esa-sceva/satcom-chunk-collection huggingface dataset:
# COMA: Propagating Complementary Multi-Level Aggregation Network for Polyp Segmentation
## 3 Results
### Experimental Results
#### 3.3.2 Qualitative Comparison  
As illustrated in Figure 2, we randomly sampled polyp images from each dataset to validate the COMMA performance through the prediction maps. The images in the first and third rows were necessarily difficult cases because they included small polyps in the low-brightness areas. Although U-Net, U-Net++, and PraNet did not predict polyp areas, the proposed method detected polyp areas with some noise. This may be helpful to clinicians performing colonoscopy by improving polyp segmentation, where reducing false negatives is important. The images in the second and fifth rows show a low color contrast with the surrounding tissue. As as result of similar issues, previous methods tend to overestimate the surrounding tissue as a polyp, whereas the proposed method accurately predicted polyps. In the fourth-row image, which contains a large-scale polyp, the existing \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{5}{c}{**CVC-ClinicDB**} & \multicolumn{5}{c}{**Kvasir**} \\ \cline{2-10}  & **mDice** & **mIoU** & \(\mathbf{S_{m}}\) & \(\mathbf{E_{m}}\) & **MAE** & **mDice** & **mIoU** & \(\mathbf{S_{m}}\) & \(\mathbf{E_{m}}\) & **MAE** \\ \hline U-Net [9] & 0.823 & 0.760 & 0.890 & 0.953 & 0.019 & 0.818 & 0.750 & 0.858 & 0.893 & 0.055 \\ U-Net++ [17] & 0.794 & 0.733 & 0.873 & 0.931 & 0.022 & 0.821 & 0.747 & 0.862 & 0.909 & 0.048 \\ ResUNet-mod [46] & 0.779 & 0.455 & n/a & n/a & n/a & 0.791 & 0.429 & n/a & n/a & n/a \\ ResUNet++ [19] & 0.796 & 0.796 & n/a & n/a & n/a & 0.813 & 0.793 & n/a & n/a & n/a \\ SFA [20] & 0.702 & 0.611 & 0.793 & 0.885 & 0.042 & 0.725 & 0.614 & 0.781 & 0.849 & 0.075 \\ PraNet \({}^{\dagger}\) [27] & 0.899 & 0.853 & 0.937 & 0.979 & 0.009 & 0.897 & 0.844 & 0.915 & 0.948 & 0.030 \\ \hline
**COMMA \({}^{*}\)** & 0.916 & 0.871 & 0.947 & 0.979 & 0.008 & **0.904** & **0.860** & **0.925** & **0.963** & **0.024** \\
**COMMA \({}^{\dagger}\)** & **0.933** & **0.891** & **0.956** & **0.985** & **0.007** & 0.901 & 0.852 & 0.919 & 0.951 & 0.027 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of COMMA performance with existing state-of-the-art methods on CVC-ClinicDB and Kvasir datasets, where n/a indicates an inaccessible prediction map, and \({}^{*}\) and \({\dagger}\) indicate that the ResNet and Res2 Net backbone encoders were employed, respectively.
# Atom Probe Tomography for Catalysis Applications: A Review
## 3 Case Studies
### Model Catalysts as Tips--Focus on the Surface
#### 3.1.2 Au-Based Alloys  
Au-based catalysts are commonly used for deNOx applications [99; 100; 101], and in this frame, two types of catalysts have been studied by APT: Pd-Au and Au-Ag.
# Detection for Frying Times of Various Edible Oils Based on Near-Infrared Spectroscopy
## Materials and Methods
### Data Processing and Analysis
#### 2.3.1 Preprocessing Method  
In the process of spectra analysis, the different spectra of the same experimental sample are slightly different due to the shift and drift caused by light scattering, refraction, and experimental conditions. To fully extract sample information from the spectrum and reduce noise interference, the original spectra need to be preprocessed. The first derivative (1D), the multiplicative scatter correction (MSC) and the standard normal variate (SNV) were used to preprocess the original spectral data. These preprocessing methods can effectively reduce noise interference, improve the signal to noise ratio, and enhance useful spectral information characteristics.  
The application of 1D can not only eliminate the baseline shift and drift in the spectra, but also effectively remove the interference from the other backgrounds to resolve the overlapped spectra peaks and improve the resolution and sensitivity. The adoption of the MSC method can eliminate the influence of the scattering caused by the uneven distribution of the particles in the sample and the different particle sizes on the spectra. SNV and MSC have a similar effect in the spectral correction. Both of them are used to correct the spectral error caused by the scattering of the particles in the sample. The only difference is that the SNV method corrects each spectrum separately.
## 4 Simulation Results
### Model Selection  
We select 2 CNN and 8 ML models on the training set using the grid search-based method for the classification of the valence and arousal scenarios. Moreover, the CNN model is also considered as the extractor to generate the deep features used as the input of the KNN model. As a result, 2 structures of the CNN extractor are selected for further estimation in combination with different ML models for the classification of the high/low \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{**Channel**} \\ \hline \multirow{2}{*}{**Valence**} & **Number of** & **Arousal** & **Number of** \\  & **Selection** & **Arousal** & **Selection** \\ \hline F91 & 52 & FC5 & 20 \\ \hline F97 & 8 & T7 & 94 \\ \hline C3 & 49 & C3 & 1 \\ \hline CP1 & 1 & Oz & 5 \\ \hline CP5 & 42 & F8 & 20 \\ \hline Oz & 5 & AF4 & 1 \\ \hline F8 & 42 & & \\ \hline Cz & 1 & Others & 0 \\ \hline Others & 0 & & \\ \hline \multicolumn{4}{c}{**Feature**} \\ \hline \multirow{2}{*}{**Valence**} & **Number of** & **Arousal** & **Number of** \\  & **Selection** & **Arousal** & **Selection** \\ \hline FD & 68 & DE & 81 \\ \hline NFD & 70 & FE & 92 \\ \hline MEA & 100 & PE & 91 \\ \hline SSC & 52 & RE & 74 \\ \hline FE & 68 & Spe & 98 \\ \hline PE & 66 & coD & 96 \\ \hline RE & 69 & HFD & 78 \\ \hline SE & 100 & H & 100 \\ \hline ShE & 77 & AM & 89 \\ \hline AR & 54 & Sw & 100 \\ \hline H & 65 & Cm & 57 \\ \hline AM & 70 & Cvbin & 88 \\ \hline Var & 64 & Kurt & 100 \\ \hline Cm & 51 & HA & 92 \\ \hline Cvbin & 83 & & \\ \hline HC & 77 & & \\ \hline BPA & 70 & Others & \textless{}50 \\ \hline Ene & 75 & & \\ \hline Others & \textless{}50 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Selected channels and features by the GA.  
valence and arousal. Table 3 represents the optimal structure of the CNN model known as the feature extractor. The grid searches are implemented to address the optimal parameter values of the models as shown in Table 4. For valence scenario, KNN with K of 37; BG with tree number of 15 and leaf number of 5; BS with learning rate of 0.9, iteration of 50, and minimum leaf of 75; RF with tree number of 10 and leaf number of 5; CNN with network depth of 3, network section of 2; learning rate of 0.01, momentum of 0.9, L2 regulation of 0.1 are the optimal ML models. The optimal CNN extractor structure is shown in Table 3 with network depth of 4, network section of 4, learning rate of 0.01, momentum of 0.8, and L2 regulation of 0.2 for both valence and arousal scenarios. The optimal parameter values of the ML models in combination with the above extractor are K of 3 for the KNN; tree number of 5 and leaf number of 75 for the BG; learning rate of 0.1, iteration of 25, and minimum leaf of 75 for the BS; tree number of 3 and leaf number of 5 for the RF.
## 8 Reduced-Order Vibroacoustic Computational Model
### Computation of the Projection Basis for the Structure
#### 8.1.2. Case of a Strong Coupling of the Structure with the Internal Acoustic Fluid  
For the computation of the appropriate basis of the structure, the practical numerical procedure is given hereinafter. Equation (28) is replaced by  
\[\left[\mathbb{K}^{S}(0)\right]\mathbb{U}=\lambda^{S}\left(\left[\mathbb{M}^{S }\right]+\left[\mathbb{M}^{A}\right]\right)\mathbb{U}\,, \tag{33}\]  
in which \([\mathbb{M}^{A}]\) is the positive symmetric \((n_{S}\times n_{S})\) real matrix (called the added mass matrix), which corresponds to the quasi-static effect of the internal acoustic fluid on the structure. It should be noted that the non-zero elements of matrix \([\mathbb{M}^{A}]\) are only related to the DOFs of the internal fluid-structure interface. This generalized eigenvalue problem admits a zero eigenvalue with multiplicity 6 (corresponding to the six rigid body motions) and admits an increasing sequence of \((n_{S}-6)\) strictly positive eigenvalues,  
\[0<\lambda_{1}^{S}\leq\ldots\leq\lambda_{\alpha}^{S}\leq\ldots\,. \tag{34}\]The eigenvectors \(\mathbb{U}_{1},\ldots,\mathbb{U}_{\alpha},\ldots\) associated with \(\lambda_{1}^{S},\ldots,\lambda_{\alpha}^{S},\ldots\) constitute a basis for the elastic structure. For \(0<N_{S}\leq n_{S}-6\), we introduce the \((n_{S}\times N_{S})\) real matrix of the \(N_{S}\) basis vectors \(\mathbb{U}_{\alpha}\) associated with the first \(N_{S}\) strictly positive eigenvalues,  
\[\left[\,\mathcal{U}\,\right]=\left[\,\mathbb{U}_{1}\ldots\mathbb{U}_{\alpha} \ldots\mathbb{U}_{N_{S}}\,\right]. \tag{35}\]  
We have the orthogonality properties,  
\[\left[\,\mathcal{U}\,\right]^{T}\left([\mathbb{M}^{S}]+[\mathbb{M}^{A}] \right)\left[\,\mathcal{U}\,\right]=[M^{\mathcal{S}A}]\,, \tag{36}\]  
\[\left[\,\mathcal{U}\,\right]^{T}\left[\mathbb{K}^{S}(0)\right]\left[\, \mathcal{U}\,\right]=[K^{S}(0)]\,, \tag{37}\]  
in which \([M^{\mathcal{S}A}]\) is a diagonal matrix of positive real numbers such that \([M^{\mathcal{S}A}]_{\alpha\beta}=\mu_{\alpha}^{S}\,\delta_{\alpha\beta}\), and where \([K^{S}(0)]\) is the diagonal matrix of the eigenvalues such that \([K^{S}(0)]_{\alpha\beta}=\mu_{\alpha}^{S}\,\lambda_{\alpha}^{S}\,\delta_{ \alpha\beta}\). It should be noted that \(\omega_{\alpha}^{S}=\sqrt{\lambda_{\alpha}^{S}}\) is not an eigenfrequency of the structure in vacuo, but is an eigenfrequency of the structure with an added mass effect. For a closed acoustic cavity and for an internal acoustic liquid with a free surface, the construction of matrix \([\mathbb{M}^{A}]\) is given hereinafter.  
_Construction of added mass matrix \([\mathbb{M}^{A}]\) for a closed acoustic cavity._ For a closed acoustic cavity, the deformations of the interface can induce a volume variation of the cavity. The positive symmetric \((n_{S}\times n_{S})\) real matrix \([\mathbb{M}^{A}]\) is written as  
\[[\mathbb{M}^{A}]=[\mathbb{C}]\,[\mathbb{S}]\,[\mathbb{C}]^{T}\,, \tag{38}\]  
in which \([\mathbb{S}]\) is the positive symmetric
# A Distance-Encoded Bloom Filter for Fast NDN Name Lookup
## 2 Related Works and Background
### Hash Table-Based Name Lookup  
The hash table-based scheme for name lookup is one of the most effective approaches because each search can be performed in \(O\) (1) time in a hash table when there is no collision. However, for each hash search, the length of the key must be determined in advance since the hash table contains prefixes of varying lengths. As a result, multiple hash searches may be required to find the longest matching prefix during the lookup process.  
Figure 1: Example of a name prefix trie.
## 3 Control Scheme Design
### Stability Analysis  
Lyapunov is a virtual energy function used to verify the stability of a system. Suitable Lyapunov functions can provide influence on the values of the parameters in the control law to enhance the stability performance of the system [29; 30]. The selection of the Lyapunov function is generally related to the error, and the tracking error and the unknown parameter error were selected as the parameters of the Lyapunov function in [30].  
In the sliding mode control part of this paper, only the tracking error needs to be considered, so the following quadratic Lyapunov function is chosen to verify the stability of the system:  
\[V_{1}=\frac{1}{2}s^{T}s \tag{39}\]  
Combining (17), (29), (38), and (39), the time derivative \(\dot{V}_{1}\) of \(V_{1}\) can be written as follows:  
\[\begin{split}\dot{V}_{1}&=s^{T}\Big{(}\Gamma\dot{e }+\bar{\mu}_{d}-\Big{(}\dot{J}(\eta)v-J(\eta)\bar{M}^{-1}(\bar{C}(v)v+\bar{D}(v )v+\bar{G}(\eta))+J(\eta)\bar{M}^{-1}\tau+J(\eta)\bar{M}^{-1}w_{\eta}\Big{)} \Big{)}\\ &=s^{T}\bigg{(}-\frac{\mu|s_{0}|+|s|}{(\alpha+\beta)\mu|s_{0}|+ \alpha|s|}\cdot ksgn(s)-ktanh(s)\bigg{)}\\ &\leq s^{T}\bigg{(}-\frac{\mu|s_{0}|+|s|}{(\alpha+\beta)\mu|s_{0} |+\alpha|s|}\cdot ksgn(s)\bigg{)}\end{split} \tag{40}\]  
The value ranges of the \(\alpha\), \(\beta\), \(\mu\), and \(k\) parameters have been defined previously. Thus, in (40), it is obvious that \(-\frac{\mu|s_{0}|+|s|}{(\alpha+\beta)\mu|s_{0}|+\alpha|s|}<0\) and \(s^{T}\cdot ksgn(s)\geq 0\), which leads to \(\dot{V}_{1}\leq 0\). Thus, the system can be shown to be globally asymptotically stable.
# Interpolating the Directional Room Impulse Response for Dynamic Spatial Audio Reproduction
## 4 Results and Analysis
### Comparative Analysis in the Great Hall
#### 4.2.1 Regular Spacing, Row 4  
Firstly, to explore the impacts of the distance between the interpolated point and the known DRIR points, three sets of positions in row 4 are chosen, with the listening point chosen as located equidistant from the known DRIR points with spacings being 1 m, 2 m, and 3 m, separately. Estimated DOA and TOA errors are shown in Figures 8 and 9, and the first peak in these figures corresponds to the direct sound followed by other five specular reflections. It can be found that in the real-world great hall in Figure 8, the proposed approach obtains, generally, equivalent azimuth and elevation estimation accuracies for three different spacings in row 4, whereas there are much smaller TOA errors when the spacing is 1 m. Similar trends can be seen when using the [PERSON]'s method. As for the [PERSON]'s method, the 2 m spacing brings the smallest azimuth and elevation errors, while the TOA errors for the three spacings are all large. Overall, the average DOA and TOA errors for the [PERSON]'s approach are larger than the other two comparative methods. For most peaks detected after FOA signal decomposition in the real-world great hall, the proposed method leads to the smallest azimuth errors (e.g., 13 out of 18 peaks in Figure 8a) and equivalently small elevation errors to that of the [PERSON]'s method.  
The experimental results in the simulated great hall in Figure 9 present different trends. The [PERSON]'s method and the proposed approach show the smallest errors when the spacing is 1 m. [PERSON]'s algorithm presents small azimuth errors when the spacing is 1 m, whilst demonstrating large elevation and TOA errors in all cases. Generally, the proposed method leads to the smallest DOA and TOA errors. The [PERSON]'s linear interpolation approach without DRIR decomposition also shows accurate DOA estimation, having four cases for azimuth and seven cases for elevation in Figure 9a that show the smallest error among all three comparative approaches.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**Classrooms**} & **Error—[PERSON]** & **Error—Southern** & **Error—Proposed** \\ \hline \multirow{4}{*}{real-world} & row 3 & 6.53 & 4.04 & 4.16 \\  & row 5 & 5.88 & 3.71 & 4.02 \\  & row 8 & 1.17 & 0.11 & 1.04 \\  & row 7 & 0.71 & 0.23 & 0.00 \\  & column 9 & 2.59 & 5.09 & 4.48 \\ \cline{2-5}  & average & 3.38 & 2.64 & 2.74 \\ \hline \multirow{4}{*}{simulated} & row 3 & 19.96 & 2.12 & 2.17 \\  & row 5 & 0.50 & 3.53 & 3.44 \\  & row 8 & 2.02 & 0.15 & 0.34 \\  & row 7 & 4.25 & 4.82 & 5.05 \\  & column 9 & 7.30 & 10.31 & 12.00 \\ \cline{2-5}  & average & 6.81 & 4.19 & 4.6 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparisons of DRR errors in the real-world and simulated classrooms (unit: dB).
# River Surface Space-Time Image Velocimetry Based on Dual-Channel Residual Network
## 4 Experiments and Discussions
### Vertical Average Velocity Comparison Experiment  
#### 4.4.1 Experimental Settings of Vertical Average Velocity Measurement  
In China's current hydrological measurement system, the velocity and discharge measured by the current meter are considered true values, which is the standard for evaluating the accuracy of various new flow measurement methods. So, to assess the practical performance of DCResNet, a comparative experiment with current meter measurements is conducted at the Panzhihua hydrological station. The current meter model used is LS25-3A. Since the current meter cannot precisely measure surface velocity, the vertical average velocity is used for comparison, following references [18; 25; 34]. The specific experimental method is as follows: during the video shooting, simultaneous measurements are taken with the current meter to ensure synchronized data collection. For the current meter method, measurement vertical lines are set at 55 m, 65 m, 90 m, 105 m, 120 m, 135 m, 155 m, 165 m, and 175 m from the starting point, respectively. At each vertical line, velocities are measured by the current meter at relative depths (the ratio between the depth of the measuring point and the depth of the vertical line) of 0.2 and 0.8, with their average representing the vertical average velocity. Based on the current meter's position in the video, testing lines are set at the same locations. After obtaining surface velocities via the FFT and DCResNet method, they are multiplied by a velocity coefficient to derive the corresponding  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Number**} & **Starting** & **FFT** & **DCResNet** & **Label Value** & \multicolumn{2}{c}{**RE (\%)**} \\  & **Distance (m)** & **(m/s)** & **(m/s)** & **(m/s)** & **FFT** & **DCResNet** \\ \hline
1 & 2 & 0.51 & 0.87 & 0.94 & 45.74 & 7.45 \\
2 & 4 & 1.65 & 1.98 & 2.16 & 23.61 & 8.33 \\
3 & 6 & 2.17 & 2.17 & 2.06 & 5.34 & 5.34 \\
4 & 8 & 2.22 & 2.25 & 2.11 & 5.21 & 6.64 \\
5 & 10 & 2.35 & 2.54 & 2.56 & 8.20 & 0.78 \\
6 & 12 & 2.34 & 2.63 & 2.46 & 4.88 & 6.91 \\
7 & 14 & 2.43 & 2.64 & 2.54 & 4.33 & 3.94 \\
8 & 16 & 1.72 & 1.7 & 2.50 & 31.20 & 32.00 \\
9 & 18 & 2.61 & 2.57 & 2.70 & 3.33 & 4.81 \\ \hline \end{tabular}
\end{table}
Table 9: Surface velocity results of Hebian station.  
Figure 22: Surface velocity distribution of test 3.  
vertical average velocity. The velocity coefficient is derived from historical statistical data at the hydrological station, which is defined as the ratio of measured discharge to the virtual discharge calculated from the surface velocity. The three indicators AE, RE, and MRE in Section 4.3.1 are still used for error evaluation, with the results of the current meter as reference values.
## 3 Results and Discussions
### Expression Change of Genes Related to Quorum-Sensing and Acid Stress Response  
\(CspA\), a gene encoding cold shock protein, was up-regulated by 7.29 times in the liquid-state fermented cells compared with the solid-state fermented cells. This gene has been reported to be involved in the response to cold stress and acid stress [70]. Gene \(rimP\) encoding ribosome maturation factor was up-regulated by 2.58 times. This gene in _Mycobacterium fortuitum_ is involved in acid stress response [71]. Gene \(rbfA\) encoding ribosome-binding factor was up-regulated by 2.53 times, and this gene in _Lactobacillus plantarum_ NMGL2 (recently reassigned as _Lactiplantiobacillus plantarum_ NMGL2) has been reported to be involved in the response to acid stress and cold stress [72]. Gene \(mazF\) was up-regulated by 2.25 times in liquid-state fermented cells, and this gene has been found to be activated under acid stress in _Bifidobacterium longum_[73]. Gene \(nagB\) encoding glucosamine-6-phosphate deaminase was up-regulated by 2.08 times, and this enzyme might be associated with acid stress response of _Lactobacillus casei_ Zhang (recently reassigned as _Lacticasibacillus paracasei_ Zhang) [30]. Twelve genes related to quorum sensing (including biofilm formation, conjugation, aggregation, and other processes) were up-regulated by 2.3 to 8.84 times. These genes might be involved in the response of bacteria to acidic environment.
# Self-Evolving Fuzzy Controller Composed of Univariate Fuzzy Control Rules
## 3 Proposed Self-Evolving FLC Design Method
### Formulation  
In this paper, the process to be controlled by the proposed self-evolving methodology is defined by following nonlinear autoregressive exogenous (NARX) model:  
\[y(k+1)=f(\mathbf{x}(k),u(k)), \tag{8}\]  
where \(\mathbf{x}(k)=[y(k),\ldots,y(k-n_{y}),u(k-1),\ldots,u(k-n_{u})]\), \(u(k)\) and \(y(k)\) are the process input and output, respectively, \(n_{y}\) and \(n_{u}\) are, respectively, the output and input orders, and \(f\) is an unknown continuous and differentiable single-input single-output (SISO) function.  
**Assumption 1**.: \(\frac{\partial f(\mathbf{x}_{u})}{\partial u}\
eq 0\) _for \(\mathbf{x}\in\mathbf{\Omega}_{\mathbf{x}}\), where \(\mathbf{x}\in\mathbf{\Omega}_{\mathbf{x}}\) is the controllability region [2, 33]._  
Assumption 1 is a controllability condition of System (8), which imposes that there is no state at which the system's output does not depend on the control signal \(u\).  
In a general way, the controller can be represented by the function \(g\) to control the system (8) [2, 31]:  
\[u(k)=g(\tilde{\mathbf{x}}(k),\mathbf{\Theta}), \tag{9}\]  
where \(\tilde{\mathbf{x}}(k)=[r(k),y(k),\ldots,y(k-n_{y}),u(k-1),\ldots,u(k-n_{u})]\), which in addition to \(\mathbf{x}(k)\) includes the reference signal \(r(k)\), and \(\mathbf{\Theta}\) are the control parameters. Fuzzy systems are universal approximators [34, 35]. Therefore, to approximate (9), the FLC (3) will be designed by the proposed self-evolving learning method.  
A temporal sliding window is created in order to allocate the variables needed to obtain the inverse function of the plant, to be used in the evolving process phase. The sliding window will  
Figure 1: Definition of membership functions for \(x_{j}\).  
be used to estimate the control estimation error in order to select the input variable that contributes to the largest estimated control error, and such a variable is selected to receive a new fuzzy control rule (if the defined criteria are met). The concept is, if a command signal \(u(k)\) generates \(y(k+1)\) at system state \(\mathbf{x}(k)\), then if the system returns again to the same state \(\mathbf{x}(k)\) and the reference is the same as the generated output, i.e., \(r(k)=y(k+1)\), then \(u(k)\) can be considered as the optimum control signal [2,31].  
The temporal sliding window, with \(T_{M}\) elements, is defined by:  
\[\mathbf{M}=[\mathbf{z}(k-T_{M})^{T},\ldots,\mathbf{z}(k-1)^{T}], \tag{10}\]  
where \(\mathbf{z}(m)=[\tilde{\mathbf{x}}(m),u(m)]\) (\(m=1,\ldots,T_{M}\)) and \(\tilde{\mathbf{x}}(m)=[y(m+1),y(m),\ldots,y(m-n_{y}),u(m-1),\)\(\ldots,u(m-n_{u})]\).
# A Population-Based Search Approach to Solve Continuous Distributed Constraint Optimization Problems
## 2 Background
### Continuous Distributed Constraint Optimization Problems  
Similarly, a _Continuous DCOP_ (C-DCOP) is a tuple \(\langle\mathbf{A},\mathbf{X},\mathbf{D},\mathbf{F},\alpha\rangle\), where \(\mathbf{A},\mathbf{F}\), and \(\alpha\) are the same as DCOP. The set of variables \(\mathbf{X}\) and the set of domains \(\mathbf{D}\) are defined as follows:  
* \(\mathbf{X}=\{x_{1},x_{2},\dots,x_{m}\}\) is the set of _continuous_ variables and each variable \(x_{j}\) is controlled by one of the agents \(a_{i}\in\mathbf{A}\).
* \(\mathbf{D}=\{D_{1},D_{2},\dots,D_{m}\}\) is the set of _continuous_ domains and each _continuous_ variable \(x_{i}\in\mathbf{X}\) takes any value from the domain \(D_{i}=[LB_{i},UB_{i}]\), where \(LB\) and \(UB\) represent the lower and upper bounds of the domain, respectively.  
The goal of a C-DCOP is the same as Equation (1). Figure 1 shows a simple example of a C-DCOP, where Figure 0(a) shows a constraint graph with four variables, and each edge represents a utility function defined in Figure 0(b). The domain \(D_{i}\) of variable \(x_{i}\) is \([-10,10]\).