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The impact of changes in global temperatures and precipitation on climate distribution remains unclear. Taking the annual global average temperatures and precipitation as the origin, this study determined the climate distribution with the distances of temperature and precipitation from their global averages as the X and Y axes. The results showed that during 1980–2019, the global temperature distribution converged toward the mean (convergence), while the precipitation distribution moved away from the mean (divergence). The combined effects of both led to a convergence in the global climate distribution. During 2025–2100, significant climate convergence is observed under two emission scenarios (SSP245 and SSP585). However, the climate convergence and the area of change in climate type remains insignificant only under SSP126, suggesting that the diversity of the global climate pattern can be maintained under a sustainable emission pathway (SSP126), whereas high emission pathways will lead to greater uniformity in global climate. Plain Language Summary: Global average temperatures and precipitation have increased significantly over recent decades. However, the distribution of affected areas remains unclear in comparison to the global mean. Taking annual temperature and precipitation averages as a reference point, this study measured temperature and precipitation anomalies from the global mean on the X and Y axes. The Euclidean distance of each grid cell represents its deviation (anomaly) from the global climate mean. These distances are termed the degree of deviation of temperature, precipitation, and climate from the global mean for each raster. The results reveal a discernible homogenization trend regarding the distribution of global climate. Among three distinct climate scenarios, climate diversity is effectively preserved under the low‐emission model (SSP126), whereas global climate distribution exhibits a substantial convergence toward the annual mean under the high‐emission models (SSP245 and SSP585). Key Points: Against the backdrop of global warming, the climate pattern is shifting toward convergenceTemperature is the primary driver behind climate convergence, while precipitation plays a central role in climate diversityLow‐level emissions are conducive to preserving the diversity of future global climate distribution [ABSTRACT FROM AUTHOR]

This paper considers the secure distributed control consensus problem of linear multi‐agent systems (MASs) under switching topologies, subject to intermittent sequential scaling attacks, which was compelled to scaling factor, attack frequency, duration and cooperative‐competitive networks. First, the scenario of a fixed topology is considered, and a novel control protocol combined with a logarithmic quantizer and relative state measurements of neighbouring agents is discussed. The sighed graph is utilized to characterize the communication topology determined by the information flow directions and captured by the graph Laplacian matrix. After that, sufficient conditions for effectiveness of the developed control methods in guiding the MASs to secure bipartite leader‐following consensus are constructed. Second, the scenario of switching topologies is considered, and it is derived that the secure bipartite consensus will be achieved if the designed state feedback control protocol with the scaling factor, the attack duration, attack frequency and switching signal are selected properly. At last, to prove the effectiveness of the designed controllers, a simulation example depended on the real‐word actual military is introduced. [ABSTRACT FROM AUTHOR]

Summary: In the presented study, the solution of the fuzzy nonlinear optimization problems (FNLOPs) is calculated using a recurrent neural network (RNN) model. Since there is a few research for solving FNLOP by RNN's, we give a new approach to solve the problem. By reducing the original program to an interval problem and then weighting problem, the Karush–Kuhn–Tucker (KKT) conditions are given. Moreover, we use the KKT conditions into a RNN as an important tool to solve the problem. Besides, the global convergence properties and the Lyapunov stability of the dynamic model are studied in this study. In the final step, some illustrative examples are considered to establish the obtained results. Reported results are compared with some others network models. [ABSTRACT FROM AUTHOR]

The paper demonstrates two approaches to constructing monotonic difference schemes for the transfer equation in divergent form from the family of semi-Lagrangian methods: Eulerian–Lagrangian and Lagrangian–Eulerian. Within each approach, a monotonic conservative difference scheme is proposed. It is shown that within the framework of the Lagrangian–Eulerian approach, based on the use of curvilinear grids formed by the characteristics of the approximated transfer operator, it is possible to construct monotonic difference schemes of second order accuracy. [ABSTRACT FROM AUTHOR]

In this paper, we consider the behaviour of solutions to a class of fully history-dependent variational-hemivariational inequalities with respect to the perturbation of the data. First, the existence and uniqueness of the solution to a class of fully history-dependent variational-hemivariational inequalities is obtained by using a fixed point theorem. Second, we obtain continuous dependence result of solutions with respect to all the data of variational-hemivariational inequalities. Meanwhile, the convergence results of the solutions for the special case of abstract variational inequalities are also given. Finally, to illustrate our main results, we consider a class of viscoelastic contact problem with a long memory. By using our abstract result, we get the continuous dependence of the solutions to frictional contact problem with respect to all the data. [ABSTRACT FROM AUTHOR]

We study the existence and uniqueness of solutions to the inverse quasi-variational inequality problem. Motivated by the dynamical approach to solving optimization problems such as variational inequality, monotone inclusion, and inverse variational problems, we consider a dynamical system associated with the inverse quasi-variational inequality problem, and establish the existence and uniqueness of a solution to the proposed system. We prove that every trajectory of the proposed dynamical system converges to the unique solution of the inverse quasi-variational inequality problem and that the system is globally asymptotically stable at its equilibrium point. We also prove that if the function which governs the inverse quasi-variational inequality problem is strongly monotone and Lipschitz continuous, then the dynamical system is globally exponentially stable at its equilibrium point. We discretize the dynamical system and show that the sequence generated by the discretization of the system converges strongly to the unique solution of the inverse quasi-variational inequality problem under certain assumptions on the parameters involved. Finally, we provide numerical examples to support and illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

We introduce an alternative closed-form objective function α-ELBO for improved parameter estimation in the Gaussian process ( G P ) based on the Rényi α-divergence. We use a decreasing temperature parameter α to iteratively deform the objective function during optimization. Ultimately, our objective function converges to the exact log-marginal likelihood function of G P. At early optimization stages, α-ELBO can be viewed as a regularizer that smoothes some unwanted critical points. At late stages, α-ELBO recovers the exact log-marginal likelihood function that guides the optimizer to solutions that best explain the observed data. Theoretically, we derive an upper bound of the Rényi divergence under the proposed objective and derive convergence rates for a class of smooth and non-smooth kernels. Case studies on a wide range of real-life engineering applications demonstrate that our proposed objective is a practical alternative that offers improved prediction performance over several state-of-the-art inference techniques. [ABSTRACT FROM AUTHOR]

• A distribution dynamics approach is employed to examine the converge of TFEE across Chinese PAA level cities. • The findings show a clear convergence in TFEE. • Convergence comes more from efficiency drops in high TFEE cities than from efficiency gains in low TFEE cities. • The environmental protection polices in key cities improved energy efficiency. • Large-sized cities show better performance in energy efficiency than small- and medium-sized cities. Improving energy efficiency is considered the most direct route to reducing carbon emissions on a massive scale. To examine the long-run trend of China's energy efficiency, this paper employs a distribution dynamics approach to analyze the convergence of total-factor energy efficiency (TFEE) across 286 Chinese cities between 2002 and 2014. The result suggests the existence of convergence, which comes more from the efficiency declines in the high TFEE cities rather than the efficiency gains in the low TFEE cities. Despite the fact that a few cities have performed well in energy efficiency, the majority of cities have converged to a low-efficiency point. Further analyses show that the inefficiency was attributed to inefficient energy use in small- and medium-sized cities. Our analysis provides strong scientific support for China's ongoing energy conservation and environmental protection policies. [ABSTRACT FROM AUTHOR]

Questions remain on whether the UCR constitutes a legitimate source for analyzing hate crime. While a handful of studies have attempted to uncover the law enforcement characteristics associated with reporting hate crime, scholars have yet to triangulate official data with other sources, namely the NCVS. In this study, I replicate past UCR-NCVS convergence analyses on hate crime incidents, determining whether these series converge and if they do so across different forms of bias motivation. Using 18 years of data from 2003 through 2020 at a national level, results indicate mixed support for convergence, drawing implications for research and policy. [ABSTRACT FROM AUTHOR]

Due to the considerable complexity of meshfree approximants, there still lacks a rational theoretical estimate on the frequency accuracy of lumped mass meshfree methods. In this study, a detailed theoretical analysis is presented for the lumped mass Galerkin meshfree formulation with particular reference to the frequency accuracy. The proposed accuracy analysis is quite general and is fully based upon the reproducing or consistency conditions of meshfree shape functions and their gradients. The theoretical findings reveal that there exists an important and interesting odd/even basis degree discrepancy feature for the frequency accuracy, i.e., (p + 2)th and (p + 1)th order accurate frequencies are attained by the lumped mass Galerkin meshfree formulation using even and odd degrees of basis functions, where p is the degree of basis function employed in the meshfree shape function construction. Furthermore, it is found that interpolatory meshfree shape functions are capable of not only circumventing the non-physical modes arising from the lumped mass Galerkin meshfree formulation using the standard non-interpolatory shape functions, but also elevating the frequency accuracy for meshfree structural vibration analysis. Numerical examples well replicate the theoretical frequency accuracy analysis results for lumped mass Galerkin meshfree methods. [ABSTRACT FROM AUTHOR]

In this paper, we study the convergence analysis of the inexact Newton–Landweber iteration method (INLIM) with frozen derivative in Hilbert as well as Banach spaces. To study the convergence analysis, we incorporate the Hölder stability of the inverse mapping and Lipschitz continuity of the Fréchet derivative of the forward mapping. Moreover, we derive the convergence rates of INLIM in Hilbert as well as Banach spaces without using any extra smoothness condition. Finally, we compare our convergence rates results with that of several other frozen methods proposed in the literature to solve inverse problems. [ABSTRACT FROM AUTHOR]

Scale morphology represents a fundamental feature of fish and a key evolutionary trait underlying fish diversification. Despite frequent and recurrent scale loss throughout fish diversification, comprehensive genome‐wide analyses of the genomic signatures associated with scale loss in divergent fish lineages remain scarce. In the current study, we investigated genome‐wide signatures, specifically convergent protein‐coding gene loss, amino acid substitutions, and cis‐regulatory sequence changes, associated with recurrent scale loss in two divergent Cypriniformes lineages based on large‐scale genomic, transcriptomic, and epigenetic data. Results demonstrated convergent changes in many genes related to scale formation in divergent scaleless fish lineages, including loss of P/Q‐rich scpp genes (e.g. scpp6 and scpp7), accelerated evolution of non‐coding elements adjacent to the fgf and fgfr genes, and convergent amino acid changes in genes (e.g. snap29) under relaxed selection. Collectively, these findings highlight the existence of a shared genetic architecture underlying recurrent scale loss in divergent fish lineages, suggesting that evolutionary outcomes may be genetically repeatable and predictable in the convergence of scale loss in fish. [ABSTRACT FROM AUTHOR]

In this paper, we extend SMSNS [Pourbagher M, Salkuyeh DK. On the solution of a class of complex symmetric linear systems. Appl Math Lett. 2018;76:14–20.] iteration method for solving a class of complex symmetric system of linear equations. We propose a successive-overrelaxation (SOR) acceleration scheme for SMSNS (SMSNSSOR), discuss the convergence conditions of it and give the optimal parameters which make the fast convergence. Numerical results demonstrate that SMSNSSOR iteration method is feasible and effective for solving complex symmetric systems, and performs better than some other usually used iteration methods. [ABSTRACT FROM AUTHOR]

Summary The convergence of filtered error and filtered reference adaptive feedforward is limited by three effects: model mismatch, unintended input‐disturbance interaction and too fast parameter adaptation. In this article, the first two effects are considered for MIMO systems under the slow parameter adaptation assumption. The convergence with model mismatch is conventionally guaranteed using a strictly positive‐real condition. This condition can be easily verified in the frequency domain, but due the high‐frequency parasitic dynamics of real systems, it is hardly ever satisfied. Nevertheless, filtered error and filtered reference adaptive feedforward have successfully been implemented in numerous applications without satisfying the strictly positive‐real condition. It is shown in this article that the strictly positive‐real condition can be relaxed to a power‐weighted integral condition, that is less conservative and provides a practical check for the convergence of filtered error adaptive feedforward for real systems in the frequency domain. The effects of input‐disturbance interaction are analysed and conditions for the stability are given in the frequency domain. Both conditions give clear indicators for frequency domain filter tuning, and are verified on an experimental active vibration isolation system. [ABSTRACT FROM AUTHOR]

Skin cancer is one of the most life-threatening diseases caused by the abnormal growth of the skin cells, when exposed to ultraviolet radiation. Early detection seems to be more crucial for reducing aberrant cell proliferation because the mortality rate is rapidly rising. Although multiple researches are available based on the skin cancer detection, there still exists challenges in improving the accuracy, reducing the computational time and so on. In this research, a novel skin cancer detection is performed using a modified falcon finch deep Convolutional neural network classifier (Modified Falcon finch deep CNN) that efficiently detects the disease with higher efficiency. The usage of modified falcon finch deep CNN classifier effectively analyzed the information relevant to the skin cancer and the errors are also minimized. The inclusion of the falcon finch optimization in the deep CNN classifier is necessary for efficient parameter tuning. This tuning enhanced the robustness and boosted the convergence of the classifier that detects the skin cancer in less stipulated time. The modified falcon finch deep CNN classifier achieved accuracy, sensitivity, and specificity values of 93.59%, 92.14%, and 95.22% regarding k-fold and 96.52%, 96.69%, and 96.54% regarding training percentage, proving more effective than literary works. [ABSTRACT FROM AUTHOR]

Whether the forelimb‐digging apparatus of tooth‐digging subterranean mammals has similar levels of specialization as compared to scratch‐diggers is still unknown. We assessed the scapular morphology and forelimb musculature of all four solitary African mole rats (Bathyergidae): two scratch‐diggers, Bathyergus suillus and Bathyergus janetta, and two chisel‐tooth diggers, Heliophobius argenteocinereus and Georychus capensis. Remarkable differences were detected: Bathyergus have more robust neck, shoulder, and forearm muscles as compared to the other genera. Some muscles in Bathyergus were also fused and often showing wider attachment areas to bones, which correlate well with its more robust and larger scapula, and its wider and medially oriented olecranon. This suggests that shoulder, elbow, and wrist work in synergy in Bathyergus for generating greater out‐forces and that the scapula and proximal ulna play fundamental roles as pivots to maximize and accommodate specialized muscles for better (i) glenohumeral and scapular stabilization, (ii) powerful shoulder flexion, (iii) extension of the elbow and (iv) flexion of the manus and digits. Moreover, although all bathyergids showed a similar set of muscles, Heliophobius lacked the m. tensor fasciae antebrachii (aiding with elbow extension and humeral retraction), and Heliophobius and Georychus lacked the m. articularis humeri (aiding with humeral adduction), indicating deeper morphogenetic differences among digging groups and suggesting a relatively less specialized scratch‐digging ability. Nevertheless, Heliophobius and Bathyergus shared some similar adaptations allowing scratch‐digging. Our results provide new information about the morphological divergence within this family associated with the specialization to distinct functions and digging behaviors, thus contributing to understand the mosaic of adaptations emerging in phylogenetically and ecologically closer subterranean taxa. This and previous anatomical studies on the Bathyergidae will provide researchers with a substantial basis on the form and function of the musculoskeletal system for future kinematic investigations of digging behavior, as well as to define potential indicators of scratch‐digging ability. [ABSTRACT FROM AUTHOR]

In the present paper, the expected-value (EV) reformulation of a class of stochastic vector variational inequalities (SVVI) is investigated. By using the regularized gap function, the EV reformulation of SVVI is transformed into a constrained optimization problem. Then a sample average approximation (SAA) method is proposed for solving the constrained optimization problem. Under suitable assumptions, the limiting behaviors of the optimal values and optimal solutions of the approximation problem are investigated. Finally, the rates of convergence in the different senses of optimal solutions for sample average approximation problem are discussed under the error bound condition. [ABSTRACT FROM AUTHOR]

The study on how equilibria behave when perturbations occur in the data of a game is a fundamental theme, since actions and payoffs of the players may be affected by uncertainty or trembles. In this paper, we investigate the asymptotic behavior and the variational stability of the subgame perfect Nash equilibrium (SPNE) in one-leader one-follower Stackelberg games under perturbations both of the action sets and of the payoff functions. To pursue this aim, we consider a general sequence of perturbed Stackelberg games and a set of assumptions that fit the usual types of perturbations. We study if the limit of SPNEs of the perturbed games is an SPNE of the original game and if the limit of SPNE-outcomes of perturbed games is an SPNE-outcome of the original game. We fully positively answer when the follower's best reply correspondence is single-valued. When the follower's best reply correspondence is not single-valued, the answer is positive only for the SPNE-outcomes; whereas the answer for SPNEs may be negative, even if the perturbation does not affect the sets and affects only one payoff function. However, we show that under suitable non-restrictive assumptions it is possible to obtain an SPNE starting from the limit of SPNEs of perturbed games, possibly modifying the limit at just one point. [ABSTRACT FROM AUTHOR]

A neural network architecture is constructed to solve Convex Multi-objective Programming Problem (CMPP). By using the weighted sum method, a single-objective optimization problem related to the CMPP is formulated, in which the scalar objective is summation of weighted original objective functions. The Pareto Optimal Solution (POS) is given by using different values of weights. A neural network framework is then designed for solving the obtained convex problem. Based on employing Lyapunov theory, the proposed model is established to be stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the convex programming problem with different values of weights. The computer simulations shows the feasibility and the efficiency of the suggested model. [ABSTRACT FROM AUTHOR]

Discrete duality finite volume (DDFV) schemes are known for their ability to approximate nonlinear and linear anisotropic diffusion operators on general meshes, but they possess several drawbacks. The most important drawback of DDFV is the simultaneous use of the cell and the node unknowns. We propose a discretization approach that incorporates DDFV ideas and the associated analysis techniques, but allows for a rapid elimination of the cell unknowns. Further, unlike the DDFV scheme, the new 'Nodal Discrete Duality' (NDD) scheme does not require specific adaptation in presence of discontinuities of the diffusion tensor along cell boundaries. We describe in detail the 2D NDD framework and its two 3D variants, focusing on the consistency properties of the discrete gradient and discrete divergence operators and on the key structural property of discrete duality. For the 2D scheme, convergence analysis is carried out and a series of numerical tests are provided for a large family of nonlinear anisotropic elliptic problems with zero Dirichlet boundary condition. [ABSTRACT FROM AUTHOR]

Unfitted finite element methods (FEM) have attractive merits for problems with evolving or geometrically complex boundaries. Conventional unfitted FEMs incorporate penalty terms, parameters, or Lagrange multipliers to impose the Dirichlet boundary condition weakly. This to some extent increases computational complexity in implementation. In this article, we propose an unfitted generalized FEM (GFEM) for the Dirichlet problem, which is free from any penalty or stabilization. This is achieved by means of partition of unity frameworks of GFEM and designing a set of new enrichments for the Dirichlet boundary. The enrichments are divided into two groups: the one is used to impose the Dirichlet boundary condition strongly, and the other one serves as energy space of variational formulations. The shape functions in energy space vanish at the boundary so that standard variational formulae like those in the conventional fitted FEM can be applied, and thus the penalty and stabilization are not needed. The optimal convergence rate in the energy norm is proven rigorously. Numerical experiments and comparisons with other methods are executed to verify the theoretical result and effectiveness of the algorithm. The conditioning of new method is numerically shown to be of same order as that of the standard FEM. [ABSTRACT FROM AUTHOR]

An efficient numerical method with high accuracy both in time and in space is proposed for solving d$$ d $$‐dimensional fractional diffusion equation with spectral fractional Laplacian. The main idea is discretizing the time by an s$$ s $$‐stage implicit Runge‐Kutta method and approximating the space by a spectral Galerkin method with Fourier‐like basis functions. In view of the orthogonality, the mass matrix of the spectral Galerkin method is an identity and the stiffness matrix is diagonal, which makes the proposed method is efficient for high‐dimensional problems. The proposed method is showed to be stable and convergent with at least order s+1$$ s+1 $$ in time, when the implicit Runge‐Kutta method with classical order p$$ p $$ (p≥s+1$$ p\ge s+1 $$) is algebraically stable. As another important contribution of this paper, we derive the spatial error estimate with optimal convergence order which depends on the regularity of the exact solution but not on the fractional parameter α$$ \alpha $$. This improves the previous result which depends on the fractional parameter α$$ \alpha $$. Numerical experiments verify and complement our theoretical results. [ABSTRACT FROM AUTHOR]

The conventional approach of the local convergence analysis of an iterative method on R m , with m a natural number, depends on Taylor series expansion. This technique often requires the calculation of high-order derivatives. However, those derivatives may not be part of the proposed method(s). In this way, the method(s) can face several limitations, particularly the use of higher-order derivatives and a lack of information about a priori computable error bounds on the solution distance or uniqueness. In this paper, we address these drawbacks by conducting the local convergence analysis within the broader framework of a Banach space. We have selected an important family of high convergence order methods to demonstrate our technique as an example. However, due to its generality, our technique can be used on any other iterative method using inverses of linear operators along the same line. Our analysis not only extends in R m spaces but also provides convergence conditions based on the operators used in the method, which offer the applicability of the method in a broader area. Additionally, we introduce a novel semilocal convergence analysis not presented before in such studies. Both forms of convergence analysis depend on the concept of generalized continuity and provide a deeper understanding of convergence properties. Our methodology not only enhances the applicability of the suggested method(s) but also provides suitability for applied science problems. The computational results also support the theoretical aspects. [ABSTRACT FROM AUTHOR]

In this work, we analyse the class of strictly pseudocontractive mappings in general metric spaces by providing a comprehensive and appropriate definition of a strictly pseudocontractive mapping, which serves as a natural extension of the existing notion. Moreover, we establish its various characterizations and explore several significant properties of these mappings in relation to fixed point theory in CAT(0) spaces. Specifically, we establish that these mappings are Lipschitz continuous, satisfying the demiclosedness-type property, and possessing a closed convex fixed point set. Furthermore, we show that the fixed points of the mappings can be effectively approximated using an iterative scheme for fixed points of nonexpansive mappings. The results in this work contribute to a deeper understanding of strictly pseudocontractive mappings and their applicability in the context of fixed point theory in metric spaces. [ABSTRACT FROM AUTHOR]

There are numerous phenomena in real world that their practical modeling in mathematics language deals with differential equations. Stochastic terms have significant roles in estimating behavior of these events such as machine tool vibrations, biology, traffic dynamics, neural networks and so on, it cannot be reasonable to consider an event without its past information, and it ends up with equations including time delays. The numerical solution of stochastic delay differential equations has always been of interest to researchers. In this paper, by using scaling function of the Daubechies wavelet, a collocation method is presented to solve a class of stochastic delay differential equations and it is tried to demonstrate the advantages of using this type of wavelet. Convergence of the method is provided and numerical experiments are reported to show application of the method in practice. [ABSTRACT FROM AUTHOR]

An explicit computational scheme is proposed for solving fractal time-dependent partial differential equations (PDEs). The scheme is a three-stage scheme constructed using the fractal Taylor series. The fractal time order of the scheme is three. The scheme also ensures stability. The approach is utilized to model the time-varying boundary layer flow of a non-Newtonian fluid over both stationary and oscillating surfaces, taking into account the influence of heat generation that depends on both space and temperature. The continuity equation of the considered incompressible fluid is discretized by first-order backward difference formulas, whereas the dimensionless Navier–Stokes equation, energy, and equation for nanoparticle volume fraction are discretized by the proposed scheme in fractal time. The effect of different parameters involved in the velocity, temperature, and nanoparticle volume fraction are displayed graphically. The velocity profile rises as the parameter I grows. We primarily apply this computational approach to analyze a non-Newtonian fluid's fractal time-dependent boundary layer flow over flat and oscillatory sheets. Considering spatial and temperature-dependent heat generation is a crucial factor that introduces additional complexity to the analysis. The continuity equation for the incompressible fluid is discretized using first-order backward difference formulas. On the other hand, the dimensionless Navier–Stokes equation, energy equation, and the equation governing nanoparticle volume fraction are discretized using the proposed fractal time-dependent scheme. [ABSTRACT FROM AUTHOR]

Summary: Data losses and noises in both forward and feedback channels significantly impact the convergence of networked iterative learning control (ILC) systems. To address this issue, this article considers a class of linear time‐invariant objects controlled by proportional ILC controllers, an optimal state filter is then designed at the ILC controller side that aims to guarantee the convergence of the input transmitted by ILC controllers. First, two data transmission processes are introduced to account for the effects of data losses and noises. Second, a filtering model is established utilizing only the object information and the aforementioned data transmission processes. Third, the optimal state filter is designed on the basis of the orthogonal projection principle. This filtered state facilitates the acquisition of actual output errors, thus improving the convergence of the input transmitted by ILC controllers. Simulation results demonstrate the effectiveness of the proposed state filters. [ABSTRACT FROM AUTHOR]

To understand how individuals navigate the complex, dynamic, and bewildering media information environment, we propose a convergence framework theorizing individuals' acquisition of information from distinct sources on multiple mediums, along with its antecedents and consequences. This study is among the first to test the convergence framework. Using a national sample during the COVID-19 pandemic, our results revealed four convergence patterns and key antecedents and outcomes of these patterns. Individuals' information verification tendency, perceived medium anonymity, and trust in alternative sources were associated with distinct patterns of convergence, which led to different risk perceptions. Future research should explore different forms of convergence and additional antecedents and outcomes of convergence. [ABSTRACT FROM AUTHOR]

The current study aims to utilize the homotopy perturbation method (HPM) to solve nonlinear dynamical models, with a particular focus on models related to predicting and controlling pandemics, such as the SIR model. Specifically, we apply this method to solve a six-compartment model for the novel coronavirus (COVID-19), which includes susceptible, exposed, asymptomatic infected, symptomatic infected, and recovered individuals, and the concentration of COVID-19 in the environment is indicated by S (t) , E (t) , A (t) , I (t) , R (t) , and B (t) , respectively. We present the series solution of this model by varying the controlling parameters and representing them graphically. Additionally, we verify the accuracy of the series solution (up to the (n − 1) t h -degree polynomial) that satisfies both the initial conditions and the model, with all coefficients correct at 18 decimal places. Furthermore, we have compared our results with the Runge–Kutta fourth-order method. Based on our findings, we conclude that the homotopy perturbation method is a promising approach to solve nonlinear dynamical models, particularly those associated with pandemics. This method provides valuable insight into how the control of various parameters can affect the model. We suggest that future studies can expand on our work by exploring additional models and assessing the applicability of other analytical methods. [ABSTRACT FROM AUTHOR]

Diverse clades of fishes adapted to feeding on the benthos repeatedly converge on steep craniofacial profiles and shorter, wider heads. But in an incipient radiation, to what extent is this morphological evolution measurable and can we distinguish the relative genetic vs. plastic effects? We use the Trinidadian guppy (Poecilia reticulata) to test the repeatability of adaptation and the alignment of genetic and environmental effects shaping poecilid craniofacial morphology. We compare wild-caught and common garden lab-reared fish to quantify the genetic and plastic components of craniofacial morphology across 4 populations from 2 river drainage systems (n  = 56 total). We first use micro-computed tomography to capture 3D morphology, then place both landmarks and semilandmarks to perform size-corrected 3D morphometrics and quantify shape space. We find a measurable, significant, and repeatable divergence in craniofacial shape between high-predation invertivore and low-predation detritivore populations. As predicted from previous examples of piscine adaptive trophic divergence, we find increases in head slope and craniofacial compression among the benthic detritivore foragers. Furthermore, the effects of environmental plasticity among benthic detritivores produce exaggerated craniofacial morphological change along a parallel axis to genetic morphological adaptation from invertivore ancestors. Overall, many of the major patterns of benthic-limnetic craniofacial evolution appear convergent among disparate groups of teleost fishes. [ABSTRACT FROM AUTHOR]

Tensor robust principal component analysis (TRPCA) aims at recovering the underlying low-rank clean tensor and residual sparse component from the observed tensor. The recovery quality heavily depends on the definition of tensor rank which has diverse construction schemes. Recently, tensor average rank has been proposed and the tensor nuclear norm has been proven to be its best convex surrogate. Many improved works based on the tensor nuclear norm have emerged rapidly. Nevertheless, there exist three common drawbacks: (1) the neglect of consideration on relativity between the distribution of large singular values and low-rank constraint; (2) the prior assumption of equal treatment for frontal slices hidden in tensor nuclear norm; (3) the missing convergence of whole iteration sequences in optimization. To address these problems together, in this paper, we propose a convex–concave TRPCA method in which the notion of convex–convex singular value separation (CCSVS) plays a dominant role in the objective. It can adjust the distribution of the first several largest singular values with low-rank controlling in a relative way and emphasize the importance of frontal slices collaboratively. Remarkably, we provide the rigorous convergence analysis of whole iteration sequences in optimization. Besides, a low-rank tensor recovery guarantee is established for the proposed CCSVS model. Extensive experiments demonstrate that the proposed CCSVS significantly outperforms state-of-the-art methods over toy data and real-world datasets, and running time per image is also the fastest. [ABSTRACT FROM AUTHOR]

In this paper, we present a comprehensive framework for studying Krylov subspace methods used to solve the linear system A x = f . These methods aim to achieve convergence within a specified number of iterations, denoted by m, given a particular initial estimate vector x 0 and its corresponding residual r 0 = f - A x 0 . Our analysis focuses on the minimal polynomial Φ m of degree m of A for the vector r 0 . We establish that these methods encompass Petrov-Galerkin methods and minimal seminorm methods as special cases. Additionally, we demonstrate that minimal seminorm methods satisfy implicit Petrov-Galerkin conditions. We provide a general formulation for the iterates based on generalized inverses. The choice of a specific left inverse and the method of constructing the Krylov basis are crucial distinguishing factors among different Krylov subspace methods. We describe and analyze the mathematical properties of these methods, emphasizing their dependency on two matrices. Notably, we prove that CMRH and QMR, as specific instances, also satisfy implicit Petrov-Galerkin orthogonality conditions. Furthermore, we explore techniques to improve the convergence behavior of these methods by carefully selecting vectors in their implementations. Through our investigation, we aim to deepen the understanding of Krylov subspace methods, provide insights into their convergence properties, and identify potential enhancements. We also consider some Krylov subspace methods, which are of product-type methods. In this case, the kth residual r k associated with the approximation x k of the exact solution is given by r k = Ψ k (A) Φ k (A) r 0 , and Ψ k is a polynomial of fixed or variable degree. We will examine particular choices of Ψ k involving local convergence, smoothing, fixed memory, and cost for each iteration. We will also give an enhancement of some product-type methods such as CGS. To illustrate the performance of the derived algorithms, we provide some numerical examples. [ABSTRACT FROM AUTHOR]

Metaheuristic algorithms are increasingly used for feature selection (FS) problems due to their robustness and searchability. This study presents a unique optimization technique called fuzzy bluefin trevally optimizer (BTO). BTO draws its inspiration from bluefin’s cooperative nature and sudden ambush behavior. The trevally will jump out of the water and attack its food in the air or even snag it off the water when it is sufficiently close to it. This study uses mathematical modeling to create an optimization algorithm to replicate dynamic patterns and behaviors. Since parameters play a critical role in optimization, we use the fuzzy concept for dynamic parameter adaptation in fuzzy BTO. By introducing the idea of signature and demonstrating that fuzzy BTO converges to the global optimal point, the mathematical basis for the proposed algorithm is provided. The convergence of fuzzy BTO is proved using the Markov chain property. On benchmark functions (BF), the effectiveness of the suggested strategies is evaluated and compared with other metaheuristic algorithms. Then the proposed algorithms are applied to a fuzzy FS problem. Then they are compared with traditional and recent metaheuristic algorithms on the UCI machine learning repository datasets. Finally, the statistical significance is examined using the Kruskal–Wallis test (KWT). [ABSTRACT FROM AUTHOR]

We describe a highly stereoconvergent radical epoxide allylation towards diastereomerically and enantiomerically enriched α‐quaternary alcohols in two steps from olefins. Our approach combines the stereospecifity and enantioselectivity of the Shi epoxidation with the unprecedented Ti(III)‐promoted intramolecular radical group transfer allylation of epoxides. A directional isomerization step via configurationally labile radical intermediates enables the selective preparation of all‐carbon quaternary stereocenters in a unique fashion. [ABSTRACT FROM AUTHOR]

English text analysis is required for quantitative grammar, phrase, and word assessment to improve its usage in conversation, drafting, etc. In particular, a teaching system requires the flawless and precise use of English words, phrases, and sentences for fundamental and knowledge-based learning. Data integration and interoperability, data volume, and data variety pose difficulties for text data analytics. This article discusses a heterogeneous English teaching system text analysis solution that integrates a Genetic Algorithm (GA) and Deep Learning (DL). The Text Analytical Model (TAM) uses fused methods (FM) to handle words and their placement for sentence framing. The framed teaching sentence is analyzed lexically for its precision and meaning with conventional features. Initially, the possible word combinations using the crossover and mutation operations of the genetic process are performed. The outcome of the genetic process forecasts different possible sentence combinations for delivering the English context to students. The mutation process identifies the most precise lexical sentence that fits the subject and context. Based on precision, the DL model is trained to reduce the initial population of the GA process; this is achieved in English teaching through repetitions or drilling performed for different sentences and words. The learning converges towards precision in delivering context-based words and sentences by reducing unnecessary crossovers in the genetic process to reduce computational complexity. This feature, therefore, achieves high-precision convergence with less computation time compared to methods of the same kind. TAM-FM improves the precision convergence, forecast probability, and population refinement by 9.5%, 11.39%, and 8.81%, respectively. TAM-FM reduces the computation time and complexity by 9.67% and 8.3%, respectively. [ABSTRACT FROM AUTHOR]

An artificial neural network (ANN) in information technology is a system of hardware or software modeled after the operation of neurons in the human brain. ANNs, often known as "neural networks," are a form of deep learning technology that falls under the umbrella of Artificial Intelligence (AI). Commercial applications of these technologies typically focus on optimization and solving complex signal processing and pattern recognition problems. Multiple types of optimization techniques are utilized to determine the optimal neural network for a model. These procedures help determine and define the model's accuracy, dependability, functionality, and capacity. The convergence of the neural network helps determine the number of training iterations required to generate the fewest errors. In this paper, we investigate an activation function to help reduce the training time of the analog-to-digital converter (ADC). A new Hopfield ADC model is proposed by using the proteretic activation function property. We supported our research by simulating the new ADC converter and comparing the traditional Hopfield ADC, the hysteretic ADC, and the proteretic ADC. Experiment and simulation demonstrate that the proteretic function provides a faster rate of convergence than other functions, thereby enhancing the performance of the ADC application. [ABSTRACT FROM AUTHOR]

Nonlinear Kawarada equations have been used to model solid fuel combustion processes in the oil industry. An effective way to approximate solutions of such equations is to take advantage of the finite difference configurations. Traditionally, the nonlinear term of the equation is linearized while the numerical stability of a difference scheme is investigated. This leaves certain ambiguity and uncertainty in the analysis. Based on nonuniform grids generated through a quenching-seeking moving mesh method in space and adaptation in time, this paper introduces a completely new stability analysis of the approximation without freezing the nonlinearity involved. Pointwise orders of convergence are investigated numerically. Simulation experiments are carried out to accompany the mathematical analysis to strengthen our conclusions. [ABSTRACT FROM AUTHOR]

In this article, two difference schemes are proposed to solve numerically a nonlinear strong damped wave equation in two dimensions. The first scheme is nonlinear implicit, the second scheme is linear implicit. It is proved that the two schemes are unique solvable, unconditionally stable. Moreover, the present numerical methods are convergent with second order accuracy both in space and time in the discrete H 1 -norm. Numerical experiments are provided to show the validity and the accuracy of the proposed difference schemes as well as their efficiency. [ABSTRACT FROM AUTHOR]

The uneven distribution of FDI contributes to inequality in economic development. Most studies on FDI in China use provincial data and parametric tools of analysis while delivering mixed findings regarding FDI’s distribution and free trade zones (FTZs) attractiveness. We investigate the convergence and transitional dynamics of relative FDI (RFDI) in China using visual tools of the distribution dynamics approach to a panel of 273 prefectural cities from 2003 to 2019. Convergence-divergence patterns are examined from inter- and intra-regional perspectives and FTZs vis-à-vis non-FTZ cities. In the long run, most entities within each region converge towards different RFDI values (from 0.05 to 0.25), far below the national average equal to one. FDI is the most unevenly distributed within the poorest western region. Furthermore, three (two) convergence clubs emerge among the non-FTZ (FTZ) entities around RFDI values of 0.05, 0.6 and 2.7 (2.5 and 10). The results corroborate the New Growth and New Economic Geography theories, indicating an absence of desirable spatial diffusion from affluent ‘core’ cities and FTZs to ‘peripheral’ entities outside the FTZs. Additionally, we provide a ‘policy priority list’ comprising western cities with above (below) average RFDI and the highest propensity to diverge further above (below) the national mean. [ABSTRACT FROM AUTHOR]

A new property of convex functions that makes it possible to achieve the linear rate of convergence of the Newton method during the minimization process is established. Namely, it is proved that, even in the case of singularity of the Hessian at the solution, the Newtonian system is solvable in the vicinity of the minimizer; i.e., the gradient of the objective function belongs to the image of the matrix of second derivatives and, therefore, analogs of the Newton method may be used. [ABSTRACT FROM AUTHOR]

Iterative learning control (ILC) algorithms appeared in connection with the problems of increasing the accuracy of performing repetitive operations by robots. They use information from previous repetitions to adjust the control signal on the current repetition. Most often, information from the previous repetition only is used. ILC algorithms that use information from several previous iterations are called higher-order algorithms. Recently, interest in these algorithms has increased in the literature in connection with robotic additive manufacturing problems. However, in addition to the fact that these algorithms have been little studied, there are conflicting estimates regarding their properties. This paper proposes new higher-order ILC algorithms for linear discrete and differential systems. The idea of these algorithms is based on an analogy with multi-step methods in optimization theory, in particular, with the heavy ball method. An example is given that confirms the possibility to accelerate convergence of the learning error when using such algorithms. [ABSTRACT FROM AUTHOR]

In engineering, most sensors can only measure the intensity information of a signal, but without the phase information. The phase retrieval problem is to reconstruct the original signal only from intensity values, which is an ill-posed problem. To address this issue, we introduce sparse prior information to overcome the ill-posed problem and propose the sparse reweighted thresholded Wirtinger flow (SRThWF) algorithm. In the SRThWF algorithm, the original signal is reconstructed from Gaussian random measurements via intensity values. In particular, SRThWF carries on iteratively in two stages: In stage one, it works with initialization by truncated spectral method restricted on support recovery of sparse signal. In the second stage, the initial estimate is refined iteratively via hard-thresholding-based adaptive reweighted gradient descent. Furthermore, the convergence of the proposed algorithm has been proved. Experimental results show that the proposed algorithm is an effective sparse phase retrieval solver in the probability of success even if the sparsity level is unknown. Not only that, the proposed algorithm exhibits a faster convergence rate and shorter running time. In addition, SRThWF is robust to the noise. [ABSTRACT FROM AUTHOR]

Purpose: This study presents a two-step numerical iteration method specifically designed to solve absolute value equations. The proposed method is valuable and efficient for solving absolute value equations. Several numerical examples were taken to demonstrate the accuracy and efficiency of the proposed method. Design/methodology/approach: We present a two-step numerical iteration method for solving absolute value equations. Our two-step method consists of a predictor-corrector technique. The new method uses the generalized Newton method as the predictor step. The four-point open Newton-Cotes formula is considered the corrector step. The convergence of the proposed method is discussed in detail. This new method is highly effective for solving large systems due to its simplicity and effectiveness. We consider the beam equation, using the finite difference method to transform it into a system of absolute value equations, and then solve it using the proposed method. Findings: The paper provides empirical insights into how to solve a system of absolute value equations. Originality/value: This paper fulfills an identified need to study absolute value equations. [ABSTRACT FROM AUTHOR]

The implementation of Newton's method for solving nonlinear equations in abstract domains requires the inversion of a linear operator at each step. Such an inversion may be computationally very expensive or impossible to find. That is why alternative iterative methods are developed in this article that require no inversion or only one inversion of a linear operator at each step. The inverse of the operator is replaced by a frozen sum of linear operators depending on the Fréchet derivative of an operator. The numerical examples illustrate that for all practical purposes, the new methods are as effective as Newton's but much cheaper to implement. The same methodology can be used to create similar alternatives to other methods using inversions of linear operators such as divided differences or other linear operators. [ABSTRACT FROM AUTHOR]

Iterative algorithms requiring the computationally expensive in general inversion of linear operators are difficult to implement. This is the reason why hybrid Newton-like algorithms without inverses are developed in this paper to solve Banach space-valued nonlinear equations. The inverses of the linear operator are exchanged by a finite sum of fixed linear operators. Two types of convergence analysis are presented for these algorithms: the semilocal and the local. The Fréchet derivative of the operator on the equation is controlled by a majorant function. The semi-local analysis also relies on majorizing sequences. The celebrated contraction mapping principle is utilized to study the convergence of the Krasnoselskij-like algorithm. The numerical experimentation demonstrates that the new algorithms are essentially as effective but less expensive to implement. Although the new approach is demonstrated for Newton-like algorithms, it can be applied to other single-step, multistep, or multipoint algorithms using inverses of linear operators along the same lines. [ABSTRACT FROM AUTHOR]

Evolutionary convergences are observed at all levels, from phenotype to DNA and protein sequences, and changes at these different levels tend to be correlated. Notably, convergent mutations can lead to convergent changes in phenotype, such as changes in metabolism, drug resistance, and other adaptations to changing environments. We propose a two-component approach to detect mutations subject to convergent evolution in protein alignments. The "Emergence" component selects mutations that emerge more often than expected, while the "Correlation" component selects mutations that correlate with the convergent phenotype under study. With regard to Emergence, a phylogeny deduced from the alignment is provided by the user and is used to simulate the evolution of each alignment position. These simulations allow us to estimate the expected number of mutations in a neutral model, which is compared to the observed number of mutations in the data studied. In Correlation, a comparative phylogenetic approach, is used to measure whether the presence of each of the observed mutations is correlated with the convergent phenotype. Each component can be used on its own, for example Emergence when no phenotype is available. Our method is implemented in a standalone workflow and a webserver, called ConDor. We evaluate the properties of ConDor using simulated data, and we apply it to three real datasets: sedge PEPC proteins, HIV reverse transcriptase, and fish rhodopsin. The results show that the two components of ConDor complement each other, with an overall accuracy that compares favorably to other available tools, especially on large datasets. [ABSTRACT FROM AUTHOR]

We study the accuracy of shock-capturing schemes for the shallow water Cauchy problems with piecewise smooth discontinuous initial data. We consider the second order balance-characteristic (CABARETM) scheme, the third order finite-difference Rusanov–Burstein–Mirin (RBM) scheme and the fifth order in space, the third order in time weighted essentially non-oscillatory (WENO5) scheme. We have shown that the maximum loss of accuracy occurs in the centered rarefaction waves of the exact solutions, where all these schemes have the first order of convergence and fairly close values of the numerical disbalances (errors), regardless of their formal approximation order on the smooth solutions. In the same time, inside the shock influence areas the considered schemes can have different convergence orders and, as a result, significantly different accuracy. In particular, when solving the Cauchy problem with periodic initial data, when the exact solution has no centered rarefaction waves, the RBM scheme has a significantly higher accuracy inside the shock influence areas, compared to the CABARETM and WENO5 schemes. It means that the combined scheme, in which the RBM scheme is a basic scheme and the CABARETM scheme is an internal one, can be effectively used to compute weak solutions of such type Cauchy problems. [ABSTRACT FROM AUTHOR]

Background Objectives Method Results and Conclusions Implications Online interaction in blended learning is leveraged through social presence and convergence. However, little systematic work currently exists on how researchers have explored these challenges in higher education institutions and no studies have synthesised these challenges.The purpose of this study is to give a novel overview of social presence and convergence to improve online interaction in blended learning in higher education. The findings will be synthesised into blended learning design principles.Two systematic literature reviews, one on each challenge, were carried out through the Web of Science databases and consulting cited sources in review articles. Accordingly, 28 distinct studies were selected through the guidelines of the PRISMA statement, using predefined selection criteria.The results show that social presence in blended learning is mostly evoked through course design, introductory f2f meetings, collaborative activities, prompt online feedback, the teacher's presence, and planned facilitation. To establish convergence, it is recommended to make basic theory available online through video clips, web‐lectures, articles, followed by simple online assignments or self‐study to increase understanding, thereby creating opportunities for deep learning during face‐to‐face through discussions and collaborative activities.This paper adds to the theory on blended learning and instructional design in higher education, and further offers an elaborate set of design principles for educational practice. Future research on instructional design may investigate in particular how a target group or student factors, are affected by the blended learning environment in order to tailor designs for a specific target group. [ABSTRACT FROM AUTHOR]

The dislocation hyperbolic augmented Lagrangian algorithm (DHALA) is a new approach to the hyperbolic augmented Lagrangian algorithm (HALA). DHALA is designed to solve convex nonlinear programming problems. We guarantee that the sequence generated by DHALA converges towards a Karush-Kuhn-Tucker point. We are going to observe that DHALA has a slight computational advantage in solving the problems over HALA. Finally, we will computationally illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

This paper focuses on distributed consensus optimization problems with coupled constraints over time-varying multi-agent networks, where the global objective is the finite sum of all agents' private local objective functions, and decision variables of agents are subject to coupled equality and inequality constraints and a compact convex subset. Each agent exchanges information with its neighbors and processes local data. They cooperate to agree on a consensual decision vector that is an optimal solution to the considered optimization problems. We integrate ideas behind dynamic average consensus and primal-dual methods to develop a distributed algorithm and establish its sublinear convergence rate. In numerical simulations, to illustrate the effectiveness of the proposed algorithm, we compare it with some related methods by the Neyman–Pearson classification problem. [ABSTRACT FROM AUTHOR]