Privacy protection in publishing set-valued data is an important problem. However, privacy notions proposed in prior works either assume that the adversary has unbounded knowledge and hence provide over-protection tha...Privacy protection in publishing set-valued data is an important problem. However, privacy notions proposed in prior works either assume that the adversary has unbounded knowledge and hence provide over-protection that causes excessive distortion, or ignore the knowledge about the absence of certain items and do not prevent attacks based on such knowledge. To address these issues, we propose a new privacy notion, （k,e）^（m,n）-privacy, which prevents both the identity disclosure and the sensitive item disclosure to a realistic privacy adversary who has bounded knowledge about the presence of items and the bounded knowledge about the absence of items. In addition to the new notion, our contribution is an efficient algorithm that finds a near-optimal solution and is applicable for anonymizing real world databases. Extensive experiments on real world databases showed that our algorithm outperforms the state of the art algorithms.展开更多
The rapid growth of biomedical data,particularly multi-omics data including genomes,transcriptomics,proteomics,metabolomics,and epigenomics,medical research and clinical decision-making confront both new opportunities...The rapid growth of biomedical data,particularly multi-omics data including genomes,transcriptomics,proteomics,metabolomics,and epigenomics,medical research and clinical decision-making confront both new opportunities and obstacles.The huge and diversified nature of these datasets cannot always be managed using traditional data analysis methods.As a consequence,deep learning has emerged as a strong tool for analysing numerous omics data due to its ability to handle complex and non-linear relationships.This paper explores the fundamental concepts of deep learning and how they are used in multi-omics medical data mining.We demonstrate how autoencoders,variational autoencoders,multimodal models,attention mechanisms,transformers,and graph neural networks enable pattern analysis and recognition across all omics data.Deep learning has been found to be effective in illness classification,biomarker identification,gene network learning,and therapeutic efficacy prediction.We also consider critical problems like as data quality,model explainability,whether findings can be repeated,and computational power requirements.We now consider future elements of combining omics with clinical and imaging data,explainable AI,federated learning,and real-time diagnostics.Overall,this study emphasises the need of collaborating across disciplines to advance deep learning-based multi-omics research for precision medicine and comprehending complicated disorders.展开更多
High-throughput transcriptomics has evolved from bulk RNA-seq to single-cell and spatial profiling,yet its clinical translation still depends on effective integration across diverse omics and data modalities.Emerging ...High-throughput transcriptomics has evolved from bulk RNA-seq to single-cell and spatial profiling,yet its clinical translation still depends on effective integration across diverse omics and data modalities.Emerging foundation models and multimodal learning frameworks are enabling scalable and transferable representations of cellular states,while advances in interpretability and real-world data integration are bridging the gap between discovery and clinical application.This paper outlines a concise roadmap for AI-driven,transcriptome-centered multi-omics integration in precision medicine(Figure 1).展开更多
Gastrointestinal tumors require personalized treatment strategies due to their heterogeneity and complexity.Multimodal artificial intelligence(AI)addresses this challenge by integrating diverse data sources-including ...Gastrointestinal tumors require personalized treatment strategies due to their heterogeneity and complexity.Multimodal artificial intelligence(AI)addresses this challenge by integrating diverse data sources-including computed tomography(CT),magnetic resonance imaging(MRI),endoscopic imaging,and genomic profiles-to enable intelligent decision-making for individualized therapy.This approach leverages AI algorithms to fuse imaging,endoscopic,and omics data,facilitating comprehensive characterization of tumor biology,prediction of treatment response,and optimization of therapeutic strategies.By combining CT and MRI for structural assessment,endoscopic data for real-time visual inspection,and genomic information for molecular profiling,multimodal AI enhances the accuracy of patient stratification and treatment personalization.The clinical implementation of this technology demonstrates potential for improving patient outcomes,advancing precision oncology,and supporting individualized care in gastrointestinal cancers.Ultimately,multimodal AI serves as a transformative tool in oncology,bridging data integration with clinical application to effectively tailor therapies.展开更多
By using cone-directed contingent derivatives, the unified necessary and sufficient optimality conditions are given for weakly and strongly minimal elements respectively in generalized preinvex set-valued optimization.
The concepts of alpha-order Clarke's derivative, alpha-order Adjacent derivative and alpha-order G.Bouligand derivative of set-valued mappings are introduced, their properties are studied, with which the Fritz Joh...The concepts of alpha-order Clarke's derivative, alpha-order Adjacent derivative and alpha-order G.Bouligand derivative of set-valued mappings are introduced, their properties are studied, with which the Fritz John optimality condition of set-valued vector optimization is established. Finally, under the assumption of pseudoconvexity, the optimality condition is proved to be sufficient.展开更多
In complete metric spaces, the common fixed point theorems for sequences of φ-type contraction set-valued mappings are established, and the corresponding random com- mon fixed point theorems for set-valued mappings a...In complete metric spaces, the common fixed point theorems for sequences of φ-type contraction set-valued mappings are established, and the corresponding random com- mon fixed point theorems for set-valued mappings are also obtained.展开更多
The set-valued optimization problem with constraints is considered in the sense of super efficiency in locally convex linear topological spaces. Under the assumption of iccone-convexlikeness, by applying the seperatio...The set-valued optimization problem with constraints is considered in the sense of super efficiency in locally convex linear topological spaces. Under the assumption of iccone-convexlikeness, by applying the seperation theorem, Kuhn-Tucker＇s, Lagrange＇s and saddle points optimality conditions, the necessary conditions are obtained for the set-valued optimization problem to attain its super efficient solutions. Also, the sufficient conditions for Kuhn-Tucker＇s, Lagrange＇s and saddle points optimality conditions are derived.展开更多
A kind of tangent derivative and the concepts of strong and weak * pseudoconvexity for a set-valued map are introduced. By the standard separation theorems of the convex sets and cones the optimality Fritz John condit...A kind of tangent derivative and the concepts of strong and weak * pseudoconvexity for a set-valued map are introduced. By the standard separation theorems of the convex sets and cones the optimality Fritz John condition of set-valued optimization under Benson proper efficiency is established, its sufficience is discussed. The form of the optimality conditions obtained here completely tally with the classical results when the set-valued map is specialized to be a single-valued map.展开更多
The optimality Kuhn-Tucker condition and the wolfe duality for the preinvex set-valued optimization are investigated. Firstly, the concepts of alpha-order G-invex set and the alpha-order S-preinvex set-valued function...The optimality Kuhn-Tucker condition and the wolfe duality for the preinvex set-valued optimization are investigated. Firstly, the concepts of alpha-order G-invex set and the alpha-order S-preinvex set-valued function were introduced, from which the properties of the corresponding contingent cone and the alpha-order contingent derivative were studied. Finally, the optimality Kuhn-Tucker condition and the Wolfe duality theorem for the alpha-order S-preinvex set-valued optimization were presented with the help of the alpha-order contingent derivative.展开更多
Several equivalent statements of generalized subconvexlike set-valued map are established in ordered linear spaces. Using vector closure, we introduce Benson proper efficient solution of vector optimization problem. U...Several equivalent statements of generalized subconvexlike set-valued map are established in ordered linear spaces. Using vector closure, we introduce Benson proper efficient solution of vector optimization problem. Under the assumption of generalized subconvexlikeness, scalarization, multiplier and saddle point theorems are obtained in the sense of Benson proper efficiency.展开更多
In this paper, we introduce a concept of quasi C-lower semicontinuity for setvalued mapping and provide a vector version of Ekeland＇s theorem related to set-valued vector equilibrium problems. As applications, we der...In this paper, we introduce a concept of quasi C-lower semicontinuity for setvalued mapping and provide a vector version of Ekeland＇s theorem related to set-valued vector equilibrium problems. As applications, we derive an existence theorem of weakly efficient solution for set-valued vector equilibrium problems without the assumption of convexity of the constraint set and the assumptions of convexity and monotonicity of the set-valued mapping. We also obtain an existence theorem of ε-approximate solution for set-valued vector equilibrium problems without the assumptions of compactness and convexity of the constraint set.展开更多
1 Introduction A discrete dynamical system can be expressed as xn+1 ?f(xn), n = 0,1,2,... where X is a metric space and f : X →X is a continuous map. The study of it tells us how the points in the base space X moved....1 Introduction A discrete dynamical system can be expressed as xn+1 ?f(xn), n = 0,1,2,... where X is a metric space and f : X →X is a continuous map. The study of it tells us how the points in the base space X moved. Nevertheless, this is not enough for the researches of biological species, demography, numerical simulation and attractors (see [1], [2]). It is necessary to know how the subsets of X moved. In this direction, we consider the set-valued discrete system associated to f, An+1 = (f|-)(An), n = 0,1,2,... where (f|-) is the natural extension of f to K(X) (the class of all compact subsets of X).展开更多
An auxiliary principle technique to study a class of generalized set-valued strongly nonlinear mixed variational-like inequalities is extended. The existence and uniqueness of the solution of the auxiliary problem for...An auxiliary principle technique to study a class of generalized set-valued strongly nonlinear mixed variational-like inequalities is extended. The existence and uniqueness of the solution of the auxiliary problem for the generalized set-valued strongly nonlinear mixed variational-like inequalities are proved, a novel and innovative three-step iterative algorithm to compute approximate solution is constructed, and the existence of the solution of the generalized set-valued strongly nonlinear mixed variational-like inequality is shown using the auxiliary principle iterative sequences generated by the algorithm technique. The convergence of three-step is also proved.展开更多
In this paper,the ε-super effcient solution for set-valued map vector optimization in locally convex space is introduced.And under the assumption of the nearly generalized cone-subconvexlikeness for set-valued maps,u...In this paper,the ε-super effcient solution for set-valued map vector optimization in locally convex space is introduced.And under the assumption of the nearly generalized cone-subconvexlikeness for set-valued maps,used new methods,the scalarization theorem and Lagrange multiplier theorem for ε-super effcient solution are established.展开更多
The definitions of cone-subconvexlike set-valued maps and generalized cone-subconvexlike set-valued maps in topological vector spaces are defined by using the relative interiors of ordering cone. The relationships bet...The definitions of cone-subconvexlike set-valued maps and generalized cone-subconvexlike set-valued maps in topological vector spaces are defined by using the relative interiors of ordering cone. The relationships between the two classes of set-valued maps are investigated, and some properties of them are shown. A Gordan type alternative theorem under the assumption of generalized cone-subconvexlikeness of set-valued maps is proved by applying convex separation theorems involving the relative interiors in infinite dimensional spaces. Finally a necessary optimality condition theorem is shown for a general kind of set-valued vector optimization in a sense of weak E-minimizer.展开更多
Structural characteristics and absolute continuities of monotone set-valued function defined by set- valued Choquet integral are discussed. Similar to the single-valued monotone set function, several important structu...Structural characteristics and absolute continuities of monotone set-valued function defined by set- valued Choquet integral are discussed. Similar to the single-valued monotone set function, several important structural characteristics of set-valued function are defined and have been proven the same as those in the original set functions, such as null-additivity, weakly null-additivity, order continuity, strong order continuity and property（S）. A counterexample shows that order continuity and strong order continuity of the original set functions are no longer kept in a monotone set-valued function when Choquet integrably bounded assumption is abandoned. Four kinds of absolute continuities are defined for set-valued function, and all been proven valid with respect to the original set functions.展开更多
Formal concept analysis （FCA） is a discipline that studied the hierarchical structures induced by a binary relation between a pair of sets, and applies in data analysis, information retrieval, knowledge discovery, e...Formal concept analysis （FCA） is a discipline that studied the hierarchical structures induced by a binary relation between a pair of sets, and applies in data analysis, information retrieval, knowledge discovery, etc. In this paper, it is shown that a formal context T is equivalent to a set-valued mapping S ： G → P（М）, and formal concepts could be defined in the set-valued mapping S. It is known that the topology and set-valued mapping are linked. Hence, the advantage of this paper is that the conclusion make us to construct formal concept lattice based on the topology.展开更多
We discuss the set-valued dynamics related to the theory of functional equations.We look for selections of convex set-valued functions satisfying set-valued Euler-Lagrange inclusions.We improve and extend upon some of...We discuss the set-valued dynamics related to the theory of functional equations.We look for selections of convex set-valued functions satisfying set-valued Euler-Lagrange inclusions.We improve and extend upon some of the results in[13,20],but under weaker assumptions.Some applications of our results are also provided.展开更多
基金supported in part by the Natural Science Foundation of Zhejiang Provice of China under Grant No. Y105700the Science and Technology Development Plan of Zhejiang Province of China under Grant No. 2006C21034
文摘Privacy protection in publishing set-valued data is an important problem. However, privacy notions proposed in prior works either assume that the adversary has unbounded knowledge and hence provide over-protection that causes excessive distortion, or ignore the knowledge about the absence of certain items and do not prevent attacks based on such knowledge. To address these issues, we propose a new privacy notion, （k,e）^（m,n）-privacy, which prevents both the identity disclosure and the sensitive item disclosure to a realistic privacy adversary who has bounded knowledge about the presence of items and the bounded knowledge about the absence of items. In addition to the new notion, our contribution is an efficient algorithm that finds a near-optimal solution and is applicable for anonymizing real world databases. Extensive experiments on real world databases showed that our algorithm outperforms the state of the art algorithms.
文摘The rapid growth of biomedical data,particularly multi-omics data including genomes,transcriptomics,proteomics,metabolomics,and epigenomics,medical research and clinical decision-making confront both new opportunities and obstacles.The huge and diversified nature of these datasets cannot always be managed using traditional data analysis methods.As a consequence,deep learning has emerged as a strong tool for analysing numerous omics data due to its ability to handle complex and non-linear relationships.This paper explores the fundamental concepts of deep learning and how they are used in multi-omics medical data mining.We demonstrate how autoencoders,variational autoencoders,multimodal models,attention mechanisms,transformers,and graph neural networks enable pattern analysis and recognition across all omics data.Deep learning has been found to be effective in illness classification,biomarker identification,gene network learning,and therapeutic efficacy prediction.We also consider critical problems like as data quality,model explainability,whether findings can be repeated,and computational power requirements.We now consider future elements of combining omics with clinical and imaging data,explainable AI,federated learning,and real-time diagnostics.Overall,this study emphasises the need of collaborating across disciplines to advance deep learning-based multi-omics research for precision medicine and comprehending complicated disorders.
文摘High-throughput transcriptomics has evolved from bulk RNA-seq to single-cell and spatial profiling,yet its clinical translation still depends on effective integration across diverse omics and data modalities.Emerging foundation models and multimodal learning frameworks are enabling scalable and transferable representations of cellular states,while advances in interpretability and real-world data integration are bridging the gap between discovery and clinical application.This paper outlines a concise roadmap for AI-driven,transcriptome-centered multi-omics integration in precision medicine(Figure 1).
基金Supported by Xuhui District Health Commission,No.SHXH202214.
文摘Gastrointestinal tumors require personalized treatment strategies due to their heterogeneity and complexity.Multimodal artificial intelligence(AI)addresses this challenge by integrating diverse data sources-including computed tomography(CT),magnetic resonance imaging(MRI),endoscopic imaging,and genomic profiles-to enable intelligent decision-making for individualized therapy.This approach leverages AI algorithms to fuse imaging,endoscopic,and omics data,facilitating comprehensive characterization of tumor biology,prediction of treatment response,and optimization of therapeutic strategies.By combining CT and MRI for structural assessment,endoscopic data for real-time visual inspection,and genomic information for molecular profiling,multimodal AI enhances the accuracy of patient stratification and treatment personalization.The clinical implementation of this technology demonstrates potential for improving patient outcomes,advancing precision oncology,and supporting individualized care in gastrointestinal cancers.Ultimately,multimodal AI serves as a transformative tool in oncology,bridging data integration with clinical application to effectively tailor therapies.
基金Supported by the National Natural Science Foundation of China (10571035)
文摘By using cone-directed contingent derivatives, the unified necessary and sufficient optimality conditions are given for weakly and strongly minimal elements respectively in generalized preinvex set-valued optimization.
基金the National Natural Science Foundation(69972036) and the Natural Science Foundation of Shanxi province(995L02)
文摘The concepts of alpha-order Clarke's derivative, alpha-order Adjacent derivative and alpha-order G.Bouligand derivative of set-valued mappings are introduced, their properties are studied, with which the Fritz John optimality condition of set-valued vector optimization is established. Finally, under the assumption of pseudoconvexity, the optimality condition is proved to be sufficient.
基金Foundation item： Supported by the Science Foundation from the Ministry of Education of Jiangsu Province（04KJD110168, 06KJBll0107）
文摘In complete metric spaces, the common fixed point theorems for sequences of φ-type contraction set-valued mappings are established, and the corresponding random com- mon fixed point theorems for set-valued mappings are also obtained.
基金Supported by the National Natural Science Foundation of China (10461007)the Science and Technology Foundation of the Education Department of Jiangxi Province (GJJ09069)
文摘The set-valued optimization problem with constraints is considered in the sense of super efficiency in locally convex linear topological spaces. Under the assumption of iccone-convexlikeness, by applying the seperation theorem, Kuhn-Tucker＇s, Lagrange＇s and saddle points optimality conditions, the necessary conditions are obtained for the set-valued optimization problem to attain its super efficient solutions. Also, the sufficient conditions for Kuhn-Tucker＇s, Lagrange＇s and saddle points optimality conditions are derived.
文摘A kind of tangent derivative and the concepts of strong and weak * pseudoconvexity for a set-valued map are introduced. By the standard separation theorems of the convex sets and cones the optimality Fritz John condition of set-valued optimization under Benson proper efficiency is established, its sufficience is discussed. The form of the optimality conditions obtained here completely tally with the classical results when the set-valued map is specialized to be a single-valued map.
基金Project supported by the National Natural Science Foundation of China (No. 10371024) the Natural Science Foundation of Zhejiang Province (No.Y604003)
文摘The optimality Kuhn-Tucker condition and the wolfe duality for the preinvex set-valued optimization are investigated. Firstly, the concepts of alpha-order G-invex set and the alpha-order S-preinvex set-valued function were introduced, from which the properties of the corresponding contingent cone and the alpha-order contingent derivative were studied. Finally, the optimality Kuhn-Tucker condition and the Wolfe duality theorem for the alpha-order S-preinvex set-valued optimization were presented with the help of the alpha-order contingent derivative.
文摘Several equivalent statements of generalized subconvexlike set-valued map are established in ordered linear spaces. Using vector closure, we introduce Benson proper efficient solution of vector optimization problem. Under the assumption of generalized subconvexlikeness, scalarization, multiplier and saddle point theorems are obtained in the sense of Benson proper efficiency.
基金supported by the National Natural Science Foundation of China (11061023)
文摘In this paper, we introduce a concept of quasi C-lower semicontinuity for setvalued mapping and provide a vector version of Ekeland＇s theorem related to set-valued vector equilibrium problems. As applications, we derive an existence theorem of weakly efficient solution for set-valued vector equilibrium problems without the assumption of convexity of the constraint set and the assumptions of convexity and monotonicity of the set-valued mapping. We also obtain an existence theorem of ε-approximate solution for set-valued vector equilibrium problems without the assumptions of compactness and convexity of the constraint set.
文摘1 Introduction A discrete dynamical system can be expressed as xn+1 ?f(xn), n = 0,1,2,... where X is a metric space and f : X →X is a continuous map. The study of it tells us how the points in the base space X moved. Nevertheless, this is not enough for the researches of biological species, demography, numerical simulation and attractors (see [1], [2]). It is necessary to know how the subsets of X moved. In this direction, we consider the set-valued discrete system associated to f, An+1 = (f|-)(An), n = 0,1,2,... where (f|-) is the natural extension of f to K(X) (the class of all compact subsets of X).
基金Project supported by the National Natural Science Foundation of China (No.10472061)
文摘An auxiliary principle technique to study a class of generalized set-valued strongly nonlinear mixed variational-like inequalities is extended. The existence and uniqueness of the solution of the auxiliary problem for the generalized set-valued strongly nonlinear mixed variational-like inequalities are proved, a novel and innovative three-step iterative algorithm to compute approximate solution is constructed, and the existence of the solution of the generalized set-valued strongly nonlinear mixed variational-like inequality is shown using the auxiliary principle iterative sequences generated by the algorithm technique. The convergence of three-step is also proved.
基金Supported by the Natural Science Foundation of the Education Department of Henan Province（2004110008）
文摘In this paper,the ε-super effcient solution for set-valued map vector optimization in locally convex space is introduced.And under the assumption of the nearly generalized cone-subconvexlikeness for set-valued maps,used new methods,the scalarization theorem and Lagrange multiplier theorem for ε-super effcient solution are established.
文摘The definitions of cone-subconvexlike set-valued maps and generalized cone-subconvexlike set-valued maps in topological vector spaces are defined by using the relative interiors of ordering cone. The relationships between the two classes of set-valued maps are investigated, and some properties of them are shown. A Gordan type alternative theorem under the assumption of generalized cone-subconvexlikeness of set-valued maps is proved by applying convex separation theorems involving the relative interiors in infinite dimensional spaces. Finally a necessary optimality condition theorem is shown for a general kind of set-valued vector optimization in a sense of weak E-minimizer.
基金Sponsored by the National Natural Science Foundation of China (70771010)
文摘Structural characteristics and absolute continuities of monotone set-valued function defined by set- valued Choquet integral are discussed. Similar to the single-valued monotone set function, several important structural characteristics of set-valued function are defined and have been proven the same as those in the original set functions, such as null-additivity, weakly null-additivity, order continuity, strong order continuity and property（S）. A counterexample shows that order continuity and strong order continuity of the original set functions are no longer kept in a monotone set-valued function when Choquet integrably bounded assumption is abandoned. Four kinds of absolute continuities are defined for set-valued function, and all been proven valid with respect to the original set functions.
基金the Young Foundation of Sichuan Province(06ZQ026-037) the Education Department Foundation of Sichuan Province(2005A1212006A084)
文摘Formal concept analysis （FCA） is a discipline that studied the hierarchical structures induced by a binary relation between a pair of sets, and applies in data analysis, information retrieval, knowledge discovery, etc. In this paper, it is shown that a formal context T is equivalent to a set-valued mapping S ： G → P（М）, and formal concepts could be defined in the set-valued mapping S. It is known that the topology and set-valued mapping are linked. Hence, the advantage of this paper is that the conclusion make us to construct formal concept lattice based on the topology.
文摘We discuss the set-valued dynamics related to the theory of functional equations.We look for selections of convex set-valued functions satisfying set-valued Euler-Lagrange inclusions.We improve and extend upon some of the results in[13,20],but under weaker assumptions.Some applications of our results are also provided.
