A novel framework is proposed to obtain physiologically meaningful features for Alzheimer's disease(AD)classification based on sparse functional connectivity and non-negative matrix factorization.Specifically,the ...A novel framework is proposed to obtain physiologically meaningful features for Alzheimer's disease(AD)classification based on sparse functional connectivity and non-negative matrix factorization.Specifically,the non-negative adaptive sparse representation(NASR)method is applied to compute the sparse functional connectivity among brain regions based on functional magnetic resonance imaging(fMRI)data for feature extraction.Afterwards,the sparse non-negative matrix factorization(sNMF)method is adopted for dimensionality reduction to obtain low-dimensional features with straightforward physical meaning.The experimental results show that the proposed framework outperforms the competing frameworks in terms of classification accuracy,sensitivity and specificity.Furthermore,three sub-networks,including the default mode network,the basal ganglia-thalamus-limbic network and the temporal-insular network,are found to have notable differences between the AD patients and the healthy subjects.The proposed framework can effectively identify AD patients and has potentials for extending the understanding of the pathological changes of AD.展开更多
Let（Ω , E, P） be a probability space, F a sub-σ-algebra of E, L^p（E）（1 p ＋∞） the classical function space and LF^p（E） the L^0（F）-module generated by L^p（E）, which can be made into a random normed modul...Let（Ω , E, P） be a probability space, F a sub-σ-algebra of E, L^p（E）（1 p ＋∞） the classical function space and LF^p（E） the L^0（F）-module generated by L^p（E）, which can be made into a random normed module in a natural way. Up to the present time, there are three kinds of conditional risk measures, whose model spaces are L^∞（E）, L^p（E）（1 p ＋∞） and LF^p（E）（1 p ＋∞） respectively, and a conditional convex dual representation theorem has been established for each kind. The purpose of this paper is to study the relations among the three kinds of conditional risk measures together with their representation theorems. We first establish the relation between L^p（E） and LF^p（E）, namely LF^p（E） = Hcc（L^p（E））, which shows that LF^p（E）is exactly the countable concatenation hull of L^p（E）. Based on the precise relation, we then prove that every L^0（F）-convex L^p（E）-conditional risk measure（1 p ＋∞） can be uniquely extended to an L^0（F）-convex LF^p（E）-conditional risk measure and that the dual representation theorem of the former can also be regarded as a special case of that of the latter, which shows that the study of L^p-conditional risk measures can be incorporated into that of LF^p（E）-conditional risk measures. In particular, in the process we find that combining the countable concatenation hull of a set and the local property of conditional risk measures is a very useful analytic skill that may considerably simplify and improve the study of L^0-convex conditional risk measures.展开更多
Functionality represents a blueprint of a product and plays a crucial role in problem-solving such as design.This article discusses the model representation from the angle of functional ontology by function deployment...Functionality represents a blueprint of a product and plays a crucial role in problem-solving such as design.This article discusses the model representation from the angle of functional ontology by function deployment.We construct a framework of functional ontology which decomposes the function and contains a library of vocabulary to comprehensively represent the conceptual design model.The ontology enables the automatic identification system to search in the functional space.Furthermore,the functional ontology can form a systematic representation for the model so that it can be reused in the conceptual design and can be applied in the domain of knowledge fusion in our further work.展开更多
In this expository paper,we describe the study of certain non-self-adjoint operator algebras,the Hardy algebras,and their representation theory.We view these algebras as algebras of (operator valued) functions on thei...In this expository paper,we describe the study of certain non-self-adjoint operator algebras,the Hardy algebras,and their representation theory.We view these algebras as algebras of (operator valued) functions on their spaces of representations.We will show that these spaces of representations can be parameterized as unit balls of certain W*-correspondences and the functions can be viewed as Schur class operator functions on these balls.We will provide evidence to show that the elements in these (non commutative) Hardy algebras behave very much like bounded analytic functions and the study of these algebras should be viewed as noncommutative function theory.展开更多
The present work is much motivated by finding an explicit way in the construction of the Jack symmetric function,which is the spectrum generating function for the Calogero-Sutherland (CS) model.To accomplish this work...The present work is much motivated by finding an explicit way in the construction of the Jack symmetric function,which is the spectrum generating function for the Calogero-Sutherland (CS) model.To accomplish this work,the hidden Virasoro structure in the CS model is much explored.In particular,we found that the Virasoro singular vectors form a skew hierarchy in the CS model.Literally,skew is analogous to coset,but here specifically refer to the operation on the Young tableaux.In fact,based on the construction of the Virasoro singular vectors,this hierarchical structure can be used to give a complete construction of the CS states,i.e.the Jack symmetric functions,recursively.The construction is given both in operator formalism as well as in integral representation.This new integral representation for the Jack symmetric functions may shed some insights on the spectrum constructions for the other integrable systems.展开更多
基金The Foundation of Hygiene and Health of Jiangsu Province(No.H2018042)the National Natural Science Foundation of China(No.61773114)the Key Research and Development Plan(Industry Foresight and Common Key Technology)of Jiangsu Province(No.BE2017007-3)
文摘A novel framework is proposed to obtain physiologically meaningful features for Alzheimer's disease(AD)classification based on sparse functional connectivity and non-negative matrix factorization.Specifically,the non-negative adaptive sparse representation(NASR)method is applied to compute the sparse functional connectivity among brain regions based on functional magnetic resonance imaging(fMRI)data for feature extraction.Afterwards,the sparse non-negative matrix factorization(sNMF)method is adopted for dimensionality reduction to obtain low-dimensional features with straightforward physical meaning.The experimental results show that the proposed framework outperforms the competing frameworks in terms of classification accuracy,sensitivity and specificity.Furthermore,three sub-networks,including the default mode network,the basal ganglia-thalamus-limbic network and the temporal-insular network,are found to have notable differences between the AD patients and the healthy subjects.The proposed framework can effectively identify AD patients and has potentials for extending the understanding of the pathological changes of AD.
基金supported by National Natural Science Foundation of China(Grant Nos.11171015 and 11301568)
文摘Let（Ω , E, P） be a probability space, F a sub-σ-algebra of E, L^p（E）（1 p ＋∞） the classical function space and LF^p（E） the L^0（F）-module generated by L^p（E）, which can be made into a random normed module in a natural way. Up to the present time, there are three kinds of conditional risk measures, whose model spaces are L^∞（E）, L^p（E）（1 p ＋∞） and LF^p（E）（1 p ＋∞） respectively, and a conditional convex dual representation theorem has been established for each kind. The purpose of this paper is to study the relations among the three kinds of conditional risk measures together with their representation theorems. We first establish the relation between L^p（E） and LF^p（E）, namely LF^p（E） = Hcc（L^p（E））, which shows that LF^p（E）is exactly the countable concatenation hull of L^p（E）. Based on the precise relation, we then prove that every L^0（F）-convex L^p（E）-conditional risk measure（1 p ＋∞） can be uniquely extended to an L^0（F）-convex LF^p（E）-conditional risk measure and that the dual representation theorem of the former can also be regarded as a special case of that of the latter, which shows that the study of L^p-conditional risk measures can be incorporated into that of LF^p（E）-conditional risk measures. In particular, in the process we find that combining the countable concatenation hull of a set and the local property of conditional risk measures is a very useful analytic skill that may considerably simplify and improve the study of L^0-convex conditional risk measures.
基金the National Natural Science Foundation of China (Nos.50575142,50775140 and 60304015)the National High Technology Research and Development Program (863) of China (No.2008AA04Z113)+2 种基金the National Basic Research Program (973) of China (No.2006CB705400)the Shanghai Committee of Science and Technology (Nos.08JC1412000,09DZ1121400 and 07XD14016)the Research Fund for the Doctoral Program of Higher Education (No.200802480036)
文摘Functionality represents a blueprint of a product and plays a crucial role in problem-solving such as design.This article discusses the model representation from the angle of functional ontology by function deployment.We construct a framework of functional ontology which decomposes the function and contains a library of vocabulary to comprehensively represent the conceptual design model.The ontology enables the automatic identification system to search in the functional space.Furthermore,the functional ontology can form a systematic representation for the model so that it can be reused in the conceptual design and can be applied in the domain of knowledge fusion in our further work.
基金supported by a grant from the U.S.-Israel Binational Science Foundation (Grant No. 200641)supported by the Technion V.P.R. Fund
文摘In this expository paper,we describe the study of certain non-self-adjoint operator algebras,the Hardy algebras,and their representation theory.We view these algebras as algebras of (operator valued) functions on their spaces of representations.We will show that these spaces of representations can be parameterized as unit balls of certain W*-correspondences and the functions can be viewed as Schur class operator functions on these balls.We will provide evidence to show that the elements in these (non commutative) Hardy algebras behave very much like bounded analytic functions and the study of these algebras should be viewed as noncommutative function theory.
基金Supported by the Chinese Academy of Sciences Program "Frontier Topics in Mathematical Physics" (KJCX3-SYW-S03)Supported Partially by the National Natural Science Foundation of China under Grant No.11035008
文摘The present work is much motivated by finding an explicit way in the construction of the Jack symmetric function,which is the spectrum generating function for the Calogero-Sutherland (CS) model.To accomplish this work,the hidden Virasoro structure in the CS model is much explored.In particular,we found that the Virasoro singular vectors form a skew hierarchy in the CS model.Literally,skew is analogous to coset,but here specifically refer to the operation on the Young tableaux.In fact,based on the construction of the Virasoro singular vectors,this hierarchical structure can be used to give a complete construction of the CS states,i.e.the Jack symmetric functions,recursively.The construction is given both in operator formalism as well as in integral representation.This new integral representation for the Jack symmetric functions may shed some insights on the spectrum constructions for the other integrable systems.
