esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 The Role of Mining Tailings in Advancing Sustainable Construction Practices
### Mining Tailings in Cement Production  
Mining tailings, typically composed of silica (SiO\({}_{2}\)), alumina (Al\({}_{2}\)O\({}_{3}\)), iron oxide (Fe\({}_{2}\)O\({}_{3}\)), and lime (CaO), offer a valuable resource for the cement industry [158]. These chemical components are crucial for the formation of cement clinker, which is the core ingredient in cement production. By substituting or supplementing traditional raw materials with tailings, cement manufacturers can utilize a waste product beneficially while maintaining the essential chemical reactions required for high-quality cement. One of the primary advantages of using mining tailings in cement production is the potential to lower the sintering temperature needed for clinker formation [159]. Typically, the process of sintering cement clinker requires temperatures up to 1450 \({}^{\circ}\)C. However, when tailings rich in iron oxide and alumina are introduced, they can act as fluxing agents, reducing the temperature required to between 1300 \({}^{\circ}\)C and 1350 \({}^{\circ}\)C [160]. This reduction is particularly effective when tailings are used in conjunction with medium calcium limestone, which is a common raw material in cement production [161]. By decreasing the sintering temperature, the cement production process becomes significantly more energy-efficient, which not only reduces operational costs but lessens carbon emissions--both critical factors in the industry's push towards sustainability. Additionally, the incorporation of tailings has been shown to enhance the mechanical properties of cement. Specifically, tailings can improve the burnability of the raw mix [159], which refers to the ease with which the raw materials combine to form clinker minerals under high temperatures. Improved burnability leads to a more consistent and complete reaction, enhancing the overall quality of the clinker. Furthermore, tailings can promote the formation of tricalcium silicate (C3S), the mineral primarily responsible for the strength developed in the early stages of cement setting [162]. The specific mineral compositions in tailings can vary depending on the source and type of mining activity, providing unique benefits in cement production. The presence of certain trace elements in the tailings, such as manganese [163], or vanadium or titanium [164], can act as mineralizers, facilitating the formation of C3S and improving the speed of clinker formation. The tailings from iron ore mining, which are high in Fe\({}_{2}\)O\({}_{3}\), can contribute to early strength development in cement ([PERSON] et al., 2024) [165]. By contrast, the tailings from aluminum ore processing might offer advantages in terms of durability and resistance to chemical attack [166].
# A Snapshot of the Microbiome of a Portuguese Abandoned Gold Mining Area
###### Abstract  
Microbial communities are known to contribute deeply to geochemical cycles, including weathering, protection from erosion and mineral precipitation. Studies aiming to understand mining areas' microbiomes are of high relevance since they can help pinpoint the occurrence of environmental shifts, key bioremediation species, environmental metals recovery strategies, and microorganisms with relevant industrial properties. Nonetheless, so far, the study of Portuguese gold-rich areas' microbiomes has been largely neglected. The main goal of this study was to apply high-throughput sequencing methods to study the microbiome (Bacteria and Fungi) and predict their functional/metabolic profiles in an abandoned Portuguese gold mining area (considering zones without a history of mining, the tailings and the flooded mine interior). The results obtained revealed high bacterial and fungal diversities at these sites while also pinpointing the presence of relative homogenous bacterial and heterogenous fungal communities. Areas without mining history were mainly dominated by WD2101 soil groups, _Sphingomonas_, Candidatus _Solibacter_, _Heliotales_, unclassified _Fungi_ and _Arzotrichum_. The tailings were mainly colonized by _Byobacter_, WD2101 soil groups, WPS-2 genera, _Starmerella_, _Heliotales_ and _Mollisia_. On the other hand, the mine area displayed a dominance of _Crossiella_, _Gemmataceae_, _Aicobacteriaceae_ (Subgroup 1), _Acidipillium_, _Mortierella_, unclassified _Fungi_ and _Chaetohydriales_. Furthermore, we verified that contrary to bacteria, the fungal structural diversity is somewhat more restricted to each site. In addition, metabolic, functional and ecological profiles revealed a strong distinction for both bacterial and fungal communities while also revealing the presence of well-adapted communities to each of the particular microenvironments considered.  
gold mine; metabarcoding; microbiome; bacteria; fungi; tailings +
Footnote †: journal: Applied sciences
## 4 System Identification Methods  
System identification is the process of determining the fundamental dynamic parameters of a mathematical model based on measured input and output data. The choice of a system identification method is contingent on the particular problem, making a universal method for flutter derivative extraction impractical. In this study, the logarithmic decrement method (LDM), the Hilbert transform method (HTM), the modified Ibrahim time domain (MITD) method, and the iterative least squares (ILS) method are implemented for the identification of parameters in an SDOF system, while only ILS and MITD are used for a 2 DOF system.
## 1 Introduction
[14] investigated several image sharpness methods for improving Vickers hardness measurement and suggested that the Brenner autofocus function provides the best compromise between computational effort and accuracy. However, typical image processing approaches often fail to detect indentations in materials with poor surface uniformity, rough surfaces, surfaces with noise patterns, distorted indentation shapes, or cracks, leading to accurate detection and segmentation of indentations in Vickers images remaining challenging. In order to address the issue, data-driven and machine learning approaches have recently been proposed. For example, [PERSON] et al. [15] proposed a microstructure-informatic strategy with random forests and linear LASSO models to predict HVs. [PERSON] et al. [9] extracted microstructure features through image processing tools and developed a machine learning model to measure hardness. [PERSON] et al. [16], [PERSON] et al. [17], [PERSON] et al. [18], [PERSON] et al. [19], and [PERSON] et al. [20] proposed to leverage the convolutional neural network (CNN) [21] to obtain location information in the convolutional layer, representing the edges or corners of feature vectors for accurate localization and segmentation of Vickers indentations (see Figure 1a). However, these methods still relied on the indentations generated by forcing a pyramidal diamond indenter, which may result in noisy surfaces containing cracks, sparkles, and other distortions in the created images. The purpose of this study is to use deep-learning-based methods to measure Vickers hardness by directly analyzing optical images of the SCM 440 steel. Considering the indentation procedure illustrated in Figure 1, it is time-consuming and requires trained operators, noisy surfaces, distorted indentation shapes, and cracks of the created Vickers images affect the accuracy and robustness of automated methods developed in previous works. In this regard, we propose a data-driven approach to develop a neural network model that can directly analyze the pixels in an image, capturing geometrical patterns in microstructures to measure Vickers hardness. The feasibility of the proposed method is evaluated on a real dataset specifically collected for this study, along with a report of the performance comparison among several state-of-the-art CNN models applied for the task.
## 3 Methodology
### Local Seasonal Information Encoder  
For weather and PV power series, the seasonal part contains the main volatility feature, which is the key to accurate prediction. Therefore, we introduce series decomposition blocks to the LSI encoder to extract seasonal patterns from local measurement data. As shown in the middle of Figure 1, the LSI encoder is staked with \(L_{\text{LSI}}\) LSI encoder layers. Given the input of the LSI encoder \(\mathbf{X}_{\text{LS}}^{0}\in\mathbb{R}^{L_{\text{in}}\times D}\) that is embedded from \(\mathbf{X}_{\text{LS}}\in\mathbb{R}^{L_{\text{in}}\times D_{\text{DS}}}\), the procedure in \(l\)-th LSI encoder layer is  
\[\begin{split}&\mathbf{S}_{\text{LS},1^{\prime}-}^{l}=\text{SDBlock}( \text{Attention}(\mathbf{X}_{\text{LS}}^{l-1})+\mathbf{X}_{\text{LS}}^{l-1}), \\ &\mathbf{S}_{\text{LS},2^{\prime}-}^{l}=\text{SDBlock}(\text{FeedFoward}( \mathbf{S}_{\text{LS},1}^{l})+\mathbf{S}_{\text{LS},1}^{l}),\\ &\mathbf{X}_{\text{LS}}^{l}=\mathbf{S}_{\text{LS},2}^{l},\end{split} \tag{10}\]  
where \"\(-\)\" is the ignored trend part; \(\mathbf{S}_{\text{LS},i}^{l},i\in\{1,2\}\) denotes the seasonal part in the \(l\)-th layer; \(\mathbf{Z}_{\text{LS}}=\mathbf{X}_{\text{LS}}^{L_{\text{LSI}}}\) denotes the output of the LSI encoder.
## 2 Results and Discussion
### VOCs Produced during Fermentation  
LB672, which is an obligatory heteroformetative LAB, ferment sugars via the PK pathway and produces a mixture of primary products such as lactic acid, acetic acid, ethanol, and CO\({}_{2}\) as well as hundreds of volatile secondary metabolites. These volatile secondary metabolites are responsible for flavour notes or flavour precursors [28; 44]. A total of 267 mass peaks (\(m/z\)) were extracted from the raw PTR-ToF-MS data obtained from the headspace of vials containing LB672 growing at either 25 or 35 \({}^{\circ}\)C. After the removal of isotopologues and \(m/z\) that were not significantly (\(p>0.05\)) different from the baseline data, the number of \(m/z\) was reduced from 267 to a finalised list of a 104 \(m/z\) (Table S1). The tentative identification (t.i.) of each of the 104 \(m/z\) was based on its exact mass, supporting HS-SPME-GC-MS identification for 29 of the 104 (Tables 2, 3 and S1), fastGC-PTR-ToF-MS identification and/or literature data. The concentrations of all finalised \(m/z\) were highest after 7 days. At 14 days, the concentration of most \(m/z\) decreased as growth stopped and gas flushing removed the VOCs. Therefore, in order to better determine the effects of carbon sources on the VOCs produced, only the data obtained after 0 and 7 days of fermentation were compared. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Medium**} & \multirow{2}{*}{**Initial pH**} & \multicolumn{2}{c}{**at 25 \({}^{\circ}\)C**} & \multicolumn{2}{c}{**at 35 \({}^{\circ}\)C**} \\ \cline{3-5}  & & **pH** & **OD\({}_{600}\)** & **pH** & **OD\({}_{600}\)** \\ \hline DM & 5.67 \(\pm\) 0.035 \({}^{\mathrm{a}}\) & 4.47 \(\pm\) 0.011 \({}^{\mathrm{b}}\) & 1.40 \(\pm\) 0.005 \({}^{\mathrm{a}}\) & 4.44 \(\pm\) 0.1 \({}^{\mathrm{b}}\) & 1.20 \(\pm\) 0.005 \({}^{\mathrm{b}}\) \\ DMFr & 5.68 \(\pm\) 0.025 \({}^{\mathrm{a}}\) & 4.72 \(\pm\) 0.03 \({}^{\mathrm{b}}\) & 1.26 \(\pm\) 0.06 \({}^{\mathrm{a}}\) & 4.65 \(\pm\) 0.04 \({}^{\mathrm{b}}\) & 1.06 \(\pm\) 0.04 \({}^{\mathrm{b}}\) \\ DMCi & 6.27 \(\pm\) 0.005 \({}^{\mathrm{a}}\) & 6.27 \(\pm\) 0.0045 \({}^{\mathrm{a}}\) & 0.07 \(\pm\) 0.005 \({}^{\mathrm{a}}\) & 6.27 \(\pm\) 0.0005 \({}^{\mathrm{a}}\) & 0.05 \(\pm\) 0.0025 \({}^{\mathrm{a}}\) \\ \hline \hline \end{tabular} DM: original defined medium (glucose); DMFi: defined medium with fructose; DMCi: defined medium with citrate.  
\end{table} 
Table 1: The mean pH and OD\({}_{600}\) of the samples after 14 days of LB672 fermentation in different medium compositions. Values are the mean \(\pm\) standard error of two replicates. Values with different superscript lowercase letters (\({}^{\mathrm{a-b}}\)) in the row (either pH or OD\({}_{600}\)) are significantly different according to [PERSON]’s test at \(p\)\(<0.05\).
## 3 Results and Discussion
### Performance Test  
#### 3.2.1 Tensile Test  
Figures 4-6 exhibit the ultimate tensile strength (UTS), % elongation at break and E-modulus of the membranes with different sulfur loadings. The membrane with GO exhibits higher UTS and E-modulus compared to pure NBR membrane at all sulfur loadings. As evidenced from XRD results, GO dispersion could be observed for all the membranes regardless of sulfur loading. Dispersion of GO will promote good interaction between GO filler and NBR matrix and thus leads to efficient stress transfer between filler and matrix. Moreover, addition of GO as filler greatly improves membrane strength due to its excellent mechanical properties, high surface area and stiffness. The UTS and E-modulus also increase proportionally with the increment in sulfur loading.  
Figure 3: XRD pattern of GO and NBR/GO membranes at different sulfur loadings.  
Figure 4: Ultimate tensile strength (UTS) of the membranes.  
Figure 5: E-modulus of the membranes.  
This proportional relationship is due to the crosslink density. According to [PERSON] et al., the increase in sulfur loading results in higher crosslink density and therefore higher moduli, stiffness, hardness and material strength could be imparted [53]. Preparation of membranes using the latex compounding and curing method has yielded membranes with higher and comparable UTS (21-22 MPa) with polymeric membranes produced through other methods. For instance, polyvinyl chloride (PVC) membrane incorporated with 0.75 wt.% GO shows UTS value of 5.46 MPa [54], polyethersulfone-functionalized GO shows maximum UTS improvement up to 22 MPa [55] and polysulfone (PSF) membrane filled with 0.25% GO shows UTS value of 4.06 MPa [56]. Comparison of UTS with latex-based membrane is not possible because to the best of our knowledge, this research work is the first attempt to produce latex-based membranes. However, the % elongation of the membranes decreases when the sulfur loading increases. As membranes have more crosslinks, the rubber chain mobility will be restricted and the chains are unable to dissipate heat generated by deformation through molecular motion, resulting in easy and brittle rupture at low elongation [57].
## 2 Signal Model  
### Array Signal Model  
Consider \(D\) uncorrelated signals that impinge on a massive MIMO system equipped with \(N\) receive antennas from directions \(\mathbf{\theta}=[\theta_{1},\theta_{2},\cdots\theta_{D}]^{\mathrm{T}}\). The analog RF array received signal at time \(t\) is modeled as  
\[\begin{split}\mathbf{x}^{\mathrm{RF}}(t)&=\sum_{d=1}^{D }\mathbf{a}(\theta_{D})s_{d}(t)e^{i\omega_{c}t}+\mathbf{n}(t)\\ &=\mathbf{A}(\mathbf{\theta})\mathbf{s}(t)e^{i\omega_{c}t}+\mathbf{n}(t),\end{split} \tag{1}\]  
where \(\mathbf{A}(\mathbf{\theta})=[\mathbf{a}(\theta_{1}),\mathbf{a}(\theta_{2}),\cdots,\mathbf{a}( \theta_{D})]\in\mathbb{C}^{N\times D}\) denotes the array manifold matrix whose \(d\)th column \(\mathbf{a}(\theta_{d})\in\mathbb{C}^{N}\) represents the steering vector of the \(d\)th user with DOA \(\theta_{d}\), \(\mathbf{s}(t)=[s_{1}(t),s_{2}(t),\cdots,s_{D}(t)]^{\mathrm{T}}\in\mathbb{C}^{D}\) represents the signal waveform vector, \(\omega_{c}\) denotes the angular frequency of the carrier, and \(\mathbf{n}(t)\sim\mathcal{CN}(\mathbf{0},\sigma_{\mathrm{n}}^{2}\mathbf{I}_{N})\) represents the zero-mean additive white Gaussian noise (AWGN) vector.  
Figure 1 depicts the block diagram of the receiver antenna array of a massive MIMO system without performing compressed measurement. In this receiver array, each antenna is assigned with a dedicated front-end circuit, which converts the received analog RF signal to the digital base-band by performing down conversion and analog-to-digital conversion. However, dedicating a separate front-end circuit to each antenna in a massive MIMO system may be impractical, considering the hardware cost, power consumption, and computational complexity.
## 3 Models' Development and Results
### Input Selection  
Before applying boosting and bagging techniques to data, an input selection has been conducted. As previously mentioned, this study adopted a likelihood ratio test for selecting the most relevant inputs for predicting the E. The candidate inputs included DD, Vp, Qtz, Mica, Chl, Plg, and Kpr. This test then selected Vp, Qtz, DD, and Mica, respectively, as the most relevant E prediction inputs. Figure 4 provides a series of 3D density diagrams of the selected variables and shows the frequency distribution of pairs of each input variable and the target variable (E). The inputs selected in this step will be used to develop the standard, boosting, and bagging models.  
Figure 4: 3D density diagrams of pairs of each input variable and E.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Input**} & \multicolumn{2}{c}{**Before Transformation**} & \multicolumn{2}{c}{**After Transformation**} \\ \cline{2-5}  & **Skewness** & **SD** & **Skewness** & **SD** \\ \hline Vp & 0.36 & 1137.62 & 0.36 & 0.19 \\ Qtz & 0.21 & 5.68 & 0.21 & 0.17 \\ DD & 2.75 & 0.13 & 2.75 & 0.18 \\ Mica & 0.43 & 3.56 & 0.43 & 0.21 \\ Chl & 0.85 & 1.65 & 0.85 & 0.33 \\ Plg & 0.20 & 7.86 & 0.20 & 0.15 \\ Kpr & \(-1.05\) & 5.36 & \(-1.05\) & 0.17 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Details of inputs distribution before and after the transformation.
## 4 Experiments
### Color Variation Threshold and Erosion Distance  
We re-state, for ease of reference, Equation (14) for the color variation \(\mathsf{CLV}^{V}\) of a video \(V\) and Equation (16) for the color variation's scaled threshold \(\Theta^{V}\).  
\[\mathsf{CLV}^{V}=\mathsf{STD}(\mathsf{MXV}^{V})\]  
\[\Theta^{V}=\theta_{t}+(\theta_{u}-\theta_{l})(\mathsf{CLV}^{V}-\mathsf{CLV}_{l} )/(\mathsf{CLV}_{u}-\mathsf{CLV}_{l})\]  
When we computed \(\mathsf{CLV}^{V}\) for each video in the testbed set, we observed that the rounded values of \(\mathsf{CLV}^{V}\) ranged from 5 to 210 and set \(\mathsf{CLV}_{l}\) to 5 and \(\mathsf{CLV}_{u}\) to 210. We also observed that for all of the videos the rounded values of \(\mathsf{CLV}^{V}\) ranged from 9 to 65. In particular, for the videos with lower bee traffic, \(\mathsf{CLV}^{V}\) tended toward 9 and for the videos with higher bee traffic-toward 65. Thus, we set the values of \(\theta_{l}\) and \(\theta_{u}\) to 9 and 65, respectively. Consequently, in the current implementation of BeePIV, the value of \(\Theta^{V}\) is computed according to Equation (32).  
\[\Theta^{V}=9.0+\frac{65.0-9.0}{210.0-5.0}(\mathsf{CLV}^{V}-5.0)=9.0+\frac{56.0} {205.0}(\mathsf{CLV}^{V}-5)\approx 9.0+0.27(\mathsf{CLV}^{V}-5.0) \tag{32}\]  
Recall that in Equation (15) we postulated the existence of functions \(\Gamma:\mathbb{R}\to\mathbb{R}\times\mathbb{R}\) from reals to 2-tuples of reals that maps video-specific color variation \(\mathsf{CLV}^{V}\) values to video-specific color variation threshold \(\Theta^{V}\) and erosion distance \(d^{V}\) values that are used to convert smoothed difference frames \(S_{t,\mathsf{A}}\) to motion frames \(W_{t}\) with uniform background. In the current implementation of BeePIV, the function \(\Gamma(\mathsf{CLV}^{V})\) is computed in accordance with Equation (33).  
\[\Gamma(\mathsf{CLV}^{V})=(\Theta^{V},\gamma(\Theta^{V})), \tag{33}\]  
where  
\[\gamma(x)=\begin{cases}5&\text{ if }0\leq x<22;\\ 3&\text{ if }22\leq x.\end{cases}\]  
In Equation (33), we chose the specific ranges for \(d^{V}\) in \(\gamma(x)\) on the basis of our experiments with the 20 videos in the testbed set. We observed that the \(\Theta^{V}\) values computed from the videos with lower to medium bee traffic ranged from 9 to \(\approx\)21.5 and for the videos with medium to higher traffic ranged from 22 to 65. The average size of an individual honey bee in 60 \(\times\) 80 video frames that BeePIV processes is \(\approx\)10 pixels. In lower traffic videos, where bees do not tend to fly in close proximity, we chose to set the value of \(d^{V}\) to approximately 1/2 the size of the bee so that local maxima positions that farther apart than half the bee are not eroded. In higher traffic videos, where bees tend to fly in closer proximity, we set the value of \(d^{V}\) to approximately 1/3 the size of the bee so that local maxima positions that are farther apart than a third of the bee are not eroded.
## 3 Optical Receiver Filter Equation-MGF Optimisation Procedure
### MGF and LMGF for Optical Receiver Signal  
The MGF uniquely determines the probability density function (PDF) of the underlying random variable by using the MGF's first and second derivatives as the mean and variance of the underlying random variable [28]. After applying the definition of the ordinary MGF [28] on \(r_{f}(t)\) signal component only in Equation (5) and taking into consideration the DSPP photoelectron generation process, we obtain the following [15; 16]:  
\[M_{r_{f(m)}}(s)=Exp[\int_{-\infty}^{\infty}\lambda_{m}(t)(Exp[sh_{f}(\tau-t)] -1)d\tau], \tag{7a}\] \[L_{r_{f(m)}}(s)=\int_{-\infty}^{\infty}\lambda_{m}(t)(Exp[sh_{f}(\tau-t)]-1)d\tau, \tag{7b}\]  
where m = [0, 1] and based on Equation (6), \(\lambda_{1}(t)=\varphi_{1}(t)+\varphi_{dc}\) is for the ON bit and \(\lambda_{0}(t)=\varphi_{0}(t)+\varphi_{dc}\) is for the OFF bit. s \(\epsilon\) [-1,1] is the transformation parameter [28]. For the sake of simplicity, we will drop the infinity notation in the limits of the integral. In a typical optical receiver, the colored ATGN variance [10]:  
\[\sigma^{2}=\frac{N_{0}}{2}\ \int\left(\ h_{f}^{2}(t)+\frac{{h_{f}^{\prime}}^{2}(t) }{w_{0}^{2}}\right)dt. \tag{8a}\]  
Then, the MGF and its corresponding LMGF for the AGTN noise component \(r_{th}(t)\) in Equation (5) takes the form [10]:  
\[M_{r_{th}}(s)=Exp\left[\frac{s^{2}N_{0}}{4}\ \int\left(\ h_{f}^{2}(t)+\frac{{h_{f}^ {\prime}}^{2}(t)}{w_{0}^{2}}\right)dt\ \right]\, \tag{8b}\]  
\[L_{r_{th}}(s)=\frac{s^{2}N_{0}}{4}\ \int\left(\ h_{f}^{2}(t)+\frac{{h_{f}^{ \prime}}^{2}(t)}{w_{0}^{2}}\right)\,dt, \tag{8c}\]  
\(h_{f}^{\prime}(t)\) is the first derivative of \(h_{f}(t)\), \(w_{0}\) is the central noise power spectral frequency, and \(N_{o}\) is a Gaussian process's signal-sided thermal noise spectral density. The first term of Equation (8) represents the white AGTN. Since \(r_{sig}(t)\) and \(r_{th}(t)\) are statistically independent components of \(r_{f}(t)\), then the overall MGF and LMGF are:  
\[M_{r_{f}}(s)=M_{r_{sig}}(s)\cdot M_{r_{th}}(s)\, \tag{9a}\]\[L_{r_{f}}\left(s\right)=L_{r_{sig}}(s)+L_{r_{th}}(s), \tag{9b}\]  
where L\({}_{()}\)(s) is the Log Moment Generating Function (LMGF) of (.). Hence, Equation (9) models the values taken by the filter output at the sampling time, i.e., at the input of the decision unit in Figure 3. In the rest of this paper, we will drop the notation of (s) inside the MGF and LMGF. In Equation (5), if we set \(h_{f}(t)\equiv sh_{f}(t-\tau)\) and \(\lambda_{m}(t)\equiv\varphi_{m}(t)+\varphi_{dc}\), we can write the LMGF for \(r_{sig}(t)\) for OFF (m = 0) and ON (m= 1) bits as follows:  
\[L_{r_{f(m)}}=(-1)^{m}\int\lambda_{m}(t)(Exp[\ (-1)^{m}\ h_{f}(t)]-1)dt+\frac{N_{0} }{4}\ \int\left(\ h_{f}^{2}(t)+\frac{{h^{\prime}_{f}}^{2}(t)}{w_{0}^{2}} \right)\ dt\, \tag{10}\]  
where m \(\in\{0,1\}\).