [35]. The prevalence of vitamin D\({}_{3}\) deficiency reaches a pandemic extent and can be observed in every age, gender, and ethnicity group, and is most commonly associated with inadequate exposure to sunlight [36].
## Materials and Methods
### Description of the Statistical Modeling Methodology  
The first modelling approach that we will utilize is linear regression, with several input predictors (radon and aggregated particle channels) and one target variable (small ion concentration). General form of linear regression equation with several input predictors and one target is given by  
\[y_{i}=a_{0}+a_{1}\cdot x_{i1}+\ldots+a_{p}\cdot x_{ip}+z_{i} \tag{7}\]  
where \(p\) is number of predictors, \(i\) is number of points we use for fitting model parameters \(a_{0},a_{1},\ldots a_{p}\), \(y_{i}\) is sample of target, \(x_{i1},x_{i2}\ldots x_{ip}\) are samples of predictors and \(z_{i}\) represents noise in \(i\)-th sample. Model parameters are determined by ordinary least squares i.e., by minimizing \(\sum z_{i}{}^{2}\)(summed over all samples). Input was transformed by subtracting median, since it is a more robust statistical measure than mean. Thus, the linear model built around Equation (6) can be considered as Taylor expansion around median. Note that particular linear scaling of input has no effect on R\({}^{2}\) score of the linear model, but serves to aid interpretation of coefficients in Equation (6).  
Second approach we utilize for statistical modeling is a simple feed-forward artificial neural network (ANN) with one hidden layer. Such shallow feed-forward ANNs were previously used successfully in a number of contexts, and recently for calibration of low-cost sensors [19]. Input was scaled using standard normalization scaling (transforming it to zero mean and unit standard deviation). The hidden layer uses rectified linear unit (ReLU) activation function, which is known to have certain benefits such as non-vanishing gradient compared to commonly used, sigmoid transfer function. Implementation of the network was done via software library scikit-learn [20]. Network optimization procedure is the default 'adam' solver used in multi-layer perceptron (MLP)-regressor in scikit-learn, and further details can be found in [21]. Class MLPregressor implements a multi-layer perceptron (MLP) with no activation function in the output layer. It uses the squared error as the loss function, and the output is a set of continuous values. Model selection criterion was based on R2 score, and two requirements: to have as high as possible R2 score, and also a balanced result on training and test set. These criterions were examined via parametric sweep of number of input PCA components and neurons in the hidden layer. Since it is not generally possible to prescribe physical meaning to model parameters in the ANN models we will only compare the predictive power of the models.
# Thermoelectricity Modeling with Cold Dipole Atoms in Aubry Phase of Optical Lattice
## 3 Results
### Figure of Merit  
To obtain the value of \(ZT\) we need to compute the conductivity of atoms, \(\sigma\), and their thermal conductivity, \(\kappa\). The value of \(\sigma\) is defined through the current \(J\) of atoms induced by a static force \(f_{dc}\) for a chain with periodic boundary conditions: \(j=v\sigma_{at}/2\pi\) where \(v_{at}\) is the average velocity of atoms and \(\sigma=j/f_{dc}\); for \(K=0\), we have \(\sigma=\sigma_{0}=\
u/(2\pi\eta)\). The heat flow \(J\) is induced by the temperature gradient due to the Fourier law with the thermal conductivity \(\kappa=J/(\partial T/\partial x)\). The heat flow is computed as it is described in [9,15] and in Appendix B. The values of \(\sigma\) and \(\kappa\) drop exponentially with the increase of \(K\) inside the Aubry phase at \(K>K_{c}\) (see Figures 13 and 14 in Appendix B). The computations performed for various chain lengths at fixed density confirm that the obtained values of \(S,\sigma,\kappa\) are independent of the chain length for \(T>K_{c}\) confirming that the results are obtained in the thermodynamic limit (see Figure 15 in Appendix C). For \(T\ll K_{c}\), the pinning is too strong and much larger computation times are needed for numerical simulations to reduce the fluctuations.  
We note that, for cold atoms in an optical lattice, a static force can be created by a modification of the lattice potential or by lattice acceleration. There is now a significant progress with the temperature control of cold ions and atoms (see, for example, [28, 29, 30]) and we expect that a generation of temperature gradients for measurements of \(\kappa\) and \(S\) can be realized experimentally.  
With the computed values of \(\sigma,\kappa,S\), we determine the figure of merit \(ZT\). Its dependence on \(K\) and \(T\) is shown in Figure 5 for \(\
u\approx 1.618\) and \(2.618\) (additional data are given in Figures 16 and 17 in Appendices D and E). For \(\
u\approx 1.618\), we obtain the maximal values \(ZT\approx 5\) being comparable with those of ion chain reported in [15]. However, for \(\
u\approx 2.618\), we find significantly larger maximal values with \(ZT\approx 25\). We attribute such large \(ZT\) values to the significantly more rapid spatial drop of dipole  
Figure 4: Dependence of the Seebeck coefficient \(S\) on the rescaled potential amplitude \(K/K_{c}\) (**left** column) and temperature \(T/K_{c}\) (**right** column) for \(N/L=34/21=\
u\approx 1.618\) (**top** row) and \(N/L=55/21=\
u\approx 2.618\) (**bottom** row). Left: color curves show the cases \(T/K_{c}=0.5,1,2,3,4\) for \(N/L=34/21\) and \(T/K_{c}=0.3,0.8,1.3,1.6,2.3\) for \(N/L=55/21\) (black, violet, blue, green, red from top to bottom curves). Right: \(K/K_{c}=0,2,4,6,8\) for \(N/L=34/21\) and \(N/L=55/21\) (black, violet, blue, green, red from bottom to top curves). Here, \(K_{c}=0.019\) for \(\
u=34/21\) and \(K_{c}=0.14\) for \(\
u=55/21\).  
interactions comparing to the Coulomb case, arguing that this produces a rapid decay of the heat conductivity with the increase of \(K>K_{c}\).
## 3 The Models
### Optimal Decisions in Policy \(T\)  
In this subsection, models are formulated and the optimal decision is derived in Policy T. A similar type of subsidy policy is discussed in the forward SC setting by several researchers [59]. For example, to strengthen sustainable innovation, $400 million was allotted to fund the R&D of energy technologies as a part of the American Recovery and Reinvestment Act of 2009 [48]. The demand function in this policy becomes \(D_{i}^{T}=a-p_{i}^{T}+\beta\theta_{i}^{T}\), and the corresponding profit functions of the manufacturer and retailer; and SW remains similar with previous subsections, and they are obtained as follows:  
\[\pi_{ri}^{T}(p_{i}^{T})=(p_{i}^{T}-w_{i}^{T})D_{i}^{T}, \tag{7}\]  
\[\pi_{mi}^{T}(w_{i}^{T},\theta_{i}^{T},\tau_{i}^{T})=(w_{i}^{T}-\lambda_{1} \theta_{i}^{T})D_{i}^{T}+X\tau_{i}^{T}D_{i}^{T}-\kappa\tau_{i}^{T}{}^{2}-(1-\mu_ {i}^{\[\pi_{gi}^{T}(\mu_{i}^{T})=\pi_{ri}^{T}+\pi_{mi}^{T}+\frac{{D_{f}^{T}}^{2}}{2}-\mu_{ i}^{T}\lambda_{2}{\theta_{i}^{T}}^{2}. \tag{9}\]  
Note that the manufacturer receives a subsidy on the total R&D investment, not on per unit product \(\lambda_{1}{\theta_{i}^{T}},i=m,r\). If \(\lambda_{1}=0\) and \(\mu_{i}^{T}=0\), the profit functions become similar to [PERSON] and [PERSON] [18], as well as [PERSON] and [PERSON] [19], where the authors examined the optimal decision for a forward SC setting where the government does not provide any subsidy. Similar to previous subsections, we derive the optimal decision for Policy T and omit the detailed derivation. Lemma 5,6 characterize the optimal decisions under the MS and RS games, respectively.  
Optimal decision in Scenario MT are obtained as follows:  
\(\mu_{m}^{T}=\frac{6\kappa}{N_{5}}\); \(w_{m}^{T}=\frac{N_{5}YZ\kappa+N_{4}(aN_{2}+c_{m}\kappa)\lambda_{2}}{\Delta_{3m }}\); \(p_{m}^{T}=  
**Lemma 8**.: _Optimal decision in the absence of a subsidy under the RS game is as follows: \(w_{r}^{N}=\frac{(a+c_{m})N_{1}\lambda_{2}+(YZ+c_{m}M_{2})\kappa}{2\Delta_{4r}}\); \(p_{r}^{N}=\frac{2 nN_{1}\lambda_{2}+(aM_{1}+YZ+2c_{m}\lambda_{2})\kappa}{2\Delta_ {4r}}\); \(\theta_{r}^{N}=\frac{(a-c_{m})Z\kappa}{2\Delta_{4r}}\); \(\tau_{r}^{N}=\frac{(a-c_{m})X\lambda_{2}}{2\Delta_{4r}}\); \(\pi_{mr}^{N}=\frac{(a-c_{m})^{2}\kappa\lambda_{2}}{4\Delta_{4r}}\); \(\pi_{rr}^{N}=\frac{(a-c_{m})^{2}\kappa\lambda_{2}}{2\Delta_{4r}^{2}}\); \(Q_{r}^{N}=\frac{(a-c_{m})\kappa\lambda_{2}}{\Delta_{4r}}\), where \(\Delta_{4r}=N_{2}\lambda_{2}-\kappa Z^{2}\)._  
Unlike optimal decisions in Policy C, the outcomes differ between the MS and RS game in the absence of a subsidy. In this regards, one can conclude that government can weaken the effect of power of CLSc members by implementing Policy C. We use results of above two lemmas as the benchmark to compare outcomes.
## 4 Results and Discussion
### Results of the Joint SOH and RUL Evaluation  
Both SOH and RUL can be used to evaluate the aging state of a battery. However, SOH is evaluated based on the current battery capacity state, while RUL is evaluated based on the number of cycles remaining in the battery. During battery use, the presence of capacity regeneration may cause the battery to have the same SOH in different cycling cycles. However, this does not mean that the battery has recovered to the previous degree of aging at the corresponding SOH, and therefore further judgment is required. Given the more obvious phenomenon of capacity regeneration in B0005, two points with the same SOH but different RUL in B0005 were selected for comparative analysis.  
As shown in Table 6, the remaining usable capacity of the B0005 battery is comparable between cycles 111 and 121, but the RUL of the two differ by 10 cycles. This indicates that although SOH can reflect the current capacity state of the battery, the degree of battery aging cannot be comprehensively and accurately assessed by SOH alone. The joint estimation  
Figure 8: Results of the RUL prediction: (**a**) B0005; (**b**) B0006; (**c**) Cell1; (**d**) Cell2.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Evaluation Metrics** & **B0005** & **B0006** & **Cell1** & **Cell2** \\ \hline MAE & 0.3600 & 0.7778 & 0.7692 & 0.7143 \\ RMSE & 0.6000 & 1.1055 & 1.1094 & 1.0000 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Results of RUL prediction error.  
method proposed in this paper can simultaneously predict the SOH and RUL of the battery at the current moment, and the prediction results are both well-fitted to the real values with high prediction accuracy and reliability. Combining SOH and RUL estimation results helps to assess battery health more comprehensively and accurately.
## 3 Challenges
### Power Consumption  
CR wireless sensors are power constraint devices with a limited energy source. In addition to the energy needed for spectrum sensing, channel negotiation, route discovery, transmission and reception of data packets, backoff, and data processing, CR wireless sensors also require energy for frequent spectrum handoff. A CR wireless sensor needs to sense the PUs' activities on the channel. Many applications require multiple antennas to monitor the PUs' activities, hence more energy is consumed.  
Although there are several proposals for energy harvesting [56; 57; 58], these techniques have their own limitations. In some application scenarios, energy harvesting or the replenishment of power resources is not possible. Such limitations are well studied in [59; 60; 61].  
In _ad hoc_ CRNs, power consumption is an important design factor, but not the primary consideration. However, in CR-WSNs, it is one of the main performance metrics that directly affect the network lifetime.
## 2 Materials and Methods
### Meta-Analysis  
While the datasets were initially normalized and preprocessed according to standard microarray protocols, we additionally applied log transformation to stabilize the variance and enhance cross-sample comparability. Since the datasets originated from different microarray platforms, batch effect correction was performed based on the Combat algorithm of the \"sva\" R package (v3.50.0) [22] to minimize platform-specific biases and ensure uniformity across studies. For meta-analysis, expression matrices were harmonized by mapping probe sets to their corresponding gene symbols; in cases where multiple probes mapped to the same gene, the mean expression value was used to generate a unified gene-level profile. Meta-analysis was conducted using the \"MetaVolcanR\" [23] package (v1.16.0) in R, employing [PERSON]'s \(p\)-value combination method to integrate statistical significance across studies. This approach increases analytical power by aggregating independent \(p\)-value, enabling robust identification of differentially expressed genes (DEGs) across heterogeneous datasets. Two thresholds were used for gene selection. First, genes that fulfilled the lenient criteria of an adjusted \(p\)-value \(<\) 0.05 and an absolute log\({}_{2}\) fold change greater \(\geq\) 0.85 were chosen for ML modeling. This lenient cutoff expands the feature pool by including moderately regulated genes, enabling models to learn subtler expression patterns and reducing overfitting in small-sample settings. Then we applied a stringent criterion of an adjusted \(p\)-value \(<\) 0.05 and an absolute log\({}_{2}\) fold change \(>\)1 to focus on the strongest signals, and the genes that fulfilled the condition were selected and further used to identify key genes from the ML analysis.
# High-Throughput Bit-Pattern Matching under Heavy Interference on FPGA
###### Abstract  
Bit-pattern matching is an important technological capability, used in many fields such as network intrusion detection (NID) and packet classification systems. Essentially, it involves the matching of an input bit pattern to a bit-pattern entry of a memory structure inside the system. Contemporary methods focus on the decomposition of the input bit pattern into smaller and more manageable parts, with the subsequent parallel processing of these elements. This fragmentation promotes the use of advanced pipeline techniques and hardware optimizations, enabling these methods to achieve very high throughputs and reasonable efficiency. However, the functionality of their respective circuits is limited to only performing pattern matching when there is no interference. In this article, we intend to present a circuit that performs pattern matching under heavy interference; instead of fragmentation, a more holistic approach will be adopted. To improve the throughput of the circuit, long bit sequences will be directly compared to many memory entries simultaneously. The minimization of hardware consumption and maximization of efficiency in these comparisons will be achieved with the use of novel hardware architecture that is based on pipelined adder trees and comparators. The platform of implementation is an FPGA (Field-Programmable Gate Array).  
bit-pattern matching; high interference; high throughput; VHDL; FPGA +
Footnote †: journal: Electronics Letters