Mathematics

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15 pages, 562 KiB

Open AccessArticle

Hill Climbing-Based Efficient Model for Link Prediction in Undirected Graphs

by Haji Gul, Feras Al-Obeidat, Adnan Amin, Fernando Moreira and Kaizhu Huang

Mathematics 2022, 10(22), 4265; https://doi.org/10.3390/math10224265 - 15 Nov 2022

Cited by 4 | Viewed by 1879

Link prediction is a key problem in the field of undirected graph, and it can be used in a variety of contexts, including information retrieval and market analysis. By “undirected graphs”, we mean undirected complex networks in this study. The ability to predict [...] Read more.

Link prediction is a key problem in the field of undirected graph, and it can be used in a variety of contexts, including information retrieval and market analysis. By “undirected graphs”, we mean undirected complex networks in this study. The ability to predict new links in complex networks has a significant impact on society. Many complex systems can be modelled using networks. For example, links represent relationships (such as friendships, etc.) in social networks, whereas nodes represent users. Embedding methods, which produce the feature vector of each node in a graph and identify unknown links, are one of the newest approaches to link prediction. The Deep Walk algorithm is a common graph embedding approach that uses pure random walking to capture network structure. In this paper, we propose an efficient model for link prediction based on a hill climbing algorithm. It is used as a cost function. The lower the cost is, the higher the accuracy for link prediction between the source and destination node will be. Unlike other algorithms that predict links based on a single feature, it takes advantage of multiple features. The proposed method has been tested over nine publicly available datasets, and its performance has been evaluated by comparing it to other frequently used indexes. Our model outperforms all of these measures, as indicated by its higher prediction accuracy. Full article

(This article belongs to the Special Issue Modeling and Analysis of Complex Networks)

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14 pages, 319 KiB

Open AccessArticle

Recursive Convex Model for Optimal Power Flow Solution in Monopolar DC Networks

by Oscar Danilo Montoya, Farhad Zishan and Diego Armando Giral-Ramírez

Mathematics 2022, 10(19), 3649; https://doi.org/10.3390/math10193649 - 5 Oct 2022

Cited by 9 | Viewed by 1392

Abstract

This paper presents a new optimal power flow (OPF) formulation for monopolar DC networks using a recursive convex representation. The hyperbolic relation between the voltages and power at each constant power terminal (generator or demand) is represented as a linear constraint for the [...] Read more.

This paper presents a new optimal power flow (OPF) formulation for monopolar DC networks using a recursive convex representation. The hyperbolic relation between the voltages and power at each constant power terminal (generator or demand) is represented as a linear constraint for the demand nodes and generators. To reach the solution for the OPF problem a recursive evaluation of the model that determines the voltage variables at the iteration

t + 1

(

v^{t + 1}

) by using the information of the voltages at the iteration t (

v^{t}

) is proposed. To finish the recursive solution process of the OPF problem via the convex relaxation, the difference between the voltage magnitudes in two consecutive iterations less than the predefined tolerance is considered as a stopping criterion. The numerical results in the 85-bus grid demonstrate that the proposed recursive convex model can solve the classical power flow problem in monopolar DC networks, and it also solves the OPF problem efficiently with a reduced convergence error when compared with semidefinite programming and combinatorial optimization methods. In addition, the proposed approach can deal with radial and meshed monopolar DC networks without modifications in its formulation. All the numerical implementations were in the MATLAB programming environment and the convex models were solved with the CVX and the Gurobi solver. Full article

(This article belongs to the Special Issue Modeling and Analysis of Complex Networks)

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34 pages, 485 KiB

Open AccessArticle

Optimal Selection of Conductor Sizes in Three-Phase Asymmetric Distribution Networks Considering Optimal Phase-Balancing: An Application of the Salp Swarm Algorithm

by Brandon Cortés-Caicedo, Luis Fernando Grisales-Noreña and Oscar Danilo Montoya

Mathematics 2022, 10(18), 3327; https://doi.org/10.3390/math10183327 - 14 Sep 2022

Cited by 1 | Viewed by 1721

Abstract

This paper presents a new methodology to simultaneously solve the optimal conductor selection and optimal phase-balancing problems in unbalanced three-phase distribution systems. Both problems were represented by means of a mathematical model known as the Mixed-Integer Nonlinear Programming (MINLP) model, and the objective [...] Read more.

This paper presents a new methodology to simultaneously solve the optimal conductor selection and optimal phase-balancing problems in unbalanced three-phase distribution systems. Both problems were represented by means of a mathematical model known as the Mixed-Integer Nonlinear Programming (MINLP) model, and the objective function was the minimization of the total annual operating costs. The latter included the costs associated with energy losses, investment in conductors per network segment, and phase reconfiguration at each node in the system. To solve the problem addressed in this study, a master–slave methodology was implemented. The master stage employs a discrete version of the Salp Swarm Algorithm (SSA) to determine the set of conductors to be installed in each line, as well as the set of connections per phase at each of the nodes that compose the system. Afterward, the slave stage uses the three-phase version of the backward/forward sweep power flow method to determine the value of the fitness function of each individual provided by the master stage. Compared to those of the Hurricane-based Optimization Algorithm (HOA) and the Sine Cosine Algorithm (SCA), the numerical results obtained by the proposed solution methodology in the IEEE 8- and 25-node test systems demonstrate its applicability and effectiveness. All the numerical validations were performed in MATLAB. Full article

(This article belongs to the Special Issue Modeling and Analysis of Complex Networks)

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14 pages, 392 KiB

Open AccessArticle

Rule Fusion of Privacy Protection Strategies for Co-Ownership Data Sharing

by Tinghuai Ma, Yuming Su, Huan Rong, Yurong Qian and Najla Al-Nabhan

Mathematics 2022, 10(6), 969; https://doi.org/10.3390/math10060969 - 18 Mar 2022

Cited by 2 | Viewed by 1512

Abstract

With the rapid development of social networks, personal privacy leakage has become more and more serious. A social network is a shared platform. Resources in a social network may be shared by multiple owners. In order to prevent privacy leakage, each owner assigns [...] Read more.

With the rapid development of social networks, personal privacy leakage has become more and more serious. A social network is a shared platform. Resources in a social network may be shared by multiple owners. In order to prevent privacy leakage, each owner assigns a corresponding privacy protection strategy. For the same shared contents, integrating the privacy protection strategies of all owners is the key problem for sharing. This paper proposes a rule fusion method of privacy protection for the co-ownership of data shared in social networks. First, the content of the protection is defined according to different privacy requirements. Second, this paper uses predicate logic formulas to abstract the natural language-based description of privacy protection and further provides a logical model of privacy protection rules. Third, this paper gives the definition of privacy protection heterogeneous rules and provides a rule fusion algorithm to ensure no conflict exists among these rules. The experimental results show that the proposed rule-based fusion method of privacy protection strategy performs at a higher level than the privacy protection strategy fusion. Full article

(This article belongs to the Special Issue Modeling and Analysis of Complex Networks)

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11 pages, 29350 KiB

Open AccessArticle

Clustering Based on Continuous Hopfield Network

by Yao Xiao, Yashu Zhang, Xiangguang Dai and Dongfang Yan

Mathematics 2022, 10(6), 944; https://doi.org/10.3390/math10060944 - 15 Mar 2022

Cited by 3 | Viewed by 2346

Abstract

Clustering aims to group n data samples into k clusters. In this paper, we reformulate the clustering problem into an integer optimization problem and propose a recurrent neural network with

n \times k

neurons to solve it. We prove the stability and convergence [...] Read more.

Clustering aims to group n data samples into k clusters. In this paper, we reformulate the clustering problem into an integer optimization problem and propose a recurrent neural network with

n \times k

neurons to solve it. We prove the stability and convergence of the proposed recurrent neural network theoretically. Moreover, clustering experiments demonstrate that the proposed clustering algorithm based on the recurrent neural network can achieve the better clustering performance than existing clustering algorithms. Full article

(This article belongs to the Special Issue Modeling and Analysis of Complex Networks)

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16 pages, 3395 KiB

Open AccessArticle

Natural Gas Scarcity Risk in the Belt and Road Economies Based on Complex Network and Multi-Regional Input-Output Analysis

by Ruijin Du, Qi Wu, Ziwei Nan, Gaogao Dong, Lixin Tian and Feifan Wu

Mathematics 2022, 10(5), 788; https://doi.org/10.3390/math10050788 - 1 Mar 2022

Cited by 6 | Viewed by 3080

Abstract

Natural gas scarcity poses a significant risk to the global economy. The risk of production loss due to natural gas scarcity can be transferred to downstream economies through globalized supply chains. Therefore, it is important to quantify and analyze how natural gas scarcity [...] Read more.

Natural gas scarcity poses a significant risk to the global economy. The risk of production loss due to natural gas scarcity can be transferred to downstream economies through globalized supply chains. Therefore, it is important to quantify and analyze how natural gas scarcity in some regions affects the Belt and Road (B&R) economies. The embodied natural gas scarcity risks (EGSRs) of B&R economies are assessed and the EGSR transmission network is constructed. The built network shows a small-world nature. This illustrates that any interruption in key countries will quickly spread to neighboring countries, potentially affecting the global economy. The top countries, including Turkey, China, Ukraine, and India are identified in EGSR exports, which also have relatively high values of closeness centrality. The findings illustrate that the shortage of natural gas supply in these countries may have a significant impact on downstream countries or sectors and the resulting economic losses spread rapidly. These countries are critical to the resilience of the B&R economies to natural gas scarcity. The top nations, including Turkmenistan, Macedonia, and Georgia are also identified in EGSR imports, highlighting their vulnerability to natural gas scarcity. Further, the community analysis of the network provides a fresh perspective for formulating fair and reasonable allocation policies of natural gas resources and minimizing the large-scale spread of economic losses caused by natural gas scarcity. Full article

(This article belongs to the Special Issue Modeling and Analysis of Complex Networks)

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17 pages, 905 KiB

Open AccessArticle

A Distributed Optimization Accelerated Algorithm with Uncoordinated Time-Varying Step-Sizes in an Undirected Network

by Yunshan Lü, Hailing Xiong, Hao Zhou and Xin Guan

Mathematics 2022, 10(3), 357; https://doi.org/10.3390/math10030357 - 25 Jan 2022

Viewed by 2350

Abstract

In recent years, significant progress has been made in the field of distributed optimization algorithms. This study focused on the distributed convex optimization problem over an undirected network. The target was to minimize the average of all local objective functions known by each [...] Read more.

In recent years, significant progress has been made in the field of distributed optimization algorithms. This study focused on the distributed convex optimization problem over an undirected network. The target was to minimize the average of all local objective functions known by each agent while each agent communicates necessary information only with its neighbors. Based on the state-of-the-art algorithm, we proposed a novel distributed optimization algorithm, when the objective function of each agent satisfies smoothness and strong convexity. Faster convergence can be attained by utilizing Nesterov and Heavy-ball accelerated methods simultaneously, making the algorithm widely applicable to many large-scale distributed tasks. Meanwhile, the step-sizes and accelerated momentum coefficients are designed as uncoordinate, time-varying, and nonidentical, which can make the algorithm adapt to a wide range of application scenarios. Under some necessary assumptions and conditions, through rigorous theoretical analysis, a linear convergence rate was achieved. Finally, the numerical experiments over a real dataset demonstrate the superiority and efficacy of the novel algorithm compared to similar algorithms. Full article

(This article belongs to the Special Issue Modeling and Analysis of Complex Networks)

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14 pages, 8717 KiB

Open AccessArticle

Fixed-Time Synchronization of Neural Networks Based on Quantized Intermittent Control for Image Protection

by Wenqiang Yang, Li Xiao, Junjian Huang and Jinyue Yang

Mathematics 2021, 9(23), 3086; https://doi.org/10.3390/math9233086 - 30 Nov 2021

Cited by 7 | Viewed by 1772

Abstract

This paper considers the fixed-time synchronization (FIXTS) of neural networks (NNs) by using quantized intermittent control (QIC). Based on QIC, a fixed-time controller is designed to ensure that the NNs achieve synchronization in finite time. With this controller, the settling time can be [...] Read more.

This paper considers the fixed-time synchronization (FIXTS) of neural networks (NNs) by using quantized intermittent control (QIC). Based on QIC, a fixed-time controller is designed to ensure that the NNs achieve synchronization in finite time. With this controller, the settling time can be estimated regardless of initial conditions. After ensuring that the system has stabilized through this strategy, it is suitable for image protection given the behavior of the system. Meanwhile, the encryption effect of the image depends on the encryption algorithm, and the quality of the decrypted image depends on the synchronization error of NNs. The numerical results show that the designed controller is effective and validate the practical application of FIXTS of NNs in image protection. Full article

(This article belongs to the Special Issue Modeling and Analysis of Complex Networks)

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14 pages, 1615 KiB

Open AccessArticle

Multimodal Identification Based on Fingerprint and Face Images via a Hetero-Associative Memory Method

by Qi Han, Heng Yang, Tengfei Weng, Guorong Chen, Jinyuan Liu and Yuan Tian

Mathematics 2021, 9(22), 2976; https://doi.org/10.3390/math9222976 - 22 Nov 2021

Viewed by 2042

Abstract

Multimodal identification, which exploits biometric information from more than one biometric modality, is more secure and reliable than unimodal identification. Face recognition and fingerprint recognition have received a lot of attention in recent years for their unique advantages. However, how to integrate these [...] Read more.

Multimodal identification, which exploits biometric information from more than one biometric modality, is more secure and reliable than unimodal identification. Face recognition and fingerprint recognition have received a lot of attention in recent years for their unique advantages. However, how to integrate these two modalities and develop an effective multimodal identification system are still challenging problems. Hetero-associative memory (HAM) models store some patterns that can be reliably retrieved from other patterns in a robust way. Therefore, in this paper, face and fingerprint biometric features are integrated by the use of a hetero-associative memory method for multimodal identification. The proposed multimodal identification system can integrate face and fingerprint biometric features at feature level when the system converges to the state of asymptotic stability. In experiment 1, the predicted fingerprint by inputting an authorized user’s face is compared with the real fingerprint, and the matching rate of each group is higher than the given threshold. In experiment 2 and experiment 3, the predicted fingerprint by inputting the face of an unauthorized user and the stealing authorized user’s face is compared with its real fingerprint input, respectively, and the matching rate of each group is lower than the given threshold. The experimental results prove the feasibility of the proposed multimodal identification system. Full article

(This article belongs to the Special Issue Modeling and Analysis of Complex Networks)

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