As Convergence Research Articles

Factor price convergence in OECD economies: the case of three profit rates indicators

Abstract This paper examines profit rate (rates of return to capital) convergence in OECD economies in the periods of 1960-2016 and relevant sub-periods. It also performs comparison of profit rates convergence in selected developed and developing economies, using the data for 1973-2003 period. Economy-wide, productive economy and manufacturing rates are estimated and three convergence concepts are considered (beta, sigma, and stochastic convergence). We use a combination of cross-sectional and univariate time series models and density distribution analysis. For each profit rate measure, a strong evidence of beta convergence is provided. In contrast, sigma convergence is indicated only in the case of productive economy profit rate; while in other cases, sigma divergence or the absence of either convergence or divergence are likely. Stochastic convergence is present in a smaller number of economies and is confined to productive economy and manufacturing. The comparison of convergence dynamics in developed versus developing economies confirmed beta convergence in both groups and for their aggregate, but did not establish sigma convergence, given the significant diversity of economies and their different economic trajectories.

Stochastic homogenisation of free-discontinuity functionals in randomly perforated domains

Abstract In this paper, we study the asymptotic behaviour of a family of random free-discontinuity energies E ε {E_{\varepsilon}} defined in a randomly perforated domain, as ε goes to zero. The functionals E ε {E_{\varepsilon}} model the energy associated to displacements of porous random materials that can develop cracks. To gain compactness for sequences of displacements with bounded energies, we need to overcome the lack of equi-coerciveness of the functionals. We do so by means of an extension result, under the assumption that the random perforations cannot come too close to one another. The limit energy is then obtained in two steps. As a first step, we apply a general result of stochastic convergence of free-discontinuity functionals to a modified, coercive version of E ε {E_{\varepsilon}} . Then the effective volume and surface energy densities are identified by means of a careful limit procedure.

Mean convergence theorems to generalized acute points for generalized pseudocontractions

Convergence theorems required more assumptions on parameters than fixed point theorems. In this paper we generalize the concept of acute point and we introduce some convergence theorems that holds under the same assumptions on parameters as fixed point theorems.

On the discontinuous solutions of explicit neutral delay differential equations

This paper considers explicit neutral delay differential equations (NDDE) with piecewise continuous initial functions. We explain how the discontinuities in the solutions arise and present a perturbing scheme, in combination with an adaptive Legendre–Gauss–Radau collocation method, to deal with this type of problems computationally. The pointwise and mean convergence of the continuous solution of the perturbed NDDE to the discontinuous solution of the original NDDE are proved. Our new method for discontinuous NDDEs and the rigorous theoretical analysis provided are particularly important since explicit NDDEs have received little attention in the literature. Numerical results are given to show that the proposed method can be implemented in an efficient and accurate manner.

Analysis of Spatial and Temporal Evolution Characteristics and Influencing Factors of the Water Footprint in Xinjiang from 2000 to 2020

Xinjiang is home to one of the most serious resource-based water shortages, and at the same time, it is an important main production area of grain, cotton, and high-quality fruits and vegetables in China, placing a heavy burden on water resources. Based on this, this paper determines the basic condition of water resources in regions of Xinjiang using the water footprint method. It then identifies the drivers of water footprint changes using the population scale effect, policy support effect, investment–output effect, economic structure effect, water use efficiency effect, and water use structure effect via the LMDI decomposition model. Finally, this paper illustrates the trajectory of the regional water footprint through individual stochastic convergence. This study found the following: (1) The water footprint of Xinjiang showed a fluctuating upward trend, and the total water footprint varied significantly between regions. From a compositional standpoint, most regions were dominated by the agricultural water footprint, while spatially, the regional water footprint had a high distribution trend in the south and a low distribution in the north. (2) The driving effects of the water footprint, policy support, population scale, and water use structure were incremental, while the effects of water use efficiency, economic structure, and investment output were decremental. (3) Most regions in Xinjiang showed individual stochastic convergence trends, indicating that regions converged to their respective compensating difference equilibrium levels. In this regard, it is necessary to strengthen R&D and the promotion of water use technology, further optimize the industrial structure, and leverage the positive effect of government investment to alleviate the regional water constraint dilemma and promote high-quality regional economic development.

Numerical convergence does not mean mathematical convergence: Examples of simple saturated steady-state groundwater models with pumping wells

Groundwater numerical studies do not include H-convergence tests, contrarily to computational fluid dynamics (CFD) studies. In regional groundwater studies with pumping wells, the grids may exceed 106 nodes. The authors examine whether H-convergence tests can help to calculate the numerical errors made by using large grids with element sizes in the 10–500 m range. First, the differences between numerical and mathematical convergences are explained. Then, a method is proposed that most users may easily implement for their groundwater studies to assess the numerical error linked to the element size, ES, and the aspect ratio, AR. A single problem, forming a simple part of a regional groundwater study, was examined and solved by using many uniform grids. The results show that most regional groundwater studies make errors in the 50–500% range, considering their usual values for ES and AR. The numerical convergence domain, NCD, is shown to be larger than the mathematical convergence domain, MCD. This means that the codes can provide a numerical solution for a large range of ES values, even for many values outside the MCD, which is a risky situation for designers who are unaware of the difference between NCD and MCD and ignore the H-convergence tests.

Toward carbon peaking and neutralization: The heterogeneous stochastic convergence of CO2 emissions and the role of digital inclusive finance

This article explores the dynamic distribution of city-level CO2 emissions from China's national and regional perspectives. For this, we apply a q-σ stochastic convergence model to inspect the heterogeneous convergence trend of carbon emissions at different quantiles. A panel time-varying quantile regression model with a factor structure was employed to determine the absolute and conditional q-β stochastic convergence of CO2 emissions and to examine the dynamic influence of digital inclusive finance on the convergence of carbon emissions. The results show (i) CO2 emissions exhibit a spatially imbalanced distribution pattern of being low in east and high in the west. The dynamic progression of carbon emissions in different areas presents huge differences in which Eastern, Central and Western China show insignificant and significant changes of distribution trending in CO2 emissions. (ii) Excluding the central region, country's CO2 emissions in eastern and western regions display dynamic q-σ convergence and dynamic absolute q-β convergence at different quantiles. In contrast, a conditional q-β convergence of CO2 emissions in the whole country and each region is found across 5%–95% quantiles. (iii) At national and regional emissions, the dynamic q-σ convergence, absolute and conditional q-β convergence typically becomes more pronounced at mid-high quantile than at low quantile. (iv) Development of digital inclusive finance across the country and in Central and Western China generally facilitates carbon emissions convergence, but the opposite result for the eastern region. Finally, comprehensive finance growth, digital finance and low-carbon technological efforts can be a better fit for achieving dual-carbon goals.

Современные культурные противоречия глобализации мировой экономики

The article discusses the interactions between globalization and culture and the various theoretical scenarios for exploring these synergies. These scenarios include homogenization and hybridization. It is argued that cul-tures are indeed influenced and changed by contact with other cultures, but this does not necessarily mean cultural standardization or convergence with the global cultural model. Cultural openness acknowledges the differences between cultures, but does not necessarily mix them and allows cultures to benefit from the rich-ness of other crops. The authors conclude that the interaction between globalization and culture has significant implications for both society and organizations, with the latter needing to adapt standardized practices from a local cultural perspective.

Widely linear complex-valued hyperbolic secant adaptive filtering algorithm and its performance analysis

To achieve good estimation in the impulsive noise environment, some hyperbolic functions have been introduced as cost functions to develop robust adaptive filtering algorithms in recent years. However, the hyperbolic functions have rarely been studied for complex-valued signals. In this paper, a robust adaptive algorithm is introduced for processing both circular and non-circular complex-valued signals by utilizing the complex hyperbolic secant cost functions. Moreover, its performance is thoroughly analyzed, including mean convergence, mean-square transient behavior, and mean-square steady-state behavior. Finally, the simulation results show the advantages of the proposed algorithm for complex-valued signal processing in non-Gaussian environments and verify the accuracy of the theoretical performance analysis.

Process control of mAb production using multi-actor proximal policy optimization

Monoclonal antibodies (mAb) are biopharmaceutical products that improve human immunity. In this work, we propose a multi-actor proximal policy optimization-based reinforcement learning (RL) for the control of mAb production. Here, manipulated variable is flowrate and the control variable is mAb concentration. Based on root mean square error (RMSE) values and convergence performance, it has been observed that multi-actor PPO has performed better as compared to other RL algorithms. It is observed that PPO predicts a 40 % reduction in the number of days to reach the desired concentration. Moreover, the performance of PPO is improved as the number of actors increases. PPO agent shows the best performance with three actors, but on further increasing, its performance deteriorated. These results are verified based on three case studies, namely, (i) for nominal conditions, (ii) in the presence of noise in raw materials and measurements, and (iii) in the presence of stochastic disturbance in temperature and noise in measurements. The results indicate that the proposed approach outperforms the deep deterministic policy gradient (DDPG), twin delayed deep deterministic policy gradient (TD3), and proximal policy optimization (PPO) algorithms for the control of the bioreactor system.

Machine learning models to predict the tunnel wall convergence

Deformation and damage of the rock mass induced by excavation operations can result in the tunnel wall convergence. Accurate prediction of the convergence is crucial for ensuring safe, economical, and efficient construction of tunnel projects. In this study, six popular and reliable machine learning (ML) models, including back-propagation neural network (BPNN), general regression neural network (GRNN), extreme learning machine (ELM), kernel extreme learning machine (KELM), least squares support vector machine (LSSVR) and random forest (RF) were selected to predict the tunnel wall convergence. The jellyfish search optimizer (JSO) was utilized to find the optimal hyperparameters of these models. A total of 142 sets of highway tunnel convergence data were collected for model training and testing, six parameters including overburden thickness (H), rock mass rating index (RMR), rock mass quality index (Q), rock mass cohesion (Crm), deformation modulus of rock mass (Erm), and internal friction angle of rock mass (φrm) were used as input variables and the mean convergence of tunnel wall (Y) was considered as the output variable. Mean absolute error (MAE), root mean squared error (RMSE), coefficient of determination (R2), and variance accounted for (VAF) as evaluation indicators were used to compare the predictive performance of the proposed models. The results from various evaluation methods demonstrate that the overall performance of the JSO-RF model is superior, with MAE, RMSE, R2, and VAF values of 4.288, 6.219, 0.917, and 89.480 during the training phase, and 3.141, 3.958, 0.939, and 93.164 during the testing phase. When compared with RF, multivariate regression (MVR), and empirical equations, the JSO-RF model also exhibits better predictive performance. The importance results of all input variables showed that φrm, Erm, and H were more important input variables than other variables.

Mean convergence of Lagrange interpolation

In this note we prove mean convergence of Lagrange interpolation at the zeros of para-orthogonal polynomials for measures on the unit circle which do not belong to Szegő’s class. When the measure is in Szegő’s class, mean convergence of Lagrange interpolation is proved for functions in the disk algebra.

Regional Differences and Convergence of Technical Efficiency in China’s Marine Economy under Carbon Emission Constraints

With the continuous development of China’s marine economy and the increasing pollution in marine-related industries, how to implement a sustainable development strategy in the marine economy has become an important issue. Under the stochastic frontier analysis framework, this paper measures the technical efficiency of the marine economy in 11 coastal provinces in China under carbon emission constraints from 2006 to 2016 and analyzes regional differences and the dynamic evolution of technical efficiency and its influencing factors. Panel unit root test is applied to analyze the stochastic convergence of technical efficiency of the inter-regional marine economy. The result shows that: in the reference period, the technical efficiency of the marine economy is on the rise. Guangdong and Shanghai are in the lead. Technical level and industrial structure have a positive impact on technical efficiency, while the structure of property rights, FDI, energy prices, and energy structure have a negative effect on it. On the whole, the changes in the technical efficiency of coastal provinces present a process from concentration to differentiation. There is a stochastic convergence between the Pan-Pearl River Delta and the Yangtze River Delta. Raising the technological level, promoting low-carbon production in the marine industry, and strengthening inter-regional cooperation have a certain effect on the improvement of the technical efficiency of the marine economy.

RETRACTED ARTICLE: Convergence in quadratic mean of averaged stochastic gradient algorithms without strong convexity nor bounded gradient

We, the Editors and Publisher of Statistics, have retracted the following article: Antoine Godichon-Baggioni. Convergence in quadratic mean of averaged stochastic gradient algorithms without strong convexity nor bounded gradient. Statistics. 57:3. 2023. 637–668. doi:10.1080/02331888.2023.2213371 The author raised concern regarding an error from an inequality (9) on page 647. This inequality cannot be verified if the gradient is bounded. We have been informed in our decision-making by our policy on publishing ethics and integrity and the COPE guidelines on retractions. The retracted article will remain online to maintain the scholarly record, but it will be digitally watermarked on each page as “Retracted”.

A Stochastic Convergence Result for the Nelder–Mead Simplex Method

We prove that the Nelder–Mead simplex method converges in the sense that the simplex vertices converge to a common limit point with a probability of one. The result may explain the practical usefulness of the Nelder–Mead method.

Exploring the use of emoji in museum social network sites

This paper aims to explore how emoji make meaning in interaction with other semiotic resources in museum social media posts. In so doing, it examines to what extent emoji are changing the way museums communicate with their audiences. The analysis is based on a corpus of museum social posts and grounded in Systemic Functional Linguistics. Findings show that emoji make meaning not only in interaction with language, working as a paralinguistic resource, but also in interaction with visual content. The analysis highlights the presence of image-driven emoji, which create a convergence of meaning in association with details of the post image, limiting or excluding the textual component of the caption from the intermodal semiosis. Image-driven emoji often lead to playful effects and can be exploited by museum communicators for engagement purposes, to create quizzes and games. The study therefore suggests that emoji can contribute to add an informal component to museum communication, according to the 'post-museum' style, which is characterised by a more direct interactional attitude towards the audience.

Stochastic convergence problems on switching networks: An event-triggered method

The paper investigates stochastic convergence problems of multi-agent systems with double-integrator dynamics. Based on the consideration of external interference and dynamic topology, a robust controller is proposed to avoid continuous communication between agents via time-dependent event-triggered protocol. The advantage of time-dependent event-triggered protocol is that its effectiveness does not decrease with the increase of the number of agents. Then, in the framework of fixed topology and Markov switching topologies, the convergence conditions are obtained respectively. In addition, singular triggering and Zeno phenomena are excluded. Finally, the effectiveness of the proposed theory is verified by numerical simulations.

Does the frequency of stochastic convergence in per capita ecological footprint matter?

Among the environmental economics research issues, the issue of convergence has received quite a lot of attention, which is also known as stationary analysis. In this research strand, whether shocks to the time series variable are permanent or temporary is tested via the unit root tests. In this study, based on the theory and empirical works of stochastic convergence, we evaluate the convergence for the BASIC member countries, including Brazil, South Africa, India, and China. We use a variety of methodologies to see whether the convergence of ecological footprint holds for these countries or not. We first use the wavelet decomposition technique to decompose the series into the short run, middle run, and long run, and then we run several unit root tests to confirm the stationarity property of the series. The methodologies implemented in this study allow us to apply econometric tests to the original series as well as to the decomposed series. The results of panel CIPS test demonstrate that the null hypothesis of unit root could be rejected for the short run but not for the middle and long run, implying that long-lasting impact might prevail due to any shocks to the ecological footprint in the middle and long run. The results for individual countries varied.

Mean convergence theorems for arrays of dependent random variables with applications to dependent bootstrap and non-homogeneous Markov chains

Mean convergence theorems for arrays of dependent random variables with applications to dependent bootstrap and non-homogeneous Markov chains

Stochastic convergence analysis of US state economic freedom sub‐components: Evidence from unit root tests for bounded processes

AbstractThis study tests for convergence of the three main sub‐components of economic freedom (government spending, taxation, and labor market freedom) for the 50 US states from 1981 to 2019. In particular, we test for stochastic convergence using unit root tests that account for structural breaks and bounded processes. By controlling for these sources of parameter instability, we find limited evidence in favor of stochastic convergence across the three sub‐components of economic freedom. However, we find more evidence of stochastic convergence with respect to the sub‐components than in the case of the overall economic freedom at the US state level. Our results highlight the distinct nature of the institutional quality across states as represented by government spending, taxation, and labor market freedom.