esa-sceva/satcom-chunk-collection huggingface dataset:
# Physics-Informed Neural Networks for Modal Wave Field Predictions in 3D Room Acoustics
## 3 Physics-Informed Neural Networks for Wave-Based Room Acoustics
### Locally Adaptive Activation Functions  
The locally adaptive activation function (LAAF) with slope recovery [27] is a method designed to improve the training speed and performance of physics-informed neural networks. It introduces a scalable parameter, a so-called activation slope \(na_{i}^{\ell}\) (for layer \(\ell\) and neuron \(i\)), to the activation function optimized during training (see Figure 3). The locally adaptive activation function neural network (at the neuron level) is defined as  
\[\begin{split}\text{Input layer: }&\mathcal{N}^{0}( \mathbf{x})=\mathbf{x}\in\mathbb{R}^{d_{\text{in}}}\\ \text{Hidden layers:}&\qquad 1\leq\ell\leq L-1, \\ &\sigma\Big{(}na^{\ell}\mathcal{N}^{\ell}(\mathbf{x})\Big{)}= \sigma\Big{(}na^{\ell}(\mathbf{W}^{\ell}\sigma\Big{(}na^{\ell-1}\mathcal{N}^ {\ell-1}(\mathbf{x})\Big{)}+\mathbf{b}^{\ell})\Big{)}\in\mathbb{R}^{N_{\ell}},\\ \text{Output layer: }&\mathcal{N}^{L}(\mathbf{x})= \mathbf{W}^{L}\sigma\Big{(}na^{L-1}\mathcal{N}^{L-1}(\mathbf{x})\Big{)}+ \mathbf{b}^{L}\in\mathbb{R}^{d_{\text{out}}}\,;\end{split} \tag{17}\]  
The output prediction at the output layer \(L\) is calculated by  
\[\hat{p}=\mathcal{N}^{L}\circ\sigma\circ na^{L-1}\mathcal{N}^{L-1}\circ\sigma \circ\cdots\circ\sigma\circ na^{1}\mathcal{N}^{1}\circ\mathbf{x}\,, \tag{18}\]  
a series of transformation functions. The slope recovery term  
\[S(a)=\frac{L-1}{\sum_{\ell=1}^{L-1}\exp\left(\frac{\sum_{i=1}^{N_{\ell}}a_{i}^{ \ell}}{N_{\ell}}\right)} \tag{19}\]  
encourages the network to increase the activation slope, leading to faster training. The loss function is extended to include the slope recovery term by  
\[\mathcal{L}=w_{\text{PDE}}\mathcal{L}_{\text{PDE}}+w_{\text{NBC}}\mathcal{L} _{\text{NBC}}+w_{\text{a}}S(a)\,. \tag{20}\]  
The analysis in [27] shows that LAAFs effectively multiply the gradients by conditioning matrices, accelerating convergence without explicitly calculating these matrices. Experiments demonstrated that LAAF works for deep neural networks in the application of standardized datasets MNIST [41], Fashion-MNIST [42], KMNIST [43], Semeion [44], SVHN [45], and CIFAR [46]. Compared to fixed and global adaptive activations, neuron wise LAAF exhibited faster training speeds when approximating a discontinuous function and, in combination with PINNs, the inverse problem of identifying the material coefficient of Poisson's equation and Burgers' equation in 2D. LAAF contributes to the overall challenge of reducing the number of iterations needed for convergence compared to the fixed activation function. This feature was tested with the backend TensorFlow 1 in DeepXDE and \(n=10\) for the reliable hyperparameters with a network depth of \(L-1=2\), each layer consisting of 180 neurons; \(w_{\text{NBC}}=5\), the \(n\) of the DeepXDE implementation of layer-wise (a uniform \(a_{i}^{\ell}=a^{\ell}\) for all neurons in the layer) LAAF is selected to be 2. The parameters selected were a good compromise for the standard PINN.
## 1 Introduction
[14, 15] revealed the influence of this load on the soil parameters around the pile by establishing a numerical model of a single pile. [PERSON] et al. [16, 17] and [PERSON] et al. [18] carried out the monopile model tests to investigate soil deformation around the monopile under cyclic loading. They found that the soil around the pile caused subsidence during the early number of cyclic, after which the convective motions of soil particles would occur. Therefore, during the operation of offshore wind turbines, cyclic lateral loading causes the variation of soil important parameters such as modulus, density, and so on. Hence, in OWT design, notably, soil parameter fluctuations lead to natural frequency variations in OWT, a key deviation factor [19]. [PERSON] et al. [20] and [PERSON] et al. [21] explored how changes in soil parameters affect the natural frequency of wind turbine structural systems, drawing on model tests of cyclic loading on offshore wind turbines; they indicated that the maximum deviation of natural frequency reached 30% by cyclic loading. Furthermore, findings reveal that the soil around the monopile imposes a notable impact on the natural frequency of the wind turbine structure, but the number of cyclic loadings is far less than 108. [PERSON] et al. [22] used the p-y curve model to simulate nonlinear soil-pile interaction, with a focus on the effects of varying clay stiffness on the natural frequency of OWT structures. They noted that when the stiffness of clay diminishes, the overall natural frequency of the OWT system tends to move closer to the 1P harmonic. [PERSON] et al. [23] highlighted that natural frequency deviation constitutes the primary factor inducing structural resonance in offshore wind turbines. However, systematic analysis of how cyclic loading affects OWT natural frequency is lacking. In conclusion, quick natural frequency calculation for OWT is achievable via certain methods. When considering the effect of soil-pile interaction, the natural frequency of OWT is less than not considering the effect of soil-pile interaction, so when the foundation stiffness is changed, the natural frequency will be also changed, and the maximum deviation reaches 30%. Assessment of how sustained cyclic loads alter OWT natural frequency remains unaddressed in existing methods. For OWT structural design, quantifying how persistent cyclic loading alters natural frequency is a critical focus of this research, but little research has been conducted in this area. FLAC3D-based integration of a soil degradation stiffness model enables investigation into amplitude/cycle-dependent vibration characteristics of the monopile offshore wind energy conversion system. Convergence of numerical data with established simplified methods yields a novel framework for evaluating long-term cyclic load impacts on structural dynamics. Finally, under the condition of long-term cyclic loading, the characteristic vibration value of 3.6 MW offshore wind energy conversion systems is evaluated using the proposed method.
# Blockchain Based Trust Model Using Tendermint in Vehicular Adhoc Networks
## 5 Implementation and Results
### Packet Delivery Ratio (PDR)  
This applies to the ratio of packets received successfully to the cumulative number of packets transmitted across the network [35]. Mathematically, it is given by:  
\[PDR=\frac{P_{r}}{P_{s}} \tag{10}\]  
where \(P_{r}\) is the total number of packets received and \(P_{s}\) is the total number of packets sent.  
Figure 7 illustrates the packet delivery ratio for the proposed consensus scheme, i.e., Tendermint incurred a higher PDR, improved by 7.8%, 5.6% and 2.4% compared to PoW, PoS and Hybrid, respectively.
## 4 C-Monoa
### Objective Function Design  
In C-MONOA, support, confidence, the Kulc metric, and comprehensibility are used as the objectives of the metaheuristic algorithm to evaluate rules in order to obtain a set of rules that are frequent, simple, and accurate. The support and confidence measures aim to mine reliable rules that occur frequently and have a strong correlation between conditions and results. Support measures the frequency of rules appearing in the dataset, while confidence evaluates the probability of results occurring under given conditions. These two indicators jointly ensure the effectiveness and reliability of rules. Kulc measures the imbalance between antecedent and consequent, which helps extract effective rules from numerical data, while comprehensibility focuses on the simplicity of rules, ensuring that the final rule set is easy to interpret and apply [43].  
Support: support refers to the proportion of transactions containing itemset \(AB\) to the total number of transactions in the dataset [44].  
\[Sup(AB)=\frac{Items(AB)}{N} \tag{22}\]  
Confidence level: the confidence of a rule measures the likelihood that consequent \(B\) will happen given that antecedent \(A\) occurs, indicating how reliable the rule is [45].  
\[Confidence(A\Rightarrow B)=\frac{Sup(AB)}{Sup(A)}=\frac{P(AB)}{P(A)} \tag{23}\]  
Kulc metric: This is a measurement method that considers the frequency difference of a term appearing before and after a rule. The Kulc metric is derived from [PERSON] et al., who first proposed it in 1928 [46]. By calculating the frequency imbalance between the front and back terms of a rule, the Kulc metric can identify rules that exhibit a significant imbalance between the front and back terms, which often have more practical significance. The Kulc metric has zero invariance, which means it can maintain stable evaluation results even if there are a large number of zero transactions in the dataset.  
\[Kulc(A,B)=\frac{1}{2}(P(A\mid B)+P(B\mid A)) \tag{24}\]  
Comprehensibility is a measure of the simplicity and interpretability of rules. Simple rules are characterized by fewer items, making them easier to understand and interpret. \(NC(A\Rightarrow B)\) is the count of characteristics in a rule, and the fewer characteristics there are, the higher the value of comprehensibility [47].  
\[Comprehensibility=\frac{1}{NC(A\Rightarrow B)} \tag{25}\]
## 2 Materials and Methods
### System Configurations  
In this study, three configurations for refrigeration cycles were chosen and investigated. A single-stage cycle (SS) comprising the compressor, condenser, expansion valve, and evaporator was considered a reference, and the performance of the other configurations was compared with this cycle. The second configuration was a single-stage cycle with an internal heat exchanger (IHX). In this configuration, a heat exchanger is added between the suction line and the liquid line to reduce the liquid temperature before the expansion valve, employing transferred heat from the liquid line to the suction line. Finally, the third configuration was a two-stage refrigeration cycle with a flash tank vapor injection  
\begin{table}
\begin{tabular}{l c c c c} \hline  & **R290** & **R600a** & **R1270** & **R134a** \\ \hline Formula & C\({}_{3}\)H\({}_{8}\) & C\({}_{4}\)H\({}_{10}\) & C\({}_{3}\)H\({}_{6}\) & C\({}_{2}\)H\({}_{3}\)F\({}_{4}\) \\ Molecular mass (g mol\({}^{-1}\)) & 44 & 58 & 42 & 102 \\ Ozone depletion potential, ODP & 0 & 0 & 0 & 0 \\
100-year global warming potential, GWP\({}_{100}\) & 3 & 3 & 3 & 1430 \\ Safety classification & A3 & A3 & A3 & A1 \\ Critical temperature (K) & 369.9 & 407.8 & 364.2 & 374.2 \\ Critical pressure (MPa) & 4.25 & 3.63 & 4.55 & 4.06 \\ Saturation pressure at 280 K (MPa) & 0.588 & 0.201 & 0.716 & 0.377 \\ Enthalpy of vaporization at 280 K (kj kg\({}^{-1}\)) & 364.5 & 347.4 & 366.6 & 193.2 \\ Vapor density at 280 K (kg m\({}^{-3}\)) & 12.8 & 5.4 & 15.05 & 18.7 \\ Volumetric capacity at 280 K (kj m\({}^{-3}\)) & 4646.9 & 1868.9 & 3197 & 3604.6 \\ Saturation pressure at 341 K (MPa) & 2.50 & 1.05 & 2.96 & 2.04 \\ \hline \end{tabular}
\end{table}
Table 1: Properties of baseline and alternative hydrocarbon refrigerants.  
(ECO). It is noted that there are other advanced configurations for the vapor compression system that improve the performance of the system. In this study, the single-stage cycle with an IHX was studied as an excellent design to ensure dry compression and improve system performance. The ECO cycle design, which includes a flash tank to inject saturated vapor instead of superheated vapor, is another promising configuration to improve the performance compared with a single-stage vapor compression cycle. The schematic and P-h diagram of these configurations are presented in Figure 1.  
Figure 1: Schematic and P-h diagrams of refrigeration systems: **(a)** SS, **(b)** IHX, and **(c)** ECO.
## 3 Results and Discussion
### Crystalline Structure  
X-ray diffraction patterns and crystalline parameters of the BRS from the 16 banana cultivars covering different genome groups are presented in Figure 5. These patterns were used to study the type and level of BRS crystallinity over the different cultivars. Previous studies have reported that natural banana starch exhibits three types of crystal structures, including type A [33], type B [10; 34], and type C [35]. In our study, all particles were found to exhibit a weak diffraction peak at 5.6 \({}^{\circ}\)O and a broad peak ranging from 22\({}^{\circ}\) to 24 \({}^{\circ}\)O, suggesting that they were B- or C-type crystals rather than A-type crystals. Saba (ABB), Jinfen 1 (ABB), Meishi 2 (AAB), Poingo (AAB), and GN 60A (AAA) were identified as C-type crystals with a weak peak at 5.7\({}^{\circ}\), moderate peaks at 15.0\({}^{\circ}\), 19.5\({}^{\circ}\), and 22.0 \({}^{\circ}\)O, and a strong peak at 17.0 \({}^{\circ}\)O. The C-type pattern was a mixture of A-type crystal and B-type crystal. The other 11 BRS samples contained reflections at 20 values of 5.6\({}^{\circ}\), 15.0\({}^{\circ}\), 17.0\({}^{\circ}\), and 23.0 \({}^{\circ}\)O, which are attributed to the B-type crystal. These results revealed that the different BRS granules had different crystal types. Even samples of BRS with the same genome had different crystals, showing the banana genotypes did not significantly impact the crystalline pattern of the starch. Instead, the growth conditions of the banana cultivars were considered to play a crucial role in shaping the crystalline structure of the starch [10].  
To estimate the degree of structural order, the crystallinity index (CI) of the BRS granules from the 16 banana cultivars was calculated. The BRS granules ranged between 57.8-63.3%, which were much higher than the cultivars of India (2.04-12.22%) reported by [3] and Thailand (24.2-31.3%) reported by [PERSON] et al. [36]. It was reported that the double-helical arrangement of the branched-chain structures in the crystalline region determined the CI value, relevant to enzyme hydrolysis [37]. In our study, the CI values of the BRS from the 16 banana cultivars were close to the same, with a ratio of maximum to minimum of 1.09. In addition, [PERSON] et al. [38] found that the B-type and C-type crystals of the resistant starch were more compact and resistant to enzymatic digestion. The BRS samples from the three genome groups exhibited B-type or C-type structures, suggesting  
Figure 5: X-ray diffraction patterns and crystallinity indexes of BRS from 16 banana cultivars.  
they were less affected by digestive enzymes in the glycemic index experiment, which might explain the low pGI values (Table 2).
## 3 Research Questions and Communication Efficient Methods
### RQ2-How Can Communication Be More Efficient in an FL Environment?
#### 3.2.3 Reducing Model Updates  
Once the global model is downloaded by connected devices in the FL environment, each device starts to train the devices locally. As each device computes and updates the model, these updates are communicated back to the central server [6]. The number of communication rounds between the devices and central server can be costly, and perhaps having fewer but more efficient model updates could be a solution. This section introduces some techniques that discuss a possible reduction in communication for these model updates and could potentially reduce the cost.  
The authors in [72] introduce an efficient way of training models; their proposed approach adapts to the concept of drifts and trains models equally well through different phases of model training. Their approach leads to reducing the communication substantially without depreciating the model's predictive performance.  
In another study [73], the authors introduce a partitioned variational inference (PVI) for probabilistic models that work well over federated data. They train a Bayesian neural network (BNN) over an FL environment that is allowed for both synchronous or asynchronous model updates across many machines. Their proposed approach, and the integration of other methods, could allow for a more communication-efficient training of BNN on non-iid federated data.  
In contrast to most of the current FL methods that include iterative optimization techniques over numerous communication rounds [6; 74], the authors in [75] introduce a one-shot communication round approach where only a single round of communication is conducted between the central server and the number of connected devices [75]. Instead of computing increments, the authors suggest that each device trains a local model to completion and then applies ensemble methods to capture information regarding device-specific models effectively. Applying ensemble learning techniques could be better suited for global modeling than averaging techniques [75].  
In an FL setting, the rate at which model convergence occurs can sometimes take a large number of communication rounds, creating a delay towards model training while simultaneously increasing network resources [76]. An intelligent algorithm called FOLB is introduced by the authors in [76]. The algorithm performs a smart sampling of participating devices over each round to optimize the expected convergence speed. The algorithm can estimate the participating device's capabilities; this is achieved by adapting to devices' aggregations.  
If the mere frequency in which the model updates are shared is reduced, the overall communication between the devices and the central server is also reduced. Having an effective way of determining how these updates are computed reduces the overall communication rounds that are needed. Fewer rounds could result in a greater efficiency.
# Multiellipsoidal Mapping Algorithm
## 2 Mathematical Background
### Geometric Algebra  
GAs are Clifford Algebras [11; 18] constructed over a bilinear form of the vector space \(\mathbb{R}^{p,q,r}\), where \((p,q,r)\) is the algebraic signature. This GA is denoted by \(\mathbb{G}_{p,q,r}\) and it is an equivalent notation for \(C\ell_{p,q,r}(\mathbb{R})\). The elements that belong to this algebra are called multivectors. Let us denote by \"\(\circ\)\" the Clifford product, by \"\(\bullet\)\" the inner product and by \"\(\wedge\)\" the outer product. Then, for two basis vectors, (1) states the Clifford product behavior, where \(e_{i}\wedge e_{j}\) is a bivector or a 2-vector element; all vectors in \(\mathbb{R}^{p,q,r}\) are included in \(\mathbb{G}_{p,q,r}\) as 1-vectors (a \(k\)-vector describe a multivector span by \(k\) basis vectors). In addition, the properties of the bilinear form shown in (2) are present, where \"\(\cdot\)\" is the common dot product used in linear algebra, thus \(\mathbb{R}^{p,q,r}\subset\mathbb{G}_{p,q,r}\).  
\[e_{i}\circ e_{j}=\left\{\begin{array}{cl}e_{i}\wedge e_{j}&\text{if }i\
eq j\\ 1&\text{if }1\leq i=j\leq p\\ -1&\text{if }p<i=j\leq q\\ 0&\text{if }q<i=j\leq r\end{array}\right. \tag{1}\]  
\[a\circ a=a\bullet a=a\cdot a,\quad a\in\mathbb{R}^{p,q,r} \tag{2}\]GAs are associative and anticommutative algebras; additionally, due to the generality of the Clifford product, many properties of other mathematical frameworks are present [11] such as complex numbers, quaternions, and other Cayley-Dickson algebras, in addition to Pauli matrices and spinor algebras.  
Nevertheless, GAs are not only useful for integrating multiple mathematical frameworks but also present attractive features for geometric entity representation. In a GA, multivectors by themselves could represent geometric entities in their inner or outer product representation instead of the traditional geometric locus. The importance of this feature is that the geometric entities, as well as their operators, are represented as elements of the same algebra (both are represented as multivectors).
## 4 Discrete Time Markov Chain Models and Analysis
### Multi-Link Access with End-Time Alignment (MLA-A)  
In the MLA-A case, the Markov Chain model is exactly the same as MLA-S's. As shown in Figure 4d, the link where the transmission starts is the link with the shortest backoff counter. The difference is that there are opportunities to access the channel during the transmission if backoff counter is expired on the other link. Hence, we just need to modify throughput equation, \(S_{MLA-A}\).  
As you can see in Figure 4d, the station on auxiliary link needs to know how long to wait for the backoff counter to expire. To this end, an absolute difference value between two uniform random variables needs to be calculated. Denote \(D_{i}\) be the distribution of absolute difference value of two uniform random variables in the stage \(i\). For instance, as seen in Figure 4d, selected backoff counters at first are 2 and 5, respectively. Assuming the MLD is in the initial stage, then \(D_{0}=|5-2|=3\).  
At first, the probability that the remaining (that is, difference) backoff counter is \(k\), \(P[D_{i}=k]\) is as follows:  
\[P[D_{i}=k]=\left\{\begin{array}{ll}\frac{1}{W_{i}},&k=0\\ \frac{2(W_{i}-k)}{W_{i}^{2}},&k\in[1,W_{i}-1]\end{array}\right.. \tag{36}\]  
Then, the number of remaining slots in stage \(i\), \(E[D_{i}]\) can be derived as follows:  
\[E[D_{i}] =\sum_{k=0}^{W_{i}-1}k\cdot P[D_{i}=k] \tag{37}\] \[=\sum_{k=0}^{W_{i}-1}\frac{2k(W_{i}-k)}{W_{i}^{2}}\] \[=\frac{1}{W_{i}^{2}}\sum_{k=0}^{W_{i}-1}\Big{(}-2k^{2}+2W_{i}\cdot k \Big{)}\] \[=\frac{W_{i}^{2}-1}{3W_{i}}\]  
This value can be approximated to \(W_{i}/3\) for a relatively large \(W_{i}\). We need to derive the number of remaining slots regardless of the stage \(E[D]\) as follows.  
\[E[D] =\sum_{i=0}^{m}E[D_{i}]P(s=i|TX) \tag{38}\] \[=\frac{W_{0}(1-p)\Big{(}1-(2p)^{m+1}\Big{)}}{3(1-p^{k+1})(1-2p)}\]where \(W_{i}=2^{i}W_{0}\). Then, throughput equation for MLA-A can be expressed as follows:  
\[S_{MLA-A}=\frac{P_{s,MLA-A}P_{tr,MLA-A}E[P]\Big{\{}1+\Big{(}1-\frac{E[D]\sigma}{T_ {data}}\Big{)}\Big{\}}}{(1-P_{tr,MLA-A})\sigma+P_{tr,MLA-A}P_{s,MLA-A}T_{s}+P_{tr, MLA-A}(1-P_{s})T_{c}} \tag{39}\]  
where \(T_{data}\) stands for the data transmission duration and \(1-\frac{E[D]\sigma}{T_{data}}\) represents the percentage of the average accessible time duration on auxiliary link to the average data transmission duration on primary link.