The Convergence Rate of Fréchet Distribution under the Second-Order Regular Variation Condition

In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.

Valence Bands Convergence in p-Type CoSb_(3) through Electronegative Fluorine Filling

Band convergence is considered to be a strategy with clear benefits for thermoelectric performance,generally favoring the co-optimization of conductivity and Seebeck coefficients,and the conventional means include elemental filling to regulate the band.However,the influence of the most electronegative fluorine on the CoSb_(3) band remains unclear.We carry out density-functional-theory calculations and show that the valence band maximum gradually shifts downward with the increase of fluorine filling,lastly the valence band maximum converges to the highly degenerated secondary valence bands in fluorine-filled skutterudites.

Call for Papers——Feature Topic Vol.22,No.3,2025 Special Issue of China Communications:Convergence of 6G empowered Edge Intelligence and Generative AI:Theories,Algorithms,and Applications

Generative artificial intelligence(AI),as an emerging paradigm in content generation,has demonstrated its great potentials in creating high-fidelity data including images,texts,and videos.Nowadays wireless networks and applications have been rapidly evolving from achieving“connected things”to embracing“connected intelligence”.Generative AI has been recognized as a fundamentally innovative technology to drive the advancement of intelligent wireless communications and networks.

Diagnostic values of questionnaires of Convergence Insufficiency Symptom Survey and College of Optometrists Vision Development Quality of Life in the screening of convergence insufficiency

AIM:To compare and analyse the diagnostic efficacy of the College of Optometrists Vision Development Quality of Life Questionnaire(COVD-QOL)and the Convergence Insufficiency Symptom Survey(CISS)in detecting convergence insufficiency and to compare their diagnostic value in clinical applications.METHODS:Using the diagnostic test method,62 adult patients with convergence insufficiency(age:24.74±3.75y)and 62 normal participants(age:23.61±3.13y)who visited the Optometry Clinic of West China Hospital of Sichuan University from April 2021 to January 2023 were included.All subjects completed the CISS and COVD-QOL.Statistical analysis of the sensitivity and specificity of the CISS and COVD-QOL and comparison and joint experimental analysis of their diagnostic efficacy were performed.RESULTS:The sensitivity of the CISS and COVD-QOL for convergence insufficiency was 64.5%and 71.0%,respectively,while the specificity was 96.8%and 67.7%,respectively.Compared to the CISS alone,the combination of the CISS and COVD-QOL demonstrated lower sensitivity and specificity.The areas under the receiver operating characteristic curve of CISS,COVD-QOL and CISS combined with COVD-QOL were 0.806,0.694 and 0.782,respectively.CONCLUSION:Considering the low sensitivity of the CISS and the low specificity of the COVD-QOL,it is recommended to supplement these questionnaires with other screening tests for the detection of convergence insufficiency.

Some convergence theorems of fuzzy concave integral on fuzzyσ-algebra

In this paper,we consider the extension of the concave integral from classical crispσ-algebra to fuzzyσ-algebra of fuzzy sets.Firstly,the concept of fuzzy concave integral on a fuzzy set is introduced.Secondly,some important properties of such integral are discussed.Finally,various kinds of convergence theorems of a sequence of fuzzy concave integrals are proved.

Quantitative analysis and prediction of the sound field convergence zone in mesoscale eddy environment based on data mining methods

The mesoscale eddy(ME)has a significant influence on the convergence effect in deep-sea acoustic propagation.This paper use statistical approaches to express quantitative relationships between the ME conditions and convergence zone(CZ)characteristics.Based on the Gaussian vortex model,we construct various sound propagation scenarios under different eddy conditions,and carry out sound propagation experiments to obtain simulation samples.With a large number of samples,we first adopt the unified regression to set up analytic relationships between eddy conditions and CZ parameters.The sensitivity of eddy indicators to the CZ is quantitatively analyzed.Then,we adopt the machine learning(ML)algorithms to establish prediction models of CZ parameters by exploring the nonlinear relationships between multiple ME indicators and CZ parameters.Through the research,we can express the influence of ME on the CZ quantitatively,and achieve the rapid prediction of CZ parameters in ocean eddies.The prediction accuracy(R)of the CZ distance(mean R:0.9815)is obviously better than that of the CZ width(mean R:0.8728).Among the three ML algorithms,Gradient Boosting Decision Tree has the best prediction ability(root mean square error(RMSE):0.136),followed by Random Forest(RMSE:0.441)and Extreme Learning Machine(RMSE:0.518).

On power series statistical convergence and new uniform integrability of double sequences

In the present paper,we mostly focus on P_(p)^(2)-statistical convergence.We will look into the uniform integrability via the power series method and its characterizations for double sequences.Also,the notions of P_(p)^(2)-statistically Cauchy sequence,P_(p)^(2)-statistical boundedness and core for double sequences will be described in addition to these findings.

Multi-modal knowledge graph inference via media convergence and logic rule

Media convergence works by processing information from different modalities and applying them to different domains.It is difficult for the conventional knowledge graph to utilise multi-media features because the introduction of a large amount of information from other modalities reduces the effectiveness of representation learning and makes knowledge graph inference less effective.To address the issue,an inference method based on Media Convergence and Rule-guided Joint Inference model(MCRJI)has been pro-posed.The authors not only converge multi-media features of entities but also introduce logic rules to improve the accuracy and interpretability of link prediction.First,a multi-headed self-attention approach is used to obtain the attention of different media features of entities during semantic synthesis.Second,logic rules of different lengths are mined from knowledge graph to learn new entity representations.Finally,knowledge graph inference is performed based on representing entities that converge multi-media features.Numerous experimental results show that MCRJI outperforms other advanced baselines in using multi-media features and knowledge graph inference,demonstrating that MCRJI provides an excellent approach for knowledge graph inference with converged multi-media features.

Application of the Conditional Nonlinear Local Lyapunov Exponent to Second-Kind Predictability

In order to quantify the influence of external forcings on the predictability limit using observational data,the author introduced an algorithm of the conditional nonlinear local Lyapunov exponent(CNLLE)method.The effectiveness of this algorithm is validated and compared with the nonlinear local Lyapunov exponent(NLLE)and signal-to-noise ratio methods using a coupled Lorenz model.The results show that the CNLLE method is able to capture the slow error growth constrained by external forcings,therefore,it can quantify the predictability limit induced by the external forcings.On this basis,a preliminary attempt was made to apply this method to measure the influence of ENSO on the predictability limit for both atmospheric and oceanic variable fields.The spatial distribution of the predictability limit induced by ENSO is similar to that arising from the initial conditions calculated by the NLLE method.This similarity supports ENSO as the major predictable signal for weather and climate prediction.In addition,a ratio of predictability limit(RPL)calculated by the CNLLE method to that calculated by the NLLE method was proposed.The RPL larger than 1 indicates that the external forcings can significantly benefit the long-term predictability limit.For instance,ENSO can effectively extend the predictability limit arising from the initial conditions of sea surface temperature over the tropical Indian Ocean by approximately four months,as well as the predictability limit of sea level pressure over the eastern and western Pacific Ocean.Moreover,the impact of ENSO on the geopotential height predictability limit is primarily confined to the troposphere.

Spatial Differentiation and Convergence Trend of High-quality Development Level of China’s Tourism Economy

This paper aims to interpret the connotation of high-quality development of tourism economy(HQTE)from the perspective of the new development concepts of innovation,coordination,green,openness and sharing,and then to evaluate the spatial differenti-ation of China’s HQTE based on provincial panel data from 2009 to 2018.Specifically,we employ the spatial convergence model to ex-plore the absolute and conditionalβconvergence trends of HQTE in the whole country and the eastern,central and western regions of China.Our empirical results reveal that:1)within the decade,from 2009 to 2018,regions of China with the highest HQTE index is its eastern region followed by the central region and then the western region,but the fastest growing one is the western region of China fol-lowed by the central region and then the eastern region.2)Whether or not the spatial effect is included,there are absolute and condition-alβconvergence in HQTE in the whole country and aforementioned three regions.3)The degree of government attention as well as the level of economic development and location accessibility are the positive driving factors for the convergence of HQTE in the whole country and the three regions.The degree of marketization and human capital have not passed the significance test either in the whole country or in the three regions.The above conclusions could deepen the understanding of the regional imbalance and spatial conver-gence characteristics of HQTE,clarify the primary development objects,and accomplish the goal of China’s HQTE.

Conditional Generative Adversarial Network Enabled Localized Stress Recovery of Periodic Composites

Structural damage in heterogeneousmaterials typically originates frommicrostructures where stress concentration occurs.Therefore,evaluating the magnitude and location of localized stress distributions within microstructures under external loading is crucial.Repeating unit cells(RUCs)are commonly used to represent microstructural details and homogenize the effective response of composites.This work develops a machine learning-based micromechanics tool to accurately predict the stress distributions of extracted RUCs.The locally exact homogenization theory efficiently generates the microstructural stresses of RUCs with a wide range of parameters,including volume fraction,fiber/matrix property ratio,fiber shapes,and loading direction.Subsequently,the conditional generative adversarial network(cGAN)is employed and constructed as a surrogate model to establish the statistical correlation between these parameters and the corresponding localized stresses.The stresses predicted by cGAN are validated against the remaining true data not used for training,showing good agreement.This work demonstrates that the cGAN-based micromechanics tool effectively captures the local responses of composite RUCs.It can be used for predicting potential crack initiations starting from microstructures and evaluating the effective behavior of periodic composites.

Convergence of Hyperbolic Neural Networks Under Riemannian Stochastic Gradient Descent

We prove,under mild conditions,the convergence of a Riemannian gradient descent method for a hyperbolic neural network regression model,both in batch gradient descent and stochastic gradient descent.We also discuss a Riemannian version of the Adam algorithm.We show numerical simulations of these algorithms on various benchmarks.

Convergence over AI Governance Amid Differences

As the EU passes the first AI law,the U.S.grapples with bipartisanship,and China proactively advances the issue-based approach and advocates the Global AI Governance Initiative,will AI become“a force for good,ensuring safety,and promoting fairness”?

Selective Technology Importation and the Convergence in the Late Qing Dynasty: Evidence from Wired Telegraph

Using the adoption and expansion of wired telegraph in China during the late 19^(th) century,this paper investigates the effect of cost reductions for knowledge exchange on China’s industrial growth before the outbreak of the War of Resistance Against Japanese Aggression(1931-1945),thus testing Baldwin’s theory of“the Great Convergence”in which developing countries are empowered by information and communication technologies.Based on panel data of 1858-1937,we found that wired telegraph access had a significantly positive effect,as well as a long-term growth effect,on the entry of industrial enterprises.Our mechanism analysis indicates that wired telegraph access accelerated early-stage industrialization in localities by encouraging market integration,human capital accumulation,and auxiliary commercial organizations.Only a few countries firmly asserted their telegraph sovereignty and set up their own workforce educational system during telegraph adoption.This explains why the Great Convergence arising from technology importation only occurred in a small number of countries.Our findings contribute to understanding the source of China’s modern industrial progress,as well as why global inequities remain.

Tunnel, Infrastructure Convergences/Monitoring and Engineering Role

Worldwide we see that the construction industry is expanding, requiring new directions, new perspectives that can help reduce time, cost, and make transportation easy, safe, and affordable. For decades now, most of the large cities have completed their surface infrastructure. It has become urgent to address their issues for overpopulated cities where nowadays all infrastructure is overwhelmed, these issues must be addressed, solved and have vision to build underground infrastructure. Developed countries are focused on expanding their infrastructure for road systems, subway network, railway, storm, and sanitary systems. The emergency for underground infrastructure development requires more large-scale projects to be built and it is becoming more crucial building tunnels/underground structures for the future than ever before. Engineering focus, scientific searches are looking to develop their ideas for designing and delivering project underground, but government, agencies and engineers are concerned about the safety, durability, functionality, and the lifetime of this structures planned to be functional for decades. To address all this concerns this study provides information of how to identify the risk on tunnels and underground structures by capturing data from the beginning phases of construction, to analyze, evaluate and produce bulletins and engineering reports through convergences and monitoring. Convergences are the key factor on development of infrastructure underground as it is the only way to explore and analyze the rock mass disturbance during excavation. Convergences and monitoring in infrastructure are the safety coefficient for building underground, preventing accidents, and assessing real risks associated with tunnel/mine works and ensuring progress of the construction in underground structures. This study delves into the engineering role of convergence monitoring, during construction activities on project excavated using New Austrian Tunnelling method and Sequential Excavation Method. The primary objective of convergence monitoring is to gather critical information on ground movements and disturbances, thereby enhancing safety measures during tunnel construction. The monitoring process serves as an early warning system offering evidence of the real risks associated with underground infrastructure, bringing results and engineering data to be used for the design as key coefficient for structural design, type of material, type and strength of the concrete, rebars, concrete mix design. By using the convergence and monitoring system on underground infrastructure this study represents information that can contribute to risk assessment, structural analysis, and the lifetime of a project.

Convergence Phenomenon with Fourier Series of tg(x2)and Alike

The Fourier series of the 2π-periodic functions tg(x2)and 1sin(x)and some of their relatives (first of their integrals) are investigated and illustrated with respect to their convergence. These functions are Generalized functions and the convergence is weak convergence in the sense of the convergence of continuous linear functionals defining them. The figures show that the approximations of the Fourier series possess oscillations around the function which they represent in a broad band embedding them. This is some analogue to the Gibbs phenomenon. A modification of Fourier series by expansion in powers cosn(x)for the symmetric part of functions and sin(x)cosn−1(x)for the antisymmetric part (analogous to Taylor series) is discussed and illustrated by examples. The Fourier series and their convergence behavior are illustrated also for some 2π-periodic delta-function-like sequences connected with the Poisson theorem showing non-vanishing oscillations around the singularities similar to the Gibbs phenomenon in the neighborhood of discontinuities of functions. .

Mixed D-vine copula-based conditional quantile model for stochastic monthly streamflow simulation

Copula functions have been widely used in stochastic simulation and prediction of streamflow.However,existing models are usually limited to single two-dimensional or three-dimensional copulas with the same bivariate block for all months.To address this limitation,this study developed a mixed D-vine copula-based conditional quantile model that can capture temporal correlations.This model can generate streamflow by selecting different historical streamflow variables as the conditions for different months and by exploiting the conditional quantile functions of streamflows in different months with mixed D-vine copulas.The up-to-down sequential method,which couples the maximum weight approach with the Akaike information criteria and the maximum likelihood approach,was used to determine the structures of multivariate Dvine copulas.The developed model was used in a case study to synthesize the monthly streamflow at the Tangnaihai hydrological station,the inflow control station of the Longyangxia Reservoir in the Yellow River Basin.The results showed that the developed model outperformed the commonly used bivariate copula model in terms of the performance in simulating the seasonality and interannual variability of streamflow.This model provides useful information for water-related natural hazard risk assessment and integrated water resources management and utilization.

Attribute Reduction of Hybrid Decision Information Systems Based on Fuzzy Conditional Information Entropy

The presence of numerous uncertainties in hybrid decision information systems(HDISs)renders attribute reduction a formidable task.Currently available attribute reduction algorithms,including those based on Pawlak attribute importance,Skowron discernibility matrix,and information entropy,struggle to effectively manages multiple uncertainties simultaneously in HDISs like the precise measurement of disparities between nominal attribute values,and attributes with fuzzy boundaries and abnormal values.In order to address the aforementioned issues,this paper delves into the study of attribute reduction withinHDISs.First of all,a novel metric based on the decision attribute is introduced to solve the problem of accurately measuring the differences between nominal attribute values.The newly introduced distance metric has been christened the supervised distance that can effectively quantify the differences between the nominal attribute values.Then,based on the newly developed metric,a novel fuzzy relationship is defined from the perspective of“feedback on parity of attribute values to attribute sets”.This new fuzzy relationship serves as a valuable tool in addressing the challenges posed by abnormal attribute values.Furthermore,leveraging the newly introduced fuzzy relationship,the fuzzy conditional information entropy is defined as a solution to the challenges posed by fuzzy attributes.It effectively quantifies the uncertainty associated with fuzzy attribute values,thereby providing a robust framework for handling fuzzy information in hybrid information systems.Finally,an algorithm for attribute reduction utilizing the fuzzy conditional information entropy is presented.The experimental results on 12 datasets show that the average reduction rate of our algorithm reaches 84.04%,and the classification accuracy is improved by 3.91%compared to the original dataset,and by an average of 11.25%compared to the other 9 state-of-the-art reduction algorithms.The comprehensive analysis of these research results clearly indicates that our algorithm is highly effective in managing the intricate uncertainties inherent in hybrid data.

Convergence Issues Associated with Cutoff Energies and Ab Initio Studies of Adsorption of CO on W and Pt

The experimental research programs of 1950s, to understand the adsorption of CO on W surfaces, changed to ab initio studies in 2000s. The goals were to seek improved practical applications. Most of the studies were based on density functional theory. Many studies also used programs, such as VASP (Vienna Abinitio simulation package) and CPMD. The computational procedures used plane wave approximations. This needed studies with selection of K points and cutoff energy selection to assure convergence in energy calculations. Observations and analysis of papers published from 2006 to 2022 indicate that the cutoff energies were selected arbitrarily without any needed convergence studies. By selecting a published 2006 paper, this paper has clearly showed that an arbitrary selection of cutoff energy, such as 460 eV, is not in the range of, cutoff energies that assure convergence of energy calculations, with ab initio methods and have indicated correction procedures. .

Almost Sure Convergence of Proximal Stochastic Accelerated Gradient Methods

Proximal gradient descent and its accelerated version are resultful methods for solving the sum of smooth and non-smooth problems. When the smooth function can be represented as a sum of multiple functions, the stochastic proximal gradient method performs well. However, research on its accelerated version remains unclear. This paper proposes a proximal stochastic accelerated gradient (PSAG) method to address problems involving a combination of smooth and non-smooth components, where the smooth part corresponds to the average of multiple block sums. Simultaneously, most of convergence analyses hold in expectation. To this end, under some mind conditions, we present an almost sure convergence of unbiased gradient estimation in the non-smooth setting. Moreover, we establish that the minimum of the squared gradient mapping norm arbitrarily converges to zero with probability one.