We prove that a generic matrix of bounded rank is uniquely recoverable - up to a permutation of its rows and columns - from an arbitrary permutation of its entries. This can be viewed as an extension of the existing u...
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For k-valued(control) networks, two types of(control) invariant subspaces are proposed,namely, the state-invariant and dual-invariant subspaces, which are subspaces of the state space and dual space, respectively. Alg...
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For k-valued(control) networks, two types of(control) invariant subspaces are proposed,namely, the state-invariant and dual-invariant subspaces, which are subspaces of the state space and dual space, respectively. Algorithms are presented to check whether a dual subspace is dual-(control)invariant, and to construct state feedback controls. The bearing space of k-valued(control) networks is introduced. Using the structure of the bearing space, the universal invariant subspace is presented,which is independent of the dynamics of particular networks. Finally, the relation between the stateinvariant subspaces and the dual-invariant subspaces of a network is investigated. A duality property shows that if a dual subspace is invariant, then its perpendicular state subspace is also invariant, and vice versa.
We consider the problem of regularization by noises for the three-dimensional magnetohydrodynamical(3D MHD) equations. It is shown that in a suitable scaling limit, the multiplicative noise of transport type gives ris...
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We consider the problem of regularization by noises for the three-dimensional magnetohydrodynamical(3D MHD) equations. It is shown that in a suitable scaling limit, the multiplicative noise of transport type gives rise to bounds on the vorticity fields of the fluid velocity and magnetic fields. As a result, if the noise intensity is big enough, then the stochastic 3D MHD equations admit a pathwise unique global solution for large initial data with high probability.
In a mathematical program with generalized complementarity constraints(MPGCC),complementarity relation is imposed between each pair of variable *** includes the traditional mathematical program with complementarity co...
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In a mathematical program with generalized complementarity constraints(MPGCC),complementarity relation is imposed between each pair of variable *** includes the traditional mathematical program with complementarity constraints(MPCC)as a special *** account of the disjunctive feasible region,MPCC and MPGCC are generally difficult to *** l_(1)penalty method,often adopted in computation,opens a way of circumventing the *** it remains unclear about the exactness of the l_(1)penalty function,namely,whether there exists a sufficiently large penalty parameter so that the penalty problem shares the optimal solution set with the original *** this paper,we consider a class of MPGCCs that are of multi-affine objective *** problem class finds applications in various fields,e.g.,the multi-marginal optimal transport problems in many-body quantum physics and the pricing problems in network *** first provide an instance from this class,the exactness of whose l_(1)penalty function cannot be derived by existing *** then establish the exactness results under rather mild *** results cover those existing ones for MPCC and apply to multi-block contexts.
Efficient cross-border tourism flows are a critical dimension of a country's economic integration into the global economy. This paper introduces an innovative application of the Stochastic Frontier Gravity Model(S...
Efficient cross-border tourism flows are a critical dimension of a country's economic integration into the global economy. This paper introduces an innovative application of the Stochastic Frontier Gravity Model(SFGM) to analyze and measure international tourism efficiency. By integrating natural determinants(e.g., geographical distance, economic size, and price indices) with man-made factors(e.g., social, political, economic, and policy preferences), the study provides a comprehensive framework for assessing tourism efficiency relative to theoretical gravity frontier levels. The findings reveal that, while China has achieved approximately 80% of its tourism potential on average, significant inefficiencies persist, particularly across different origin countries and regions. The study highlights the complementary relationship between human and goods flows, emphasizing the importance of cultural proximity and trade intensity in reducing inefficiencies. Furthermore, it demonstrates the robustness of the SFGM framework in capturing the dynamic and uneven patterns of tourism efficiency over time. By addressing gaps in the application of SFGM to tourism research, this paper advances the theoretical and methodological understanding of tourism efficiency and provides actionable policy recommendations for enhancing China's tourism market integration.
Continuous glucose monitoring(CGM) technology has grown rapidly to track real-time blood glucose levels and trends with improved sensor accuracy. The ease of use and wide availability of CGM will facilitate safe and e...
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Continuous glucose monitoring(CGM) technology has grown rapidly to track real-time blood glucose levels and trends with improved sensor accuracy. The ease of use and wide availability of CGM will facilitate safe and effective decision making for diabetes management. Here, we developed an attention-based deep learning model, CGMformer, pretrained on a well-controlled and diverse corpus of CGM data to represent individual's intrinsic metabolic state and enable clinical applications. During pretraining, CGMformer encodes glucose dynamics including glucose level, fluctuation, hyperglycemia, and hypoglycemia into latent space with self-supervised learning. It shows generalizability in imputing glucose value across five external datasets with different populations and metabolic states(MAE = 3.7 mg/d L). We then fine-tuned CGMformer towards a diverse panel of downstream tasks in the screening of diabetes and its complications using task-specific data, which demonstrated a consistently boosted predictive accuracy over direct fine-tuning on a single task(AUROC = 0.914 for type 2 diabetes(T2D) screening and 0.741 for complication screening). By learning an intrinsic representation of an individual's glucose dynamics,CGMformer classifies non-diabetic individuals into six clusters with elevated T2D risks, and identifies a specific cluster with lean body-shape but high risk of glucose metabolism disorders, which is overlooked by traditional glucose measurements. Furthermore, CGMformer achieves high accuracy in predicting an individual's postprandial glucose response with dietary modelling(Pearson correlation coefficient = 0.763)and helps personalized dietary recommendations. Overall, CGMformer pretrains a transformer neural network architecture to learn an intrinsic representation by borrowing information from a large amount of daily glucose profiles, and demonstrates predictive capabilities fine-tuned towards a broad range of downstream applications, holding promise for the ear
In the previous works [1] and [2], we solved the optimal strategy of the human player against a machine player who makes decisions based on Fictitious Play in infinitely repeated 2 × 2 games, in which the informa...
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Dear editor, Erasure codes are increasingly adopted in modern storage systems (such as Windows Azure Storage [1] and Facebook storage [2]) to ensure fault-tolerant storage with low redundancy. Meanwhile, efficient rep...
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Dear editor, Erasure codes are increasingly adopted in modern storage systems (such as Windows Azure Storage [1] and Facebook storage [2]) to ensure fault-tolerant storage with low redundancy. Meanwhile, efficient repair of node failures becomes a central issue in coding for distributed storage. The repair efficiency is usually measured by the repair bandwidth which is the amount of data transmitted from the helper nodes during the repair process.
The classical noise is unavoided in the real world. In what way classical part impact quantum dynamics and whether classical part impact controllability of quantum system have become problems. To figure out these two ...
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WE are in an exciting new intelligent era where various Web 3.0 systems emerge and flourish.[1]–[3].In this new epoch,the collaboration of data and knowledge,humans and machines,actual and virtual worlds is undergoin...
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WE are in an exciting new intelligent era where various Web 3.0 systems emerge and flourish.[1]–[3].In this new epoch,the collaboration of data and knowledge,humans and machines,actual and virtual worlds is undergoing an unprecedented diversification and community-driven transformation,unveiling an open future full of boundless ***,the value of dispersed data extends far beyond passive storage and application.
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