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The level of privacy may vary across different parts of an image. This paper proposes a semi-visual obfuscation algorithm for images that takes into account the varying levels of privacy in different areas of the image. Firstly, we present a novel One-dimensional Uniform Chaotic Amplifier (1_DUCA) aimed at expanding the parameter range and enhancing the uniformity of the standard one-dimensional chaotic map. Next, we employ a detection algorithm or autonomous frame selection to identify the precise location of the area with strong privacy. Finally, we apply noise to blur the selected area and conceal vital bit information within the image. At this point, the image has certain visual effects, and only people with prior knowledge can recognize the image. Furthermore, in the last stage of image encryption, we employ a weight scrambling and high-low bit coupled diffusion technology to completely obscure the visual effects of the image. It is noteworthy that the experimental results and performance analysis have verified the practicality and security of the encryption algorithm. Moreover, they have also demonstrated the robust amplification effect of the employed amplifier. • A semi-visual fuzzy encryption scheme for images with varying privacy levels is proposed. • This paper presents a self-hiding fuzzy algorithm using noise blur and information hiding techniques. • Proposes a scrambling method that perturbs pixel positions based on their own weight, enhancing security and robustness. • This encryption scheme introduces a novel high-low coupling diffusion method to enhance pixel coupling. [ABSTRACT FROM AUTHOR]

Variational inequalities are a universal optimization paradigm that incorporate classical minimization and saddle point problems. Nowadays more and more tasks require to consider stochastic formulations of optimization problems. In this paper, we present an analysis of a method that gives optimal convergence estimates for monotone stochastic finite-sum variational inequalities. In contrast to the previous works, our method supports batching, does not lose the oracle complexity optimality and uses an arbitrary Bregman distance to take into account geometry of the problem. Paper provides experimental confirmation to algorithm's effectiveness. • We consider stochastic variational inequalities and present a new method for them. • An analysis of the method gives optimal convergence estimates. • Our method supports batching, does not lose the oracle complexity optimality. • Our method uses an arbitrary Bregman distance to take into account geometry of the problem. [ABSTRACT FROM AUTHOR]

This paper creatively proposes a type of cubic fractal matrix and a new spatiotemporal chaotic system named logistic-logistic cascade coupled map lattice (L-LCCML). Furthermore, based on cubic fractal matrix and L-LCCML, this paper proposes a novel image encryption algorithm. The proposed cubic fractal matrix is three-dimensional, irregular, and self-similar. In particular, the proposed L-LCCML system adopts cascade coupling parameter to ensure the dynamic effect of coupling. Therefore, L-LCCML has excellent chaos and is suitable for information encryption. To provide a more secure approach, the proposed algorithm contains two diffusion operations, one permutation operation, and does not require multiple rounds of encryption. The diffusion operation is based on the cubic fractal matrix, which has good security and high encryption efficiency. In addition, the algorithm adopts sorting permutation based on L-LCCML, which provides good randomness for encryption. Experimental results show that the proposed algorithm has the characteristics of large key space, high sensitivity, fast encryption speed, good statistical properties of cipherd images, and etc. Therefore, the proposed algorithm is a usable alternative for practical secure communication. [ABSTRACT FROM AUTHOR]

A new fractional-order 5D hyperchaotic system based on memristor is constructed in this paper, with the speciality that the system exists chaotic and hyperchaotic states in the fractional-order case, while in periodic state in the integer-order. In addition, it has a variety of special phenomena at fractional-order such as infinite initial value range, parameter-dependent offset-boosting and amplitude control, attractor coexistence, and fractional order complexity greater than integer order. The correctness and feasibility of the system is verified by analog circuit simulation and hardware circuit implementation. Combining this system with image encryption algorithms, two new scrambling algorithms and a diffusion algorithm are proposed. And a high-quality encryption scheme that can be applied to a wide range of color images is proposed. The scheme is found to have excellent security after verification by various security analyses and comparison with other literatures. This paper provides a basis for the superiority of fractional-order chaotic systems and provides new methods in the field of image encryption. • We construct a fractional-order 5D hyperchaotic system based on memristor. • The system is chaotic only to fractional-order and has a rich and complex dynamical behavior. • We propose a possible mechanism for the generation of attractor coexistence. • Designed new encryption algorithms and proposed a new color image encryption scheme [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive security analysis on an improved chaos-based image encryption algorithm. The initial algorithm, proposed by Li et al., involves permutation related to the sum of plaintext pixel values and diffusion associated with 9 specific pixel values in the permuted image. However, a thorough analysis conducted by Liu et al. reveals two major flaws in it: firstly, the 9 specific pixel values are not involved in the diffusion process; secondly, the permutation method exhibits significant vulnerabilities. In response to these shortcomings, Liu et al. proposed targeted improvements on it, which include incorporating a permutation step for the 9 specific pixels and enhancing the original permutation method. In this study, we analyze the improved algorithm and discover that it still possesses security vulnerabilities, rendering it susceptible to chosen-plaintext attack. By constructing three categories of special plaintexts, one can decipher the equivalent permutation and diffusion. Theoretical analysis and experimental results provide strong evidence for the effectiveness of our analysis in this paper. [ABSTRACT FROM AUTHOR]

Urban rail transit networks have become the most important traffic modal and greatly improve the traffic environment and travel efficiency of metropolis, and the critical station identification and robustness assessment of urban rail transit networks have become more and more important. In this paper, we propose a comprehensive vote-rank (CVR) algorithm to identify the critical stations, and adopt mutual information and k -center clustering algorithm to analyze the similar characteristics of passenger flow on different dates of urban rail transit networks. Meanwhile, Shanghai metro network is chosen as the example and we find that the optimal classification of passenger flow on different dates is 2 categories, and the passenger flows have the significant differences between conventional day and unconventional day. The results show that the critical stations on unconventional day are farther from the city center than the critical stations on conventional day, and some critical stations locate in the suburbs on unconventional day. Moreover, we study the structural and functional robustness characteristics of urban rail transit networks subjected to continuous malicious attacks to the top critical nodes, and the results show that Shanghai metro network has the worse robustness subjected to malicious attacks. Compared with the existed methods, we can declare that the proposed CVR algorithm is the most effective method for critical station identification and robustness assessment among the discussed methods in this paper, and this study will provide theoretical and practical support for the safe operation of urban rail transit networks. [ABSTRACT FROM AUTHOR]

This paper proposes a 1-D enhanced Log-logistic chaotic map (1-DELLCM) and an asymmetric generalized Gaussian apertured fractional Fourier transform (AGGAFrFT). The 1-DELLCM is a new chaotic map that introduces the nonlinear function log 2 (1 + x) into the traditional logistic map. This modification leads to a more intricate behavior and an expanded spectrum of chaos. On the other hand, the AGGAFrFT utilizes the asymmetric generalized Gaussian distribution with three shaping parameters as the soft aperture in the fractional Fourier optical system. This design choice enables the AGGAFrFT to exhibit a low-pass filtering performance, which helps to resist noise attacks to some extent. To bolster the sensitivity of the three shaping parameters, an iterative image encryption algorithm has been devised to create an apertured phase mask utilized for encrypting images. Based on the experimental outcomes, the sensitivities of the three shaping parameters, fractional order, and wavelength for AGGAFrFT are found to be at least up to 10 − 15. Additionally, experimental findings demonstrate that incorporating 1-DELLCM and AGGAFrFT into the proposed algorithm significantly bolsters the encryption process's security, rendering it resilient against diverse attacks, particularly noise attacks. • A new chaotic map 1-DELLCM using log 2 (1 + x) has been proposed. • AGG aperture is introduced into FrFT to form AGGAFrFT. • A novel IE scheme based on 1-DELLCM and AGGAFrFT has been proposed. • The three shaping parameters of AGG aperture are designed as cipher keys. • The maximum sensitivity of three shaping parameters can reach 10 − 15. [ABSTRACT FROM AUTHOR]

In this paper, we propose universal proximal mirror methods to solve the variational inequality problem with Hölder-continuous operators in both deterministic and stochastic settings. The proposed methods automatically adapt not only to the oracle's noise (in the stochastic setting of the problem) but also to the Hölder continuity of the operator without having prior knowledge of either the problem class or the nature of the operator information. We analyzed the proposed algorithms in both deterministic and stochastic settings and obtained estimates for the required number of iterations to achieve a given quality of a solution to the variational inequality. We showed that, without knowing the Hölder exponent and Hölder constant of the operators, the proposed algorithms have the least possible in the worst-case sense complexity for the considered class of variational inequalities. We also compared the resulting stochastic algorithm with other popular optimizers for the task of image classification. • Proposed universal proximal mirror methods (UMPs) for the variational inequalities. • UMPs adapt to the oracle's noise and also to the Holder continuity of the operator. • UMPs have no prior knowledge of the nature of the operator information. • Obtained the optimal convergence rate of UMP in the deterministic setting. • Analyzed UMP in the stochastic setting and concluded its optimal convergence rate. • Compared stochastic UMP with other algorithms for the task of image classification. [ABSTRACT FROM AUTHOR]

This paper presents a novel algorithm for ranking nodes in graph-structured data using Graph Convolutional Networks (GCNs) combined with mini-batch training. The proposed method integrates local and global structural information, enabling a comprehensive understanding of node importance within complex networks. By employing a multi-layer GCN architecture with residual connections and dropout regularization, our approach captures intricate graph patterns while mitigating common issues such as vanishing gradients and overfitting. The node importance scores are computed using a Multi-Layer Perceptron (MLP), with the entire model trained using Mean Squared Error (MSE) loss optimized via the Adam algorithm. We demonstrate the scalability and effectiveness of our method through extensive experiments on various benchmark datasets, showcasing its superior performance in node ranking tasks compared to existing approaches. [ABSTRACT FROM AUTHOR]

In this paper, the Parameter Switching (PS) algorithm is used to numerically approximate attractors of a Hopfield Neural Network (HNN) system. The PS algorithm is a convergent scheme designed for approximating the attractors of an autonomous nonlinear system, depending linearly on a real parameter. Aided by the PS algorithm, it is shown that every attractor of the HNN system can be expressed as a convex combination of other attractors. The HNN system can easily be written in the form of a linear parameter dependence system, to which the PS algorithm can be applied. This work suggests the possibility to use the PS algorithm as a control-like or anticontrol-like method for chaos. • Attractor decomposition as a convex combination of other attractors. • The Parameter Switching algorithm to approximate attractors. • Attractors of a HNN system are expressed as a convex combination of his attractors. [ABSTRACT FROM AUTHOR]

The influence maximization problem grapples with issues such as low infection rates and high time complexity. Many existing methods prove unsuitable for large-scale networks due to their time complexity or heavy reliance on free parameters. This paper introduces a solution to these challenges through a local heuristic that incorporates shell decomposition, node representation. This strategic approach selects candidate nodes based on their connections within network shells and topological features, effectively reducing the search space and computational overhead. The algorithm employs a deep learning-based node embedding technique to generate a low-dimensional vector for candidate nodes, calculating the dependency on spreading for each node based on local topological features. In the final phase, influential nodes are identified using results from previous phases and newly defined local features. Evaluation using the independent cascade model demonstrates the competitiveness of the proposed algorithm, highlighting its ability to deliver optimal performance in terms of solution quality. When compared to the Collective-Influence (CI) global algorithm, the presented method has a significant improvement in the differential infection rate due to its faster execution. • Using deep learning-based node embedding technique to reduce the search space • Identifying influential nodes based on global diffusion and spreading scores • Applying autoencoder-based node embedding to learning representation graph [ABSTRACT FROM AUTHOR]

Two gradient descent based fractional methods are proposed for systems with outliers in this paper. The outliers in the collected data usually causes biased estimates, resulting in a poor identification model. Tradition fractional gradient descent (FGD) algorithm has an assumption that the fractional derivative is a scalar, which leads to slow convergence rates, especially for systems with an ill-conditioned matrix. The proposed algorithms in this paper have several advantages over the traditional identification methods: (1) can get unbiased estimates; (2) have faster convergence rates; (3) enrich the FGD estimation framework. Simulation examples demonstrate the effectiveness of the proposed algorithms. • Can get unbiased estimates. • Have faster convergence rates. • Enrich the FGD estimation framework. [ABSTRACT FROM AUTHOR]

The paper introduces a novel memristive chaotic system characterized by an infinite number of index-2 saddle foci, enabling it to generate multiscroll chaos and exhibit extreme multistability. Bifurcation diagrams, phase portraits and other methods are employed to examine the stabilities of equilibria and complex dynamics. It shows that by modifying the function of memristor, the system can produce multiscroll attractors with varying scroll counts. Furthermore, it can be decomposed into coexisting chaotic attractors at different locations, and this decomposition is influenced by adjustments in parameters and initial values, illustrating the impact of initial-relied and parameter-relied offset boosting. With variations in the parameter, the coexisting chaotic attractors will undergo a bifurcation, ultimately transforming into coexisting periodic attractors. The image encryption application of the system is explored, introducing an efficient chaos-based algorithm applied to encrypt Internet of Medical Things (IoMT) images, followed by a comprehensive performance evaluation. • New memristive system with multiscroll chaos and offset boosting is presented. • Complex dynamics of the system are theoretically and numerically studied. • New chaos-based image encryption algorithm with high security is designed. [ABSTRACT FROM AUTHOR]

For an undirected network G = (V , E) with removal cost on each node, the generalized network dismantling problem is to find a node subset S ⊆ V with the minimum overall removal cost, such that the size of each connected component in G − S is not larger than a given integer K. This issue has wide applications at network destruction (e.g., combating crime network) or network defense (e.g., strengthening the infrastructure), and has gained growing attentions from various research fields. In graph theory, cut nodes play important roles in ensuring network connectivity, which could of course be regarded as potential removal candidates for this network dismantling problem. This paper is primarily dedicated to this point. Here, having the aid of an auxiliary block-cut tree, we transform the network dismantling problem into a relatively simple problem − − tree dismantling problem, and then design a bottom-up dynamic programming algorithm (abbreviated as DPA) to dismantle this auxiliary tree by removing cut nodes with minimum overall removal costs. This DPA dismantling strategy has been tested on both synthetic networks and real-world networks, and numerical experiments demonstrate the superiority of this method. Our results shed light on more explorations of network structure from the cut-node perspectives. • Allowed to take arbitrary non-negative real values as removal costs. • An auxiliary tree-structure built to create an efficient dynamic programming algorithm. • Randomization verifies superiority in handling generalized dismantling problems. [ABSTRACT FROM AUTHOR]

Banach's contraction principle is a fundamental result in pure and applied mathematics, and all the fields of physics. In this paper a new type of contraction, called in the text partial contractivity, is presented in the framework of b-metric spaces (an extension of the usual metric spaces). The new mappings generalize the classical Banach contractions, that appear as a particular case. The properties of the new self-maps are studied, giving sufficient conditions for the existence and uniqueness of their fixed points. Afterwords three different iterative algorithms for the approximation of critical points (Picard, Ishikawa and Karakaya) are considered, concerning their convergence and stability. These findings are applied to the approximation of fractal functions, coming from contractive and non-contractive operators. • Definition of a new type of contraction. • Existence and uniqueness of fixed points for this self-map. • Study of Ishikawa and Karakaya algorithms for the approximation of critical points. • Analysis of convergence and stability of these procedures. • Application to the approximation of fractal functions. [ABSTRACT FROM AUTHOR]

Cryptography and steganography are usual methods for safe transfer of information, which encryption algorithms turn original images into unreadable noise-like images. This paper presents a novel symmetric cryptosystem designed for the transmission of RGB color images through open channels and our goal is to provide a secure cryptography algorithm against cropping and noise attacks. The encryption algorithm is based on a suitable 3D hybrid chaotic system, with high Lyapunov exponent value, leveraging the advantages of common chaos maps while addressing their inherent limitations. To further enhance security, a novel pixel shuffle operator is employed to eliminate any potential neighborhood relations between image pixels. The encryption process incorporates reversible second-order cellular automata, which are applied to the outputs of the chaotic system. Key generation is achieved through the utilization of irreversible cellular automata. The resulting key space is large enough to resist brute-force attacks and performs a high level of sensitivity. Experimental results, including analysis of histograms, entropies, and pixel correlations, confirm the effectiveness of the proposed image encryption scheme, and prove its resilient against statistical attacks and a remarkable resistance against data loss attacks. • Improving classical chaotic systems by creating a three-dimensional system with high Lyapunov exponent value. • Defining suitable functions to shuffle image pixels. • Introducing a resistant and effective encryption algorithm based on the new chaotic system and cellular automata. [ABSTRACT FROM AUTHOR]

This paper studies chaotic image encryption technology and fractal matrix theory, and proposes a synchronous permutation-diffusion encryption algorithm based on multi-parameter fractal matrix. First, this paper proposes a new Multiple Parameter Mixed Coupled Map Lattices system (MPMCML). Then, the concept of fractal matrix is introduced, and the construction process of multi-parameter fractal matrix is given. Finally, based on the multi-parameter fractal matrix, a new synchronous permutation-diffusion image encryption algorithm is proposed. Most importantly, the multi-parameter fractal matrix is very sensitive to the change of parameters, any slight change of parameters will produce a completely different fractal matrix, making the encryption result completely different. Compared with the methods of permutation before diffusion and diffusion before permutation, the synchronous permutation-diffusion method greatly improves the privacy of permutation and diffusion, and improves the anti-attack ability of the algorithm. By analyzing the encryption performance and the ability to resist various attacks, it can be determined that the proposed algorithm exhibits good security characteristics. [ABSTRACT FROM AUTHOR]

This paper presents efficient chaotic invasive weed optimization (CIWO) techniques based on chaos for solving optimal power flow (OPF) problems with non-smooth generator fuel cost functions (non-smooth OPF) with the minimum pollution level (environmental OPF) in electric power systems. OPF problem is used for developing corrective strategies and to perform least cost dispatches. However, cost based OPF problem solutions usually result in unattractive system gaze emission issue (environmental OPF). In the present paper, the OPF problem is formulated by considering the emission issue. The total emission can be expressed as a non-linear function of power generation, as a multi-objective optimization problem, where optimal control settings for simultaneous minimization of fuel cost and gaze emission issue are obtained. The IEEE 30-bus test power system is presented to illustrate the application of the environmental OPF problem using CIWO techniques. Our experimental results suggest that CIWO techniques hold immense promise to appear as efficient and powerful algorithm for optimization in the power systems. [ABSTRACT FROM AUTHOR]

The occurrence of economic management crisis has seriously affected the production and operation of enterprises, the stability of capital markets and even the economic security of the entire country and the world. The use of higher mathematics in economic management is very beneficial to the economic restructuring. For example, in the Lagrangian method for solving the constraint optimization problem, the correlation function can be listed in the Lagrangian fractional calculus equation for the economic management early warning problem with many independent variables. Then take one of the factors as the dependent variable and other factors as fixed constants, and bring them into the Lagrangian fractional calculus equation, you can find the variable solution and get the extreme value of the economic management early warning algorithm. Therefore, this paper combines normative research and empirical research to study the algorithm design, theoretical analysis and numerical experiments of Lagrangian-based methods for solving constrained optimization problems. The Lagrangian fractional calculus method is used to evaluate the early warning algorithm of economic management, improve the prediction accuracy and practicability of the model, and conduct empirical research. It is expected to find a way to effectively determine whether a listed company is caught in an economic management crisis and provide early warning for the listed company's own management. [ABSTRACT FROM AUTHOR]

Quantitative analysis of the factors affecting the energy consumption of metro trains and finding out the breakthrough points of energy conservation is of great practical significance for reducing transport costs and improving energy utilization. Train operation curve optimization is one of the main methods to reduce the energy consumption of train operation. This paper introduces the metro train energy-saving operation optimization model with fixed travel time. Firstly, taking the energy consumption index and punctuality index as the objectives, a train energy-saving operation optimization model is established. Then, the solution method based on the improved NSGA-II algorithm is developed. Finally, the developed optimization model is applied to Guangzhou Metro Line 7 to verify the performance. The results show that the energy consumption of the developed operation strategy is 24.4 % less than that of the minimum travel time strategy, and the total operation time meets the punctuality requirements. Meanwhile, the improved NSGA-II algorithm has less energy consumption than GA and PSO algorithms in the application of Guangzhou Metro Line 7. [ABSTRACT FROM AUTHOR]

In this paper, we develop a new algorithm for estimating control parameter values of ordinary differential equation (ODE) models. We call it the complex error minimization algorithm with an adaptive rate of change. It efficiently determines the parameters of ODE models even over extremely short time series. The algorithm is based on the gradient method and successfully solves its major drawback, namely getting stuck in local minima. To detect the getting stuck, we first introduce the calculation of four different errors at once. Our studies show that they achieved the global minimum only when we observe simultaneous minimization of all these errors. When getting stuck in local minima takes place, only one (or several) errors are minimized, while the others remain unchanged or grow. Thus, the algorithm accurately detects getting stuck in local minima. After this, it applies special methods based on simulated annealing to escape from local minima. The algorithm selects the most optimal path for convergence of parameter values to the global minimum by applying random restarts and multi-start methods to avoid local minima. We have tested our method on models with regular and chaotic dynamics and have found that it can work with high accuracy in these cases. Our method is suitable for actual systems with complex dynamics and an extensive set of control parameters but short time series. Thus, the proposed algorithm is an effective method for solving the inverse problem of ODE models. • Efficient algorithm estimates ODE control parameters over short time series, addressing local minima. • Simultaneous minimization of multiple errors accurately detects instances of being stuck. • Escape local minima using simulated annealing and optimal path selection for parameter convergence. • High accuracy in estimating parameters for complex systems with limited data, solving inverse ODE problems. [ABSTRACT FROM AUTHOR]

Abstract: Third part of the paper is devoted to analysis of the hyper, hyper-hyper and spatial–temporal chaos of continuous mechanical systems using the Lyapunov exponents. The constructed algorithms for the Lyapunov exponents’ computation allowed detecting and analysing novel phase transitions from chaos through hyper chaos to hyper-hyper chaos. In addition, a novel characteristic “maximal deflection versus excitation amplitude” has been introduced to study stability properties of the investigated continuous systems. It should be emphasized that the latter characteristic yields results in full agreements with those obtained via the Lyapunov exponents’ spectrum estimation. The introduced methods and tools of analysis allowed detecting the Sharkovskii windows of periodicity in all continuous mechanical systems investigated in this paper. Finally, the approach to study the space-temporal chaos exhibited by shell structural-members is also proposed. [Copyright &y& Elsevier]

• In this analysis, by developed the reproducing kernel algorithm within the Atangana–Baleanu fractional operator, the numerical solutions of Volterra integro-differential equations are discussed with respect to initial conditions of necessity. • The solution methodology involves the use of couple Hilbert spaces for both range and domain space. • Numerical algorithm and procedure of solution are assembled compatibility with the optimal formulation of the problem. • The optimal profiles show the performance of the numerical solutions and the effect of the Atangana–Baleanu fractional operator in the obtained results. • In this approach, computational simulations are introduced to delineate the suitability, straightforwardness, and relevance of the calculations created. This paper focuses on providing a novel high-order algorithm for the numerical solutions of fractional order Volterra integro-differential equations using Atangana–Baleanu approach by employing the reproducing kernel approximation. For this purpose, we investigate couples of Hilbert spaces and kernel functions, as well as, the regularity properties of Atangana–Baleanu derivative, and utilize that the representation theorem of its solution. To remove the singularity in the kernel function, using new Atangana–Baleanu approach the main operator posses smoothing solution with a better regularity properties and the reproducing kernel algorithm is designed for the required equation. The convergence properties of the proposed algorithm are also studied which proves that the new strategy exhibits a high-order of convergence with decreasing error bound. Some numerical examples of single and system formulation illustrate the performance of the approach. Summary and some notes are also provided in the case of conclusion and highlight. [ABSTRACT FROM AUTHOR]

Abstract: Evolutionary Algorithms (EAs) are stochastic and robust meta-heuristics of evolutionary computation field useful to solve optimization problems in image processing applications. Recently, as special mechanism to avoid being trapped in local minimum, the ergodicity property of chaotic sequences has been used in various designs of EAs. Three differential evolution approaches based on chaotic sequences using logistic equation for image enhancement process are proposed in this paper. Differential evolution is a simple yet powerful evolutionary optimization algorithm that has been successfully used in solving continuous problems. The proposed chaotic differential evolution schemes have fast convergence rate but also maintain the diversity of the population so as to escape from local optima. In this paper, the image contrast enhancement is approached as a constrained nonlinear optimization problem. The objective of the proposed chaotic differential evolution schemes is to maximize the fitness criterion in order to enhance the contrast and detail in the image by adapting the parameters using a contrast enhancement technique. The proposed chaotic differential evolution schemes are compared with classical differential evolution to two testing images. Simulation results on three images show that the application of chaotic sequences instead of random sequences is a possible strategy to improve the performance of classical differential evolution optimization algorithm. [Copyright &y& Elsevier]

Abstract: This paper proposes a novel particle swarm optimization (PSO) algorithm, chaotically encoded particle swarm optimization algorithm (CENPSOA), based on the notion of chaos numbers that have been recently proposed for a novel meaning to numbers. In this paper, various chaos arithmetic and evaluation measures that can be used in CENPSOA have been described. Furthermore, CENPSOA has been designed to be effectively utilized in data mining applications. [Copyright &y& Elsevier]

Abstract: The main objective of this paper is to study reduction rate of 2D DEM (digital elevation model) data profile after data reduction by the Douglas–Peucker (DP) linear simplification method and by fractal interpolation to show original terrain reconstruction. In this paper, two-dimensional data of measured geographic profiles are taken as the study object, by using the DP method and the improved Douglas–Peucker (IDP) method to reduce data. Its aim is to retain spatial linear characteristics and variations, then take reduced data points as basic points and use the random fractal interpolation approach to add more data points up to the same as the original data points, in order to reconstruct the terrain, and compare the experimental data with the random point extraction method addressed in related literature. This paper uses tolerance calibration to generate different reduction rates and utilizes four types of evaluation factors, statistical measurement, image measurement, spectral analysis and elevation cumulative probability distribution graph, to make a quantitative analysis of profile variation. The study result indicates that real profile elevation data, manipulated with varied reduction approaches, then reconstructed by means of fractal interpolation can produce data points with a higher resolution than those originally observed, thereby the reconstructed profile gets more natural and real details. [Copyright &y& Elsevier]

• We propose a new clustering method for clustering categorical data based on the fuzzy k-modes algorithm. • A new attribute weighting mechanism is used to improve the performance of the fuzzy k-modes algorithm. • In addition to weighting the attributes, we use cluster weighting to avoid poor local optima, which occurs after bad initialization. • We introduce a new distance criterion that significantly reduces sensitivity to noise. • Our method forms high quality clusters during clustering process, irrespective of the initialization. The fuzzy k-modes (FKM) is a popular method for clustering categorical data. However, the main problem of this algorithm is that it is very sensitive to the initialization of primary clusters, so inappropriate initial cluster centers lead to poor local optima. Another problem with the FKM is the equal importance of the attributes used during the clustering process, which in real applications, the importance of the attributes are different, and some attributes are more important than others. Some versions of FKM have been presented in the literature, each of which has somehow solved one of the above problems. In this paper, we propose a new clustering method (FKMAWCW) to solve mentioned problems at the same time. In the proposed clustering process, a local attribute weighting mechanism is used to weight the attributes of each cluster properly. Also, a cluster weighting mechanism is proposed to solve the initialization sensitivity. Attribute weight and cluster weight are learned simultaneously and automatically during the clustering process. In addition, to reduce the noise sensitivity, a new distance function is proposed. So, the proposed algorithm can tolerate noisy environment. Extensive experiments on 11 benchmark datasets and an artificially generated dataset show that the proposed algorithm performs better than the state-of-the-art algorithms. This paper presents mathematical analyses to obtain updating functions, providing the convergence proof of the algorithm. The implementation source code of FKMAWCW is made publicly available at https://github.com/Amin-Golzari-Oskouei/FKMAWCW. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the global robust exponential stability of interval neural networks with time delays is investigated. As far as we are aware only, few papers deals with the interval neural networks and focus on the robust exponential stability. A linear matrix inequality (LMI) approach is developed to derive sufficient conditions ensuring the delayed neural network to have a unique equilibrium point, which is globally robust exponentially stable. The proposed LMI conditions can be checked easily by a recently developed algorithms solving LMIs. [Copyright &y& Elsevier]

Abstract: LMSER PCA algorithm is a principal components analysis algorithm. It is used to extract principal components on-line from input data. The algorithm has both stability and chaotic dynamic behavior under some conditions. This paper studies the local stability of the LMSER PCA algorithm via a corresponding deterministic discrete time system. Conditions for local stability are derived. The paper also explores the chaotic behavior of this algorithm. It shows that the LMSER PCA algorithm can produce chaos. Waveform plots, Lyapunov exponents and bifurcation diagrams are presented to illustrate the existence of chaotic behavior of this algorithm. [Copyright &y& Elsevier]

Abstract: This paper presents an approach to the well-known traveling salesman problem (TSP) using self-organizing maps (SOM). There are many types of SOM algorithms to solve the TSP found in the literature, whereas the purpose of this paper is to look for the incorporation of an efficient initialization methods and the definition of a parameters adaptation law to achieve better results and a faster convergence. Aspects of parameters adaptation, selecting the number of nodes of neurons, index of winner neurons and effect of the initial ordering of the cities, as well as the initial synaptic weights of the modified SOM algorithm are discussed. The complexity of the modified SOM algorithm is analyzed. The simulated results show an average deviation of 2.32% from the optimal tour length for a set of 12 TSP instances. [Copyright &y& Elsevier]

Abstract: This paper refines existing techniques into an algorithmic method for deriving the generalization of a Lax Pair directly from a general integrable nonlinear evolution equation via the use of truncated Painlevé expansions. The resulting algorithm is also applicable to multicomponent integrable systems, and is thus expected to be of great value for complicated variants of such systems in various applications areas. Although a related method has existed for simple scalar integrable evolution equations for many years now, nevertheless no systematic procedure has been given that would work in general for scalar as well as for multicomponent systems. The method presented here largely systematizes the necessary operations in applying the Painlevé method to a general integrable evolution equation or system of equations. We demonstrate that by following the concept of enforcing integrability at each step (referred to here as the Principle of Integrability), one is led to an appropriate generalization of a Lax Pair, although perhaps in nonlinear form, called a “Lax Complex”. One new feature of this procedure is that it utilizes, as needed, a technique from the well-known Estabrook–Wahlquist method for determining necessary integrating factors. The end result of this procedure is to obtain a Lax Complex, whose integrability condition will contain the original evolution equation as a necessary condition. This in itself is sufficient to ensure that the Lax Complex may be used to construct Bäcklund solutions of the evolution equation, to obtain Darboux Transformations, and also to obtain Hirota’s tau functions, in a manner analogous to the procedure for single component systems. The additional problem of finding a general procedure for the linearization of any Lax Complex is not treated in this paper. However, we do demonstrate that a particular technique, which can be derived self-consistently from the Painlevé–Bäcklund equations, has proven to be sufficient so far. The Nonlinear Schrödinger equation is used to illustrate the method, and then the method is applied to obtain, for the first time via the Painlevé method, a Lax Complex for the vector Manakov system. Limitations in the algorithm remain, especially for cases with more than one principal branch, and these are briefly mentioned as directions for future work. [Copyright &y& Elsevier]

Abstract: A novel observer-base output feedback variable universe adaptive fuzzy controller is investigated in this paper. The contraction and expansion factor of variable universe fuzzy controller is on-line tuned and the accuracy of the system is improved. With the state-observer, a novel type of adaptive output feedback control is realized. A supervisory controller is used to force the states to be within the constraint sets. In order to attenuate the effect of both external disturbance and variable parameters on the tracking error and guarantee the states to be within the constraint sets, a robust controller is appended to the variable universe fuzzy controller. Thus, the robustness of system is improved. By Lyapunov method, the observer-controller system is shown to be stable. The overall adaptive control algorithm can guarantee the global stability of the resulting closed-loop system in the sense that all signals involved are uniformly bounded. In the paper, we apply the proposed control algorithms to control the Duffing chaotic system and Chua’s chaotic circuit. Simulation results confirm that the control algorithm is feasible for practical application. [Copyright &y& Elsevier]

This paper devises an effective image encryption algorithm that exploits a novel hyperchaotic map and is applicable to a variety of image encryption scenarios. The newly designed hyperchaotic map exhibits enhanced ergodicity, more intricate behavior, and a substantial chaotic range, as revealed by performance evaluation. The encryption algorithm under consideration utilizes a newly developed hyperchaotic map in conjunction with fission diffusion and permutation operations. Fission diffusion effectively spreads minor changes throughout the entire image, while permutation operations relocate these changes to various positions within the image. The results of the performance analysis demonstrate that the algorithm exhibits strong resilience against various attack patterns, while also exhibiting high levels of encryption efficiency. • A new large-scale hyperchaotic map is constructed and its performance is tested. • A new chaos-based image encryption algorithm with fission diffusion is designed. • The secure performance of the proposed image algorithm is thoroughly analyzed. [ABSTRACT FROM AUTHOR]

Multi-individual interactions are ubiquitous in the real world, which are usually modeled by hypergraphs. Similar to low-order networks, there are special key nodes in high-order networks that are highly influential and play a crucial role in information dissemination. The objective of the influence maximization problem is to find an optimal set of nodes that maximizes the influence of the network, while maximizing influence in hypergraphs has been neglected so far, and how to explore higher-order interactions from multiple perspectives and exploit the features of higher-order structures are still open questions. To solve the above problems, a self-optimization algorithm based on electrostatic field is proposed. The network is innovatively viewed as an electrostatic field to uncover the interaction forces of the nodes in it. The improved localized Physarum polycephalum algorithm is used to assign values to the initial charges of the nodes. The effective distance among hyperedges and nodes is redefined. Furthermore, the self-optimizing update algorithm is designed to reduce the overlap of nodes' influence ranges in the optimal set. Percolation, SIR, Top-k, and correlation experiments are conducted on eight real-world networks, and the superiority of our proposed algorithm in this paper is verified by comparing with six algorithms. • A charge initialization rule based on localized Physarum polycephalum is designed. • The distances between hyperedges and between nodes are effectively measured on a hypergraph. What's more, the global and local information in the hypergraph is combined using Coulomb's law. • In order to reduce the overlap of impact areas in the seed set, a self-optimizing update algorithm is proposed to find the node that currently has the greatest impact on the network. [ABSTRACT FROM AUTHOR]

Influence Maximization (IM) is a key algorithmic problem that has been extensively studied in social influence analysis, but most of existing researches either make sacrifices in solution accuracy or suffer high computational complexity. In this paper, we propose a new Community-based Influence Maximization (CIM) algorithm for identifying a set of seed spreaders in a social network to maximize the expected number of influenced nodes. In CIM, the initial candidate seeds are first selected based on the proposed topological potential "peak-slope-valley" structure framework. Then, we propose a recursive clustering approach and a similarity indicator based on local resource allocation to partition communities. Finally, we design a community-based regional influence indicator to select seed nodes without using any prior knowledge. Experiment datasets include three artificial benchmarks with varying community strengths, as well as nine representative networks drawn from various fields. Extensive numerical simulations on both artificial and real networks indicate that (i) community-based techniques enrich the toolbox for addressing the IM problem and (ii) the derivative algorithm outperforms recent high-performing influence maximization algorithms in terms of influence propagation and coverage redundancy of the seed set with an acceptable complexity. Furthermore, our algorithm exhibits good stability on networks of varying scales and structural characteristics. • A new algorithm is proposed to further enrich the toolbox for influence maximization. • A topological potential "peak-slope-valley" structure is proposed to identify local communities. • This study uses a proposed recursive clustering approach to identify community partition. • Experiments show that this work is an effective and efficient influence maximization algorithm. [ABSTRACT FROM AUTHOR]

Current multiple-image encryption schemes usually require a fixed number or the same size of images. Therefore, this paper proposes a multiple-image encryption algorithm that can encrypt any number, size, and type of image. Firstly, we propose a two-dimensional chaotic model, which can generate multiple types of chaotic systems to solve the defects of some existing chaotic systems and reduce the design difficulty of chaotic systems. The generated chaotic systems are proven to have better performance through bifurcation diagrams, phase diagrams, Lyapunov exponent, and sample entropy analysis. Secondly, we fuse multiple images and then use SHA-512 to generate a secret key to increase resistance to plaintext attacks. We embed the size message of the original image into the fused image pixels, eliminating the need to transmit the size message separately from the secret key. Finally, we propose a simultaneous permutation and diffusion algorithm to improve security and efficiency. Experimental simulations and security analysis show that the proposed algorithm can encrypt multiple images of different sizes and types with good attack resistance and encryption efficiency. [ABSTRACT FROM AUTHOR]

• This work proposes a new one-dimensional chaotic system with better chaotic performance. • A novel random block strategy is designed based on the new chaotic map. • Bit-level confusion method is adopted using random block strategy. • The simulation results and security results demonstrate that the algorithm can resist common attacks. With the continuous development of information technology, ensuring information security has become an important issue. Image is widely used as a multimedia tool, so this paper proposes a chaotic image encryption algorithm based on scrambling and diffusion operations. In the scrambling stage, the whole image is represented in binary form and divided into several sub images. The sub images are scrambling at bit-level using the improved zigzag method proposed in this paper. After that, the pixel-level image is randomly shuffled once. In the diffusion phase, the row-by-row strategy is adopted, which can change the pixel value of the image, making the image more difficult to crack. The chaotic sequence used in the whole encryption operation is generated by the one-dimensional Logistic Self-embedding (1DLSE) chaotic system proposed in this paper. Compared with the traditional one-dimensional chaotic system, the new chaotic system has more chaotic performance. Simulation results and security analyses demonstrate that the proposed encryption algorithm has superior security and higher efficiency in practical application. [ABSTRACT FROM AUTHOR]

• Three one-dimensional chaotic maps are improved and two new one-dimensional chaotic systems are proposed. • The dynamic row scrambling in this paper is to traverse odd rows from outside to inside and even rows from inside to outside. • Using different values of the chaotic remainder sequence, the different triangle matrices of the image are zigzag scrambled in different directions and orders. This paper introduces two new one-dimensional chaotic systems. They can be considered as an improvement of Logistic map, Sine map and Tent map. One is the chaotic system composed of Sine and Tent maps (STCS), the other is Logistic-Logistic chaotic system (L-LCS). Based on the two, an image encryption algorithm using dynamic row scrambling and Zigzag transformation is proposed. Firstly, the image is traversed in different directions of odd and even rows, and the results are scrambled with the chaotic sequence generated by STCS. Secondly, based on standard Zigzag scrambling idea, a special traversal method is used, that is, for the different permutation of the lower triangle and the upper triangle of the matrix (each triangular matrix does not contain the values on the main and sub diagonals) in order and direction. Then, combined with the chaotic sequence generated by L-LCS, two different diffusion formulas are used to diffuse the segmented image. Finally, this encryption scheme can also be extended to color images. Experimental simulation and performance analysis show that the encryption algorithm has better security. [ABSTRACT FROM AUTHOR]

In real networks, clustering is of great value to the analysis, design, and optimization of numerous complex systems in natural science and engineering, e.g. power supply systems ,modern transportation networks, and real-world networks. However, the majority of them simply pay attention to the density of edges rather than the signs of edges as the attributes to cluster, which usually suffer a high-level computational complexity. In this paper, a new rule is proposed to update the attributes flow, which can guarantee network clustering reach a state of optimal convergence. The positive and negative update rule we introduced, represent the cooperative and hostile relationship, and the attribute configuration will convergence and one can identify the reasonable cluster configuration automatically. An algorithm with high efficiency is proposed: a nearly linear relationship is found between the time complexity and the size in sparse networks. Finally, we conduct the verification of the algorithmic performance by a representative simulations on Correlates of War data. [ABSTRACT FROM AUTHOR]

Mining the community structure is an important subject in the area of social network analysis, and detecting the hidden communities within the social networks will help to better understand the topological properties of the real-life networks. Meanwhile, community detection will be also helpful to monitor the public opinion, identify the opinion leaders and perform the personalized recommendation. In comparison with the simplex user ties or contents, considering the trust features from multiple users will provide a more comprehensive account of the linking relationship between users. To this end, we propose a novel non-overlapping community detection algorithm, which is based on the trust mechanism, to recognize the community structure in this paper. At first, we propose several definitions with regard to trust relationship between users to depict the trust strength, which includes the direct, indirect and mutual trust, and then the specific trust calculation method is provided to quantitatively describe the extent of trust. Secondly, starting from the trust relationship, we integrate the edge fitness and community fitness into the non-overlapping community detection and propose a novel trust-based algorithm to comprehensively leverage the trust among nodes to further mine the communities within the networks. Finally, to deeply analyze the analyze the performance, we take use of Lesmis and Gemo data sets to carry out extensive experiments, and the results show that, compared with other classical algorithms, the community based on the newly proposed algorithm features the higher trust cohesion on the condition that the structural cohesiveness of social network is fully satisfied. The current methods will be of significance to deeply understand and effectively find out the communities within realistic networks. [ABSTRACT FROM AUTHOR]

Cryptanalysis analyses various combinations among plaintexts, ciphertexts and random keys; even using differential methods or analog methods, the attackers can interpret the keys depending upon the operations in the round functions or any subset of the algorithm. The previous research emphasizes on creation of different cryptographic functions, however the randomness of such functions has not been researched significantly so far. In this paper, we have shown a random function generator which can be used for any cryptographic algorithm. This generator outputs the combination of functions in random and cannot be traced back due its randomness. The objective of our research work is not to identify a particular boolean function that is balanced or symmetric based on its input variables, our proposed work provides a random combination of generic boolean functions as used in MD5 or SHA series, block cipher round functions and stream ciphers. Moreover, the random selection of input variables for a particular function also makes it desirable for cryptographic function modules. The results of our experimentation show that the functions generated by the proposed generator provide a good non-linearity, resiliency and balanced effect. [ABSTRACT FROM AUTHOR]

This paper proposes two fractional gradient descent algorithms for switching models. Each submodel is assigned a weight which can determine the identity of the submodel in each sampling instant. By using the fractional gradient descent algorithms, the parameters of each submodel can be obtained, and then the weights of all the submodels can be estimated based on the self-organizing maps method. These two algorithms can deal with different kinds of switching models on a case by case basis. In addition, compared with the traditional identification algorithms, the proposed methods have two advantages: (1) has faster convergence rates; (2) has less computational efforts. Simulation example demonstrates the effectiveness of the proposed methods. • The FGD-SOM algorithms have less computational efforts and faster convergence rates. • The FGD-SOM-2 algorithm has less limitation of the switching models. [ABSTRACT FROM AUTHOR]

Aiming at the problem that the current image encryption algorithms generally use dissipative chaos, which leads to the algorithms being vulnerable to reconstruction attack, and the coding rules of image encryption algorithms using biological coding are too simple, this paper proposes an image encryption algorithm based on conservative hyperchaotic and biological gene algorithms. Firstly, a new conservative hyperchaotic system is proposed, which can resist reconstruction attacks, has a larger key space, and can generate pseudorandom sequences with strong randomicity. Secondly, SHA-512 is used to calculate the hash value of plaintext image, and the initial key is generated through the key generation algorithm we devised to improve the sensitivity of the algorithm to the key and plaintext. Finally, new dynamic coding rules are designed to enrich the biological coding rules. In addition, dynamic gene uniform crossover algorithm and dynamic gene mutation algorithm are devised, and pseudorandom sequences dynamically control gene operation, further enriching coding rules and expanding key space, improving the security of the algorithm. According to experimental and analysis results, the image encryption algorithm has high security and efficiency. [ABSTRACT FROM AUTHOR]

• A new spatiotemporal chaotic system is proposed: Tent-Dynamics Coupled Map Lattices chaotic system. • Experimental tests prove that the performance of the Tent-Dynamics Coupled Map Lattices model is better than the traditional coupled mapping lattice model. • Applying the Household method to the diffusion process of image matrix. • The security analysis experiment proves that the image encryption algorithm based on Tent-Dynamics Coupled Map Lattices and diffusion of Household has good performance. This paper presents an image encryption algorithm based on Tent-Dynamics Coupled Map Lattices (TDCML) system and diffusion of Household. All aspects of the TDCML spatiotemporal chaotic system proposed in this paper meet the cryptographic characteristics and are suitable for studying image encryption. The specific image encryption algorithm first generates chaotic sequences according to the TDCML system. The image scrambling uses a cyclic shift algorithm, and the movement of each row and column is determined by the chaotic sequence. Then the image diffusion is improved according to the Household orthogonal decomposition method. Think of each column of the image matrix as a row vector, and then operate according to part of the formulas in the Household transformation to obtain a new row vector. Finally, perform the bitwise XOR operation with the specified chaotic sequence to obtain the final encrypted image. Theoretical analysis and experimental results have proved the security of this encryption algorithm. [ABSTRACT FROM AUTHOR]

• This research paper deals with a problem related to the damped materials involved in structural dynamics. • The problem considered in this paper involves a fractional-order damping coefficient in the form of fractional derivatives to present a better mathematical model of the vibration systems. • We have suggested a novel unsupervised machine learning procedure that first designs general solutions, with the help of Artificial Neural Networks (ANNs), for the fractional-order differential equation involving unknown decision weights. These weights are determined with the help of Fractional-Order Darwinian Particle Swarm Optimization (FO-DPSO) algorithm by setting a fitness function for each case. This research paper deals with a problem related to the damped materials contained in structural dynamics. The problem dealt with here involves a fractional-order damping coefficient in the form of fractional derivatives that present a better mathematical model of the vibration systems. Fractional derivatives are widely used to characterize the viscoelastic features in structural designs. Unlike the integer order differentiation, fractional-order derivatives consider local as well as the global evolution of the system. Therefore, fractional differential equations can be indicated as a reasonable choice for modeling certain physical phenomena, and to present more accurate mathematical solutions to real-world applications than the ordinary differential equations. We have proposed a novel unsupervised machine learning procedure that first designs general solutions, with the help of Artificial Neural Networks (ANNs), for the fractional-order differential equation containing unknown decision weights. These weights are worked out with the help of Fractional-Order Darwinian Particle Swarm Optimization (FO-DPSO) algorithm by setting a fitness function for each case. Results obtained from our simulations are better in the sense that they are overlapping with the analytical solutions available in the literature. [ABSTRACT FROM AUTHOR]

In this paper we obtain the rates of convergence of the algorithms given in [13] and [14] for an automatic computation of the centered Hausdorff and packing measures of a totally disconnected self-similar set. We evaluate these rates empirically through the numerical analysis of three standard classes of self-similar sets, namely, the families of Cantor type sets in the real line and the plane and the class of Sierpinski gaskets. For these three classes and for small contraction ratios, sharp bounds for the exact values of the corresponding measures are obtained and it is shown how these bounds automatically yield estimates of the corresponding measures, accurate in some cases to as many as 14 decimal places. In particular, the algorithms accurately recover the exact values of the measures in all cases in which these values are known by geometrical arguments. Positive results, which confirm some conjectural values given in [13] and [14] for the measures, are also obtained for an intermediate range of larger contraction ratios. We give an argument showing that, for this range of contraction ratios, the problem is inherently computational in the sense that any theoretical proof, such as those mentioned above, might be impossible, so that in these cases, our method is the only available approach. For contraction ratios close to those of the connected case our computational method becomes intractably time consuming, so the computation of the exact values of the packing and centered Hausdorff measures in the general case, with the open set condition, remains a challenging problem. [ABSTRACT FROM AUTHOR]

There are a number of situations in which several signals are simultaneously recorded in complex systems, which exhibit long-term power-law cross-correlations. This paper presents two-dimensional multifractal cross-correlation analysis based on the partition function (2D-MFXPF), two-dimensional multifractal cross-correlation analysis based on the detrended fluctuation analysis (2D-MFXDFA) and two-dimensional multifractal cross-correlation analysis based on the detrended moving average analysis (2D-MFXDMA). We apply these methods to pairs of two-dimensional multiplicative cascades (2D-MC) to do a comparative study. Then, we apply the two-dimensional multifractal cross-correlation analysis based on the detrended fluctuation analysis (2D-MFXDFA) to real images and unveil intriguing multifractality in the cross correlations of the material structures. At last, we give the main conclusions and provide a valuable reference on how to choose the multifractal algorithms in the potential applications in the field of SAR image classification and detection. [ABSTRACT FROM AUTHOR]

How to obtain higher-dimensional integrable systems from lower ones is a hot topic deserving deeply consideration. Recently, a deformation algorithm with the help of different conservation laws proposed by Lou, Hao and Jia has been applied to establish some higher-dimensional nonlinear systems. In this paper, the method is mainly used to establish the (2+1)-dimensional Burgers equation and higher-dimensional Burgers systems. The Lax pairs, integrable Burgers hierarchy, Lie point symmetries and kink soliton solutions are also investigated. • The most important in our article the application of the deformation method, which leads to a lot of new Lax integrable systems and creates more problems are worth deeply study. • For example, we can search for the corresponding physical model of the coupled B-KdV equation. • I think this method can be interesting. [ABSTRACT FROM AUTHOR]

Identifying influential nodes in complex networks is an essential research issue in network science since it may attribute to understand network structure and function. Majority of existing methods have been established by considering topological characteristics of networks. In this paper, we put forward a novel algorithm based on the Local Propagation Probability (LPP) model for identifying influential nodes in complex networks. The core idea of LPP algorithm is that the nodal influence is measured by total comprehensive scores of neighbor nodes within its three level neighborhood. Specially, the comprehensive score is calculated from three dimensions, namely the propagation influence score between different order neighbors, the propagation influence score in the same order neighbors and the hierarchical structure information of nodes. To validate the performance and applicability of the proposed algorithm, LPP is compared with eight state-of-the-art and competitive algorithms on nine real-world networks. Experimental results demonstrate that LPP performs better in terms of ranking accuracy, effectiveness, top- k nodes and distinguishing ability. The low time complexity allows LPP to be applied to large-scale sparse networks. • A novel algorithm is proposed to identify influential nodes in complex networks. • The proposed algorithm is designed from the perspective of propagation dynamics. • A new comprehensive score is defined to measure the nodal influence. • The proposed algorithm has better performance than eight competitive algorithms. [ABSTRACT FROM AUTHOR]

This work studies pseudomonotone equilibrium problems. The modified inertial viscosity subgradient extragradient is proposed for obtaining strong convergence, and it is proved under the assumption that the bifunction satisfies the Lipchitz-type condition. Flexible use of different stepsize parameters is offered. Moreover, the proposed algorithm is applied to solve diabetes mellitus classification problems. The algorithm's efficiency is shown by comparing with many existing methods with 80.3% high accuracy. The training-validation loss and accuracy plots are presented to consider our good model fitting. • The paper proposed an algorithm for solving pseudomonotone equilibrium problems. • The strong convergence result has been established subject to certain conditions. • Predict diabetes mellitus through the proposed algorithm by ELM. • The algorithm's effectiveness is up to 80.3% accuracy. [ABSTRACT FROM AUTHOR]