esa-sceva/satcom-chunk-collection huggingface dataset:
# Diverse Decoding for Abstractive Document Summarization
## 3 Neural Abstractive Summarization with Diverse Decoding
### Structure of the Neural Network Model  
The base neural model uses a bi-directional LSTM encoder and a single-layer LSTM decoder, as shown in Figure 2. The encoder takes the source text \(x=\{w_{1},w_{2},\dots,w_{n}\}\) as input and produces a sequence of encoder hidden states \(\{h_{1},\ h_{2},\dots,h_{n}\}\).  
\[e_{i}^{t}=v^{T}\tanh\left(w_{h}h_{i}+w_{s}s_{t}+b_{attn}\right) \tag{1}\]  
The task is to predict the summary sequence \(y=\{y_{1},\ y_{2},\dots,y_{n}\}\). At each step \(t\), the decoder receives the word embedding of the previous word and produces the decoder state \(s_{t}\). Notice that all the following probability expressions are conditional probabilities. The attention distribution at each decoding time step is:  
\[\text{a}^{t}=\text{softmax}\left(e^{t}\right) \tag{2}\]  
where \(v\), \(w_{h}\), \(w_{s}\), and \(b_{attn}\) are learnable parameters. The attention distribution can help the decoder to focus on a specific part of the input when predicting the next word. Next, the attention distribution is used to calculate the context vector, which is the weighted sum of encoder hidden states and can be used to produce the vocabulary distribution:  
\[h_{t}^{*}=\ \sum_{i}a_{i}^{t}h_{i} \tag{3}\]  
\[P_{vocab}=\text{softmax}\left(V^{\prime}\left(V\left[s_{t},\ h_{t}^{*}\right] +b\right)+b^{\prime}\right) \tag{4}\]  
where \(V^{\prime}\), \(V\), \(b\), \(b^{\prime}\) are learnable parameters. \(P_{vocab}\) is the probability over all words in the vocabulary. Then, we add the pointer mechanism, which works as a switch, to choose whether to generate a word from the fixed vocabulary or to copy OOV words from the input. The generation probability \(P_{gen}\) for time step \(t\) is calculated as:  
\[P_{gen}=\text{e}\left(w_{h^{*}}^{T}+w_{s}^{T}s_{t}+w_{x}^{T}x_{t}+b_{ptr}\right) \tag{5}\]  
Figure 2: Illustration of the attentional sequence-to-sequence model. The model attends to relevant words in the source text to generate words of the output sequence.  
where vectors \(w_{h*},\ w_{s},\ w_{x}\), and scalar \(b_{ptr}\) are learnable parameters and ce is the sigmoid function. We finally obtain the following probability distribution:  
\[P\left(y_{t}\right)=P_{gen}P_{vocab}\left(y_{t}\right)+\left(1-P_{gen}\right) \sum_{iy_{t}=y_{t}}a_{i}^{t} \tag{6}\]  
During training, we use the human-written summary as the target sequence \(y^{*}=\left\{y_{1}^{*},\ y_{2}^{*},\ldots,y_{n}^{*}\right\}\); the loss for time step \(t\) is the negative log likelihood of the target word \(y_{t}^{*}\); and the overall loss for the whole sequence is:  
\[\text{loss}=\frac{1}{T}\ \sum_{t=0}^{T}-\text{log}P\left(y_{t}^{*}\right) \tag{7}\]
## 5 Extended Kalman Filter Tracking
### Tracking Preliminaries
To do so, we first define a weighting factor \(\mathbf{K}\) by normalizing the acting transition function \(\mathbf{H}\) by the error covariance matrices in the predicting parameters and measurements, \(\mathbf{\hat{P}}\) and \(\mathbf{S}\), respectively. This takes the form:  
\[\mathbf{K}^{(n-1)}=\mathbf{\hat{p}}^{(n-1)}_{(-)}{\mathbf{H}^{(n-1)}}^{T} \mathbf{S}^{(n-1)-1}, \tag{30}\]  
with which we make the corrections  
\[\hat{\mathbf{x}}^{(n-1)}=\hat{\mathbf{x}}^{(n-1)}_{(-)}+\mathbf{K}^{(n-1)}( \mathbf{z}^{(n-1)}-\hat{\mathbf{z}}^{(n-1)}_{(-)})\, \tag{31}\]  
\[\mathbf{\hat{p}}^{(n-1)}=(\mathbf{I}_{|\mathbf{x}|}-\mathbf{K}^{(n-1)}\mathbf{ H}^{(n-1)})\mathbf{\hat{p}}^{(n-1)}_{(-)}\, \tag{32}\]  
where \(|\mathbf{x}|\) is the number of state space parameters. To maintain the resolution of one estimate per frame, we extrapolate between cycles; the estimates \(\hat{\mathbf{x}}^{(n)}\) are extrapolated using  
\[\hat{\mathbf{x}}^{(n)}=\mathbf{F}\!\left(l^{(n-1)}_{A}\right)\hat{\mathbf{x}} ^{(n-1)}. \tag{33}\]  
Using this construction, we formulate the first- and second-order joint delay-offset tracking algorithm described in Algorithm 1. ```
1:while flight duration do
2:\(\hat{\mathbf{x}}^{(n-1)}_{(-)}\!=\!\mathbf{F}\!\left(l^{(n-1)}_{A}\right)\hat{ \mathbf{x}}^{(n-3)}\)
3:\(\mathbf{\hat{p}}^{(n-1)}_{(-)}\!=\!\mathbf{F}^{(n-1)}\mathbf{\hat{p}}^{(n-3)} \mathbf{F}^{(n-1)}\!+\!\mathbf{Q}^{(n-1)}\)
4:\(\hat{\mathbf{z}}^{(n-1)}_{(-)}\!=\!\mathbf{u}^{(n-1)}\!+\!\mathbf{h}(\hat{ \mathbf{x}}^{(n-1)}_{(-)})\)
5:\(\mathbf{H}^{(n-1)}=\frac{\partial\mathbf{h}(\mathbf{x})}{\partial\mathbf{x}} \Big{|}_{(-)}\)
6:\(\mathbf{S}^{(n-1)}\!=\!\mathbf{H}^{(n-1)}\mathbf{\hat{p}}^{(n-1)}_{(-)}\mathbf{ H}^{(n-1)}\mathbf{H}^{(n-1)}\mathbf{T}\!+\!\mathbf{R}^{(n-1)}\)
7:\(\mathbf{z}^{(n-1)}_{(-)}\!=\!\mathbf{u}^{(n-1)}\!+\!\mathbf{h}(\hat{ \mathbf{x}}^{(n-1)}_{(-)})\)
8:\(\mathbf{K}^{(n-1)}=\mathbf{\hat{p}}^{(n-1)}_{(-)}\mathbf{H}^{(n-1)}\mathbf{S} ^{(n-1)}\mathbf{\hat{p}}^{(n-1)}_{(-)}\)
9:\(\hat{\mathbf{x}}^{(n-1)}=\mathbf{\hat{x}}^{(n-1)}_{(-)}\mathbf{+K}^{(n-1)}( \mathbf{z}^{(n-1)}\mathbf{-z}^{(n-1)}_{(-)})\)
10:\(\mathbf{\hat{p}}^{(n-1)}=(\mathbf{I}_{|\mathbf{x}|}-\mathbf{K}^{(n-1)}\mathbf{ H}^{(n-1)})\mathbf{\hat{p}}^{(n-1)}_{(-)}\)
```  
**Algorithm 1** Extended Kalman Filter Tracking Algorithm
## 4 Experimental Research
### Construction of Feature Vector  
After performing multiscale analysis for MI-EEG on all channels, a variety of forms can be used to construct the feature vector. If the multiscale fuzzy entropies of MI-EEG on all channels are fused serially, the feature vector is obtained by Equation (15):  
\[F^{1}=[MFE^{1}_{\text{C3}},MFE^{1}_{\text{C4}},MFE^{1}_{\text{Cz}}]\in R^{1 \times(3\times\tau_{\text{max}})}, \tag{15}\]  
where \(\tau_{\text{max}}\) is the maximum of \(\tau\); \(MFE^{1}_{\text{C3}}\), \(MFE^{1}_{\text{C4}}\), and \(MFE^{1}_{\text{Cz}}\) can be calculated by Equation (12) and stand for the MFE of MI-EEG on channels C3, C4, and Cz, respectively.  
Considering the ERD/ERS phenomenon of MI-EEG on channels C3 and C4, we can also flexibly select the MFE values of MI-EEG on those channels to construct a feature vector after a specific operation to guarantee the sharp distinction between two imaginary tasks. The result is as shown in Equation (16):  
\[F^{2}=[MFE^{1}_{\text{C3}}-MFE^{1}_{\text{C4}},MFE^{1}_{\text{Cz}}]\in R^{1 \times(2\times\tau_{\text{max}})}. \tag{16}\]  
In calculations for fuzzy entropy on different scale factors, parameters \(m\), \(n\), and \(r\) were set to 2, 2, and 0.1 \(SD\), respectively; \(SD\) was the standard deviation of the original MI-EEG signal, and \(\tau_{\text{max}}\) was equal to 4.  
To find the best means of feature vector construction, some experiments were conducted on a public dataset using SVM as a classifier. In addition, to eliminate the contingency in the feature extraction process and increase the objectivity of feature evaluation, 10-fold Cross-Validation (CV) was employed. This means that the data, including 280 trials, were randomly divided into 10 subsets, each of which was used as a validation set. Experiment environment: Win7 operating system, memory 4G, programming language is Matlab R2014a. The experiment results of 10-fold CV are listed in Table 1.  
Table 1 shows that the feature vector \(F^{2}\) constructed by Equation (16) has certain advantages over \(F^{1}\) constructed by Equation (15), and the highest classification accuracy and average classification rate with 10-fold CV were 100% and 90.36%, respectively. It is obvious that the feature vector \(F^{2}\) is more conducive to mining and characterizes more and deeper feature information contained in the MI-EEG signal. Therefore, feature vector \(F^{2}\) is employed in the following experiments.
# Technique Evolutions for Microorganism Detection in Complex Samples: A Review
## 2 Current Detection Methods
### Individual Cells Detection Methods
#### 2.2.1 Solid Phase Cytometry  
Microorganisms are trapped on a filter membrane and stained with a fluorophore that only emits light for viable cells. Viable microorganisms are detected by epifluorescence, with a single-cell resolution. Due to this high sensitivity, the usual incubation step is not required. Microbial contaminants can be detected within a few hours, even the viable and non-culturable ones. A wider field of view allows a faster scanning of the membrane [24]. Appropriate software is required to distinguish between viable microorganisms and auto-fluorescent particles. Otherwise, the confusion leads to false positives. The more general version of this method is named direct epifluorescent filtration technique (DEFT), in which other fluorescent dyes can be used (DAPI, CTC, etc.).
## 4 Discussion
#### Uncertainty and Limitations  
Despite that, the newly launched MSWEP revealed a better performance in estimating the spatial precipitation distribution and erroneousness than all other products. However, it still has some uncertainty in estimating the accurate magnitude of daily precipitation over highly mountainous areas. Thus, users of MSWEP must be circumspect about overestimating light precipitation occurrence, particularly in this type of study area. The finer spatial (0.1\({}^{\circ}\)) resolution and long-term data availability with considerable bias correction will favor the MSWEP product in hydro-climatic applications. However, bias correction is recommended for all GPPs before they can be used in any kind of meteorological investigation over the JRB and a similar topographic characteristic catchment. Lately, due to the inaccessibility of recently observed data, this study was only limited from (1981-2009). For that, the continuous monitoring of precipitation variation within the study scope using recently observed data is open for future research.
# Review of Remote Sensing Methods to Map Coffee Production Systems
## 3 Results
### Spectral Pixel-Based Approaches
The addition of the precipitation correlation to the seasonal model (with elevation) gave them a further bump of 1% to 90.5% overall accuracy.
## 2 Materials and Methods  
### Chemicals and Reagents  
Catechins, namely (+)-catechin (C, 98%-C1251), (-)-epicatechin (EC, 98%-E4018), (-)-epigallocatechin (EGC, 98%-E3768), (-)-epigallocatechin-3-gallate (EGCG, 95%-E4143), (-)-epicatechin-3-gallate (ECG, 98%-E3893), (+)-gallocatechin (GC, 98%-G6657) and (-)-gallocatechin-3-gallate (GCG, 98%-G6782), caffeine (CAF, 99%-C0750), gallic acid (98%-G7384), rutin, 2,2-diphenyl-l-picrylhydrazyl (DPPH), butylated hydroxytoluene (BHT), ethylenediaminetetraacetic disodium salt (EDTA), Folin-Ciocalteu reagent (FCR), potassium ferricyanide, iron (II) chloride (FeCl\({}_{2}\)), iron (III) chloride (FeCl\({}_{3}\)), aluminum chloride (AlCl\({}_{3}\)), ferrozine, and trichloroacetic acid (TCA), were all obtained from Sigma-Aldrich (St. Louis, MO, USA). Sodium carbonate (Na\({}_{2}\)CO\({}_{3}\)), potassium acetate (KCH\({}_{3}\)CO\({}_{2}\)), sodium phosphate, and orthophosphoric acid were purchased from E. Merck (Darmstadt, Hessen, Germany). Acetonitrile, methanol, chloroform, and ethyl acetate, HPLC-grade, were obtained from Riedel-de Haen (Aktiengesellschaft, Seelze, Germany). Ultrapure glass-distilled water that was deionized with the Millipore Milli-Q purification system (Millipore, Bedford, MA, USA) was used throughout all the experiments.
## 3 Experimental Results
### Analysis and Comparison of Experimental Results
#### 3.2.3 Deformation Capacity  
Table 3 lists the displacement of the specimen at the yield strength (\(\Delta_{y}\)), maximum strength (\(\Delta_{\text{pank}}\)), ultimate strength (\(\Delta_{u}\)) and specimen ductility (\(\mu=\Delta_{u}/\Delta_{y}\)). The ductility \(\mu\) of the IP specimen is 110% greater than that of the SSP specimen. The integrated member specimens exhibit high deformation capacity with an ultimate displacement \(\Delta_{u}\) in the range of 4.7%-5.6%. Furthermore, the stud-reinforced specimens exhibit higher ultimate displacement and ductility than the IP-only specimen. Thus, the reinforcement of the integrated member with studs imparts strength, but slightly reduces the deformation capacity of the specimen.
# Life Cycle Assessment for the Production Phase of Nano-Silica-Modified Asphalt Mixtures
## 1 Introduction
There have been several studies that attempt to assess the environmental impact of asphalt materials and some studies have also been conducted on asphalt binders modified with additives [12; 13; 14; 15]. However, to the author's knowledge, no studies that assess the complete LCA for the production phase of nano-silica-modified asphalt mixtures have previously been published. A new material being used as a modifier, there are uncertainties regarding the environmental impacts associated with nanomaterials. Therefore, it is of paramount importance to investigate the extent to which the use of nano-silica-modified asphalt mixtures for asphalt concrete pavement is beneficial from an environmental perspective. This study presents the assessment of a Nano-Silica-Modified Asphalt Mixtures in terms of materials production emissions through LCA methodology. The environmental impacts of a conventional asphalt mixture were assessed so that a comparison could be made to understand the impact contribution of nano-silica in the asphalt mixture. In addition, to be able to compare the relative significance of each impact category, the normalized score was computed for each impact category using impact scores and normalization factors. The application of LCA to NMAM has the potential to guide decision-makers on the selection of pavement modification additives to realize the full benefits of the use of nanomaterials in pavements while avoiding potential environmental risks.
## 2 Literature Review  
The initial and recent versions of BATMAN have been compared to other similar routing protocols in [18; 19]. As a proactive routing protocol, BATMAN is similar to most proactive routing protocols, including AODV [20] and OLSR, which it is most alike [21]. The initial work of the BATMAN routing protocol was derived and inspired by IETF Optimized Link State Routing Protocol (OLSR) [22]. Both routing protocols maintain a neighbor table with 2-hop nodes [23]; OLSR selects Multipoint Relays (MP), while BATMAN uses all the available neighbors to pass information [24]. Neighbor discovery in OLSR is carried out with HELLO messages, while the same function is carried out by Originator Messages (OGM). The only difference is that the link quality is also measured through OGM while OLSR separates Topology Control (TC) messages to announce network information. Some authors have also compared BATMAN with Destination Sequenced Distance Vector (DSDV), concluding that DSDV is much closer to BATMAN as both use sequence numbers to identify and discard obsolete information and prevent routing loops in the topology [25]. Some of the works carried out on the BATMAN routing protocol are discussed below in Table 1.
# Design of a Dynamic Secondary Mirror Truss Adjustment Mechanism for Large Aperture Telescopes
## 6 Results and Discussion  
The dynamic secondary mirror truss adjustment mechanisms designed in this study provide a particular reference value for designing SMAMs for large aperture telescopes. As an essential part of the telescope system, the telescope's secondary mirror truss adjustment mechanism must be designed in a large mode to meet the control system requirements for control bandwidth. The designed SMAM has an absolute accuracy of better than 16 \(\upmu\)m for movement in the z-direction and 20 \(\upmu\)m for requirements and an absolute positioning accuracy of better than 6.4\({}^{\circ}\) for deflection in the x-direction and 8\({}^{\circ}\) for requirements. In the travel also, all meet the requirements of use, as shown in Table 2.  
In the future, the study will consider other important factors, including the adjustment speed of the mechanism and the effect of different temperatures on the adjustment accuracy. The core components will be optimized to improve the resonance and increase the resolution and positioning accuracy.  
Conceptualization, B.L. and F.W.; methodology, B.L.; software, B.L.; validation, B.L., F.W. and B.Z.; formal analysis, B.L.; investigation, B.L.; resources, B.L.; data curation, B.L.; writing--original draft preparation, B.L.; writing--review and editing, B.L.; visualization, B.L.; supervision, B.L.; project administration, B.L.; funding acquisition, F.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded by The Jilin Science and Technology Development Program, grant number 20210402065 GH; Excellent Member of Youth Innovation Promotion Association CAS, grant number Y202053; International Partnership Program of the Chinese Academy of Sciences, grant number 181722 KYSB20200001; National Natural Science Foundation of China (NSFC); grant number 11973040; and National Key R&D Program of China; grant number 2017 YFE0102900.
# Precedence Table Construction Algorithm for CFGs Regardless of Being OPGs
## 2 Basic Definitions  
### Context-Free Grammars and Languages  
Within [PERSON]'s hierarchy [15], context-free grammars play a significant role in programming and compilation language applications by addressing the syntactic structure of programming languages.  
A _context-free grammar_ (CFG) \(G\) generates a language \(L(G)\), commonly called _context-free language_ (CFL), which is composed of the strings generated by the CFG. The CFG is defined as a 4-tuple \(G(S)=<T,N,S,P>\), where:  
* \(T\) represents the set of terminal symbols that create the strings within the CFL generated by the CFG.
* \(N\) represents the set of non-terminal symbols or syntactic variables that determine strings leading to CFL generation.
* \(S\) is the initial non-terminal symbol from which all strings defined by the GFC are generated.
* \(P\) is the set of productions or rules that group terminals and non-terminals to generate the strings. A production takes the form \(A\longrightarrow\alpha\), where \(A\) represents a non-terminal and \(\alpha\) is a combination of terminals and non-terminals. The \(\longrightarrow\) is pronounced \"produce\". Thus, the production is read \"\(A\) produce alpha\".  
The following notation will be used: lowercase letters from the beginning of the alphabet represent terminal symbols \((a,b,c,\ldots\in T)\); uppercase letters from the beginning of the alphabet represent non-terminal symbols \((A,B,C,\ldots\in N)\); lowercase letters late in the alphabet represent terminal strings \((u,v,w,x,y,z\in T^{+})\); lowercase Greek letters generally represent terminal and/or non-terminal strings \((a,\beta,\gamma,\ldots\in(T\cup N)^{*})\), and the empty string will be represented by \(\varepsilon\) (this Greek letter will be the exception to the above convention).
# An EV SRM Drive and Its Interconnected Operations Integrated into Grid, Microgrid, and Vehicle
## 4 G2V/V2G Operations
### Bidirectional CLLC Resonant Converter
#### 4.1.2 Control Scheme  
The control schemes of the CLLC resonant converter in two operation modes are shown in Figure 15a,b.  
Figure 14: Schematic of bidirectional CLLC resonant converter.  
Figure 15: CLLC resonant converter control schemes: (**a**) charging mode; (**b**) discharging mode.  
1. Charging mode (1) Normal G2V charging In the control system shown in Figure 15a, the battery voltage command is set at 158 V. And the current command \(i_{b}^{*}\) is yielded by the outer voltage loop and is limited at 10 A. Hence, before the battery voltage reaches 158 V, the battery charges in a constant current mode at 10 A. Then, the constant voltage mode is applied after the voltage reaches 158 V. Through trial-and-error, the voltage feedback controller and current feedback controller are set to PI type as: \[G_{cv}(s)=K_{pv}+\frac{K_{iv}}{s}=3+\frac{50}{s}\] (17) \[G_{ci}(s)=K_{pi}+\frac{K_{ii}}{s}=1+\frac{100}{s}\] (18) (2) Trickle charging The self-discharging phenomenon will reduce the battery store energy and the driving endurance range. To compensate this loss, the current command in Figure 15a is set as \(i_{b}^{*}=i_{ht}^{*}\) with a suitably low value for making the trickle charge [67; 68]. (b) Discharging mode In the discharging mode, only the voltage loop is arranged. The DC-link voltage is well-regulated at \(v_{dc}=400\) V via modulated switching frequency. Through trial-and-error, the voltage feedback controller is set to PI type as follows: \[G_{cv}(s)=K_{pv}+\frac{K_{iv}}{s}=3+\frac{50}{s}\] (19)
## 3 Experimental Results and Analysis
### Comparisons with the State of the Arts
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{2}{c}{**Computational**} & \multicolumn{3}{c}{**AIDS**} & \multicolumn{3}{c}{**WBDS**} \\  & \multicolumn{2}{c}{**Efficiency**} & & & & & & & \\ \hline \multirow{6}{*}{DANet} & Params & FLOPs & \multirow{2}{*}{IoU} & \multirow{2}{*}{precision} & \multirow{2}{*}{Recall} & \multirow{2}{*}{F1} & \multirow{2}{*}{IoU} & \multirow{2}{*}{precision} & \multirow{2}{*}{Recall} & \multirow{2}{*}{F1} \\  & (\(\times 10^{6}\)) & (\(\times 10^{9}\)) & & & & & & & \\ \cline{1-1}  & 46.19 & 125.14 & 79.68 & 88.25 & 89.14 & 88.69 & 77.95 & 94.07 & 81.98 & 87.61 \\ \cline{1-1}  & DeepLab v3+ & 40.35 & 17.36 & 82.98 & **96.73** & 85.37 & 90.70 & 85.12 & 95.99 & 88.25 & 91.96 \\ \cline{1-1}  & U-Net & 34.53 & 65.52 & 83.53 & 96.10 & 86.47 & 91.03 & 85.17 & 93.55 & 90.43 & 91.97 \\ \cline{1-1}  & ViT & 87.80 & 24.28 & 84.29 & 96.08 & 87.30 & 91.48 & 83.78 & 94.79 & 87.82 & 91.17 \\ \cline{1-1}  & TransUNet & 93.23 & 32.23 & 87.11 & 96.20 & 90.22 & 93.11 & 87.89 & 94.05 & 93.07 & 93.56 \\ \cline{1-1}  & CMTFNet & 30.07 & 8.56 & 88.05 & 94.26 & 93.03 & 93.64 & 86.21 & 90.12 & **95.21** & 92.59 \\ \cline{1-1}  & UANet & **26.73** & **7.45** & 88.83 & 94.90 & 93.28 & 94.08 & 88.50 & 92.73 & 95.09 & 93.90 \\ \cline{1-1}  & 93.23 & 32.23 & 90.12 & 95.67 & 93.95 & 94.80 & **92.07** & **96.65** & 95.11 & **95.87** \\ \cline{1-1}  & Ours & 93.23 & 32.23 & \multirow{2}{*}{**90.83**} & \multirow{2}{*}{95.58} & \multirow{2}{*}{**94.80**} & \multirow{2}{*}{**95.19**} & \multirow{2}{*}{90.30} & \multirow{2}{*}{95.80} & \multirow{2}{*}{94.02} & \multirow{2}{*}{94.90} \\ \cline{1-1}  & 30.28 & 19.93 & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparisons of different models on the AIDS and WBDS datasets. The boldfaced values indicate the optimal result.
## 5 Cross-Referencing Bloom-Filter-Based Data Integrity Framework
### Memory Overhead Analysis  
#### 5.3.1 Memory Requirements of a Standard Bloom-Filter-Based Data Integrity Solution  
This section analyzes the memory requirements of a standard Bloom-filter-based data integrity solution [38].  
We consider the dataset as shown in Table 2.  
Given a dataset and a false-positive probability, the total number of bits required for a data integrity solution can be calculated by substituting \(n\) in Equation (7).  
\[m=-\frac{(N\times S)lne}{ln2^{2}} \tag{8}\]  
\begin{table}
\begin{tabular}{c c} \hline \hline Files in the dataset & \(N\) \\ \hline Objects per file & \(S\) \\ \hline Total objects in the dataset & \((N\times S)\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Dataset specification.  
If we assume that the total number of files in the dataset (\(S\)) is equal to the number of objects per file (\(N\)), and we ignore any constant values, then the total bits required can be approximated as  
\[m\approx(N^{2}) \tag{9}\]