esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Methodology
### Material Assessment
#### 2.1.3 Multiple Objective Decision Making (MODM) Examinations  
After the MADM step, two conflicting objective functions of [PERSON]'s approach [31; 32] are used to examine whether the ranking goals agree with two primary LHTES performance objectives: high energy density and fast heat transfer.  
To maximize the thermal energy stored in a certain volume and minimize the thermal inertia, the volumetric energy density and equivalent diffusivity of the PCM are selected as the objective functions \(f_{1}\) and \(f_{2}\),  
\[f_{1}=\left(dH+c_{\mathrm{P}}\cdot\Delta T\right)\cdot\rho \tag{8}\]  
\[f_{2}=k_{\mathrm{PCM}}/\left(c_{\mathrm{P}}\cdot\rho\right) \tag{9}\]  
where \(\Delta T\) [K] is the temperature change during charging/discharging.  
High \(f_{1}\) value indicates that the LHTES unit stores more thermal energy by using this material, while high \(f_{2}\) allows for faster charging and discharging of the LHTES unit. The \(f_{1}\) and \(f_{2}\) values of the materials are plotted in an objective map with the conflicting objectives \(f_{1}\) and \(f_{2}\) being the \(x\) and \(y\) axes. Preferred material alternatives should perform better than nonpreferred materials for both \(f_{1}\) and \(f_{2}\), indicating that they have relatively higher \(dH\), \(C_{\mathrm{P}}\), and \(k_{\mathrm{PCM}}\) at the same time, which are the key desired properties of PCMs [3; 33; 34]. An illustration about how to plot the properties of PCMs in an objective map is provided in Figure 3.  
If the MADM ranking results mostly overlap with the MODM examination results, the best material alternatives will serve as the material candidates for the geometrical assessment. Otherwise, the designer should adjust the weights of the MADM ranking. After several rounds of iteration, the final decision will be a combination of both the engineers' preference and the LHTES performance objectives [26].  
Detailed explanation and illustration of how the MADM ranking and MODM examination work jointly to rank the PCMs can be found in [PERSON] et al. [26; 27].
# Mycotoxin Level in Winter Wheat Grain as Impacted by Nitrogen and Manganese Fertilisation
## 4 Discussion
### Grain Yield  
Net nitrogen productivity varied widely during the study years, and weather conditions largely decided the effectiveness of nitrogen fertilisation [64]. The grain yield determined in the current study was mainly affected by the varied weather conditions during the wheat-growing periods. Neither nitrogen nor manganese fertilisation differentiated the wheat grain yield. It has been shown in many studies [65; 66] that foliar application of small amounts of micronutrients (alone or in combination with other essential nutrients) can increase the yield and its components, thereby improving wheat growth and quality. The grain yield was correlated with _Fusarium_ spp. infestation since _Fusarium_ head blight has an adverse impact on wheat grain yield [67]. This disease, as examined by Spanic [68], reduced the grain yield in some wheat cultivars by up to 64%.
## 4 Test Experiments and Discussion of DMMAEO
### Scalability Comparison Analysis  
The scalability test is conducted in this subsection, which is used to test the optimization performance of the proposed DMMAEO in different dimensions. The scalability experiments are carried out on the optimization problems with 30, 50, and 100 dimensions, respectively. Except for the change in dimension setting, other experimental parameters are consistent with the previous subsection. The results for the scalability tests in different dimensions are shown in Table 6.  
According to the results in Table 6, the optimization performance of EO gradually declines with the increase in dimension. In contrast, the optimization ability of DMMAEO remains stable in more functions, although the optimization ability of DMMAEO also declines with the increasing dimensionality. Moreover, the DMMAEO still shows better optimization ability than EO in most functions with the increase in dimension. Therefore, the scalability experiment shows that the proposed DMMAEO has more stable optimization ability than the canonical EO in the case of dimensional change.
## 3 Results
### Modified method of the NPs fabrication  
Within the present study we have elaborated a modified nanoprecipitation method, according to which the surfactant was dissolved in the organic solvent and added dropwise to the aqueous phase, i.e., pure water. All the neutral AABB polymers **1F6**, **1L6**, **4F4** and **8L6**, and five of eight surfactants were included in these experiments. The parameters (invariable and variable) of the NPs fabrication process are given in table below:  
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{5}{c}{**Parameters of the Process**} \\ \hline  & **Invariable** & & **Variable** \\ \hline \(\bullet\) & solvent--DMI & \(\bullet\) & polymers (four)—**1F6**, **1L6**, **4F4** and **8L6** \\ \(\bullet\) & concentration of the polymer in organic & \(\bullet\) & surfactants (five)— Tween 20, Triton X-100, \\  & phase--6.0 mg/mL & & Brij 010, Mowiol 4-88 and Mowiol 8-88 \\ \(\bullet\) & concentration of the surfactant in the organic & & & \\ phase--50.0 mg/mL & & & & \\ \(\bullet\) & O/W ratio--1:10 & & & \\ \(\bullet\) & organic phase dropping rate--12 drops/min & & & \\ \(\bullet\) & stirring rate of the water phase--700 rpm. & & & \\ \hline \hline \end{tabular}  
The conditions of the NPs fabrication were as follows: the solvent: DMI; the polymer concentration in the organic phase: 6.0 mg/mL; the surfactant concentration in the organic phase: 50.0 mg/mL; the O/W ratio: 1:10; the organic phase dropping rate: 12 drops/min; and the stirring rate of the water phase: 700 rpm. The results obtained for all the AABB polymers using five surfactants in terms of the MPD and PDI of the NPs are listed in Tables 10-13.  
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{5}{c}{**Surfactant**} \\ \cline{2-6}  & **Tween 20** & **Triton X-100** & **Brij 010** & **Mowiol 4-88** & **Mowiol 8-88** \\ \cline{2-6}  & \multicolumn{5}{c}{**MPD (nm) \(\pm\) SD**} & **[PDI] \(\pm\) SD** & \\ \hline \multirow{2}{*}{NM} & **143 \(\pm\) 6** & **148 \(\pm\) 6** & **160 \(\pm\) 10** & **321 \(\pm\) 4** & **328 \(\pm\) 2** \\  & [0.123 \(\pm\) 0.019] & [0.116 \(\pm\) 0.004] & [0.268 \(\pm\) 0.009] & [0.053 \(\pm\) 0.015] & [0.075 \(\pm\) 0.019] \\ \hline \multirow{2}{*}{MNM} & **121 \(\pm\) 4** & **113 \(\pm\) 5** & **108 \(\pm\) 3** & **222 \(\pm\) 7** & **199 \(\pm\) 4** \\  & [0.230 \(\pm\) 0.024] & [0.180 \(\pm\) 0.011] & [0.213 \(\pm\) 0.006] & [0.092 \(\pm\) 0.020] & [0.087 \(\pm\) 0.014] \\ \hline \hline \end{tabular}  
Figure 7: The influence of the stirring rate of the water phase on the mean diameter of the **1F6** (**A**) and **4F4** (**B**) NPs.
# Sigfox and LoRaWAN Datasets for Fingerprint Localization in Large Urban and Rural Areas
## 1 Introduction
This paper presents three LPWAN datasets which can be used to evaluate fingerprinting methods in outdoor environments. All datasets were collected in real outdoor environments, no simulations or propagation models were used. Firstly, we created a Sigfox dataset in a large rural area between Antwerp and Ghent, Belgium. Secondly, an urban Sigfox dataset was built in the city center of Antwerp. Lastly, an urban LoRaWAN dataset was also built in the city center of Antwerp. In the near future, we also intend to create a rural LoRaWAN dataset in the large area between Antwerp and Ghent, as well as a rural and urban NB-IoT dataset. The remainder of the paper is structured as follows. Section 2 describes three state-of-the-art LPWAN standards, two of which were used to create our datasets. Section 3 explains how the messages were collected and stored in a fingerprint database. Section 4 illustrates how the dataset can be used by the research community. In Section 5, the results of our analysis are listed. These results are then discussed in Section 6. Finally, Section 7 concludes the paper and states the intended future work.
# Removal of Antibiotics by Biochars: A Critical Review
## 4 A Critical Review of Biochar-Based Adsorption Processes
### Biochar Properties
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Feedstock** & \begin{tabular}{c} **Pyolysis** \\ **Temperature (\({}^{\circ}\)C)** \\ \end{tabular} & \begin{tabular}{c} **Char Yield (\%)** \\ \end{tabular} & \begin{tabular}{c} **Surface Area** \\ **m\({}^{2}\)/g** \\ \end{tabular} & \begin{tabular}{c} **Pore Volume** \\ **cm\({}^{3}\)/g** \\ \end{tabular} & \begin{tabular}{c} **Ash Content** \\ **(\%)** \\ \end{tabular} & \begin{tabular}{c} **Reference** \\ **Reference** \\ \end{tabular} \\ \hline Rice straw & 700 & - & 20.6 & 0.019 & - & [113] \\ \hline Rapeseed & 550 & - & \
\begin{tabular}{c} 25.4 (BET) \\ 18.3 (Micro) \\ 7.1 (Meso) \\ \end{tabular} & 0.0480 & 24.9 & [114] \\ \hline Rapeseed & 700 & 29.6 & 19.3 & 1.254 & 14.4 & [115] \\ \hline Maize & 600 & 29.54 & 70 & 0.06 & 27.2 & [116] \\ \hline Sugarcane & 300 & - & 224.1 & & 4.2 & \\ bagasse (SGB) & 400 & - & 361.8 & & 4.2 & [117] \\ \hline Giant _Miscanthus_ & 500 & 27.2 & 181 & & - & [118] \\ \hline Peanut shell & 700 & 25.1 & 369 & & - & [118] \\ \hline Peanut shell & 700 & 21.9 & 448.2 & 0.200 & 8.9 & [108] \\ \hline Palm kernel shell & 400 & 46.7 & 4.5 & 0.011 & 8.1 & \\ 500 & 37.5 & 12 & 0.086 & 5.2 & \\ 600 & 35.4 & 260 & 0.17 & 8.9 & [77] \\ \cline{2-6}  & 700 & 32.8 & 370 & 0.19 & 8.4 & \\ \hline Olive stones & 400 & - & 476.3 & & 36.2 & [119] \\ \cline{2-6}  & 600 & - & 173.3 & & 41.2 & [119] \\ \hline Alfafa (_Melicago sativa_) & 500 & - & 31.1 & & 31.3 & [120] \\ \hline Orange peel & 700 & 22.2 & 201.0 & 0.035 & 2.8 & [121] \\ \hline Tire rubber & 400 & 59.3 & 24.2 & 0.080 & 15.4 & \\  & 600 & 54.5 & 51.5 & 0.120 & 15.6 & [122] \\  & 800 & 43.0 & 50.0 & 0.110 & 10.5 & \\ \hline \multirow{4}{*}{Grape seeds} & \multirow{4}{*}{700} & \multirow{4}{*}{28} &
\begin{tabular}{c} 124 (N\({}_{2}\)) \\ 454 (CO\({}_{2}\)) \\ 66 (Ar77) \\ \end{tabular} & & \multirow{4}{*}{-} & \multirow{4}{*}{[93]} \\  & & & 110 (N\({}_{2}\)) & & \\  & 600 & 31 & 424 (CO\({}_{2}\)) & & \\  & & 57 (Ar77) & & & \\ \hline Wood & & 23.3 & 127 & & 1.3 & \\ Straw & & 25.2 & 22 & & 24.5 & \\ Green waste & & 24.4 & 46 & & 13.4 & \\ Dry algae & & 22.9 & 19 & & 73.0 & \\ \hline Cow manure & & 57.2 & 21.9 & 0.028 & 67.5 & \\ Pig manure & & 38.5 & 47.4 & 0.075 & 48.4 & \\ Shrimp hull & & 33.4 & 13.3 & 0.039 & 53.8 & \\ Bone dregs & & 48.7 & 113 & 0.278 & 77.6 & \\ Wastewater & & 45.9 & 71.6 & 0.060 & 61.9 & \\ sludge & & & & & \\ Waste paper & 500 & 36.6 & 133 & 0.084 & 53.5 & [124] \\ Sawdust & & 28.3 & 203 & 0.125 & 9.9 & \\ Grass & & 27.8 & 333 & 0.010 & 20.8 & \\ Wheat straw & & 29.8 & 33.2 & 0.051 & 18.0 & \\ Peanut shell & & 32.0 & 43.5 & 0.040 & 10.6 & \\ _Chlorella_ & & 40.2 & 2.78 & 0.010 & 52.6 & \\ Waterweeds & & 58.4 & 3.78 & 0.009 & 63.5 & \\ \hline Spruce wood & & & 40.4 & & 4.7 & \\ Poplar wood & 525 & - & 55.7 & & 6.8 & [125] \\ Wheat straw & & & 14.2 & & 12.7 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._
## 6 Conclusions and Discussions  
1. In this study, ANN was applied to estimate the viscosity of various bulk solutions of the most widely-used EOR polymers (FlopaamTM 3330S, FlopaamTM 3630S and AN-125) based on shear rate, polymer concentration, NaCl concentration, Ca2+ concentration and temperature. As a result, three ANN models, one for each of the EOR polymers, were presented.
2. The viscosity estimated using the ANN models is in good agreement with the measured viscosity. Based on the AARD calculations, the ANN models show higher accuracy than the Carreau model using [PERSON]'s correlation, which is the only method to estimate the unmeasured viscosity of a polymer solution for enhanced oil recovery.  
Figure 11: Average absolute relative deviation (AARD) of the viscosity estimated by the ANN model and by the Carreau model using [PERSON]’s correlation. (**a**) FlopaamTM 3330S. (**b**) FlopaamTM 3630S. (**c**) AN-125.  
In some conditions (low salinity or FlopaamTM 3630S), the viscosity estimation by the Carreau model using [PERSON]'s correlation is not accurate. It is possible that the relationship between the influential parameters and viscosity can change under certain conditions, such as low salinity (0.1 wt % NaCl) or high molecular weight polymers (20 million). The ANN models proposed in this study are less affected by this effect than the Carreau model using [PERSON]'s correlation considering the higher accuracy for all conditions of polymer solutions.
4. It is concluded that the ANN models proposed in this study can be utilized for quick estimation of the viscosity of the bulk polymer solution prior to experimental measurement, which is a time-consuming process.
5. One interesting finding is that the same structure of the ANN model can provide accurate estimation despite the different polymer structures of HPAM and poly(AM-co-AMPS). Considering that ANN can easily be expanded to include other factors, such as polymer characteristics (polymer structure and degree of hydrolysis, among others), it would be possible to develop an ANN model to estimate the viscosity of other EOR polymers if a method for the quantification of polymer structures can be established.  
This work was supported by the Energy Efficiency & Resources program of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) (No. 20122010300020) and the Korea Energy and Mineral Resources Engineering Program (KEMREP) with a grant funded by the Ministry of Trade, Industry and Energy, Republic of Korea.  
[PERSON] is the main researcher who analyzed the data and designed the ANN structure for this research. [PERSON] gave guidance from a theoretical point of view on the data analysis and ANN designing. [PERSON] gave field experience and guidance on polymer rheology for enhanced oil recovery. All authors have given approval to the final version of the manuscript.  
The authors declare no conflict of interest.
## 3 Experimental and Computational Methods  
### De Laval Nozzle Experiments  
In the experiments carried out by [PERSON] et al. [10; 11], the condensation was recorded in the converging-diverging nozzle (also known as a de Laval Nozzle). The setup of the experiments is shown in Figure 3 and the experimental conditions in terms of total pressure (\(P_{t}\)) and temperature (\(T_{t}\)) are provided in Table 1. The experiments were carried out over a wide range of pressures. The liquid CO\({}_{2}\) flows from the high pressure tank on the left. The transparent observation section of the de Laval nozzle is in the center of the experiment (between the two valves) to which the gaseous CO\({}_{2}\) is passed. This gas is then collected in the dump tank connected to the outlet at the exit of the nozzle, which is then connected to the vacuum pump to evacuate the collected gas. To control the flow, high-response time valves are connected near the inlet and outlet of the test nozzle section.  
The experiments start with a subcritical inlet pressure furthest from the critical point of pure CO\({}_{2}\) (case 1 and case 2), and progressively carry out four further series of experiments where the inlet pressure of case 3 is closest to the critical pressure point of pure CO\({}_{2}\), then cases 4 and 5 are taken into supercritical pressure states still relative to the critical point of pure CO\({}_{2}\) (\(P_{c}\) = 7.377 MPa and \(T_{c}\) = 304.128 K). The resulting database mainly comprises the following:  
* The steady state pressure profiles along the nozzle;
* The shadography images of the the nozzle showing the two-phase (condensation) region.  
The work in references [10; 11] mentions CO\({}_{2}\) as the fluid used, however, the paper does not address the exact amount of impurities present initially in the CO\({}_{2}\) gas used in the experiments. Our hypothesis is that, even if the CO\({}_{2}\) used is of high quality, it still has traces of impurities that play a role, even if they enter the test section through the presence of air before the test section is filled with the working fluid. This current work focuses on the effect of impurities on the condensation observed in the de Laval nozzle. Thus, for the scope of this paper, we limit our study with the operating details shown in Table 1.
# Mapless Collaborative Navigation for a Multi-Robot System Based on the Deep Reinforcement Learning
## 3 Methods
### Problem Formulation  
This paper aims to provide an end-to-end navigation method for multi-robot systems. We try to find such a learnable policy module \(\pi\):  
\[a_{t}^{i}=\pi(x_{t}^{i},\varphi_{t}^{i},a_{t-1}^{i}), \tag{1}\]  
where \(x_{t}^{i}\) is the observation from the raw lidar sensor information of robot \(i\) at timestep \(t\), \(\varphi_{t}^{i}\) is the relative parameters about the target, and \(a_{t-1}^{i}\) is the control action in the last timestep. In the multi-robot reinforcement learning system, these inputs can be regarded as the state of whole system \(s_{t}=(x_{t},\varphi_{t})\). For a single robot at each timestep \(t\), the robot makes observations \(s_{t}\in\mathcal{S}\) and selects actions \(a_{t}\in\mathcal{A}\) with respect to its policy \(\pi\colon\mathcal{S}\to\mathcal{P}(\mathcal{A})\), which maps states to a probability distribution over the actions. Then, the robot can receive the reward \(r(s_{t},a_{t})\) and arrive at the next state. The state-action value function describes the expected return of a state-action trajectory according to \(\pi\). It is commonly used to evaluate the quality of a policy as defined in Equation (2):  
\[Q_{\pi}(s,a)=\mathbb{E}\left[\sum_{t=0}^{\infty}\gamma^{t}r\left(s_{t},a_{t} \right)\right]\ \ where\ \ s_{t}\sim p\left(\cdot|s_{t-1},a_{t-1}\right),a_{t}=\pi\left(s_{t}\right). \tag{2}\]  
The recursive form of the state-action value function, known as the Bellman equation, can be defined as Equation (3). The policy module \(\pi\) directly maps the state perception to the control law of robots with the collaborative consideration. \(E\) represents the environment. In addition, the notation \(\sim\) means the former variable follows the distribution of the latter:  
\[Q^{\pi}\left(s_{t},a_{t}\right)=\mathbb{E}_{r_{t},s_{t+1}\sim E}\left[r\left( s_{t},a_{t}\right)+\gamma\mathbb{E}_{a_{t+1}\sim\pi}\left[Q\left(s_{t+1},a_{t+1} \right)\right]\right]. \tag{3}\]  
In order to get a good policy module \(\pi\), the multi-robot system has to overcome several challenges. First of all, it is difficult to extract valuable information from the raw sensor data and merge it properly with the relative parameters of robot state. Then, based on the processed information, a policy module needs to learn a stable transition rule between the perceptions and the decision to make. Additionally, the robots need to avoid the collision and consider the collaboration in some situation.
# Lateral Control Calibration and Testing in a Co-Simulation Framework for Automated Vehicles
###### Abstract  
Lateral vehicle control is of high importance in automated vehicles as it directly influences the vehicle's performance and safety during operation. The linear quadratic regulator (LQR) controller stands out due to its high-performance characteristics and is used in the open source for self-driving functions. However, a notable limitation of the current approach is the manual calibration of LQR controllers based on the experience and intuition of the designers, leading to empirical uncertainties. To address this issue and enhance the lateral control performance, this paper concentrates on refining the LQR by employing three optimization algorithms: artificial bee colony optimization (ABC), genetic algorithm (GA), and particle swarm optimization (PSO). These algorithms aim to overcome the reliance on empirical methods and enable a data-driven approach to LQR calibration. By comparing the outcomes of these optimization algorithms to the manual LQR controller within an offline multibody simulation as a testing platform, this study highlights the superiority of the best-performing optimization approach. Following this, the optimal algorithm is implemented on a real-time system for the full vehicle level, revealing the model-in-the-loop and the hardware-in-the-loop gap up to 78.89% with lateral velocity when we use the relative error criterion (REC) method to validate and 2.35 m with lateral displacement when considering the maximum absolute value method.  
linear quadratic regulator; calibration optimization; virtual simulation; automated driving +
Footnote †: journal: Applied sciences
# Robust 3D Joint Inversion of Gravity and Magnetic Data: A High-Performance Computing Approach
## Appendix B Development of the 1 st Variation of the Objective Function  
We express the parametric functional \(P\) using the following notation, where \(\langle\rangle\) denotes an inner product:  
\[P^{\alpha}(m)=\langle W_{d}A(m)-W_{d}d,W_{d}A(m)-W_{d}d\rangle+ \alpha\langle L(m),L(m)\rangle+\beta\langle W_{m}(m)-W_{m}(m_{apr}),W_{m}(m)\]  
\[-W_{m}\big{(}m_{apr}\big{)}\rangle+\gamma\langle M(m),M(m)\rangle+\eta\langle N (m),N(m)\rangle+\mu G(\
abla m,\
abla\text{m})\]  
The least squares method is used to find the solution, so the first variation of the functional must be calculated and equaled to zero. Using Calculus of Variations, the Gateaux derivative is calculated, whereas most of the terms are quadratic it is trivial:  
\[\delta P^{\alpha}(m)=2\langle W_{d}F_{m}\delta m,W_{d}A(m)-W_{d}d \rangle+2\alpha+2\beta\langle W_{m}\delta m,\ W_{m}(m)-W_{m}(m_{apr})\rangle+2 \gamma\langle M\delta m,M(m)\rangle\] \[+2\eta\langle N\delta m,N(m)\rangle+\mu\delta m,I_{G}\rangle=0\]  
The variation \(\delta A(m)=F_{m}\delta m\) where \(F_{m}\) is called the Frechet derivative of \(A\). However, the Frechet derivative of a linear operator is the operator itself \(F_{m}=A\). Additionally, expressing the first variation of the coupling term in inner product form:  
\[\delta P^{\alpha}(m)=2\langle W_{d}A\delta m,W_{d}A(m)-W_{d}d \rangle+2\alpha+2\beta\langle W_{m}\delta m,\ W_{m}(m)-W_{m}(m_{apr})\rangle+2 \gamma\langle M\delta m,M(m)\rangle\] \[+2\eta\langle N\delta m,N(m)\rangle+2\mu\langle\delta m,I_{G} \rangle=0\]  
The constants are factored using the linearity property of the inner product and adjoint operators are used to obtain the expression:  
\[\delta P^{\alpha}(m)=2\big{[}\big{\langle}\delta m,\ A^{*}W_{d}^{*}(W_{d}A(m)-W _{d}d)+\alpha L^{*}L(m)+\beta W_{m}^{*}\big{(}W_{m}(m)-W_{m}(m_{apr})\big{)}+ \gamma M^{*}M(m)\ =0\]  
\[+\eta N^{*}N(m)+\mu I_{G}\big{]}=0\]From the above expression we obtain the Euler equation whose main characteristic is that it expresses the minimum of the parametric functional \(I(m)\), i.e., the parameters \(m\) with which the parametric functional finds a minimum are a solution to the Euler equation.  
\[I(m)=A^{*}W_{d}^{*}W_{d}A(m)-A^{*}W_{d}^{*}W_{d}d+\alpha L^{*}L(m)+\beta W_{m}^{* }W_{m}(m)-\beta W_{m}^{*}W_{m}(m_{apr})+\gamma M^{*}M(m)+\eta N^{*}N(m)+\mu I_{G}\]  
Adjoint operators such as \(A^{*}=\overline{A^{T}}\) simplify to transposes \(A^{T}\). Since they belong to the reals \(\mathbb{R}\) they have no imaginary part:  
\[I(m)=A^{T}W_{d}^{T}W_{d}A(m)-A^{T}W_{d}^{T}W_{d}d+\alpha L^{T}L(m)+\beta W_{m}^{ T}W_{m}(m)-\beta W_{m}^{T}W_{m}\big{(}m_{apr}\big{)}+\gamma M^{T}M(m)+\eta N^{T}N (m)+\mu I_{G}\]  
\[I(m)=A^{T}W_{d}^{2}A(m)-A^{T}W_{d}^{2}d+\alpha L^{T}L(m)+\beta W_{m}^{2}(m)- \beta W_{m}^{2}(m_{apr})+\gamma M^{T}M(m)+\eta N^{T}N(m)+\mu I_{G}\]  
The terms can also be regrouped in the following way, which will be useful later:  
\[I(m)=(A^{T}W_{d}^{2}A+\alpha L^{T}L+\beta W_{m}^{2}+\gamma M^{T}M+\eta N^{T}N)m -(A^{T}W_{d}^{2}d+\beta W_{m}^{2}(m_{apr}))+\mu I_{G}\]