We study embeddings of spaces of Besov-Morrey type, MB p1^s1 q1^r1（R^d）→MB p2^s2 q2^r2（R^d） and obtain necessary and sufficient conditions for this. Moreover, we can also charaeterise the special weighted situat...We study embeddings of spaces of Besov-Morrey type, MB p1^s1 q1^r1（R^d）→MB p2^s2 q2^r2（R^d） and obtain necessary and sufficient conditions for this. Moreover, we can also charaeterise the special weighted situation Bp1^s1 （R^d ,w）→MB p2^s2 q2^r2（R^d） for a Muekenhoupt A∞ weight w, with wα（x） = ｜x｜^a, 〉 -d, as a typical example.展开更多
Purpose-Hate speech is an expression of intense hatred.Twitter has become a popular analytical tool for the prediction and monitoring of abusive behaviors.Hate speech detection with social media data has witnessed spe...Purpose-Hate speech is an expression of intense hatred.Twitter has become a popular analytical tool for the prediction and monitoring of abusive behaviors.Hate speech detection with social media data has witnessed special research attention in recent studies,hence,the need to design a generic metadata architecture and efficient feature extraction technique to enhance hate speech detection.Design/methodology/approach-This study proposes a hybrid embeddings enhanced with a topic inference method and an improved cuckoo search neural network for hate speech detection in Twitter data.The proposed method uses a hybrid embeddings technique that includes Term Frequency-Inverse Document Frequency(TF-IDF)for word-level feature extraction and Long Short Term Memory(LSTM)which is a variant of recurrent neural networks architecture for sentence-level feature extraction.The extracted features from the hybrid embeddings then serve as input into the improved cuckoo search neural network for the prediction of a tweet as hate speech,offensive language or neither.Findings-The proposed method showed better results when tested on the collected Twitter datasets compared to other related methods.In order to validate the performances of the proposed method,t-test and post hoc multiple comparisons were used to compare the significance and means of the proposed method with other related methods for hate speech detection.Furthermore,Paired Sample t-Test was also conducted to validate the performances of the proposed method with other related methods.Research limitations/implications-Finally,the evaluation results showed that the proposed method outperforms other related methods with mean F1-score of 91.3.Originality/value-The main novelty of this study is the use of an automatic topic spotting measure based on na€ıve Bayes model to improve features representation.展开更多
Knowledge graphs are employed in several tasks,such as question answering and recommendation systems,due to their ability to represent relationships between concepts.Automatically constructing such a graphs,however,re...Knowledge graphs are employed in several tasks,such as question answering and recommendation systems,due to their ability to represent relationships between concepts.Automatically constructing such a graphs,however,remains an unresolved challenge within knowledge representation.To tackle this challenge,we propose CtxKG,a method specifically aimed at extracting knowledge graphs in a context of limited resources in which the only input is a set of unstructured text documents.CtxKG is based on OpenIE(a relationship triple extraction method)and BERT(a language model)and contains four stages:the extraction of relationship triples directly from text;the identification of synonyms across triples;the merging of similar entities;and the building of bridges between knowledge graphs of different documents.Our method distinguishes itself from those in the current literature(i)through its use of the parse tree to avoid the overlapping entities produced by base implementations of OpenIE;and(ii)through its bridges,which create a connected network of graphs,overcoming a limitation similar methods have of one isolated graph per document.We compare our method to two others by generating graphs for movie articles from Wikipedia and contrasting them with benchmark graphs built from the OMDb movie database.Our results suggest that our method is able to improve multiple aspects of knowledge graph construction.They also highlight the critical role that triple identification and named-entity recognition have in improving the quality of automatically generated graphs,suggesting future paths for investigation.Finally,we apply CtxKG to build BlabKG,a knowledge graph for the Blue Amazon,and discuss possible improvements.展开更多
One of the critical hurdles, and breakthroughs, in the field of Natural Language Processing (NLP) in the last two decades has been the development of techniques for text representation that solves the so-called curse ...One of the critical hurdles, and breakthroughs, in the field of Natural Language Processing (NLP) in the last two decades has been the development of techniques for text representation that solves the so-called curse of dimensionality, a problem which plagues NLP in general given that the feature set for learning starts as a function of the size of the language in question, upwards of hundreds of thousands of terms typically. As such, much of the research and development in NLP in the last two decades has been in finding and optimizing solutions to this problem, to feature selection in NLP effectively. This paper looks at the development of these various techniques, leveraging a variety of statistical methods which rest on linguistic theories that were advanced in the middle of the last century, namely the distributional hypothesis which suggests that words that are found in similar contexts generally have similar meanings. In this survey paper we look at the development of some of the most popular of these techniques from a mathematical as well as data structure perspective, from Latent Semantic Analysis to Vector Space Models to their more modern variants which are typically referred to as word embeddings. In this review of algoriths such as Word2Vec, GloVe, ELMo and BERT, we explore the idea of semantic spaces more generally beyond applicability to NLP.展开更多
A Liouville type result is established for non-negative entire solutions of a weighted elliptic equation.This provides a positive answer to a problem left open by Du and Guo(2015) and Phan and Souplet(2012)(see(CJ) by...A Liouville type result is established for non-negative entire solutions of a weighted elliptic equation.This provides a positive answer to a problem left open by Du and Guo(2015) and Phan and Souplet(2012)(see(CJ) by Du and Guo(2015) and Conjecture B by Phan and Souplet(2012)). Meanwhile, some regularity results are also obtained. The main results in this paper imply that the number ps is the critical value of the Dirichlet problems of the related equation, even though there are still some open problems left. Our results also apply for the equation with a Hardy potential.展开更多
Efficient airport airside ground movement(AAGM)is key to successful operations of urban air mobility.Recent studies have introduced the use of multi-objective multigraphs(MOMGs)as the conceptual prototype to formulate...Efficient airport airside ground movement(AAGM)is key to successful operations of urban air mobility.Recent studies have introduced the use of multi-objective multigraphs(MOMGs)as the conceptual prototype to formulate AAGM.Swift calculation of the shortest path costs is crucial for the algorithmic heuristic search on MOMGs,however,previous work chiefly focused on single-objective simple graphs(SOSGs),treated cost enquires as search problems,and failed to keep a low level of computational time and storage complexity.This paper concentrates on the conceptual prototype MOMG,and investigates its node feature extraction,which lays the foundation for efficient prediction of shortest path costs.Two extraction methods are implemented and compared:a statistics-based method that summarises 22 node physical patterns from graph theory principles,and a learning-based method that employs node embedding technique to encode graph structures into a discriminative vector space.The former method can effectively evaluate the node physical patterns and reveals their individual importance for distance prediction,while the latter provides novel practices on processing multigraphs for node embedding algorithms that can merely handle SOSGs.Three regression models are applied to predict the shortest path costs to demonstrate the performance of each.Our experiments on randomly generated benchmark MOMGs show that(i)the statistics-based method underperforms on characterising small distance values due to severe overestimation;(ii)A subset of essential physical patterns can achieve comparable or slightly better prediction accuracy than that based on a complete set of patterns;and(iii)the learning-based method consistently outperforms the statistics-based method,while maintaining a competitive level of computational complexity.展开更多
Machine learning-assisted prediction of polymer properties prior to synthesis has the potential to significantly accelerate the discovery and development of new polymer materials.To date,several approaches have been i...Machine learning-assisted prediction of polymer properties prior to synthesis has the potential to significantly accelerate the discovery and development of new polymer materials.To date,several approaches have been implemented to represent the chemical structure in machine learning models,among which Mol2Vec embeddings have attracted considerable attention in the cheminformatics community since their introduction in 2018.However,for small datasets,the use of chemical structure representations typically increases the dimensionality of the input dataset,resulting in a decrease in model performance.Furthermore,the limited diversity of polymer chemical structures hinders the training of reliable embeddings,necessitating complex task-specific architecture implementations.To address these challenges,we examined the efficacy of Mol2Vec pre-trained embeddings in deriving vectorized representations of polymers.This study assesses the impact of incorporating Mol2Vec compound vectors into the input features on the efficacy of a model reliant on the physical properties of 214 polymers.The results will hopefully highlight the potential for improving prediction accuracy in polymer studies by incorporating pre-trained embeddings or promote their utilization when dealing with modestly sized polymer databases.展开更多
We establish an explicit embedding of a quantum affine sl_(n) into a quantum affine sl_(n)+1.This embedding serves as a common generalization of two natural,but seemingly unrelated,embed-dings,one on the quantum affin...We establish an explicit embedding of a quantum affine sl_(n) into a quantum affine sl_(n)+1.This embedding serves as a common generalization of two natural,but seemingly unrelated,embed-dings,one on the quantum affine Schur algebra level and the other on the non-quantum level.The embedding on the quantum affine Schur algebras is used extensively in the analysis of canonical bases of quantum affine sln and gl_(n).The embedding on the non-quantum level is used crucially in a work of Riche and Williamson on the study of modular representation theory of general linear groups over a finite field.The same embedding is also used in a work of Maksimau on the categorical representations of affine general linear algebras.We further provide a more natural compatibility statement of the em-bedding on the idempotent version with that on the quantum affine Schur algebra level.A gl_(n)-variant of the embedding is also established.展开更多
New Sobolev type embeddings for some weighted Banach spaces are established. Using such embeddings and the singular positive radial entire solutions, we construct singular positive weak solutions with a prescribed sin...New Sobolev type embeddings for some weighted Banach spaces are established. Using such embeddings and the singular positive radial entire solutions, we construct singular positive weak solutions with a prescribed singular set for a weighted elliptic equation. Our main results in this paper also provide positive weak solutions with a prescribed singular set to an equation with Hardy potential.展开更多
In this paper, we completely solve the embedding problem of simple directed triple systems by proving that the necessary conditions for the embeddings of directed triple systems are also sufficient.
Most of results of Bestvina and Mogilski [Characterizing certain incomplete infinite-di- mensional absolute retracts. Michigan Math. J., 33, 291-313 （1986）] on strong Z-sets in ANR＇s and absorbing sets is generaliz...Most of results of Bestvina and Mogilski [Characterizing certain incomplete infinite-di- mensional absolute retracts. Michigan Math. J., 33, 291-313 （1986）] on strong Z-sets in ANR＇s and absorbing sets is generalized to nonseparable case. It is shown that if an ANR X is locally homotopy dense embeddable in infinite-dimensional Hilbert manifolds and w（U） ---- w（X） （where ＂w＂is the topological weight） for each open nonempty subset U of X, then X itself i,~ homotopy dense embeddable in a Hilbert manifold. It is also demonstrated that whenever X is an AR, its weak product W（X, ＊） ---- {（xn）=l C X ： x~ = ＊ for almost all n} is homeomorphic to a pre-Hilbert space E with E EE. An intrinsic characterization of manifolds modelled on such pre-Hilbert spaces is given.展开更多
Using the relation between the set of embeddings of tori into Euclideanspaces modulo ambient isotopies and the homotopy groups of Stiefel manifolds, we prove new resultson embeddings of tori into Euclidean spaces.
The measure of non-compactness is estimated from below for various operators, including the Hardy-Littlewood maximal operator, the fractional maximal operator and the Hilbert transform, all acting between weighted Leb...The measure of non-compactness is estimated from below for various operators, including the Hardy-Littlewood maximal operator, the fractional maximal operator and the Hilbert transform, all acting between weighted Lebesgue spaces. The identity operator acting between weighted Lebesgue spaces and also between the counterparts of these spaces with variable exponents is similarly analysed. These results enable the lack of compactness of such operators to be quantified.展开更多
The weighted Poincare inequalities in weighted Sobolev spaces are discussed, and the necessary and sufficient conditions for them to hold are given. That is, the Poincare inequalities hold if, and only if, the ball me...The weighted Poincare inequalities in weighted Sobolev spaces are discussed, and the necessary and sufficient conditions for them to hold are given. That is, the Poincare inequalities hold if, and only if, the ball measure of non-compactness of the natural embedding of weighted Sobolev spaces is less than 1.展开更多
Smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 are horospherical varieties. We characterize standard embeddings of smooth Schubert varieties in rational homogeneous manifolds of Picard ...Smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 are horospherical varieties. We characterize standard embeddings of smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 by means of varieties of minimal rational tangents. In particular, we mainly consider nonhomogeneous smooth Schubert varieties in symplectic Grassmannians and in the 20-dimensional F_4- homogeneous manifold associated to a short simple root.展开更多
Purpose:With more and more digital collections of various information resources becoming available,also increasing is the challenge of assigning subject index terms and classes from quality knowledge organization syst...Purpose:With more and more digital collections of various information resources becoming available,also increasing is the challenge of assigning subject index terms and classes from quality knowledge organization systems.While the ultimate purpose is to understand the value of automatically produced Dewey Decimal Classification(DDC)classes for Swedish digital collections,the paper aims to evaluate the performance of six machine learning algorithms as well as a string-matching algorithm based on characteristics of DDC.Design/methodology/approach:State-of-the-art machine learning algorithms require at least 1,000 training examples per class.The complete data set at the time of research involved 143,838 records which had to be reduced to top three hierarchical levels of DDC in order to provide sufficient training data(totaling 802 classes in the training and testing sample,out of 14,413 classes at all levels).Findings:Evaluation shows that Support Vector Machine with linear kernel outperforms other machine learning algorithms as well as the string-matching algorithm on average;the string-matching algorithm outperforms machine learning for specific classes when characteristics of DDC are most suitable for the task.Word embeddings combined with different types of neural networks(simple linear network,standard neural network,1 D convolutional neural network,and recurrent neural network)produced worse results than Support Vector Machine,but reach close results,with the benefit of a smaller representation size.Impact of features in machine learning shows that using keywords or combining titles and keywords gives better results than using only titles as input.Stemming only marginally improves the results.Removed stop-words reduced accuracy in most cases,while removing less frequent words increased it marginally.The greatest impact is produced by the number of training examples:81.90%accuracy on the training set is achieved when at least 1,000 records per class are available in the training set,and 66.13%when too few recor展开更多
Unsupervised text simplification has attracted much attention due to the scarcity of high-quality parallel text simplification corpora. Recent an unsupervised statistical text simplification based on phrase-based mach...Unsupervised text simplification has attracted much attention due to the scarcity of high-quality parallel text simplification corpora. Recent an unsupervised statistical text simplification based on phrase-based machine translation system (UnsupPBMT) achieved good performance, which initializes the phrase tables using the similar words obtained by word embedding modeling. Since word embedding modeling only considers the relevance between words, the phrase table in UnsupPBMT contains a lot of dissimilar words. In this paper, we propose an unsupervised statistical text simplification using pre-trained language modeling BERT for initialization. Specifically, we use BERT as a general linguistic knowledge base for predicting similar words. Experimental results show that our method outperforms the state-of-the-art unsupervised text simplification methods on three benchmarks, even outperforms some supervised baselines.展开更多
New embeddings of some weighted Sobolev spaces with weights a(x)and b(x)are established.The weights a(x)and b(x)can be singular.Some applications of these embeddings to a class of degenerate elliptic problems of the f...New embeddings of some weighted Sobolev spaces with weights a(x)and b(x)are established.The weights a(x)and b(x)can be singular.Some applications of these embeddings to a class of degenerate elliptic problems of the form-div(a(x)?u)=b(x)f(x,u)in?,u=0 on??,where?is a bounded or unbounded domain in RN,N 2,are presented.The main results of this paper also give some generalizations of the well-known Caffarelli-Kohn-Nirenberg inequality.展开更多
文摘We study embeddings of spaces of Besov-Morrey type, MB p1^s1 q1^r1（R^d）→MB p2^s2 q2^r2（R^d） and obtain necessary and sufficient conditions for this. Moreover, we can also charaeterise the special weighted situation Bp1^s1 （R^d ,w）→MB p2^s2 q2^r2（R^d） for a Muekenhoupt A∞ weight w, with wα（x） = ｜x｜^a, 〉 -d, as a typical example.
文摘Purpose-Hate speech is an expression of intense hatred.Twitter has become a popular analytical tool for the prediction and monitoring of abusive behaviors.Hate speech detection with social media data has witnessed special research attention in recent studies,hence,the need to design a generic metadata architecture and efficient feature extraction technique to enhance hate speech detection.Design/methodology/approach-This study proposes a hybrid embeddings enhanced with a topic inference method and an improved cuckoo search neural network for hate speech detection in Twitter data.The proposed method uses a hybrid embeddings technique that includes Term Frequency-Inverse Document Frequency(TF-IDF)for word-level feature extraction and Long Short Term Memory(LSTM)which is a variant of recurrent neural networks architecture for sentence-level feature extraction.The extracted features from the hybrid embeddings then serve as input into the improved cuckoo search neural network for the prediction of a tweet as hate speech,offensive language or neither.Findings-The proposed method showed better results when tested on the collected Twitter datasets compared to other related methods.In order to validate the performances of the proposed method,t-test and post hoc multiple comparisons were used to compare the significance and means of the proposed method with other related methods for hate speech detection.Furthermore,Paired Sample t-Test was also conducted to validate the performances of the proposed method with other related methods.Research limitations/implications-Finally,the evaluation results showed that the proposed method outperforms other related methods with mean F1-score of 91.3.Originality/value-The main novelty of this study is the use of an automatic topic spotting measure based on na€ıve Bayes model to improve features representation.
基金The authors of this work would like to thank the Center for Artificial Intelligence(C4AI-USP)and the support from the São Paulo Research Foundation(FAPESP grant#2019/07665-4)and from the IBM CorporationFabio G.Cozman acknowledges partial support by CNPq grant Pq 305753/2022-3This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior-Brazil(CAPES)-Finance Code 001。
文摘Knowledge graphs are employed in several tasks,such as question answering and recommendation systems,due to their ability to represent relationships between concepts.Automatically constructing such a graphs,however,remains an unresolved challenge within knowledge representation.To tackle this challenge,we propose CtxKG,a method specifically aimed at extracting knowledge graphs in a context of limited resources in which the only input is a set of unstructured text documents.CtxKG is based on OpenIE(a relationship triple extraction method)and BERT(a language model)and contains four stages:the extraction of relationship triples directly from text;the identification of synonyms across triples;the merging of similar entities;and the building of bridges between knowledge graphs of different documents.Our method distinguishes itself from those in the current literature(i)through its use of the parse tree to avoid the overlapping entities produced by base implementations of OpenIE;and(ii)through its bridges,which create a connected network of graphs,overcoming a limitation similar methods have of one isolated graph per document.We compare our method to two others by generating graphs for movie articles from Wikipedia and contrasting them with benchmark graphs built from the OMDb movie database.Our results suggest that our method is able to improve multiple aspects of knowledge graph construction.They also highlight the critical role that triple identification and named-entity recognition have in improving the quality of automatically generated graphs,suggesting future paths for investigation.Finally,we apply CtxKG to build BlabKG,a knowledge graph for the Blue Amazon,and discuss possible improvements.
文摘One of the critical hurdles, and breakthroughs, in the field of Natural Language Processing (NLP) in the last two decades has been the development of techniques for text representation that solves the so-called curse of dimensionality, a problem which plagues NLP in general given that the feature set for learning starts as a function of the size of the language in question, upwards of hundreds of thousands of terms typically. As such, much of the research and development in NLP in the last two decades has been in finding and optimizing solutions to this problem, to feature selection in NLP effectively. This paper looks at the development of these various techniques, leveraging a variety of statistical methods which rest on linguistic theories that were advanced in the middle of the last century, namely the distributional hypothesis which suggests that words that are found in similar contexts generally have similar meanings. In this survey paper we look at the development of some of the most popular of these techniques from a mathematical as well as data structure perspective, from Latent Semantic Analysis to Vector Space Models to their more modern variants which are typically referred to as word embeddings. In this review of algoriths such as Word2Vec, GloVe, ELMo and BERT, we explore the idea of semantic spaces more generally beyond applicability to NLP.
基金supported by National Natural Science Foundation of China (Grant No. 11571093)
文摘A Liouville type result is established for non-negative entire solutions of a weighted elliptic equation.This provides a positive answer to a problem left open by Du and Guo(2015) and Phan and Souplet(2012)(see(CJ) by Du and Guo(2015) and Conjecture B by Phan and Souplet(2012)). Meanwhile, some regularity results are also obtained. The main results in this paper imply that the number ps is the critical value of the Dirichlet problems of the related equation, even though there are still some open problems left. Our results also apply for the equation with a Hardy potential.
基金This work was supported by the UK Engineering and Physical Sciences Research Council(grant no.EP/N029496/1,EP/N029496/2,EP/N029356/1,EP/N029577/1,and EP/N029577/2)the joint scholarship of the China Scholarship Council and Queen Mary,University of London(grant no.202006830015).
文摘Efficient airport airside ground movement(AAGM)is key to successful operations of urban air mobility.Recent studies have introduced the use of multi-objective multigraphs(MOMGs)as the conceptual prototype to formulate AAGM.Swift calculation of the shortest path costs is crucial for the algorithmic heuristic search on MOMGs,however,previous work chiefly focused on single-objective simple graphs(SOSGs),treated cost enquires as search problems,and failed to keep a low level of computational time and storage complexity.This paper concentrates on the conceptual prototype MOMG,and investigates its node feature extraction,which lays the foundation for efficient prediction of shortest path costs.Two extraction methods are implemented and compared:a statistics-based method that summarises 22 node physical patterns from graph theory principles,and a learning-based method that employs node embedding technique to encode graph structures into a discriminative vector space.The former method can effectively evaluate the node physical patterns and reveals their individual importance for distance prediction,while the latter provides novel practices on processing multigraphs for node embedding algorithms that can merely handle SOSGs.Three regression models are applied to predict the shortest path costs to demonstrate the performance of each.Our experiments on randomly generated benchmark MOMGs show that(i)the statistics-based method underperforms on characterising small distance values due to severe overestimation;(ii)A subset of essential physical patterns can achieve comparable or slightly better prediction accuracy than that based on a complete set of patterns;and(iii)the learning-based method consistently outperforms the statistics-based method,while maintaining a competitive level of computational complexity.
基金the framework of the program of state support for the centers of the National Technology Initiative(NTI)on the basis of educational institutions of higher education and scientific organizations(Center NTI"Digital Materials Science:New Materials and Substances"on the basis of the Bauman Moscow State Technical University).
文摘Machine learning-assisted prediction of polymer properties prior to synthesis has the potential to significantly accelerate the discovery and development of new polymer materials.To date,several approaches have been implemented to represent the chemical structure in machine learning models,among which Mol2Vec embeddings have attracted considerable attention in the cheminformatics community since their introduction in 2018.However,for small datasets,the use of chemical structure representations typically increases the dimensionality of the input dataset,resulting in a decrease in model performance.Furthermore,the limited diversity of polymer chemical structures hinders the training of reliable embeddings,necessitating complex task-specific architecture implementations.To address these challenges,we examined the efficacy of Mol2Vec pre-trained embeddings in deriving vectorized representations of polymers.This study assesses the impact of incorporating Mol2Vec compound vectors into the input features on the efficacy of a model reliant on the physical properties of 214 polymers.The results will hopefully highlight the potential for improving prediction accuracy in polymer studies by incorporating pre-trained embeddings or promote their utilization when dealing with modestly sized polymer databases.
基金Partially supported by NSF DMS(Grant No.1801915)。
文摘We establish an explicit embedding of a quantum affine sl_(n) into a quantum affine sl_(n)+1.This embedding serves as a common generalization of two natural,but seemingly unrelated,embed-dings,one on the quantum affine Schur algebra level and the other on the non-quantum level.The embedding on the quantum affine Schur algebras is used extensively in the analysis of canonical bases of quantum affine sln and gl_(n).The embedding on the non-quantum level is used crucially in a work of Riche and Williamson on the study of modular representation theory of general linear groups over a finite field.The same embedding is also used in a work of Maksimau on the categorical representations of affine general linear algebras.We further provide a more natural compatibility statement of the em-bedding on the idempotent version with that on the quantum affine Schur algebra level.A gl_(n)-variant of the embedding is also established.
基金supported by National Natural Science Foundation of China (Grant Nos. 11171092 and 11571093)
文摘New Sobolev type embeddings for some weighted Banach spaces are established. Using such embeddings and the singular positive radial entire solutions, we construct singular positive weak solutions with a prescribed singular set for a weighted elliptic equation. Our main results in this paper also provide positive weak solutions with a prescribed singular set to an equation with Hardy potential.
基金the Science and Technology Foundation of Shanghai Jiao Tong University
文摘In this paper, we completely solve the embedding problem of simple directed triple systems by proving that the necessary conditions for the embeddings of directed triple systems are also sufficient.
文摘Most of results of Bestvina and Mogilski [Characterizing certain incomplete infinite-di- mensional absolute retracts. Michigan Math. J., 33, 291-313 （1986）] on strong Z-sets in ANR＇s and absorbing sets is generalized to nonseparable case. It is shown that if an ANR X is locally homotopy dense embeddable in infinite-dimensional Hilbert manifolds and w（U） ---- w（X） （where ＂w＂is the topological weight） for each open nonempty subset U of X, then X itself i,~ homotopy dense embeddable in a Hilbert manifold. It is also demonstrated that whenever X is an AR, its weak product W（X, ＊） ---- {（xn）=l C X ： x~ = ＊ for almost all n} is homeomorphic to a pre-Hilbert space E with E EE. An intrinsic characterization of manifolds modelled on such pre-Hilbert spaces is given.
基金Both authors are supported in part by the Ministry of Education,Science and Sport of the Republic of Slovenia Research Program No.0101-509Research Grant No.SLO-KIT-04-14-2002
文摘Using the relation between the set of embeddings of tori into Euclideanspaces modulo ambient isotopies and the homotopy groups of Stiefel manifolds, we prove new resultson embeddings of tori into Euclidean spaces.
文摘The measure of non-compactness is estimated from below for various operators, including the Hardy-Littlewood maximal operator, the fractional maximal operator and the Hilbert transform, all acting between weighted Lebesgue spaces. The identity operator acting between weighted Lebesgue spaces and also between the counterparts of these spaces with variable exponents is similarly analysed. These results enable the lack of compactness of such operators to be quantified.
基金Project supported by the National Natural Science Foundation of China(Nos.10261004 and 10461006)the Visiting Scholar Foundation of Key Laboratory of University and the Natural Science Foundation of the Inner Mongolia Autonomous Region of China(No.200408020104)
文摘The weighted Poincare inequalities in weighted Sobolev spaces are discussed, and the necessary and sufficient conditions for them to hold are given. That is, the Poincare inequalities hold if, and only if, the ball measure of non-compactness of the natural embedding of weighted Sobolev spaces is less than 1.
基金supported by the National Researcher Program 2010-0020413 of NRFGA17-19437S of Czech Science Foundation(GACR)+3 种基金partially supported by the Simons-Foundation grant 346300the Polish Government MNi SW 2015-2019 matching fundsupported by BK21 PLUS SNU Mathematical Sciences DivisionIBS-R003-Y1
文摘Smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 are horospherical varieties. We characterize standard embeddings of smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 by means of varieties of minimal rational tangents. In particular, we mainly consider nonhomogeneous smooth Schubert varieties in symplectic Grassmannians and in the 20-dimensional F_4- homogeneous manifold associated to a short simple root.
文摘Purpose:With more and more digital collections of various information resources becoming available,also increasing is the challenge of assigning subject index terms and classes from quality knowledge organization systems.While the ultimate purpose is to understand the value of automatically produced Dewey Decimal Classification(DDC)classes for Swedish digital collections,the paper aims to evaluate the performance of six machine learning algorithms as well as a string-matching algorithm based on characteristics of DDC.Design/methodology/approach:State-of-the-art machine learning algorithms require at least 1,000 training examples per class.The complete data set at the time of research involved 143,838 records which had to be reduced to top three hierarchical levels of DDC in order to provide sufficient training data(totaling 802 classes in the training and testing sample,out of 14,413 classes at all levels).Findings:Evaluation shows that Support Vector Machine with linear kernel outperforms other machine learning algorithms as well as the string-matching algorithm on average;the string-matching algorithm outperforms machine learning for specific classes when characteristics of DDC are most suitable for the task.Word embeddings combined with different types of neural networks(simple linear network,standard neural network,1 D convolutional neural network,and recurrent neural network)produced worse results than Support Vector Machine,but reach close results,with the benefit of a smaller representation size.Impact of features in machine learning shows that using keywords or combining titles and keywords gives better results than using only titles as input.Stemming only marginally improves the results.Removed stop-words reduced accuracy in most cases,while removing less frequent words increased it marginally.The greatest impact is produced by the number of training examples:81.90%accuracy on the training set is achieved when at least 1,000 records per class are available in the training set,and 66.13%when too few recor
基金supported by the National Natural Science Foundation of China(Grant Nos.62076217 and 61906060)and the Program for Changjiang Scholars and Innovative Research Team in University(PCSIRT)of the Ministry of Education,China(IRT17R32).
文摘Unsupervised text simplification has attracted much attention due to the scarcity of high-quality parallel text simplification corpora. Recent an unsupervised statistical text simplification based on phrase-based machine translation system (UnsupPBMT) achieved good performance, which initializes the phrase tables using the similar words obtained by word embedding modeling. Since word embedding modeling only considers the relevance between words, the phrase table in UnsupPBMT contains a lot of dissimilar words. In this paper, we propose an unsupervised statistical text simplification using pre-trained language modeling BERT for initialization. Specifically, we use BERT as a general linguistic knowledge base for predicting similar words. Experimental results show that our method outperforms the state-of-the-art unsupervised text simplification methods on three benchmarks, even outperforms some supervised baselines.
基金supported by National Natural Science Foundation of China (Grant Nos. 11171092, 11571093 and 11371117)
文摘New embeddings of some weighted Sobolev spaces with weights a(x)and b(x)are established.The weights a(x)and b(x)can be singular.Some applications of these embeddings to a class of degenerate elliptic problems of the form-div(a(x)?u)=b(x)f(x,u)in?,u=0 on??,where?is a bounded or unbounded domain in RN,N 2,are presented.The main results of this paper also give some generalizations of the well-known Caffarelli-Kohn-Nirenberg inequality.
