Image smoothing is a fundamental task in digital image processing with broad applications. However, traditional texture smoothing techniques often result in the loss or blurring of small structural information and contrast. In this paper, we introduce a piecewise gradient prior aimed at overcoming this drawback. The prior is based on a four-segment piecewise (FSP) penalty function, which can process

The current research introduces a new numerical iterative method that uses a quadrature formula and successive approximations to solve certain types of equations called nonlinear delay integral equations as Hammerstein Volterra type of the second kind. The convergence analysis and numerical stability of the method are also demonstrated. Additionally, by providing the numerical applications, we show

This study investigates the stabilization of generalized asynchronous Boolean control networks under noise interference. Firstly, it involves generalized asynchronous Boolean control networks unaffected by noise interference and extends the stabilization theorem of ordinary Boolean networks to them. Secondly, a theorem is provided to determine the stabilization of networks with noise interference.

The industry and investors are closely monitoring the valuation of research and development (R&D) projects related to new energy vehicles (NEVs) as their technology advances rapidly. However, standard techniques of valuation often fail to describe the full value of R&D initiatives in an uncertain market environment, due to the significant technical hazards and uncertain results associated with these

In this paper, a dual auxiliary systems-based fault-tolerant attitude turn-on/off trigger control problem is studied for the satellite. To address the flexible performance tracking control problem under any initial condition, a new prescribed performance function is designed. Furthermore, to improve the accuracy of satellite attitude tracking errors under the saturation and fault, a novel monitor auxiliary

Evolutionary games on networks often assume that individuals do not move and adopt a uniform strategy toward all neighbors. In reality, however, individuals can migrate to seek more favorable conditions and may act differently depending on whom they interact with. Here, we fill this gap by extending the spatial public goods game on a two-dimensional lattice to include both migration and node-dynamics-based

In general, individuals with high reputation often leverage greater access to resources, influence, and opportunities, creating a differential advantage in societal hierarchies. Meanwhile, real legal systems impose stricter punishments on severe crimes to ensure proportional justice. In some social contexts, individuals who engage in punishment behavior may be perceived as more trustworthy or committed

To achieve common goals, we often use joint commitments. Our commitment helps us to coordinate with our partners and assures them that their cooperative efforts will benefit themselves. However, if one of us can exploit the other's cooperation (as in the Prisoner's Dilemma), our commitment appears less useful. It cannot remove the temptation for our partners to exploit us. Using methods from evolutionary

This paper studies the asynchronous double-source bumpless transfer (BT) finite-time secure control issue for stochastic hidden semi-Markovian jump systems (HSMJSs) with Brownian noise. The HSMJS is assumed to suffer from deception attacks governed by Bernoulli variables, which occur randomly in both sensor-controller (SC) and controller-actuator (CA) channels. Firstly, a hidden semi-Markovian model

In this research, we mainly utilize the stationary iteration method in conjunction with Krylov subspace techniques, such as GMRES, to tackle the large indefinite least squares problem. To accomplish this, the normal equation of the large indefinite least squares problem is firstly transformed into the sparse block three-by-three linear systems with non-singular diagonal blocks, then a block upper triangular

Zernike polynomials serve as an orthogonal basis on the unit disc, and have proven to be effective in optics simulations, astrophysics, and more recently in plasma simulations. Unlike Bessel functions, Zernike polynomials are inherently finite and smooth at the disc center (r=0), ensuring continuous differentiability along the axis. This property makes them particularly suitable for simulations, requiring

Dynamic mode decomposition (DMD) algorithm is widely applied to identify the flow characteristics of fluid dynamic field. However, for high-dimensional viscoelastic fluid systems, DMD might often result in unsatisfactory performance because of its huge computation cost. Therefore, we propose an improved dynamic mode decomposition algorithm, called sparsity promoting randomized dynamic mode decomposition

The paper is devoted to address the numerical preservation of the exponential mean-square contractive character of the dynamics of stochastic differential equations (SDEs), whose drift and diffusion coefficients are subject to non-global Lipschitz assumptions. The conservative attitude of stochastic θ-methods is analyzed both for Itô and Stratonovich SDEs. The case of systems with linear drift is also

For a graph G, the general Sombor (SOα) index is defined as:SOα(G)=∑vivj∈E(G)(di2+dj2)α, where α≠0 is a real number, E(G) is the edge set and di denotes the degree of a vertex vi in G. A chemical tree is a tree in which no vertex has a degree greater than 4, and a pendant vertex is a vertex with degree 1. This paper aims to completely characterize the n− vertex chemical trees with a fixed number of

Arbitrarily partitionable (AP) graphs are graphs that can have their vertices partitioned into arbitrarily many parts inducing connected graphs of arbitrary orders. Since their introduction, several aspects of AP graphs have been investigated in literature, including structural and algorithmic aspects, their connections with other fundamental notions of graph theory, and variants of the original notion

Metric dimension is a valuable parameter that helps address problems related to network design, localization, and information retrieval by identifying the minimum number of landmarks required to uniquely determine distances between vertices in a graph. Generalized Sierpiński graphs represent a captivating class of fractal-inspired networks that have gained prominence in various scientific disciplines

This study presents an efficient class of fourth-order iterative methods introduced by Ali Zein (2024) in a more abstract Banach space setting. The Convergence Order of this class is proved by bypassing the Taylor expansion. We use the mean value theorem and relax the differentiability assumptions of the involved function. At the outset, we provide a semilocal analysis, and then, using the results

This article proposes and analyzes fast and precise numerical methods for calculating the Bessel integral, which exhibits rapid oscillations and includes algebraic and Cauchy singularities. When a>0, we utilize the numerical steepest descent method with the Gauss-Laguerre quadrature formula to solve it. If a=0, we partition the integral into two parts, solving each part using the modified Filon-type

Individuals frequently engage in a multitude of concurrent games. Owing to the complexity of the interactions and the inherent diversity in players' preferences, this paper introduces a multi-issue game model tailored for structured populations characterized by heterogeneous preferences. The model incorporates several dimensions of preference diversity, including the relative weight accorded to different

In real-world social and economic systems, the provisioning of public goods generally entails continuous interactions among individuals, with decisions to cooperate or defect being influenced by dynamic factors such as timing, resource availability, and the duration of engagement. However, the traditional public goods game ignores the asynchrony of the strategy adopted by players in the game. To address

In information visualization, the position of symbols often encodes associated data values. When visualizing data elements with both a numerical and a categorical dimension, positioning in the categorical axis admits some flexibility. This flexibility can be exploited to reduce symbol overlap, and thereby increase legibility. In this paper, we initialize the algorithmic study of optimizing symbol legibility

Cooperation is the foundation of social progress, but due to rational individuals often prioritize personal interests, reciprocal cooperation is undermined. The Public Goods Game (PGG) is a classic model for studying group interactions. Traditional PGG assumes a static environment, but in reality, the environment is dynamically changing, and there is an interaction between individual behavior and the

In this paper we introduce the concept of integral hypergraphs - hypergraphs whose all adjacency eigenvalues are integers, in analogy to integral graphs. We present infinite families of integral uniform hypergraphs, especially hypergraphs built by two operations, the s-extension of a graph and the k-power of a graph. Our main result is about integrality for uniform hypercycles, obtaining a characterization

A recently introduced coupling strategy for two nonconservative hyperbolic systems is employed to investigate a collapsing vapor bubble embedded in a liquid near a solid. For this purpose, an elastic solid modeled by a linear system of conservation laws is coupled to the two-phase Baer–Nunziato-type model for isothermal fluids, a nonlinear hyperbolic system with nonconservative products. For the coupling

We define the reduced biquaternion tensor ring (RBTR) decomposition and provide a detailed exposition of the corresponding algorithm RBTR-SVD. Leveraging RBTR decomposition, we propose a novel low-rank tensor completion algorithm RBTR-TV integrating RBTR ranks with total variation (TV) regularization to optimize the process. Numerical experiments on color image and video completion tasks indicate the

Inferring information diffusion networks plays a crucial role in social network analysis and various applications. Existing methods often rely on the infection times of nodes in diffusion processes to uncover influence relationships. However, accurately monitoring real-time temporal information is challenging and resource-intensive. Additionally, some approaches that do not utilize infection timestamps

Over the last decade, high-frequency oscillations (HFOs), very high-frequency oscillations (VHFOs), and ultra-fast oscillations (UFOs) have been proposed as possible biomarkers for epileptogenic zones in individuals with drug-resistant epilepsy. Despite considerable interest, the mechanisms responsible for producing such high frequencies, significantly surpassing the physiological limits of neuronal

The main focus of this work is to study ocean-atmosphere coupling, modeled using coupled advection-diffusion equations with two coupling conditions: the Dirichlet-Neumann (DN) and the heat flux condition, defined across two non-overlapping domains. For numerical approximation, the finite-volume method (FVM) and finite-difference method (FDM) are applied. The convergence analysis of the coupled problem

In this paper, we present a novel unconstrained fractional ℓ0 regularization (FL0R) model to solve cardinality minimization. Firstly, we construct an interesting min⁡−min minimization from FL0R by introducing a middle variable of sparsity. Then, we prove that the solution to min⁡−min minimization with a given sparsity is one of FL0R. Finally, some numerical examples are presented to illustrate the

In this paper, a prescribed-time distributed algorithm is proposed to solve the resource allocation problem among the heterogeneous linear multi-agent systems over unbalanced directed networks. First, an estimator with prescribed-time convergence performance is designed to cope with the asymmetry of the unbalanced network topology. Then, a novel prescribed-time convergence result that features an adjustable

In this paper, the spatio-temporal radial basis function (RBF) collocation method based on Hausdorff fractal distance is developed and used to simulate the transient heat transfer problems in anisotropic materials governed by Hausdorff derivative heat conduction equations. We introduce Hausdorff fractal distance into the conventional RBFs, and based on this incorporation, establish a meshless method

Community structure is one of the most common features of complex networks and plays a crucial role in the game of strategy during an evolutionary process. Previous works focus on its physical characteristics of high cohesion and low coupling, we extend the existing research, by taking into consideration the capacity of communities to effectively manage and allocate resources through collective action

This paper considers anti-disturbance aperiodically intermittent control of complex dynamical networks with unmatched and matched disturbances. The unmatched ones are suppressed by the H∞ method and the matched ones are compensated via distributed disturbance observers. An event-dependent intermittent strategy is built in terms of an auxiliary function with a square root form and three segmented regions

Let G be a graph, and let k,s be two positive integers. A k-list assignment of G is called a (k,k+s)-list assignment if, for any two adjacent vertices u and v, |L(u)∪L(v)|≥k+s. A graph G is said to be (k,k+s)-choosable if, for every given (k,k+s)-list assignment, it always admits a proper coloring π such that π(v)∈L(v) for every v∈V(G). In this paper, we demonstrate that every planar graph without

Dynamic contact problems are common in engineering systems. Current dynamic contact simulations are prone to energy non-conservation and over-reliance on nodes accuracy. To address the above difficulties, a numerical algorithm based on the bipotential theory for solving the dynamic contact problems of multibody systems is proposed. Within the framework of semi-finite element method, the Uzawa iteration

The primary objective of this paper is to explore the strong convergence for a neutral McKean-Vlasov stochastic differential equation with super-linear delay driven by fractional Brownian motion with Hurst exponent H∈(1/2,1). After giving uniqueness and existence for the exact solution, we analyze the properties including boundedness of moment and propagation of chaos. Besides, we give the Euler-Maruyama

Autonomous vehicles with information exchange and precision control on the road usually form platoon with smaller gaps between vehicles to increase the road traffic volume and reduce the fossil energy consumption. This paper focuses on uncertain vehicle platoon systems (VPSs) with disturbances and designs a distributed fixed-time disturbance rejection platoon tracking control strategy based on time

This work investigates how biodiversity is affected in a cyclic spatial May-Leonard model with hierarchical and non-hierarchical rules. Here we propose a generalization of the traditional rock-paper-scissors model by considering highly reactive species, i.e., species that react in a stronger manner compared to the others in respect to either competition or reproduction. These two classes of models

In real society, different individuals have different opinions on a certain issue, and individuals with similar views tend to become close gradually, while individuals with different opinions tend to become distant. Based on this fact, we propose a weighted spatial prisoner's dilemma game model with opinions to explore the impact of link weight change influenced by differences in opinions on the evolution

In this paper, we propose a new approach to approximation of the left and the right fractional Riemann - Liouville integrals as well as the compositions of these two operators, based on a shallow neural network with ReLU as an activation function. We apply the proposed method to the fractional Euler - Bernoulli beam equation with fixed-supported and fixed-free ends, and we provide numerical simulations

This paper studies the hybridizable discontinuous Galerkin (HDG) method for solving the diffusive viscous wave equation. We provide a theoretical analysis of both the semi-discrete and fully-discrete schemes. Our results demonstrate that the displacement and the flux converge with an order of m+1 in the L2 norm where m is the degree of polynomials. We also present a superconvergence analysis, indicating

In this paper, a singularity-free fixed-time adaptive interval type-2 fuzzy fault-tolerant control scheme with user-defined tracking performance is developed for a quadrotor unmanned aerial vehicle (QUAV) with unknown actuator failures under the command-filtered backstepping control (CFBC) framework. At first, the hyperbolic tangent function and interval type-2 fuzzy logic systems (IT2FLSs) are integrated

Benefiting from the development of information science and technology, more and more scholars use various complex networks as evolutionary carriers to research evolutionary game theory, which leads to the gradual unraveling of many evolutionary mechanisms. The reputation mechanism is particularly interesting and important among many mechanisms. Therefore, it has received widespread attention and research

We consider a population game in which a group of mobile individuals must repeatedly decide between two strategies: following other neighbors or moving on their own. When following others there is an improvement due to directed motion but a sharing of the credit for any rewards obtained. Conversely, the individual strategy provides for a full share of the credit for any rewards obtained at the cost

This paper investigates the optimal tracking and regulation performance of networked control systems (NCSs) with additive colored Gaussian noise (ACGN) and finite bandwidth. The bandwidth-limited channel is described as a non-minimum phase channel, which introduces additional restrictions on performance due to potential non-minimum-phase zeros (NMPZs). The optimal tracking and regulation performance

In this paper, a novel fifth-order weighted essentially non-oscillatory (WENO) scheme by using radial basis function (RBF) is proposed to solve hyperbolic conservation laws. The key idea is to choose multi-quadric (MQ) RBF and trigonometric function to construct numerical flux and smoothness indicator respectively. First, we modify the RBF interpolation making it into the WENO reconstruction framework

This study introduces a designed L2 compact approach for the fourth-order subdiffusion models on general nonuniform meshes. Initially, we establish long-time H1-stability and estimation of the error for the L2 compact approach under general nonuniform meshes, imposing only mild conditions on the time step ratio ρk. This is achieved by leveraging the positive semidefiniteness of an essential bilinear

In population ecology, competition interactions between species are pivotal in shaping species growth and ecosystem stability. A prominent example is the phenomenon where one species preys on the offspring of another. This paper introduces and analyzes a novel stage-structured competition model to explore this ecological dynamic. Focusing on juvenile and adult life stages, we integrate two competition

This paper discusses the sampled-data control problem of Lurie systems. First, a sufficient condition is presented to ensure system stability with a predefined controller gain. This condition is then extended to design a state-feedback controller (SFC) that stabilizes the systems. Additionally, the paper introduces a cone complementary linearization iteration (CCLI) algorithm with an enhanced iteration

This work focuses on developing a virtual element framework for analyzing nonlinear partial integro-differential equations with singular Abel-type kernels. To address the singularity in the integral term, we propose two strategies: one based on linear interpolation over a uniform temporal mesh and another employing a graded mesh. Notably, while the uniform mesh fails to retain second-order temporal

This paper investigates the consensus problem of privacy protection for multi-agent systems (MASs) under conditions of compound faults. We develop a fault-tolerant observer that utilizes intermediate variables to estimate both the system state and compound faults, specifically addressing sensor and actuator faults in the physical layer of the system. To safeguard the privacy of communication data at

This paper focuses on the quasi-synchronization (Q-S) of stochastic heterogeneous delayed multi-agent systems (SHDMSs), in which a novel irregularly intermittent tactic with unbounded waving feedback gains (IIT-UWG) is imposed on the systems. By the IIT-UWG, the discontinuous control signals received outside hampers can be settled. And the presumable sabotage of actuators caused by the dramatic switching

In this study, we introduce a novel structure-preserving compact alternating direction implicit (ADI) difference scheme based on the BDF2-θ and the ADI algorithm for solving the space fractional Klein-Gordon-Schrödinger equations. The primary focus of this article lies in the theoretical analysis and computational efficiency of the proposed schemes, which encompasses rigorous proofs of the error estimation

The attempt to solve inverse scattering problems often leads to optimization and sampling problems that require handling moderate to large amounts of partial differential equations acting as constraints. We focus here on determining inclusions in a layered medium from the measurement of wave fields on the surface, while quantifying uncertainty and addressing the effect of wave solver quality. Inclusions

This paper investigates data-driven learning techniques for fractional chaotic systems (FCS), specifically those utilizing the Caputo derivative. Three machine learning (ML) methods are employed for parameter estimation: feedforward neural networks (FNN), long short-term memory (LSTM), and gated recurrent units (GRU). Optimization problems are formulated, and the well-known algorithms, Backpropagation

Klann and Ramlau [16] hypothesized fractional Tikhonov regularization as an interpolation between generalized inverse and Tikhonov regularization. In fact, fractional schemes can be viewed as a generalization of the Tikhonov scheme. One of the motives of this work is the major pitfall of the a priori parameter choice rule, which primarily relies on source conditions that are often unknown. It necessitates

The event-triggered adaptive control issue for a class of nonlinearly parameterized higher-order systems with sensor fault is investigated in this article. The difficulty lies in how to replace the actual signal with the sensor fault output signal for control design and how to use adaptive technology to deal with the resulting uncertainties and the inherent unstructured uncertainties of the system

In this paper, the classic Favard inequality in classical calculus is extended to quantum calculus, resulting in the quantum integral form of the Favard-type inequality. Furthermore, the quantum integral form under weighted conditions is considered. As q→1−, it degenerates into the classical Favard inequality.