esa-sceva/satcom-chunk-collection huggingface dataset:
# Application of the Parabola Method in Nonconvex Optimization
## 2 Univariate Optimization: Parabola Method
### The Parabola Method
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**No.** & **Function and Interval** & **Solution** & g/1 & **Record** & \(\mathbf{k}_{f}\) \\ \hline
6. & \(f(x)=-\sum\limits_{k=1}^{5}k\cos((k+1)x+k)\), & \(f^{*}=-14.50801\), & g & \(f^{\sharp}=-14.50780\) & 22 \\  & & \(x\in[-10,10]\) & \(x^{*,1}=-7.083506\) & & \(x^{\sharp}=5.483102\) & \\  & & \(x^{*,2}=-0.800321\) & & & \\  & & \(x^{*,3}=\ \ \ 5.482864\) & & & \\ \hline
7. & \(f(x)=\sin(x)+\sin\left(\frac{2\pi}{3}\right)\), & \(f^{*}=-1.905961\), & 1 & \(f^{\sharp}=-1.215982\) & 22 \\  & & \(x\in[3.1,20.4]\) & \(x^{*}=17.039199\) & & \(x^{\sharp}=5.361825\) & \\ \hline
8. & \(f(x)=-x\sin(x)\), & \(f^{*}=-7.916727\), & g & \(f^{\sharp}=-7.916727\) & 22 \\  & & \(x\in[0,10]\) & \(x^{*}=7.978666\) & & \(x^{\sharp}=7.978632\) & \\ \hline
9. & \(f(x)=2\cos(x)+\cos(2x)\), & \(f^{*}=-1.500000\), & g & \(f^{\sharp}=-1.499999\) & 21 \\  & & \(x\in[-1.57,6.28]\) & \(x^{*,1}=2.094395\) & & \(x^{\sharp}=2.094447\) & \\  & & \(x^{*,2}=4.188790\) & & & \\ \hline
10. & \(f(x)=\sin^{3}(x)+\cos^{3}(x)\), & \(f^{*}=-1.000000\), & g & \(f^{\sharp}=-0.9999999\) & 21 \\  & & \(x\in[0,6.28]\) & \(x^{*,1}=3.141593\) & & \(x^{\sharp}=4.712287\) & \\  & & \(x^{*,2}=4.712389\) & & & \\ \hline
11. & \(f(x)=-e^{-x}\sin(2\pi x)\), & \(f^{*}=-0.788595\), & 1 & \(f^{\sharp}=-0.039202\) & 20 \\  & & \(x\in[0,4]\) & \(x^{*}=0.224982\) & & \(x^{\sharp}=3.226282\) & \\ \hline
12. & \(f(x)=\frac{x^{2}-5x+6}{x^{2}+1}\), & \(f^{*}=-0.035534\), & g & \(f^{\sharp}=-0.035533\) & 22 \\  & & \(x\in[-5,5]\) & \(x^{*}=2.414214\) & & \(x^{\sharp}=2.414418\) & \\ \hline
13. & \(f(x)=x^{6}-15x^{4}+27x^{2}+250\), & \(f^{*}=7.000000\), & g & \(f^{\sharp}=7.000001\) & 21 \\  & & \(x\in[-4,4]\) & \(x^{*,1}=-3.0\) & & \(x^{\sharp}=-3.000009\) & \\  & & \(x^{*,2}=\ \ \ 3.0\) & & & \\ \hline
14. & \(f(x)=-x+\sin(3x)-1\), & \(f^{*}=-7.815675\), & 1 & \(f^{\sharp}=-5.721279\) & 21 \\  & & \(x\in[0,6.5]\) & \(x^{*}=5.872866\) & & \(x^{\sharp}=3.778193\) & \\ \hline
15. & \(f(x)=\cos(x)-\sin(5x)+1\), & \(f^{*}=-0.952897\), & g & \(f^{\sharp}=-0.952896\) & 21 \\  & & \(x\in[0,7]\) & \(x^{*}=2.839347\) & & \(x^{\sharp}=2.839196\) & \\ \hline
16. & \(f(x)=-xe^{-\sin(3x)}+1\), & \(f^{*}=-3.363290\), & g & \(f^{\sharp}=-3.363290\) & 20 \\  & & \(x\in[-3,2]\) & \(x^{*}=1.639062\) & & \(x^{\sharp}=1.638984\) & \\ \hline
17. & \(f(x)=\ln(3x)\ln(2x)-1\), & \(f^{*}=-1.041100\), & g & \(f^{\sharp}=-1.041100\) & 21 \\  & & \(x\in[0.1,7]\) & \(x^{*}=0.408248\) & & \(x^{\sharp}=0.408014\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Test problems 6–17. Let us turn now to the Parabola Method. In order to start the method, property (2) must be satisfied. The points satisfying property (2) are known as a three-point pattern (TPP) in [11]. In order to find the TPP, we propose the following procedure.
## 1 Introduction
Specifically, this paper proposes the use of fast algorithms from the shrinkage-thresholding family to improve the convergence speed achieved by FISTA during the training of an ELM-AE. In particular, two representative models of this class are considered: G-FISTA [44] and LC-FISTA [45; 46]. To evaluate the efficiency of our scheme, six datasets that are widely used in the validation of ELM algorithms are adopted: MNIST, NORB, CIFAR10, UMist, Caltech256, and Stanford Cars. The main contributions of our article are as follows:  
* We present a novel method for computing the output layer weights of the ELM-AE network that avoids the need for the Moore-Penrose inverse. Instead of solving the linear system analytically, we use first-order iterative algorithms from the class of shrinkage-thresholding algorithms to minimize the output weights of the ELM-AE. * We demonstrate experimentally that the proposed method can effectively improve the computational time of the FISTA algorithm while maintaining its generalization capability. According to the theory presented in [47], the ELM-AE experiences a better performance when it achieves the lowest training error. * Compared to FISTA, the G-FISTA, and LC-FISTA algorithms show a considerable improvement in the training time of the ELM-AE, for all of the databases, and a very competitive reconstruction capability. Thus, applying this mathematical tool in other contexts would constitute a significant scientific contribution. The rest of this work is structured as follows: in Section 2, we briefly explain the ELM-AE, FISTA, G-FISTA, and LC-FISTA algorithms. Section 3 describes the method proposed to train the ELM-AEs. The datasets and the results are presented in Section 4. The discussion of results is presented in Section 5. Finally, Section 6 gives the conclusions of this work.
# MT-CMVAD: A Multi-Modal Transformer Framework for Cross-Modal Video Anomaly Detection
## 3 Supposed Method
### Classic Transformer Encoder
#### 3.2.1 Embedding Layer  
The input image \(\mathbf{I}\in\mathbb{R}^{H\times W\times C}\) is partitioned into \(N\) non-overlapping patches of size \(P\times P\), where \(N=\frac{HW}{P^{2}}\). Each patch \(\mathbf{x}_{\text{patch}}^{i}\in\mathbb{R}^{P^{2}\times C}\) is linearly projected into a \(D\)-dimensional embedding space and augmented with learnable positional encodings:  
\[\mathbf{z}_{0}=\left[\mathbf{x}_{\text{patch}}^{1}\mathbf{W}_{e};\dots; \mathbf{x}_{\text{patch}}^{N}\mathbf{W}_{e}\right]+\mathbf{E}_{\text{pos}}, \tag{1}\]  
where \(\mathbf{W}_{e}\in\mathbb{R}^{P^{2}\times D}\) is the projection matrix, \(\mathbf{E}_{\text{pos}}\in\mathbb{R}^{N\times D}\) denotes positional embeddings, and \(D\) is the hidden dimension.
## 4 Performance Evaluation
### Simulations
#### 4.2.1 Simulation on Effectiveness of _HeaLow_ in WSNs  
In our first simulation, we set up an environment where there is a high-end smartphone offloading data from multiple sensor sources using _HeaLow_. In this scenario, we examine the applicability of our system to WSN where a powerful device is nearby. An example scenario was to have microphone based sensor nodes exploiting a user's smartphone when one is nearby. In this way, the user can utilize more microphone inputs when available, and inputs to the sensor nodes can be used with deeper understanding. Figure 5 shows the average ratio of successful processing and offloaded amounts. We simulated an environment assuming a commercial high-end smartphone that can process up to \(\times 25\). This number is based on the data in Section 4.1.1 where a low-end smartphone has \(\times 8\) to \(\times 10\) processing power. Each sensor node can only process 20% of its input. With our system, a node will try to offload the other 80% and more, although these may fail to meet deadline due to the limited capacity of the high-power device and the network bandwidth limitation. Throughout the simulation,only one high-end smartphone was placed. There was no low-end smartphone. In addition, each sensor node generates \(\times 1\) workloads.  
With any given point of our simulations, each sensor node will try to offload the same amount, which is more than 80%. As shown in the figure, when there are five sensor nodes, a node offloads roughly 90% of its workload and fails to process less than 3% of the workload. With 10 nodes, a similar result is shown with more drop rate, and we found that this is due to the network congestion. Our system asks if the offloaded device have a room for more task, and offloads only when there is. In this case, the only device that can do offloaded work is the smartphone, and the amount of each sensor's offloaded workload decreases when the smartphone does not reply. This is highly likely due to network bottleneck. The success ratio visibly drops from 20 nodes, and the offloaded amount drops significantly from 80 nodes. However, it has to be noted that the amount of offloaded data exceeds the amount of data traffic in average WSN. If we lower the sampling rate, the network bottleneck is expected to be mitigated as well. In summary, when using _HeaLow_, a smartphone device is sufficient to enable up to at least 20 sensor nodes that are not capable of processing an average acoustic sensor input.
## 5 Performance Evaluation
### Effect of the Size of Encoding Information Block \(N\) on the Network Performance  
#### 5.1.1 Network Delay  
With (full or partial) network coding, the value of \(N\), which is the number of packets included in each data block, impacts the time (network delay) of transmitting the data. We first conducted several experiments to compare GPNC (based on partial network coding) and VBF_NC (based on full network coding) in terms of network delay impacted by the selection of \(N\). As shown in Figure 6, with the increase of \(N\), network delay increases for both GPNC and VBF_NC. The average delay of GPNC is smaller than that of VBF_NC when \(N<8\), and especially the improvement is about 22% when \(3\leq N\leq 5\). When \(N>5\), improvement of delay effect is not obvious and when \(N>8\), the delay of GPNC even exceeds that of VBF_NC. The longer delay for \(N>5\) is caused by the increase of the number of data packets to be decoded. Figure 7 further explains this phenomenon.  
Normally, VBF-NC requires \(N\) encoded data packets to decode them back to the \(N\) original data packets, or the possibility of linear dependency is very small, which never exceeds \(N+2\). When \(N<5\), the number of required data packets for decoding in GPNC is similar to that in VBF-NC. However when \(N>8\), the number of required data packets for decoding in GPNC will exceed that in VBF-NC, leading to the increase of network delay and the decrease of network performance. The reason behind this is the essential difference between partial and full network coding algorithms. The partial network coding algorithm randomly selects packets for encoding when forwarding data. As a result, the same packets may be repeatedly encoded when \(N\) gets bigger, reducing the linear independency between packets and increasing the number of packets to be decoded and consequently the network delay. In contrast, the full network coding algorithm always maintains the linear independency between packets such that decoding can only be done after the \(N\) linearly independent packets have all been received by a receiving node.
## 3 Results
### Power Consumption Measurement Strategy
Our experiments have revealed that the sensor node integrated with the ATMEGA328P MCU stands out as the most power-efficient platform among the options. However, we encountered reliability issues when operating the system with a 2.5 V voltage supply. It became evident that this MCU platform requires a minimum voltage supply of 2.7 V for reliable operation. Another strong contender is the TI-CC2650 Launchpad, which showcases comparable power consumption levels and consistently reliable operation. Our data also suggest that employing the TI-CC2650 Launchpad MCU with the internal timer \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**DC**} & \multicolumn{6}{c}{**Broadcast Time Interval [s]**} \\ \cline{3-8}
**MCU Platform** & **Supply** & **5** & **15** & **30** & **60** & **120** & **300** & **600** \\  & **[V]** & & & & **Power Consumption [\(\mu\)W]** & & & \\ \hline ATMEGA328P + TPL5110 TIMER & & 1291.4 & 431.79 & 216.88 & 109.43 & 55.700 & 23.464 & 12.719 \\ TI-CC2650 + INTERNAL TIMER & **2.5** & 1493.6 & 550.01 & 314.09 & 196.14 & 137.16 & 101.78 & 89.980 \\ TI-CC2650 + TPL5110 TIMER & & 1863.6 & 621.28 & 310.68 & 155.39 & 77.740 & 31.151 & 15.621 \\ ADAFRUIT + TPL5110 TIMER & & 4217.5 & 1405.9 & 702.99 & 351.54 & 175.81 & 70.374 & 35.228 \\ \hline ATMEGA328P + TPL5110 TIMER & & 1502.5 & 502.71 & 252.77 & 127.80 & 65.318 & 27.827 & 15.329 \\ TI-CC2650 + INTERNAL TIMER & **3** & 1713.9 & 631.40 & 360.75 & 225.43 & 157.77 & 117.17 & 103.64 \\ TI-CC2650 + TPL5110 TIMER & & 2263.8 & 754.68 & 377.40 & 188.75 & 94.433 & 37.840 & 18.976 \\ ADAFRUIT + TPL5110 TIMER & & 5553.1 & 1851.1 & 925.61 & 462.86 & 231.49 & 92.662 & 46.387 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experimentally measured power consumption of each sensor node using different MCU platforms at all possible configurations and at different broadcast frequencies. can be advantageous for reducing power consumption, especially in applications with broadcast time intervals longer than 30 s. However, for shorter broadcast intervals, the power consumption tends to be comparable or even slightly higher, as illustrated in Figure 8.  
As the next step, we explore the viability of using our proposed harvester designs, depicted in Figure 1, as sustainable power sources for our sensing system. We utilized the same power management and conditioning circuits as described in [38]. This investigation comprises two main parts. Initially, we examined the system's performance with a Lithium-Ion battery serving as a power storage unit and a backup plan for potential system failures. Subsequently, we replaced the battery with a supercapacitor to deliver the high current required during the active phase. This allowed us to assess the possibility of operating the entire system autonomously without the need for a traditional battery.
## 3 Methodology
### Problem Definition
#### 3.1.2 Encoder  
Chinese is hieroglyphic, and character shapes and character sound features contain important information. Similar to the recent CSC methods utilizing multimodal information [7; 8], we use ChineseBERT [11] as an encoder, as shown in Figure 4 ChineseBERT is a pre-trained language model that incorporates both Chinese pinyin and glyph information in a pre-trained language model to extract semantic, phonological and morphological  
Figure 3: SPMSpell overall framework.  
features for the CSC task. Since the multimodal information of characters is captured and fused by the same model without adding additional networks, the problem of ambiguity between different feature information can be largely mitigated; furthermore, using only ChineseBERT as a multimodal encoder further simplifies the architectural complexity of the overall model of the CSC; on the other hand, in terms of the degree of pinyin feature extraction, the model uses a fine-grained level, i.e., the consonants, rhymes and tones of characters are extracted as graphemic features instead of capturing the whole pinyin as in previous work. Fine-grained pronunciation feature capture allows for better modeling of the phonetic similarity between the target character and the error character. Specifically, for each character \(X_{i}\) in the input sentence \(X\), the encoder first generates all its character embeddings, pinyin embeddings, and grapheme embeddings with embedding size \(D\). These three embeddings are then concatenated in series and mapped to the D-dimensional fusion embeddings via a fully connected layer. Afterward, as in most other pre-trained language models, the fusion embeddings are added to the positional embeddings and fed into the Transformer's stack to generate a contextual representation \(h_{i}\in R^{D}\) of the input character \(x_{i}\). We denote the representation of the character after this encoding process as \(H=\{h_{1},h_{2}\ldots,h_{n}\}\).
## 5 Results and Analysis
### Qualitative Scores  
After implementing the proposed model, we found that the MTS-TGAN can simultaneously learn to produce representations, encode characteristics and iterate across time. We further compared MTS-TGAN to Time-GAN [8], the best available alternative, and assessed it using qualitative visualizations and quantitative metrics. Graphs of the columns Low, High, Close, Open, Adj Close and Volume of the Google dataset [17] and columns Running and Jumping of the UniMIB dataset [18] are plotted to show the visual representation of the real and the synthetic data. Some generated samples are shown in Figures 6-12. Real and synthetic data both continue to be standardized with values between \([0,1]\) for the Google dataset [17].  
Figures 9-12 shows the distribution of age, height, and weight of all 30 subjects in the UniMIB dataset [18] as green, orange and blue colors respectively. Figures 9 and 11 show the real data from the UniMIB dataset [18], depicting that the data range from \([-3,\,3]\) for the UniMIB dataset, and Figures 6-8, 10 and 12 depict the real and synthetic samples of various sequence lengths for the data that are plotted using the Python module, Plotly [40], with the time-steps (seconds) on the x-axis and the signal values on the y-axis. For better visualization, the range of the x-axis is 25 in the case of the Google dataset [17] and 150 for the UniMIB dataset [18].  
Figure 10: Generated synthetic data for jumping column.  
Figure 9: Real data for jumping column.  
The predictive and discriminator scores show the MAE values in relation to the generated data sequence and the original data sequence, respectively, as shown in Table 5. However, the predictive and discriminative scores acquired, 0.024 and 0.092, respectively, are still significantly more accurate than the outcomes of the initial implementation [8] by 13% and 10%, respectively, as shown in Table 5.  
The predictive and discriminative scores for Google stocks compared to TimeGAN.  
\begin{table}
\begin{tabular}{l l l} \hline  & **Predictive Score** & **Discriminative Score** \\  & **(Lower the Better)** & **(Lower the Better)** \\ \hline TimeGAN [8] & 0.037 & 0.102 \\ \hline Proposed Model & 0.024 (13\% lower) & 0.092 (10\% lower) \\ \hline \end{tabular}
\end{table}
Table 5: Predictive and discriminative scores for Google stocks compared to TimeGAN.  
Figure 14: PCA and t-SNE of generated and real data for jumping parameter for UniMIB dataset.  
Figure 15: PCA and t-SNE of generated and real data for running parameter for UniMIB dataset.  
Figure 13: PCA and t-SNE of generated and real data for Google stocks dataset.
## 5 Experimental Scenarios and Results  
The dataset used in this section was examined in detail, extracting photos of vehicles with fully or partially visible ADR signs. In addition, certain basic statistics were also determined, such as the total number of vehicles and those with visible ADR signs, per hour, for March 2021, on two stations. These statistics are summarized in Table 1. Moreover, Figure 5a,b show two typical examples of highly problematic photos that make detection practically impossible. The first two ADR-Det algorithm validation experiments, outlined below, were conducted at 10:00 a.m. and 3:59 p.m.  
For the ADR-Det algorithm evaluation process, three experimental scenarios were employed to assess the algorithm's performance in execution time and detection accuracy under various input datasets. These were:  
1. ADR-Det algorithm stage 2 ADR signs detection evaluation.
2. ADR-Det algorithm Optical Character Recognition (OCR) process evaluation and improvements.
3. ADR-Det performance evaluation and requirements for its use in embedded mobile devices.  
The images used for the ADR-Det training and validation have been taken from the EGNATIA SA toll post cameras installed to take snapshots of the vehicle's front part, close  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Toll Station** & **Number of Toll Post Images** &
\begin{tabular}{c} **Number of ADR Truck Photos from** \\ **the Toll Post Images (\% Percentage)** \\ \end{tabular} \\ \hline MAL-1H & 6596 & 121 (0.016\%) \\ MAL-1K & 8837 & 30 (0.0032\%) \\ \hline Total: & 15,433 & 151 (0.01\%) \\ \hline \hline \end{tabular}
\end{table}
Table 1: dataset used during the ADR-Det validation process, of March 2021, using two toll posts (MAL-1H, MAL-1K) images.  
Figure 4: HMRT-EF OCR process with its OCR preview capabilities enabled displaying the detected Regions of Interest.  
to the license plate. However, these images were of low-resolution and had color depth (752 \(\times\) 480 \(\times\) 8-bits, 96 dpi, 40-65 KB in size). In addition, the camera modules are placed in the toll posts without proper perimetric lightning or force-activated infrared capabilities and, in some cases, without extreme care, especially at night, as shown in Figure 5a,b. This made it hard to detect the vehicle's ADR and license plates in such cases, even for the naked eye. Consequently, since no other camera equipment providing high-resolution image datasets was available at the toll posts, it was necessary to train the proposed algorithm to process low-resolution images, excluding the zero visibility ones from the training process.
## 2 Existing Systems
#### Limitations of Existing Systems  
1. Lack of digitization: Every monetary transaction and storage entry is recorded on paper. Piles of record registers take up a great amount of space in the form of filing cabinets. These are susceptible to manipulation, theft, fire, water, and bugs. Searching for a record would become a cumbersome task and would lead to a waste of time and labor.
2. Extensive corruption: The easy manipulation of records largely contributes to corruption. Authority figures might authorize a fake transit of goods, and the money would get transferred to a bogus account. The seeds are often hoarded so that a state of scarcity can be established and are then sold for a higher price.
3. Opaque operations: In the existing system, no operation is logged at any step of the supply chain. In case of any exigency, there would not be any chain of custody to identify the point where things went wrong. There is no transparency in operations, due to which it is easy to hide bogus transactions and shipments.
4. Inefficient and slow: There is no automation of any of the tasks, starting from breeder registration and ending with a farmer's purchase of a packet of seeds. Entering and searching paper records is extremely time-consuming, which becomes a burden to the entire system.
5. Security: Records are kept in a file cabinet in an unguarded room, which any intruder can visit and then view the details without any restrictions. This is conducive to data leaks, which could be catastrophic to farmers, as their account details and seed purchase routines could fall into the wrong hands.
6. Middleman: The present system comprises middlemen who take advantage of the manual system and sell seeds at a greater price than the maximum retail price by manipulating the taxes for their advantage. In addition, expired seeds are sold with normal seeds. The practice of hoarding and creating a fake demand allows middlemen to sell seeds at a higher price, which causes trouble for farmers.