esa-sceva/satcom-chunk-collection huggingface dataset:
# Dynamic Optimization of Buckling Problems for Panel Structures with Stiffening Characteristics
## 3 Optimization of the Panel with Ribs and Frames
### Method of the MMCs
#### 3.2.1 Component Description  
In the MMC method, the topological configuration of the structure is determined by the topological description function (TDF) \(\mathcal{K}^{s}\)[19].  
\[\begin{cases}\mathcal{K}^{s}(\mathbf{x})>0,&\mathbf{x}\ \in\ \Omega^{s}\\ \mathcal{K}^{s}(\mathbf{x})=0,&\mathbf{x}\ \in\ \partial\Omega^{s}\\ \mathcal{K}^{s}(\mathbf{x})<0,&\mathbf{x}\ \in\ \mathbf{D}\backslash\Omega^{s}\end{cases} \tag{18}\]  
Here, \(\mathbf{D}\) is the design domain of topology optimization, and \(\Omega^{s}\) is the area occupied by the components. From Equation (16), it can be seen that the TDF value of the area occupied by the components is greater than zero, while the area without the components is less than zero. Specifically, the TDF value on the boundary of the components is equal to zero. \(\mathcal{K}^{s}\) can be calculated by the following equation:  
\[\mathcal{K}^{s}(\mathbf{x})=max(\mathcal{K}_{1},\mathcal{K}_{2},\dots\mathcal{K} _{n}) \tag{19}\]  
Here, \(\varphi_{i}\) is the TDF value of the \(i\)th component. The TDF value of the 2 nd-order variable-thickness component can be calculated by Equation (18) [24].  
\[\mathcal{K}_{i}(x,y)=1-\left(\frac{x^{\prime}}{L_{i}}\right)^{p}-\left(\frac{ y^{\prime}}{f(x^{\prime})}\right)^{p} \tag{20}\]  
where  
\[\begin{bmatrix}x^{\prime}\\ y^{\prime}\end{bmatrix}=\begin{bmatrix}cos\theta_{i}&sin\theta_{i}\\ -sin\theta_{i}&cos\theta_{i}\end{bmatrix}\begin{bmatrix}x-x_{0i}\\ y-y_{0i}\end{bmatrix} \tag{21}\]  
\[f\big{(}x^{\prime}\big{)}=\frac{t_{i}^{1}+t_{i}^{2}-2t_{i}^{3}}{2L_{i}^{2}} \big{(}x^{\prime}\big{)}^{2}+\frac{t_{i}^{2}-t_{i}^{1}}{2L_{i}}x^{\prime}+t_{i} ^{3} \tag{22}\]  
In Equation (18), \(p\) is a relatively large even number, and usually, \(p=6\). \(x_{0i}\), \(y_{0i}\), \(\theta_{i}\), \(L_{i}\), \(t_{i}^{1}\), \(t_{i}^{2}\) and \(t_{i}^{3}\) in Equations (19) and (20) are the variables of the \(i\)th component. Figure 11 illustrates the geometry definition of these variables.  
Figure 10: Component arrangement process. (i.e., different color represents different component).
# ZenoPS: A Distributed Learning System Integrating Communication Efficiency and Security
## 3 Preliminaries
### Design Objectives  
The goal of this research is to design an integrated system resolving the critical problems in distributed machine learning: heavy communication overhead, system security, and client privacy. To be more specific, we solve the distributed optimization problem defined in (1) based on the parameter server architecture with the following additional features.  
* **Communication reduction:** Optionally, the workers can reduce the communication overhead via both infrequent synchronization and message compression. To be more specific, every worker sends updates to the central server after every \(H\) local iterations, and compresses the update with the error reset technique and an arbitrary compressor \(\mathcal{C}\) that satisfies \(\delta\)-approximation: \(\|\mathcal{C}(v)-v\|^{2}\leq(1-\delta)\|v\|^{2},\forall v\in\mathbb{R}^{d}\), where \(v\) is the message vector sent to the server.
* **Synchronization mode:** The system supports both synchronous and asynchronous training.
* **Byzantine tolerance:** The system supports Byzantine tolerance on the server side, with multiple choices of defense methods, including a coordinate-wise trimmed mean and score-based validation approaches.
* **Local differential privacy:** We show the theoretical guarantees that the local differential privacy of releasing updates from the workers to the servers can be achieved by randomly replacing the correct values with arbitrary (Byzantine) values. To be more specific, we use the following definition for local differential privacy (LDP).  
**Definition 5** (\(\xi\)-Lpp [48]).: _Given the domain \(\mathcal{D}\) of the datasets and a query function query : \(\mathcal{D}\rightarrow\mathbb{R}^{d}\), a mechanism \(\mathcal{M}\) with domain \(\mathbb{R}^{d}\) is \(\xi\)-LDP if, for any \(\mathcal{S}\subseteq Range(\mathcal{M})\) and two arbitrary datasets \(D_{1},D_{2}\in\mathcal{D}\),_  
\[\Pr[\mathcal{M}(\textit{query}(D_{1}))\in\mathcal{S}]\leq\exp(\xi)\Pr[ \mathcal{M}(\textit{query}(D_{2}))\in\mathcal{S}].\]  
In the case of distributed SGD, the queries are the gradients or updates released by the workers. Note here that the result does not refer to differential privacy of the full training pipeline, but only to differential privacy of a single step with the following threat model: We assume that the attackers are the curious servers, from which we want to protect the workers and of which we want to avoid the servers recovering the private updates from individual workers. There are various mechanisms or protocols that achieve LDP [49; 50; 51; 52; 53; 54; 55; 56]. Furthermore, some LDP mechanisms can also provide \(\xi\)-DP guarantees [48; 57] for the full training process, at the expense of increased \(\xi\) for LDP.
## 3 Results and Discussion
### Diagnosis of the Potential Sources of PD across the Major Insulation  
Figure 9 shows the voltage waveforms of various cases investigated for diagnosis of PD sources across the major-insulation. The same normal case plot (Figure 5a), which was obtained under inter-turn free and discharge-free condition), was retained as the signature plot of the transformer and reproduced as Figure 9a. The tests for diagnosis of PD cases (PD-3-major and PD-4-major) were conducted by applying a switching impulse voltage of 37.5 kV and the corresponding waveforms were obtained and are shown in Figure 9b,c, respectively.  
The following observations were made from the Figure 9. Firstly, the presence of a potential PD source across major insulation of transformer winding is identifiable when the magnitude switching voltages are sufficient to incept the discharges: there were distortions like chopping in the waveform, pulses appearing over the base impulse waveform and the swings in response voltage (V2) to the opposite polarity. These changes were distinguishable from the changes due to the presence of internal shorts (Figure 5b,c). Sparks was also visible across the electrodes of PD model and confirmed the occurrence of PD.  
Secondly, the peak magnitude of the chopped waves is lower when the PD location (87.5% tapping) is near the impulsed end and comparatively higher for PD location (62.5% tapping) situated away from the impulsed end. The difference indicates that the identification of the occurrence of PD and its location is possible with the switching impulse voltage response.  
Figure 10 shows the EEV TF plots that were developed for analyzing the usefulness of IFRA approach in the diagnosis of the potential sources of PD across the major insulation.  
Figure 10 shows a comparison between the 'Normal case' and the two PD cases (PD-3-major and PD-4-major). The following observations were made in the transfer function plots as shown in  
Figure 8: Comparison of EEV TF plots for the diagnosis of sources of PDs across minor insulation: Normal case (vs) PD-1-minor (vs) PD-2-minor.  
Figure 9: Comparison of the input and response voltage waveforms for the diagnosis of sources of PDs across major insulation (**a**) Normal case (**b**) PD-3-major (**c**) PD-4-major.  
Figure 10. In the EEV TF plots of the PD cases, many changes were observed at different frequencies in the form of alterations in the magnitudes and locations of spikes (Ups & Dips). There was a disappearance of spikes and appearance new spikes. These changes demonstrate that the transfer function plots developed with IFRA can be useful in PD identification, location and discrimination.  
Though these differences are differently unique for different PD cases, they are available all along with the low-, mid-, and high-frequency ranges, and it should be carefully interpreted. Capitalizing such variations in TF plots for PD location and discrimination requires experience. Hence, further investigations with feature extraction through statistical parameter were carried out for the interpretation of experimental results.
###### Abstract  
After the construction of desert highway, the physiognomy changes caused by surface wind erosion and accumulation not only seriously threaten the stability of road structure, but also have a tremendous impact on the safety of the highway operation and the maintenance work on the highway. The purpose of this paper is to explore the change of sand sedimentation and the law of sand transport along the highway in the moving dune areas, and to clarify the change of sand flow and the formation mechanism of sand damage in the moving dune areas. Taking the test section of Wuhai-Maqin Expressway in the hinterland of Tengger Desert as the research object, the on-site observation of sand accumulation and the recording of wind information by small weather stations were adopted, supplemented by CFD numerical simulation method, in order to provide reference for the construction of sand control system in moving dune areas. The study results show that: (1) Dunes not only obstruct wind-drift sand but are also the sediment source condition for forming road sand. The windward dunes near the road are affected by wind and the deposition of sand will quickly bury the road in the strong wind season. (2) Compared with highways with flat terrain, the existence of dunes affects the flow field structure and the distribution of sand sedimentation on the highway, in which, under the influence of the gathering effect, the flow velocity reaches the maximum at the top of the dune and a large low-speed recirculation zone is formed on the lee side of the dune, easily causing sand accumulation. (3) Sediment accumulates at the windward side of the embankment or dune where sandy air current is easy to saturate. However, with the increase of wind speed, in addition to the grit carried by the sandy air current itself, new sand rolled up on the windward side of the dunes also form deposits on the road surface and the amount of sand-accumulation on highway surface and leeward side tends to increase. As a result, for the highway in drifting sand dunes areas, sediment prevention and control measures should be taken actively. It is necessary to remove sediment from the road in time and reduce the moving speed of sand dunes and the deposition range of wind-sand flow, ultimately for the purpose of reducing the damage wind-sand activity causes to the highway in desert.  
highway in desert; movement of sediment; sand-accumulation principle; numerical simulation; flow field structure +
Footnote †: journal: Applied Sciences
## 5 Analysis of the Dynamic Response Law of Non-Homogeneous Slopes
### Dynamic Response Analysis of Non-Homogeneous Slopes
#### 5.2.1 Variable Sensitivity Analysis
Overall, the effects of variations in cohesion conditions and variations in friction angle conditions on the dynamic response of the slope surface are relatively similar. As illustrated in Figures 16b and 17b, in the slope interior, when the shape parameter \(\beta=1\), the PGA values due to variations in the elastic modulus exhibit a pattern where they are smaller than the reference condition (no variations) between relative elevations of 0 to 0.3, but greater between relative elevations of 0.3 to 1.0, with an increased degree of fluctuation. Conversely, in the slope interior, when the shape parameter \(\beta=9\), the PGA values due to variations in the elastic modulus generally remain consistent with the reference condition. As shown in Figures 16b and 17b, in the slope interior, when the shape parameter \(\beta=1\), the variations in PGA due to changes in cohesion and friction angle are relatively consistent with the reference condition (no variations) between relative elevations of 0 to 0.5. However, between relative elevations of 0.5 to 1.0, the PGA is greater than the reference condition, with a significant difference in PGA values. Conversely, in the slope interior, when the shape parameter \(\beta=9\), the variations in PGA due to changes in cohesion and friction angle are relatively consistent with the reference condition. Hence, it is evident that the PGA of slope blasting-induced vibration waves is most sensitive to changes in the elastic modulus, followed by cohesion and friction angle, with sensitivity to the latter two being relatively similar. Between relative elevations of 0.5 to 1.0, the sensitivity of the PGA to changes in these parameters is greater than between relative elevations of 0 to 0.5. Moreover, as the shape parameter increases, the sensitivity of the PGA to changes in these parameters decreases.
## 4 Capacities of the Single Bucket Foundation  
Before establishing the bridge connecting the tetrapod bucket foundations and the single bucket foundation, the vertical, maximum horizontal and moment capacity factors of single bucket foundation should be expressed. In existing studies, due to the different locations of RP (e.g., on the mud's surface [20] or at the foundation base [21,44]) and different definitions of undrained soil shear strength at a specific depth (\(s_{\mathrm{u}0}\)) used to non-dimensionalize the capacity (e.g., at the foundation base [21] or at a specific depth below the foundation's base [8,20]), the capacities of the single bucket foundation can be expressed in different formulas. In addition, the formula for the maximum horizontal capacity of the single bucket foundation remains scarce. In this study, the location of RP was set at the center of the single bucket foundation on the mud's surface and \(s_{\mathrm{u}0}\) was adopted at depth \(D/4\) below the skirt tip level, as suggested by [PERSON] and [PERSON] [8]. Then, the vertical, maximum horizontal and moment capacity factors of single bucket foundations (\(N_{Vs}\), \(N_{Hmax,s}\) and \(N_{M,s}\)) with different foundation embedment depth ratios (\(d/D\)) and soil  
Figure 4: Comparisons between finite-element results in this study and (a) analytic solutions of a single bucket foundation or (b) model tests of the tetrapod bucket foundations.  
strength heterogeneity indices (\(\kappa\)) can be deduced from the finite-element results in this study, as expressed in Equations (3)-(5), respectively.  
\[N_{V,s}=a_{1}+b_{1}e^{c_{1}\kappa} \tag{3}\]  
where \(a_{1}=12.8-9.14\times 0.32^{d/D}\), \(b_{1}=2.18+0.27\times 4.05^{d/D}\), \(c_{1}=-0.83+0.83\times 0.24^{d/D}\), \(0.25\leq d/D\leq 1.0\), \(0\leq\kappa\leq\)20;  
\[N_{H\mathrm{max},s}=a_{2}+b_{2}e^{c_{2}\kappa} \tag{4}\]  
where \(a_{2}=-15.2+15.38\times 1.35^{d/D}\), \(b_{2}=-7.24+7.94\times 1.74^{d/D}\), \(c_{2}=-1.54+1.31\times 0.55^{d/D}\), \(0.25\leq d/D\leq 1.0\), \(0\leq\kappa\leq\)20;  
\[N_{M,s}=a_{3}+b_{3}e^{c_{3}\kappa} \tag{5}\]  
where \(a_{3}=-0.68+0.9\times 2.75^{d/D}\), \(b_{3}=0.21+0.23\times 6.98^{d/D}\), \(c_{3}=-0.09-0.67d/D\), \(0.25\leq d/D\leq 1.0\), \(0\leq\kappa\leq\)20.  
The good agreement between the finite-element results and the fitted curves plotted according to Equations (3)-(5), as shown in Figure 5, validates the fact that the formulas established in this study are suitable to evaluate the capacity factors of the single bucket foundation.
## 2 Materials and Methods
### Confocal Microscopy for Detecting NRF2 Expression in DPCs  
The DPCs were seeded at a density of 4 \(\times\) 10\({}^{4}\) cells per well in a slide chamber and then treated with essential oils for 24 h. Following washing with PBS, the cells were fixed with 4% paraformaldehydeheyde in PBS for 10 min, then permeabilized with PBS containing 0.5% TritonX-100 (PBS-T) for 15 min. An anti-NRF2 antibody (sc-722, 1:100; Santa Cruz Biotechnology, Dallas, TX, USA) was added to the cells and incubated for 1 h in PBS-T containing 1% bovine serum albumin, followed by overnight incubation at 4 \({}^{\circ}\)C with the Alexa Fluor 488 goat anti-rabbit IgG (A11034, H + L, 1:500; Invitrogen, Carlsbad, CA, USA). Cell staining was visualized by confocal microscopy with a 20\(\times\) objective on a laser scanning microscope (LSM510; Carl Zeiss, Jena, Germany) and analyzed using LSM 5 browser imaging software [29].  
Reverse Transcriptase-Polymerase Chain Reaction (RT-PCR) for NRF2, Phase II Enzymes Genes, and the Hair Growth Factors Genes VEGF and IGF1 in DPCs  
Total RNA was extracted with an RNeasy mini kit (Qiagen, Fremont, CA, USA), and 1 mg of total RNA was reverse-transcribed with an Omniscript RT kit (Qiagen). RT-PCR was performed with the primers described in Table 1 using a HiPi Plus 5\(\times\) PCR Premix (ELPIS, Daejeon, Republic of Korea) [29]. The PCR products were analyzed in 1.5% agarose gels. This was followed by staining with Sybr Safe DNA gel stain buffer (Invitrogen, Carlsbad, CA, USA). For quantification, endogenous glyceraldehyde-3-phosphate dehydrogenase (GAPDH) was used to normalize the mRNA levels for each tested molecule.
## 2 Predicting the Seismic Response by Applying the Energy Balance Concept
### Estimation of the Elastic Vibrational Energy \(W_{e}\)  
To estimate the elastic vibrational energy \(W_{e}\), the nonlinear spring of the first story that represents the frame is replaced by an undamped elastic continuous shear beam of length \(h_{1}\) and shear stiffness \(G_{1 st}\) (=\(s_{k1}\)\(h_{1}\)). The contribution of the damper to \(G_{1 st}\) and therefore to \(W_{e}\) is disregarded. This is a conservative assumption since it implies underestimating the energy absorption capacity of the structure in terms of elastic strain energy, and it is justified because the damper yielding displacement \(s_{k}\delta_{y1}\) must be marginal when compared to \(\rho\delta_{y1}\) in order to effectively protect the frame against plastic deformations. Hence, the amount of elastic energy provided by the hysteretic dampers is negligible when compared to the rest of the system, and it is not considered. As a result, to estimate \(W_{e}\) the entire structure is represented by a cantilever elastic shear beam with two different shear stiffnesses: \(G_{1 st}\) from \(x=0\) to \(x=h_{1}\) and \(G_{upper}\) from \(x=h_{1}\) to \(x=H\). The mass per unit length \(m\) is assumed constant and taken as \(m=\sum m_{i}/M\). Here \(x_{i}\) is the distance from the ground to the \(i\)-th floor and \(m_{i}\) is the mass at each level. The partial differential equation of this cantilever under a ground motion acceleration at the base \(\ddot{z}_{g}(t)\) can be resolved by applying modal analysis, and the elastic vibrational energy is obtained from the following expression [9]:  
\[W_{e}=\frac{Mg^{2}T_{1}^{2}}{4\pi^{2}}\Big{(}\frac{e}{a^{2}}\Big{)}\frac{ \pi^{2}_{max,1}}{2} \tag{7}\]  
where \(T_{1}\) is the fundamental period of the frame (without dampers), \(M\) is the total mass of the system, \(g\) is the gravity acceleration and \(\rho\alpha_{max,1}\) (=\(\rho Q_{max,1}/Mg\)) is the base shear force coefficient of the frame, defined as the ratio between the maximum base shear sustained by the frame, \(\rho Q_{max,1}\), and the total weight of the building, \(Mg\). In Equation (7), the ratio \(e/a^{2}\) is a constant that depends on the dynamic properties of the system and the \(V\)-\(T\) spectrum that characterises the ground motion. For structures with a soft first story, the following expression has been proposed [9] to estimate \(e/a^{2}\):  
\[\frac{e}{a^{2}}=\bigg{[}0.35-0.33\bigg{(}\frac{h_{1}}{H}\bigg{)}\bigg{]}e^{ \frac{-(\frac{G_{upper}}{G_{1 st}})}{2\pi T_{1}(\frac{h_{1}}{H})}}+\bigg{[}1.04+ 0.25\bigg{(}\frac{h_{1}}{H}\bigg{)}\bigg{]} \tag{8}\]
## 3 Model Formulation
### Covariate Bands Estimation
#### 3.5.1 Clustering Technique  
In this research, GMM was employed to define the band ranges. Its superior performance in clustering, easy interpretation, and robustness has been demonstrated, surpassing other clustering techniques like K-means in previous studies. GMM is a probabilistic clustering algorithm that represents a dataset as a mixture of multiple Gaussian distributions. It estimates the parameters of these distributions, including means and covariances, and assigns data points to clusters based on the likelihood of belonging to each component by a probability distribution.  
The training process depends on the data volume of the dataset. If working with high-volume datasets, the data points are simplified using Sturges' rule to streamline computation, dividing it into equivalent subgroups with representative class marks for use in the model. However, Sturges' rule should be avoided when working with low-volume datasets to evade possible data bias.  
To identify the optimal number of clusters for GMM, this research utilized the Akaike values (AIC and BIC). The guiding principle for decision-making is to select the number of clusters associated with the lowest values of these criteria.
## 3 Results and Discussion  
### Thermodilatometry  
Figure 1 shows the thermodilatometric measurements up to 1500 \({}^{\circ}\)C under air for calcined powders of BCZN ceramic materials. This experiment was performed in order to optimize the sintering temperature. As can be seen on the graph, shrinkage was observed to start at \(\sim\)1090 \({}^{\circ}\)C. In addition, the derivative curve indicates a high densification rate (\(-\)1.7% min\({}^{-1}\)) at 1350 \({}^{\circ}\)C and the maximum densification of BCZN is achieved at 1450 \({}^{\circ}\)C. Thus, two temperatures 1350 and 1450 \({}^{\circ}\)C, have been chosen to sinter the pellets with a heating and cooling rate of 200 \({}^{\circ}\)C\(\cdot\)h\({}^{-1}\) under air atmosphere. Regarding the durations, two sintering times were studied: 2 h and 30 h at 1350 \({}^{\circ}\)C and also at 1450 \({}^{\circ}\)C. It turned out that the best results are achieved by using a high temperature (1450 \({}^{\circ}\)C) during a short time (2 h) or by using a longer treatment (30 h) at a lower temperature (1350 \({}^{\circ}\)C). Taking into account these results and in order to study the effect of the heat treatment on the dielectric properties of the BCZN ceramics, we decided to describe here the sintering processes that provided the best dielectrics proprieties. Therefore, we chose to present the sintered pellets at 1350 \({}^{\circ}\)C for 30 h and at 1450 \({}^{\circ}\)C for 2 h under air atmosphere with a heating and cooling rate of 200 \({}^{\circ}\)C\(\cdot\)h\({}^{-1}\).