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Plant root-nodule symbiosis (RNS) with mutualistic nitrogen-fixing bacteria is restricted to a single clade of angiosperms, the Nitrogen-Fixing Nodulation Clade (NFNC), and is best understood in the legume family. Nodulating species share many commonalities, explained either by divergence from a common ancestor over 100 million years ago or by convergence following independent origins over that same time period. Regardless, comparative analyses of diverse nodulation syndromes can provide insights into constraints on nodulation-what must be acquired or cannot be lost for a functional symbiosis-and the latitude for variation in the symbiosis. However, much remains to be learned about nodulation, especially outside of legumes. Here, we employed a large-scale phylogenomic analysis across 88 species, complemented by 151 RNA-seq libraries, to elucidate the evolution of RNS. Our phylogenomic analyses further emphasize the uniqueness of the transcription factor NIN as a master regulator of nodulation and identify key mutations that affect its function across the NFNC. Comparative transcriptomic assessment revealed nodule-specific upregulated genes across diverse nodulating plants, while also identifying nodule-specific and nitrogen-response genes. Approximately 70% of symbiosis-related genes are highly conserved in the four representative species, whereas defense-related and host-range restriction genes tend to be lineage specific. Our study also identified over 900 000 conserved non-coding elements (CNEs), over 300 000 of which are unique to sampled NFNC species. NFNC-specific CNEs are enriched with the active H3K9ac mark and are correlated with accessible chromatin regions, thus representing a pool of candidate regulatory elements for genes involved in RNS. Collectively, our results provide novel insights into the evolution of nodulation and lay a foundation for engineering of RNS traits in agriculturally important crops.

This article examines equity market perceptions of fair value reporting for tangible assets. We identify six events—four designated as increasing, two as decreasing—affecting the likelihood of U.S. adoption of fair value reporting for investment property (i.e., real estate) assets, one of the largest asset classes in the world. Fair value adoption in the United States would facilitate convergence of one of the widest remaining disparities between U.S. reporting and International Financial Reporting Standards (IFRS): accounting for tangible investment property assets, where the United States (IFRS) requires depreciated historical cost (recognized or disclosed fair values). Using a sample of U.S. investment property firms, we document an average positive market reaction for movement toward fair value reporting. We further find predictable cross-sectional variation, with the market reaction increasing for firms with greater commitment to high-quality reporting, greater investor demand for fair values, higher financial risk, and staler asset values. Overall, the results are consistent with U.S. equity markets perceiving net benefits to movement toward a fair value reporting approach for this asset class. [ABSTRACT FROM AUTHOR]

Abstract: Convergence science is an intrepid form of interdisciplinarity defined by the US National Research Council as ‘the coming together of insights and approaches from originally distinct fields’ to strategically address grand challenges. Despite its increasing relevance to science policy and institutional design, there is still no practical framework for measuring convergence. We address this gap by developing a measure of disciplinary distance based upon disciplinary boundaries delineated by hierarchical ontologies. We apply this approach using two widely used ontologies—the Classification of Instructional Programs and the Medical Subject Headings—each comprised of thousands of entities that facilitate classifying two distinct research dimensions, respectively. The social dimension codifies the disciplinary pedigree of individual scholars, connoting core expertise associated with traditional modes of mono-disciplinary graduate education. The conceptual dimension codifies the knowledge, methods, and equipment fundamental to a given target problem, which together may exceed the researchers’ core expertise. Considered in tandem, this decomposition facilitates measuring social-conceptual alignment and optimizing team assembly around domain-spanning problems—a key aspect that eludes other approaches. We demonstrate the utility of this framework in a case study of the human brain science (HBS) ecosystem, a relevant convergence nexus that highlights several practical considerations for designing, evaluating, institutionalizing, and accelerating convergence. Econometric analysis of 655,386 publications derived from 9,121 distinct HBS scholars reveals a 11.4% article-level citation premium attributable to research featuring full topical convergence, and an additional 2.7% citation premium if the social (disciplinary) configuration of scholars is maximally aligned with the conceptual (topical) configuration of the research.

Populations can adapt to novel selection pressures through dramatic frequency changes in a few genes of large effect or subtle shifts in many genes of small effect. The latter (polygenic adaptation) is expected to be the primary mode of evolution for many life-history traits but tends to be more difficult to detect than changes in genes of large effect. Atlantic cod (Gadus morhua) were subjected to intense fishing pressure over the twentieth century, leading to abundance crashes and a phenotypic shift toward earlier maturation across many populations. Here, we use spatially replicated temporal genomic data to test for a shared polygenic adaptive response to fishing using methods previously applied to evolve-and-resequence experiments. Cod populations on either side of the Atlantic show covariance in allele frequency change across the genome that are characteristic of recent polygenic adaptation. Using simulations, we demonstrate that the degree of covariance in allele frequency change observed in cod is unlikely to be explained by neutral processes or background selection. As human pressures on wild populations continue to increase, understanding and attributing modes of adaptation using methods similar to those demonstrated here will be important in identifying the capacity for adaptive responses and evolutionary rescue. This article is part of the theme issue 'Detecting and attributing the causes of biodiversity change: needs, gaps and solutions'.

In addition to the negative effects generated by the pandemic period, nowadays, the digital and ecological transition exerts additional pressure on the economy and society, especially on the labor market. Digital transformation is changing people\’s live, offering new opportunities to increase productivity and to improve the well-being of the citizens. To get the desired results, the EU\’s policies and measures must put people at the center of the actions by ensuring an equitable transition. Gender equality is a key factor in promoting an inclusive and sustainable growth. The digital transformation provides new tools to increase the participation of women in the labor market and to close the gender gap. In this context, the main objective of this paper is to examine the evolution of gender disparities between Member States and to show how Europe\’s digital decade can contribute to remarkable progress towards gender convergence by improving the labor market conditions.

Abstract 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.

In this paper, we investigate the numerical solution of the Brusselator system using a meshless method. A numerical scheme is derived employing the formulas of the Generalized Finite Difference Method, and the convergence of the approximate solution to the exact solution is examined. In order to demonstrate the applicability and accuracy of the method, several examples are proposed.

We have suggested a new modified iterative scheme for approximating a common fixed point of two $ G $-nonexpansive mappings. Our approach was based on an iterative scheme in the context of Banach spaces via directed graphs. First, we proved a weak convergence theorem using the Opial's property of the underlying space. A weak convergence result without the Opial's property was also given. After this, we established several strong convergence theorems using various mild conditions. We also carried out some numerical simulations to examine the main techniques. Eventually, we obtained an application of our result to solve split feasibility problems (SFP) in the context of $ G $-nonexpansive mappings.

As China's economy transitions from a stage of high-speed growth to a stage of high-quality development, the concept of low-carbon and green economic development has gained increasing popularity. Mastering the regional differences and changing patterns of low-carbon economy and economic growth quality is an important prerequisite for further promoting low-carbon economic development and improving the quality of economic growth. Taking the data of 21 prefecture-level cities in Guangdong Province from 2008 to 2019 as examples, we calculated the low-carbon economy and the quality index of economic growth, and analyzed the convergences between them through coefficient of variation analysis and a panel data convergence model with fixed effects. The results showed that: First, the convergence of low-carbon economy was better than the convergence of economic growth quality. Second, the low-carbon economy of Guangdong Province had σ convergence, and the imbalance between regions of low-carbon economy was alleviated, but the quality of economic growth of Guangdong Province did not have σ convergence. Third, there was absolute and conditional β convergence in the quality of low-carbon economy and economic growth in Guangdong Province. Fourth, the convergence rate of low-carbon economy in Guangdong Province showed "club difference"; the same was true of σ convergence, absolute β convergence, conditional β convergence, and dimensional convergence of economic growth quality in various regions of Guangdong Province. The exploration conducted in this article was conducive to better grasping the changing patterns of low-carbon economy and economic growth quality, enriching relevant research. The conclusions of this paper can provide decision-making basis for China to formulate urban and regional economic policies, achieve high-quality economic development, and "double carbon goal".

Abstract Background The persistently high out-of-pocket health spending (OOPHE) in Africa raise significant concern about the prospect of reaching SDG health targets and UHC. The study examines the convergence hypothesis of OOPHE in 40 African countries from 2000 to 2019. Methods We exploit the $${\text{log }}t$$ log t , club clustering, and merging methods on a panel of dataset obtained from the World Development Indicators, the World Governance Indicators, and the World Health Organization. Then, we employ the multilevel linear mixed effect model to examine whether countries' macro-level characteristics affect the disparities in OOPHE in the African regional economic communities (RECs). Results The results show evidence of full panel divergence, indicating persistent disparities in OOPHE over time. However, we found three convergence clubs and a divergent group for the OOPHE per capita and as a share of the total health expenditure. The results also show that convergence does not only occur among countries affiliated with the same regional economic grouping, suggesting disparities within the regional groupings. The findings reveal that countries' improved access to sanitation and quality of governance, increased childhood DPT immunization coverage, increased share of the elderly population, life expectancy at birth, external health expenditure per capita, and ICT (information and communication technology) significantly affect within-regional groupings’ disparities in OOPHE per capita. The results also show that an increasing countries’ share of elderly and younger populations, access to basic sanitation, ICT, trade GDP per capita, life expectancy at birth, childhood DPT immunization coverage, and antiretroviral therapy coverage have significant impacts on the share of OOPHE to total health expenditure within the regional groupings. Conclusion Therefore, there is a need to develop policies that vary across the convergence clubs. These countries should increase their health services coverage, adopt planned urbanization, and coordinate trade and ICT access policies. Policymakers should consider hidden costs associated with access to childhood immunization services that may lead to catastrophic health spending.

In Romania, the issue of economic inequalities and regional convergence is one of the current important topics on which the attention of economic specialists and the decision-making factors is focused. In the actual context, the regional policy in Romania is implemented at regional level, the regions being formed by counties that have voluntarily associated on the basis of a convention signed by the representatives of the County Councils, respectively of the General Council of Bucharest. After the year 2000, the development regions faced two major crises: the global financial crisis (2008-2009) and the one caused by the COVID-19 pandemic (2020-2021). Both crises have caused important effects at regional level and both have been supported by a number of territorial strategies and policies, to which there was added the cohesion and regional development policy financed by the EU Structural Funds. The paper is based on the analysis of the differences between the regions of Romania, in the period 2008-2022, during the COVID-19 pandemic, by highlighting the differences between the dynamics of certain indicators, of the analysis of the GINI coefficients for measuring inequalities, trying to answer the question which of the two crises, financial or health, affected the level of territorial inequalities more and what was the evolution of the regions of Romania in these two sub-periods. Regarding the financial crisis versus the pandemic one, in the majority of the indicators, it was shown that the values of the Gini Coefficients in the 2020-2022 were higher than the ones in 2008-2010 and also after the COVID-19 crisis the tendency of increased disparities was maintained. The only domains that were least affected by the pandemic were demography (rural population), transportation infrastructure and economic potential (companies with 10-49 employees).

Abstract Background The convergence of hypervirulence and carbapenem resistance in the bacterial pathogen Klebsiella pneumoniae represents a critical global health concern. Hypervirulent K. pneumoniae (hvKp) strains, frequently from sequence type 23 (ST23) and having a K1 capsule, have been associated with severe community-acquired invasive infections. Although hvKp were initially restricted to Southeast Asia and primarily antibiotic-sensitive, carbapenem-resistant hvKp infections are reported worldwide. Here, within the carbapenemase production Enterobacterales surveillance system headed by the Chilean Public Health Institute, we describe the isolation in Chile of a high-risk ST23 dual-carbapenemase-producing hvKp strain, which carbapenemase genes are encoded in a single conjugative plasmid. Results Phenotypic and molecular tests of this strain revealed an extensive resistance to at least 15 antibiotic classes and the production of KPC-2 and VIM-1 carbapenemases. Unexpectedly, this isolate lacked hypermucoviscosity, challenging this commonly used hvKp identification criteria. Complete genome sequencing and analysis confirmed the K1 capsular type, the KpVP-1 virulence plasmid, and the GIE492 and ICEKp10 genomic islands carrying virulence factors strongly associated with hvKp. Although this isolate belonged to the globally disseminated hvKp clonal group CG23-I, it is unique, as it formed a clade apart from a previously reported Chilean ST23 hvKp isolate and acquired an IncN KPC-2 plasmid highly disseminated in South America (absent in other hvKp genomes), but now including a class-I integron carrying bla VIM−1 and other resistance genes. Notably, this isolate was able to conjugate the double carbapenemase plasmid to an E. coli recipient, conferring resistance to 1st -5th generation cephalosporins (including combinations with beta-lactamase inhibitors), penicillins, monobactams, and carbapenems. Conclusions We reported the isolation in Chile of high-risk carbapenem-resistant hvKp carrying a highly transmissible conjugative plasmid encoding KPC-2 and VIM-1 carbapenemases, conferring resistance to most beta-lactams. Furthermore, the lack of hypermucoviscosity argues against this trait as a reliable hvKp marker. These findings highlight the rapid evolution towards multi-drug resistance of hvKp in Chile and globally, as well as the importance of conjugative plasmids and other mobile genetic elements in this convergence. In this regard, genomic approaches provide valuable support to monitor and obtain essential information on these priority pathogens and mobile elements.

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

In recent years, gambling has become increasingly prominent in everyday life; the term 'gamblification' first emerged in the late 2000s and was used to describe the colonisation of sports and sporting cultures by the gambling industry. Since that time, gamblification has been used to describe a range of phenomena in increasingly diffuse contexts; it has been variously used as a proxy for the convergence of gaming and gambling, to describe specific monetisation practices, or as a means of motivating consumer behaviours. Conceptual clarity has been further muddied by the positioning of gamblification as a form of gamification. This work provides a definition of gamblification, which draws upon and consolidates existing uses of the term while also providing a lens through which the differing aspects of gamblification can be understood and appraised. By doing so, this work will establish a clear conceptual framework, which can structure in-depth discussions of this multi-dimensional phenomenon. [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]

Globalization has fueled the rise of international family disputes, which raise difficult legal issues that cannot be addressed by any court or jurisdiction working alone. These challenges require a considered and coherent response on the international front, supported by the willingness of individual family judges to communicate and cooperate to identify and implement practical solutions. To meet these new challenges, this paper proposes a vision of international family justice as collaborative justice. There are three aspects or phases to the proposed endeavor: (a) the articulation of common aspirations and values; (b) continuing cooperation and communication between family courts and institutions; and (c) convergence in the substantive norms and practice of international family law. Key points for the family court community: International family disputes raise difficult issues which cannot be addressed by any court or jurisdiction working alone. Such disputes call for cross‐border collaboration between judges, family lawyers, and a team of allied family justice professionals.Such collaboration should be directed toward three goals: (a) articulating common aspirations and values for family justice; (b) deepening cooperation and communication between family courts and other family justice institutions; and (c) promoting convergence in the substantive norms and practice of international family law. [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]

This paper is concerned with the inverse scattering of the rough surfaces with multi-frequency phase and phaseless measurements. We present a high-order recursive iteration method based on the homotopy iteration technique to reconstruct the rough surfaces. The convergence for the multi-frequency homotopy iteration method is obtained under some conditions. Some numerical experiments show the effectiveness of the proposed algorithm. [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]

In this study, we start from a Follow-the-Leaders model for traffic flow that is based on a weighted harmonic mean (in Lagrangian coordinates) of the downstream car density. This results in a nonlocal Lagrangian partial differential equation (PDE) model for traffic flow. We demonstrate the well-posedness of the Lagrangian model in the L 1 sense. Additionally, we rigorously show that our model coincides with the Lagrangian formulation of the local LWR model in the "zero-filter" (nonlocal-to-local) limit. We present numerical simulations of the new model. One significant advantage of the proposed model is that it allows for simple proofs of (i) estimates that do not depend on the "filter size" and (ii) the dissipation of an arbitrary convex entropy. [ABSTRACT FROM AUTHOR]

In this paper, we intend to utilize the generalized scalar auxiliary variable (GSAV) approach proposed in recent paper (Ju et al., SIAM J. Numer. Anal., 60 (2022), 1905–1931) for the nonlocal coupled sine-Gordon equation to construct a class of fully decoupled, linear, and second-order accurate energy-preserving scheme. The unconditional unique solvability and discrete energy conservation law of the proposed scheme are rigorously discussed, and the unconditional convergence is then proved by the mathematical induction. Particularly, the convergence analysis covers the proposed scheme in multiple dimensions due to the corresponding nonlinear terms satisfy the global Lipschitz continuity straightforwardly. Finally, time evolution of dynamical behavior of the governing equation with different nonlocal parameters are observed, and ample numerical comparisons demonstrate that the proposed scheme manifests high efficiency in long-time computations. [ABSTRACT FROM AUTHOR]

This paper proposes and analyzes an uncoupled and linearized compact finite difference scheme for the generalized dissipative symmetric regularized long‐wave (GDSRLW) equations. The unique solvability and some a priori estimates of the proposed difference scheme are rigorously proved based on the mathematical induction method. To obtain the ‖·‖∞$$ {\left\Vert \cdotp \right\Vert}_{\infty } $$‐norm estimation of numerical solutions, the discrete energy method is used to prove the convergence and stability of the difference scheme. The proposed difference scheme preserves the original energy dissipation property, and the convergence of the scheme is proved to be fourth‐order in space and second‐order in time in the ‖·‖∞$$ {\left\Vert \cdotp \right\Vert}_{\infty } $$‐norm for both u$$ u $$ and ρ$$ \rho $$. Some numerical experiments are given to verify the theoretical analysis and the reliability of the proposed difference scheme. [ABSTRACT FROM AUTHOR]