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Multi-modal knowledge graph inference via media convergence and logic rule
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作者 Feng Lin Dongmei Li +5 位作者 Wenbin Zhang Dongsheng Shi Yuanzhou Jiao Qianzhong Chen Yiying Lin Wentao Zhu 《CAAI Transactions on Intelligence Technology》 SCIE EI 2024年第1期211-221,共11页
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 intro... 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. 展开更多
关键词 logic rule media convergence multi-modal knowledge graph inference representation learning
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Spatial Differentiation and Convergence Trend of High-quality Development Level of China’s Tourism Economy
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作者 CAO Shanshan HE Zhaoli +2 位作者 NIU Jinlan WANG Songmao ZHAO Lei 《Chinese Geographical Science》 SCIE CSCD 2024年第2期230-249,共20页
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 e... 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. 展开更多
关键词 new development concepts high-quality development of tourism economy(HQTE) spatial convergence China
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Almost Sure Convergence of Proximal Stochastic Accelerated Gradient Methods
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作者 Xin Xiang Haoming Xia 《Journal of Applied Mathematics and Physics》 2024年第4期1321-1336,共16页
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 stocha... 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. 展开更多
关键词 Proximal Stochastic Accelerated Method Almost Sure convergence Composite Optimization Non-Smooth Optimization Stochastic Optimization Accelerated Gradient Method
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Valence Bands Convergence in p-Type CoSb_(3) through Electronegative Fluorine Filling
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作者 黄写格 李家良 +5 位作者 马浩钦 李昌隆 刘天乐 段波 翟鹏程 李国栋 《Chinese Physics Letters》 SCIE EI CAS CSCD 2024年第7期87-94,共8页
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 ele... 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. 展开更多
关键词 VALENCE convergence BANDS
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Diagnostic values of questionnaires of Convergence Insufficiency Symptom Survey and College of Optometrists Vision Development Quality of Life in the screening of convergence insufficiency
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作者 Ling Xiong Qian Chen Ye Wu 《International Journal of Ophthalmology(English edition)》 SCIE CAS 2024年第5期904-908,共5页
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 convergenc... 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. 展开更多
关键词 convergence insufficiency symptom survey College of Optometrists Vision Development Quality of Life Questionnaire convergence insufficiency ASTHENOPIA
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Quantitative analysis and prediction of the sound field convergence zone in mesoscale eddy environment based on data mining methods
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作者 Ming Li Yuhang Liu +1 位作者 Yiyuan Sun Kefeng Liu 《Acta Oceanologica Sinica》 SCIE CAS CSCD 2024年第5期110-120,共11页
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 co... 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). 展开更多
关键词 convergence zone mesoscale eddy statistic analysis quantitative prediction machine learning
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Tunnel, Infrastructure Convergences/Monitoring and Engineering Role
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作者 Sali Bedaj 《Engineering(科研)》 2024年第5期134-147,共14页
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 th... 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. 展开更多
关键词 TUNNEL INFRASTRUCTURE convergence/Monitoring Underground Monitoring
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The Convergence Rate of Fréchet Distribution under the Second-Order Regular Variation Condition
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作者 Xilai Dai 《Journal of Applied Mathematics and Physics》 2024年第5期1597-1605,共9页
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 ... 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. 展开更多
关键词 convergence Rate Second-Order Regular Variation Condition Fréchet Distribution Extreme Value Index
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Complete moment convergence for ND random variables under the sub-linear expectations
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作者 FENG Feng-xiang WANG Ding-cheng WU Qun-ying 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2023年第3期444-457,共14页
In this article,we establish a general result on complete moment convergence for arrays of rowwise negatively dependent(ND)random variables under the sub-linear expectations.As applications,we can obtain a series of r... In this article,we establish a general result on complete moment convergence for arrays of rowwise negatively dependent(ND)random variables under the sub-linear expectations.As applications,we can obtain a series of results on complete moment convergence for ND random variables under the sub-linear expectations. 展开更多
关键词 complete convergence complete moment convergence ND random variables sub-linear expectation
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On the Feasibility of the Chinese County-Level Convergence Media Centers in Participating in International Communication:Evidence from CDHT’s First-Hand Communication Practice
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作者 Wu Jun 《Contemporary Social Sciences》 2023年第1期75-88,共14页
With the advent of new technologies,China is faced with the practical need to enhance its international communication capacity and address reforms in the modes,content,and channels of international communication.There... With the advent of new technologies,China is faced with the practical need to enhance its international communication capacity and address reforms in the modes,content,and channels of international communication.Therefore,more efforts should be made to further enrich the participants in international communication by optimizing China’s four-level journalism communication system and crafting a“great external publicity pattern.”Guiding and promoting county-level convergence media centers to participate in international communication is conducive to promoting the building of a vertical international communication system and a multi-level integrated communication matrix and facilitating the resource alignment and information sharing between domestic and international communication.In practice,some county-level convergence media centers in China have achieved certain results in international communication.A good example is the Chengdu Hi-tech Industrial Development Zone(CDHT),a pioneer in the reform of Chinese county-level convergence media.Therefore,this paper has used CDHT as an example to discuss the reality and basic conditions for Chinese county-level convergence media centers to participate in international communication and put forward general paths for county-level convergence media centers to engage in international communication. 展开更多
关键词 International communication county-level convergence media centers media convergence Chengdu Hitech Industrial Development Zone
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THE SINGULAR CONVERGENCE OF A CHEMOTAXIS-FLUID SYSTEM MODELING CORAL FERTILIZATION
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作者 杨明华 孙晋易 +1 位作者 傅尊伟 王政 《Acta Mathematica Scientia》 SCIE CSCD 2023年第2期492-504,共13页
The singular convergence of a chemotaxis-fluid system modeling coral fertilization is justified in spatial dimension three.More precisely,it is shown that a solution of parabolic-parabolic type chemotaxis-fluid system... The singular convergence of a chemotaxis-fluid system modeling coral fertilization is justified in spatial dimension three.More precisely,it is shown that a solution of parabolic-parabolic type chemotaxis-fluid system modeling coral fertilization■converges to that of the parabolic-elliptic type chemotaxis-fluid system modeling coral fertiliz ation■in a certain Fourier-Herz space asε^(-1)→0. 展开更多
关键词 CHEMOTAXIS singular convergence recation diffusion Fourier-Herz space
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THE UNIFORM CONVERGENCE OF A DG METHOD FOR A SINGULARLY PERTURBED VOLTERRA INTEGRO-DIFFERENTIAL EQUATION
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作者 陶霞 谢资清 《Acta Mathematica Scientia》 SCIE CSCD 2023年第5期2159-2178,共20页
The purpose of this work is to implement a discontinuous Galerkin(DG)method with a one-sided flux for a singularly perturbed Volterra integro-differential equation(VIDE)with a smooth kernel.First,the regularity proper... The purpose of this work is to implement a discontinuous Galerkin(DG)method with a one-sided flux for a singularly perturbed Volterra integro-differential equation(VIDE)with a smooth kernel.First,the regularity property and a decomposition of the exact solution of the singularly perturbed VIDE with the initial condition are provided.Then the existence and uniqueness of the DG solution are proven.Then some appropriate projection-type interpolation operators and their corresponding approximation properties are established.Based on the decomposition of the exact solution and the approximation properties of the projection type interpolants,the DG method achieves the uniform convergence in the L2 norm with respect to the singular perturbation parameter e when the space of polynomials with degree p is used.A numerical experiment validates the theoretical results.Furthermore,an ultra-convergence order 2p+1 at the nodes for the one-sided flux,uniform with respect to the singular perturbation parameter e,is observed numerically. 展开更多
关键词 singularly perturbed VIDE DG method Shishkin mesh uniform convergence
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Local pointwise convergence of the 3D finite element
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作者 LIU Jing-hong ZHU Qi-ding 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2023年第2期210-222,共13页
For an elliptic problem with variable coefficients in three dimensions,this article discusses local pointwise convergence of the three-dimensional(3D)finite element.First,the Green's function and the derivative Gr... For an elliptic problem with variable coefficients in three dimensions,this article discusses local pointwise convergence of the three-dimensional(3D)finite element.First,the Green's function and the derivative Green's function are introduced.Secondly,some relationship of norms such as L^(2)-norms,W^(1,∞)-norms,and negative-norms in locally smooth subsets of the domainΩis derived.Finally,local pointwise convergence properties of the finite element approximation are obtained. 展开更多
关键词 nite element local convergence Green's function
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Fully asynchronous distributed optimization with linear convergence over directed networks
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作者 SHA Xingyu ZHANG Jiaqi YOU Keyou 《中山大学学报(自然科学版)(中英文)》 CAS CSCD 北大核心 2023年第5期1-23,共23页
We study distributed optimization problems over a directed network,where nodes aim to minimize the sum of local objective functions via directed communications with neighbors.Many algorithms are designed to solve it f... We study distributed optimization problems over a directed network,where nodes aim to minimize the sum of local objective functions via directed communications with neighbors.Many algorithms are designed to solve it for synchronized or randomly activated implementation,which may create deadlocks in practice.In sharp contrast,we propose a fully asynchronous push-pull gradient(APPG) algorithm,where each node updates without waiting for any other node by using possibly delayed information from neighbors.Then,we construct two novel augmented networks to analyze asynchrony and delays,and quantify its convergence rate from the worst-case point of view.Particularly,all nodes of APPG converge to the same optimal solution at a linear rate of O(λ^(k)) if local functions have Lipschitz-continuous gradients and their sum satisfies the Polyak-?ojasiewicz condition(convexity is not required),where λ ∈(0,1) is explicitly given and the virtual counter k increases by one when any node updates.Finally,the advantage of APPG over the synchronous counterpart and its linear speedup efficiency are numerically validated via a logistic regression problem. 展开更多
关键词 fully asynchronous distributed optimization linear convergence Polyak-Łojasiewicz condition
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Improved High Order Model-Free Adaptive Iterative Learning Control with Disturbance Compensation and Enhanced Convergence
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作者 Zhiguo Wang Fangqing Gao Fei Liu 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第1期343-355,共13页
In this paper,an improved high-order model-free adaptive iterative control(IHOMFAILC)method for a class of nonlinear discrete-time systems is proposed based on the compact format dynamic linearization method.This meth... In this paper,an improved high-order model-free adaptive iterative control(IHOMFAILC)method for a class of nonlinear discrete-time systems is proposed based on the compact format dynamic linearization method.This method adds the differential of tracking error in the criteria function to compensate for the effect of the random disturbance.Meanwhile,a high-order estimation algorithmis used to estimate the value of pseudo partial derivative(PPD),that is,the current value of PPD is updated by that of previous iterations.Thus the rapid convergence of the maximumtracking error is not limited by the initial value of PPD.The convergence of the maximumtracking error is deduced in detail.This method can track the desired output with enhanced convergence and improved tracking performance.Two examples are used to verify the convergence and effectiveness of the proposed method. 展开更多
关键词 Pseudo partial derivative enhanced convergence tracking error disturbance compensation
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A multi-modal clustering method for traditonal Chinese medicine clinical data via media convergence
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作者 Jingna Si Ziwei Tian +6 位作者 Dongmei Li Lei Zhang Lei Yao Wenjuan Jiang Jia Liu Runshun Zhang Xiaoping Zhang 《CAAI Transactions on Intelligence Technology》 SCIE EI 2023年第2期390-400,共11页
Media convergence is a media change led by technological innovation.Applying media convergence technology to the study of clustering in Chinese medicine can significantly exploit the advantages of media fusion.Obtaini... Media convergence is a media change led by technological innovation.Applying media convergence technology to the study of clustering in Chinese medicine can significantly exploit the advantages of media fusion.Obtaining consistent and complementary information among multiple modalities through media convergence can provide technical support for clustering.This article presents an approach based on Media Convergence and Graph convolution Encoder Clustering(MCGEC)for traditonal Chinese medicine(TCM)clinical data.It feeds modal information and graph structure from media information into a multi-modal graph convolution encoder to obtain the media feature representation learnt from multiple modalities.MCGEC captures latent information from various modalities by fusion and optimises the feature representations and network architecture with learnt clustering labels.The experiment is conducted on real-world multimodal TCM clinical data,including information like images and text.MCGEC has improved clustering results compared to the generic single-modal clustering methods and the current more advanced multi-modal clustering methods.MCGEC applied to TCM clinical datasets can achieve better results.Integrating multimedia features into clustering algorithms offers significant benefits compared to single-modal clustering approaches that simply concatenate features from different modalities.It provides practical technical support for multi-modal clustering in the TCM field incorporating multimedia features. 展开更多
关键词 graph convolutional encoder media convergence multi-modal clustering traditional Chinese medicine
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Receded near point of convergence as a predictor of mild cognitive impairment in the general geriatric population:results from a population-based study
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作者 Asgar Doostdar Hassan Hashemi +2 位作者 Payam Nabovati Amir Asharlous Mehdi Khabazkhoob 《International Journal of Ophthalmology(English edition)》 SCIE CAS 2023年第4期623-629,共7页
AIM:To investigate the relationship between near point of convergence(NPC)and mild cognitive impairment(MCI)in the general elderly population.METHODS:The present report is a part of the Tehran Geriatric Eye Study(TGES... AIM:To investigate the relationship between near point of convergence(NPC)and mild cognitive impairment(MCI)in the general elderly population.METHODS:The present report is a part of the Tehran Geriatric Eye Study(TGES):a population-based crosssectional study conducted on individuals 60 years of age and above living in Tehran,Iran using the multi-stage stratified random cluster sampling method.Cognitive status was assessed using the Persian version of the Mini-Mental State Examination(MMSE).All study participants underwent complete ocular examination including measurement of uncorrected and best-corrected visual acuity,objective and subjective refraction,cover testing,NPC measurement,and slit-lamp biomicroscopy.RESULTS:The data of 1190 individuals were analyzed for this report.The mean age of the participants analyzed was 66.82±5.42(60-92y)and 728(61.2%)of them were female.Patients with MCI had a significantly more receded NPC compared to subjects with normal cognitive status(10.89±3.58 vs 7.76±2.71 cm,P<0.001).In the multivariable logistic regression model and in the presence of confounding variables,a receded NPC was statistically significantly associated with an increased risk of MCI(odds ratio:1.334,95%confidence interval:1.263 to 1.410,P<0.001).According to receiver operating characteristic(ROC)analysis,a cut point NPC>8.5 cm(area under the curve:0.764,P<0.001)could predict the presence of MCI with a sensitivity and specificity of 70.9%and 69.5%,respectively.CONCLUSION:A receded NPC can be clinically proposed as a predictor of MCI in older adults.It is recommended that elderly with a receded NPC>8.50 cm undergo detailed cognitive screening for a definite diagnosis of MCI.In this case,the necessary interventions can be carried out to slow down MCI progression to dementia. 展开更多
关键词 near point of convergence mild cognitive impairment GERIATRICS population-based study
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Pearl S. Buck’s Values of “Cultural Convergence” and Their Application
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作者 WANG Yan ZHU Ze-yuan SHI Hui-ge 《Cultural and Religious Studies》 2023年第1期9-18,共10页
The typical features of internal and external integration of cultures as revealed by the conception of“cultural convergence”provide a new perspective on the study of cultural exchanges and mutual learning.In the con... The typical features of internal and external integration of cultures as revealed by the conception of“cultural convergence”provide a new perspective on the study of cultural exchanges and mutual learning.In the context of“a global community of shared future for humankind”,this paper adopts the novel idea of“cultural convergence”to probe the growth of Pearl S.Buck’s cultural values and the specific contents and representation of Pearl S.Buck’s conception of“cultural convergence”,highlighting the application of Pearl S.Buck’s values to cultural education,growth and success,family education,cultural exchanges,humanistic practices,etc.Feasible suggestions and countermeasures are put forward to better promote the cultural exchanges and mutual learning as well as the convergence of different cultures. 展开更多
关键词 Pearl S.Buck values of“cultural convergence applied research
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Modification of the Convergence of GG-PPA for Solving Generalized Equations
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作者 Asraful Alom Zaidur Rahman +1 位作者 Bayezid Gazi Imran Hossain 《Journal of Applied Mathematics and Physics》 2023年第1期260-275,共16页
A modified Gauss-type Proximal Point Algorithm (modified GG-PPA) is presented in this paper for solving the generalized equations like 0 &#8712;T(x), where T is a set-valued mapping acts between two different Bana... A modified Gauss-type Proximal Point Algorithm (modified GG-PPA) is presented in this paper for solving the generalized equations like 0 &#8712;T(x), where T is a set-valued mapping acts between two different Banach spaces X and Y. By considering some necessary assumptions, we show the existence of any sequence generated by the modified GG-PPA and prove the semi-local and local convergence results by using metrically regular mapping. In addition, we give a numerical example to justify the result of semi-local convergence. 展开更多
关键词 Set-Valued Mappings Metrically Regular Mappings Semi-Local convergence Lipschitz Continuous Fixed Point Lemma
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About Upper and Lower Strong Fractional Weighted Mean Convergence by Moduli for Triple Sequences
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作者 Amelia Bucur 《Journal of Applied Mathematics and Physics》 2023年第5期1304-1318,共15页
In article, I present a study on upper and lower statistical convergence, and upper and lower strong fractional weighted mean convergence by moduli for triple sequences. One of the generalizations of the discrete oper... In article, I present a study on upper and lower statistical convergence, and upper and lower strong fractional weighted mean convergence by moduli for triple sequences. One of the generalizations of the discrete operator Cesàro, was weighted mean operators, which are linear operators, too. Given a modulus function f, I established that a triple sequence that is f-upper or lower strong fractional weighted mean convergent, in some supplementary conditions, is also f-lower or upper statistically convergent. The results of this paper adapt the results obtained in [1] and [2] to upper and lower strong fractional weighted mean convergence and to triple sequence concept. Furthermore, new concepts can be applied to the approximation theory, topology, Fourier analysis, analysis interdisciplinary with applications electrical engineering, robotics and other domains. 展开更多
关键词 Upper and Lower Statistical convergence Triple Sequences Unbounded Modulus Function Numerical Analysis
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