Toward Personalized Vibrotactile Support When Learning Motor Skills*Algorithms* **2017**, *10*(1), 15; doi:10.3390/a10010015 (registering DOI) - 16 January 2017**Abstract **

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Personal tracking technologies allow sensing of the physical activity carried out by people. Data flows collected with these sensors are calling for big data techniques to support data collection, integration and analysis, aimed to provide personalized support when learning motor skills through varied

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Personal tracking technologies allow sensing of the physical activity carried out by people. Data flows collected with these sensors are calling for big data techniques to support data collection, integration and analysis, aimed to provide personalized support when learning motor skills through varied multisensorial feedback. In particular, this paper focuses on vibrotactile feedback as it can take advantage of the haptic sense when supporting the physical interaction to be learnt. Despite each user having different needs, when providing this vibrotactile support, personalization issues are hardly taken into account, but the same response is delivered to each and every user of the system. The challenge here is how to design vibrotactile user interfaces for adaptive learning of motor skills. TORMES methodology is proposed to facilitate the elicitation of this personalized support. The resulting systems are expected to dynamically adapt to each individual user’s needs by monitoring, comparing and, when appropriate, correcting in a personalized way how the user should move when practicing a predefined movement, for instance, when performing a sport technique or playing a musical instrument.
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Kernel Clustering with a Differential Harmony Search Algorithm for Scheme Classification*Algorithms* **2017**, *10*(1), 14; doi:10.3390/a10010014 (registering DOI) - 14 January 2017**Abstract **

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This paper presents a kernel fuzzy clustering with a novel differential harmony search algorithm to coordinate with the diversion scheduling scheme classification. First, we employed a self-adaptive solution generation strategy and differential evolution-based population update strategy to improve the classical harmony search. Second,

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This paper presents a kernel fuzzy clustering with a novel differential harmony search algorithm to coordinate with the diversion scheduling scheme classification. First, we employed a self-adaptive solution generation strategy and differential evolution-based population update strategy to improve the classical harmony search. Second, we applied the differential harmony search algorithm to the kernel fuzzy clustering to help the clustering method obtain better solutions. Finally, the combination of the kernel fuzzy clustering and the differential harmony search is applied for water diversion scheduling in East Lake. A comparison of the proposed method with other methods has been carried out. The results show that the kernel clustering with the differential harmony search algorithm has good performance to cooperate with the water diversion scheduling problems.
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A Fault Detection and Data Reconciliation Algorithm in Technical Processes with the Help of Haar Wavelets Packets*Algorithms* **2017**, *10*(1), 13; doi:10.3390/a10010013 (registering DOI) - 14 January 2017**Abstract **

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This article is focused on the detection of errors using an approach that is signal based. The proposed algorithm considers several criteria: soft, hard and very hard recognition error. After the recognition of the error, the error is replaced. In this sense, different

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This article is focused on the detection of errors using an approach that is signal based. The proposed algorithm considers several criteria: soft, hard and very hard recognition error. After the recognition of the error, the error is replaced. In this sense, different strategies for data reconciliation are associated with the proposed criteria error detection. Algorithms in several industrial software platforms are used for detecting errors of sensors. Computer simulations confirm the validation of the presented applications. Results with actual sensor measurements in industrial processes are presented.
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Coupled Least Squares Identification Algorithms for Multivariate Output-Error Systems*Algorithms* **2017**, *10*(1), 12; doi:10.3390/a10010012 - 12 January 2017**Abstract **

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This paper focuses on the recursive identification problems for a multivariate output-error system. By decomposing the system into several subsystems and by forming a coupled relationship between the parameter estimation vectors of the subsystems, two coupled auxiliary model based recursive least squares (RLS)

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This paper focuses on the recursive identification problems for a multivariate output-error system. By decomposing the system into several subsystems and by forming a coupled relationship between the parameter estimation vectors of the subsystems, two coupled auxiliary model based recursive least squares (RLS) algorithms are presented. Moreover, in contrast to the auxiliary model based recursive least squares algorithm, the proposed algorithms provide a reference to improve the identification accuracy of the multivariate output-error system. The simulation results confirm the effectiveness of the proposed algorithms.
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Acknowledgement to Reviewers of *Algorithms* in 2016*Algorithms* **2017**, *10*(1), 11; doi:10.3390/a10010011 - 10 January 2017**Abstract **
The editors of *Algorithms* would like to express their sincere gratitude to the following reviewers for assessing manuscripts in 2016.[...]
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Estimating the Local Radius of Convergence for Picard Iteration*Algorithms* **2017**, *10*(1), 10; doi:10.3390/a10010010 - 9 January 2017**Abstract **

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In this paper, we propose an algorithm to estimate the radius of convergence for the Picard iteration in the setting of a real Hilbert space. Numerical experiments show that the proposed algorithm provides convergence balls close to or even identical to the best

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In this paper, we propose an algorithm to estimate the radius of convergence for the Picard iteration in the setting of a real Hilbert space. Numerical experiments show that the proposed algorithm provides convergence balls close to or even identical to the best ones. As the algorithm does not require to evaluate the norm of derivatives, the computing effort is relatively low.
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Modeling Delayed Dynamics in Biological Regulatory Networks from Time Series Data*Algorithms* **2017**, *10*(1), 8; doi:10.3390/a10010008 - 9 January 2017**Abstract **

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Background: The modeling of Biological Regulatory Networks (BRNs) relies on background knowledge, deriving either from literature and/or the analysis of biological observations. However, with the development of high-throughput data, there is a growing need for methods that automatically generate admissible models. Methods: Our

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Background: The modeling of Biological Regulatory Networks (BRNs) relies on background knowledge, deriving either from literature and/or the analysis of biological observations. However, with the development of high-throughput data, there is a growing need for methods that automatically generate admissible models. Methods: Our research aim is to provide a logical approach to infer BRNs based on given time series data and known influences among genes. Results: We propose a new methodology for models expressed through a timed extension of the automata networks (well suited for biological systems). The main purpose is to have a resulting network as consistent as possible with the observed datasets. Conclusion: The originality of our work is three-fold: (i) identifying the sign of the interaction; (ii) the direct integration of quantitative time delays in the learning approach; and (iii) the identification of the qualitative discrete levels that lead to the systems’ dynamics. We show the benefits of such an automatic approach on dynamical biological models, the DREAM4(in silico) and DREAM8 (breast cancer) datasets, popular reverse-engineering challenges, in order to discuss the precision and the computational performances of our modeling method.
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Elite Opposition-Based Social Spider Optimization Algorithm for Global Function Optimization*Algorithms* **2017**, *10*(1), 9; doi:10.3390/a10010009 - 8 January 2017**Abstract **

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The Social Spider Optimization algorithm (SSO) is a novel metaheuristic optimization algorithm. To enhance the convergence speed and computational accuracy of the algorithm, in this paper, an elite opposition-based Social Spider Optimization algorithm (EOSSO) is proposed; we use an elite opposition-based learning strategy

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The Social Spider Optimization algorithm (SSO) is a novel metaheuristic optimization algorithm. To enhance the convergence speed and computational accuracy of the algorithm, in this paper, an elite opposition-based Social Spider Optimization algorithm (EOSSO) is proposed; we use an elite opposition-based learning strategy to enhance the convergence speed and computational accuracy of the SSO algorithm. The 23 benchmark functions are tested, and the results show that the proposed elite opposition-based Social Spider Optimization algorithm is able to obtain an accurate solution, and it also has a fast convergence speed and a high degree of stability.
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Backtracking-Based Iterative Regularization Method for Image Compressive Sensing Recovery*Algorithms* **2017**, *10*(1), 7; doi:10.3390/a10010007 - 6 January 2017**Abstract **

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This paper presents a variant of the iterative shrinkage-thresholding (IST) algorithm, called backtracking-based adaptive IST (BAIST), for image compressive sensing (CS) reconstruction. For increasing iterations, IST usually yields a smoothing of the solution and runs into prematurity. To add back more details, the

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This paper presents a variant of the iterative shrinkage-thresholding (IST) algorithm, called backtracking-based adaptive IST (BAIST), for image compressive sensing (CS) reconstruction. For increasing iterations, IST usually yields a smoothing of the solution and runs into prematurity. To add back more details, the BAIST method backtracks to the previous noisy image using L2 norm minimization, i.e., minimizing the Euclidean distance between the current solution and the previous ones. Through this modification, the BAIST method achieves superior performance while maintaining the low complexity of IST-type methods. Also, BAIST takes a nonlocal regularization with an adaptive regularizor to automatically detect the sparsity level of an image. Experimental results show that our algorithm outperforms the original IST method and several excellent CS techniques.
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Using Force-Field Grids for Sampling Translation/Rotation of Partially Rigid Macromolecules*Algorithms* **2017**, *10*(1), 6; doi:10.3390/a10010006 - 4 January 2017**Abstract **

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An algorithm is presented for the simulation of two partially flexible macromolecules where the interaction between the flexible parts and rigid parts is represented by energy grids associated with the rigid part of each macromolecule. The proposed algorithm avoids the transformation of the

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An algorithm is presented for the simulation of two partially flexible macromolecules where the interaction between the flexible parts and rigid parts is represented by energy grids associated with the rigid part of each macromolecule. The proposed algorithm avoids the transformation of the grid upon molecular movement at the expense of the significantly lesser effect of transforming the flexible part.
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Efficient Algorithms for the Maximum Sum Problems*Algorithms* **2017**, *10*(1), 5; doi:10.3390/a10010005 - 4 January 2017**Abstract **

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We present efficient sequential and parallel algorithms for the maximum sum (MS) problem, which is to maximize the sum of some shape in the data array. We deal with two MS problems; the maximum subarray (MSA) problem and the maximum convex sum (MCS)

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We present efficient sequential and parallel algorithms for the maximum sum (MS) problem, which is to maximize the sum of some shape in the data array. We deal with two MS problems; the maximum subarray (MSA) problem and the maximum convex sum (MCS) problem. In the MSA problem, we find a rectangular part within the given data array that maximizes the sum in it. The MCS problem is to find a convex shape rather than a rectangular shape that maximizes the sum. Thus, MCS is a generalization of MSA. For the MSA problem, $O\left(n\right)$ time parallel algorithms are already known on an $(n,n)$ 2D array of processors. We improve the communication steps from $2n-1$ to *n*, which is optimal. For the MCS problem, we achieve the asymptotic time bound of $O\left(n\right)$ on an $(n,n)$ 2D array of processors. We provide rigorous proofs for the correctness of our parallel algorithm based on Hoare logic and also provide some experimental results of our algorithm that are gathered from the Blue Gene/P super computer. Furthermore, we briefly describe how to compute the actual shape of the maximum convex sum.
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Dependent Shrink of Transitions for Calculating Firing Frequencies in Signaling Pathway Petri Net Model*Algorithms* **2017**, *10*(1), 4; doi:10.3390/a10010004 - 31 December 2016**Abstract **

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Despite the recent rapid progress in high throughput measurements of biological data, it is still difficult to gather all of the reaction speed data in biological pathways. This paper presents a Petri net-based algorithm that can derive estimated values for non-valid reaction speeds

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Despite the recent rapid progress in high throughput measurements of biological data, it is still difficult to gather all of the reaction speed data in biological pathways. This paper presents a Petri net-based algorithm that can derive estimated values for non-valid reaction speeds in a signaling pathway from biologically-valid data. In fact, these reaction speeds are reflected based on the delay times in the timed Petri net model of the signaling pathway. We introduce the concept of a “dependency relation” over a transition set of a Petri net and derive the properties of the dependency relation through a structural analysis. Based on the theoretical results, the proposed algorithm can efficiently shrink the transitions with two elementary structures into a single transition repeatedly to reduce the Petri net size in order to eventually discover all transition sets with a dependency relation. Finally, to show the usefulness of our algorithm, we apply our algorithm to the IL-3 Petri net model.
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A Pilot-Pattern Based Algorithm for MIMO-OFDM Channel Estimation*Algorithms* **2017**, *10*(1), 3; doi:10.3390/a10010003 - 28 December 2016**Abstract **

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An improved pilot pattern algorithm for facilitating the channel estimation in multiple input multiple output-orthogonal frequency division multiplexing (MIMO-OFDM) systems is proposed in this paper. The presented algorithm reconfigures the parameter in the least square (LS) algorithm, which belongs to the space-time block-coded

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An improved pilot pattern algorithm for facilitating the channel estimation in multiple input multiple output-orthogonal frequency division multiplexing (MIMO-OFDM) systems is proposed in this paper. The presented algorithm reconfigures the parameter in the least square (LS) algorithm, which belongs to the space-time block-coded (STBC) category for channel estimation in pilot-based MIMO-OFDM system. Simulation results show that the algorithm has better performance in contrast to the classical single symbol scheme. In contrast to the double symbols scheme, the proposed algorithm can achieve nearly the same performance with only half of the complexity of the double symbols scheme.
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A Tensor Decomposition Based Multiway Structured Sparse SAR Imaging Algorithm with Kronecker Constraint*Algorithms* **2017**, *10*(1), 2; doi:10.3390/a10010002 - 25 December 2016**Abstract **

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This paper investigates a structured sparse SAR imaging algorithm for point scattering model based on tensor decomposition. Several SAR imaging schemes have been developed by researchers for improving the imaging quality. For a typical SAR target scenario, the scatterers distribution usually has the

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This paper investigates a structured sparse SAR imaging algorithm for point scattering model based on tensor decomposition. Several SAR imaging schemes have been developed by researchers for improving the imaging quality. For a typical SAR target scenario, the scatterers distribution usually has the feature of structured sparsity. Without considering this feature thoroughly, the existing schemes have still certain drawbacks. The classic matching pursuit algorithms can obtain clearer imaging results, but the cost is resulting in an extreme complexity and a huge computation resource consumption. Therefore, this paper put forward a tensor-based SAR imaging algorithm by means of multiway structured sparsity which makes full use of the above geometrical feature of the scatterers distribution. The spotlight SAR observation signal is formulated as a Tucker model considering the Kronecker constraint, and then a sparse reconstruction algorithm is introduced by utilizing the structured sparsity of the scene. The proposed tensor-based SAR imaging model is able to take advantage of the Kronecker information in each mode, which ensures the robustness for the signal reconstruction. Both the algorithm complexity analysis and numerical simulations show that the proposed method requires less computation than the existing sparsity-driven SAR imaging algorithms. The imaging realizations based on the practical measured data also indicate that the proposed algorithm is superior to the reference methods even in the severe noisy environment, under the condition of multiway structured sparsity.
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MultiAspect Graphs: Algebraic Representation and Algorithms*Algorithms* **2017**, *10*(1), 1; doi:10.3390/a10010001 - 25 December 2016**Abstract **

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We present the algebraic representation and basic algorithms for MultiAspect Graphs (MAGs). A MAG is a structure capable of representing multilayer and time-varying networks, as well as higher-order networks, while also having the property of being isomorphic to a directed graph. In particular,

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We present the algebraic representation and basic algorithms for MultiAspect Graphs (MAGs). A MAG is a structure capable of representing multilayer and time-varying networks, as well as higher-order networks, while also having the property of being isomorphic to a directed graph. In particular, we show that, as a consequence of the properties associated with the MAG structure, a MAG can be represented in matrix form. Moreover, we also show that any possible MAG function (algorithm) can be obtained from this matrix-based representation. This is an important theoretical result since it paves the way for adapting well-known graph algorithms for application in MAGs. We present a set of basic MAG algorithms, constructed from well-known graph algorithms, such as degree computing, Breadth First Search (BFS), and Depth First Search (DFS). These algorithms adapted to the MAG context can be used as primitives for building other more sophisticated MAG algorithms. Therefore, such examples can be seen as guidelines on how to properly derive MAG algorithms from basic algorithms on directed graphs. We also make available Python implementations of all the algorithms presented in this paper.
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Which, When, and How: Hierarchical Clustering with Human–Machine Cooperation*Algorithms* **2016**, *9*(4), 88; doi:10.3390/a9040088 - 21 December 2016**Abstract **

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Human–Machine Cooperations (HMCs) can balance the advantages and disadvantages of human computation (accurate but costly) and machine computation (cheap but inaccurate). This paper studies HMCs in agglomerative hierarchical clusterings, where the machine can ask the human some questions. The human will return the

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Human–Machine Cooperations (HMCs) can balance the advantages and disadvantages of human computation (accurate but costly) and machine computation (cheap but inaccurate). This paper studies HMCs in agglomerative hierarchical clusterings, where the machine can ask the human some questions. The human will return the answers to the machine, and the machine will use these answers to correct errors in its current clustering results. We are interested in the machine’s strategy on handling the question operations, in terms of three problems: (1) Which question should the machine ask? (2) When should the machine ask the question (early or late)? (3) How does the machine adjust the clustering result, if the machine’s mistake is found by the human? Based on the insights of these problems, an efficient algorithm is proposed with five implementation variations. Experiments on image clusterings show that the proposed algorithm can improve the clustering accuracy with few question operations.
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Evaluation of Cloud Services: A Fuzzy Multi-Criteria Group Decision Making Method*Algorithms* **2016**, *9*(4), 84; doi:10.3390/a9040084 - 16 December 2016**Abstract **

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This paper presents a fuzzy multi-criteria group decision making method for evaluating the performance of Cloud services in an uncertain environment. Intuitionistic fuzzy numbers are used to better model the subjectivity and imprecision in the performance evaluation process. An effective algorithm is developed

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This paper presents a fuzzy multi-criteria group decision making method for evaluating the performance of Cloud services in an uncertain environment. Intuitionistic fuzzy numbers are used to better model the subjectivity and imprecision in the performance evaluation process. An effective algorithm is developed based on the technique for order preference by similarity to the ideal solution and the Choquet integral operator for adequately solving the performance evaluation problem. An example is presented for demonstrating the applicability of the proposed method for solving the multi-criteria group decision making problem in real situations.
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A No Reference Image Quality Assessment Metric Based on Visual Perception*Algorithms* **2016**, *9*(4), 87; doi:10.3390/a9040087 - 16 December 2016**Abstract **

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Nowadays, how to evaluate image quality reasonably is a basic and challenging problem. In view of the present no reference evaluation methods, they cannot reflect the human visual perception of image quality accurately. In this paper, we propose an efficient general-purpose no reference

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Nowadays, how to evaluate image quality reasonably is a basic and challenging problem. In view of the present no reference evaluation methods, they cannot reflect the human visual perception of image quality accurately. In this paper, we propose an efficient general-purpose no reference image quality assessment (NRIQA) method based on visual perception, and effectively integrates human visual characteristics into the NRIQA fields. First, a novel algorithm for salient region extraction is presented. Two characteristics graphs of texture and edging of the original image are added to the Itti model. Due to the normalized luminance coefficients of natural images obey the generalized Gauss probability distribution, we utilize this characteristic to extract statistical features in the regions of interest (ROI) and regions of non-interest respectively. Then, the extracted features are fused to be an input to establish the support vector regression (SVR) model. Finally, the IQA model obtained by training is used to predict the quality of the image. Experimental results show that this method has good predictive ability, and the evaluation effect is better than existing classical algorithms. Moreover, the predicted results are more consistent with human subjective perception, which can accurately reflect the human visual perception to image quality.
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Moving Mesh Strategies of Adaptive Methods for Solving Nonlinear Partial Differential Equations*Algorithms* **2016**, *9*(4), 86; doi:10.3390/a9040086 - 15 December 2016**Abstract **

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This paper proposes moving mesh strategies for the moving mesh methods when solving the nonlinear time dependent partial differential equations (PDEs). Firstly we analyse Huang’s moving mesh PDEs (MMPDEs) and observe that, after Euler discretion they could be taken as one step of

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This paper proposes moving mesh strategies for the moving mesh methods when solving the nonlinear time dependent partial differential equations (PDEs). Firstly we analyse Huang’s moving mesh PDEs (MMPDEs) and observe that, after Euler discretion they could be taken as one step of the root searching iteration methods. We improve Huang’s MMPDE by adding one Lagrange speed term. The proposed moving mesh PDE could draw the mesh to equidistribution quickly and stably. The numerical algorithm for the coupled system of the original PDE and the moving mesh equation is proposed and the computational experiments are given to illustrate the validity of the new method.
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A Differentiated Anonymity Algorithm for Social Network Privacy Preservation*Algorithms* **2016**, *9*(4), 85; doi:10.3390/a9040085 - 14 December 2016**Abstract **

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Devising methods to publish social network data in a form that affords utility without compromising privacy remains a longstanding challenge, while many existing methods based on *k*-anonymity algorithms on social networks may result in nontrivial utility loss without analyzing the social network

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Devising methods to publish social network data in a form that affords utility without compromising privacy remains a longstanding challenge, while many existing methods based on *k*-anonymity algorithms on social networks may result in nontrivial utility loss without analyzing the social network topological structure and without considering the attributes of sparse distribution. Toward this objective, we explore the impact of the attributes of sparse distribution on data utility. Firstly, we propose a new utility metric that emphasizes network structure distortion and attribute value loss. Furthermore, we design and implement a differentiated *k*-anonymity *l*-diversity social network anonymity algorithm, which seeks to protect users’ privacy in social networks and increase the usability of the published anonymized data. Its key idea is that it divides a node into two child nodes and only anonymizes sensitive values to satisfy anonymity requirements. The evaluation results show that our method can effectively improve the data utility as compared to generalized anonymizing algorithms.
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