BACKGROUND Dysfunction of the glymphatic system in the brain in different stages of altered glucose metabolism and its influencing factors are not well characterized.AIM To investigate the function of the glymphatic s...BACKGROUND Dysfunction of the glymphatic system in the brain in different stages of altered glucose metabolism and its influencing factors are not well characterized.AIM To investigate the function of the glymphatic system and its clinical correlates in patients with different glucose metabolism states,the present study employed diffusion tensor imaging along the perivascular space(DTI-ALPS)index.METHODS Sample size was calculated using the pwr package in R software.This crosssectional study enrolled 22 patients with normal glucose metabolism(NGM),20 patients with prediabetes,and 22 patients with type 2 diabetes mellitus(T2DM).A 3.0T magnetic resonance imaging was used to evaluate the function of the glymphatic system.The mini-mental state examination(MMSE)was used to assess general cognitive function.The DTI-ALPS index of bilateral basal ganglia and the mean DTI-ALPS index was calculated.Further,the correlation between DTI-ALPS and clinical features was assessed.RESULTS The left-side,right-side,and mean DTI-ALPS index in the T2DM group were significantly lower than that in the NGM group.The right-side DTI-ALPS and mean DTI-ALPS index in the T2DM group were significantly lower than those in the prediabetes group.DTI-ALPS index lateralization was not observed.The MMSE score in the T2DM group was significantly lower than that in the NGM and prediabetes group.After controlling for sex,the left-side DTI-ALPS and mean DTI-ALPS index in the prediabetes group were positively correlated with 2-hour postprandial blood glucose level;the left-side DTI-ALPS index was negatively correlated with total cholesterol and low-density lipoprotein level.The right-side DTI-ALPS and mean DTI-ALPS index were negatively correlated with the glycosylated hemoglobin level and waist-to-hip ratio in the prediabetes group.The left-side,right-side,and mean DTI-ALPS index in the T2DM group were positively correlated with height.The left-side and mean DTIALPS index in the T2DM group were negatively correlated with high-density lipoprotein levels.展开更多
Nowadays the semi-tensor product(STP)approach to finite games has become a promising new direction.This paper provides a comprehensive survey on this prosperous field.After a brief introduction for STP and finite(netw...Nowadays the semi-tensor product(STP)approach to finite games has become a promising new direction.This paper provides a comprehensive survey on this prosperous field.After a brief introduction for STP and finite(networked)games,a description for the principle and fundamental technique of STP approach to finite games is presented.Then several problems and recent results about theory and applications of finite games via STP are presented.A brief comment about the potential use of STP to artificial intelligence is also proposed.展开更多
In this article,we comment on an original article published in a recent issue of the World Journal of Diabetes.That observational cross-sectional study focused on investigating the function of the glymphatic system an...In this article,we comment on an original article published in a recent issue of the World Journal of Diabetes.That observational cross-sectional study focused on investigating the function of the glymphatic system and its clinical correlates in patients with different glucose metabolism states by using diffusion tensor imaging along the perivascular space(DTI-ALPS)index.It was shown that the cerebral glymphatic system may be dysfunctional in patients with type 2 diabetes.Various clinical variables affected the DTI-ALPS index in different glucose metabolism states.In conclusion,the study by Tian et al improves the under-standing of the pathophysiology of diabetes-associated brain damage and pro-vides insights for early diagnosis.展开更多
The cross-dimensional dynamical systems have received increasing research attention in recent years.This paper characterizes the structure features of the cross-dimensional vector space.Specifically,it is proved that ...The cross-dimensional dynamical systems have received increasing research attention in recent years.This paper characterizes the structure features of the cross-dimensional vector space.Specifically,it is proved that the completion of cross-dimensional vector space is an infinite-dimensional separable Hilbert space.Hence,it means that one can isometrically and linearly embed the crossdimensional vector space into theℓ^(2),which is known as the space of square summable sequences.This result will be helpful in the modeling and analyzing the dynamics of cross-dimensional dynamical systems.展开更多
A new matrix product, called the second semi-tensor product (STP-Ⅱ) of matrices is proposed. It is similar to the classical semi-tensor product (STP-I). First, its fundamental properties are presented. Then, the equi...A new matrix product, called the second semi-tensor product (STP-Ⅱ) of matrices is proposed. It is similar to the classical semi-tensor product (STP-I). First, its fundamental properties are presented. Then, the equivalence relation caused by STP-II is obtained. Using this equivalence, a quotient space is also obtained. Finally, the vector space structure, the metric and the metric topology, the projection and subspaces, etc. of the quotient space are investigated in detail.展开更多
It is a challenge to investigate the interrelationship between the geometric structure and performance of sensor networks due to the increasingly complex and diverse architecture of them.This paper presents two new fo...It is a challenge to investigate the interrelationship between the geometric structure and performance of sensor networks due to the increasingly complex and diverse architecture of them.This paper presents two new formulations for the information space of sensor networks,including Lagrangian and energy–momentum tensor,which are expected to integrate sensor networks target tracking and performance evaluation from a unified perspective.The proposed method presents two geometric objects to represent the dynamic state and manifold structure of the information space of sensor networks.Based on that,the authors conduct the property analysis and target tracking of sensor networks.To the best of our knowledge,it is the first time to investigate and analyze the information energy-momentum tensor of sensor networks and evaluate the performance of sensor networks in the context of target tracking.Simulations and examples confirm the competitive performance of the proposed method.展开更多
The kernel function method in support vector machine(SVM)is an excellent tool for nonlinear classification.How to design a kernel function is difficult for an SVM nonlinear classification problem,even for the polynomi...The kernel function method in support vector machine(SVM)is an excellent tool for nonlinear classification.How to design a kernel function is difficult for an SVM nonlinear classification problem,even for the polynomial kernel function.In this paper,we propose a new kind of polynomial kernel functions,called semi-tensor product kernel(STP-kernel),for an SVM nonlinear classification problem by semi-tensor product of matrix(STP)theory.We have shown the existence of the STP-kernel function and verified that it is just a polynomial kernel.In addition,we have shown the existence of the reproducing kernel Hilbert space(RKHS)associated with the STP-kernel function.Compared to the existing methods,it is much easier to construct the nonlinear feature mapping for an SVM nonlinear classification problem via an STP operator.展开更多
Let φ be an Orlicz function that has a complementary function φ＊ and let lφ be an Orlicz sequence space. We prove a similar version of Rearrangement Inequality and Chebyshev＇s Sum Inequality in lφ FX, the Freml...Let φ be an Orlicz function that has a complementary function φ＊ and let lφ be an Orlicz sequence space. We prove a similar version of Rearrangement Inequality and Chebyshev＇s Sum Inequality in lφ FX, the Fremlin projective tensor product of lφ with a Banach lattice X, and in lφ iX, the Wittstock injective tensor product of lφ with a Banach lattice X.展开更多
It was noted earlier that the general relativity field equations for static systems with spherical symmetry can be put into a linear form when the source energy density equals radial stress. These linear equations lea...It was noted earlier that the general relativity field equations for static systems with spherical symmetry can be put into a linear form when the source energy density equals radial stress. These linear equations lead to a delta function energymomentum tensor for a point mass source for the Schwarzschild field that has vanishing self-stress, and whose integral therefore transforms properly under a Lorentz transformation, as though the particle is in the flat space-time of special relativity (SR). These findings were later extended to n spatial dimensions. Consistent with this SR-like result for the source tensor, Nordstrom and independently, Schrodinger, found for three spatial dimensions that the Einstein gravitational energy-momentum pseudo-tensor vanished in proper quasi-rectangular coordinates. The present work shows that this vanishing holds for the pseudo-tensor when extended to n spatial dimensions. Two additional consequences of this work are: 1) the dependency of the Einstein gravitational coupling constant κ on spatial dimensionality employed earlier is further justified;2) the Tolman expression for the mass of a static, isolated system is generalized to take into account the dimensionality of space for n ≥ 3.展开更多
Einstein theorized that Gravity is not a force derived from a potential that acts across a distance. It is a distortion of space and time in which we live by masses and energy. Consistent with Einstein’s theory, a mo...Einstein theorized that Gravity is not a force derived from a potential that acts across a distance. It is a distortion of space and time in which we live by masses and energy. Consistent with Einstein’s theory, a model of space-time curvature modes and associated curvature quanta in slightly warped space-time generated by a light Photon is derived. Both a Schr<span style="white-space:nowrap;">?</span>dinger and a Second Quantized representation of the space-time curvature mode quanta are calculated and are fourth rank tensors. The eigenvalues of these equations are radii of curvature, not energy. The Eigenfunctions are linear functions of the components of the tensor that describes the curvature of space-time.展开更多
The theory of general relativity is related to the concept of curvature of space- time induced by the presence of the massive objects. We will see through this paper that the general relativity can be linked with line...The theory of general relativity is related to the concept of curvature of space- time induced by the presence of the massive objects. We will see through this paper that the general relativity can be linked with linear Algebra and Vector Analysis without the need for concept of space-time. This is important for the unification of general relativity with quantum mechanics, gravity with electromagnetic, and a better understanding of the universe, gravity, black holes. The most important is the separation between the space-time and the big bang theory, which prove the existence of space-time before that, which leads to the existence of the creator of the universe.展开更多
The author considers relations between Yang-Baxter operators and tensor transformations, and proves that all tensor transform at ions over the category of modules of a Yang-space form a group.
It is proved that the action of the higher-dimensional gravity in Weitzenb(?)ck space reduces to the sum of the action of gravity in four-dimensional space-time and that of gauge fields. In this sense we conclude that...It is proved that the action of the higher-dimensional gravity in Weitzenb(?)ck space reduces to the sum of the action of gravity in four-dimensional space-time and that of gauge fields. In this sense we conclude that in Weitzenb(?)ck space the higher-dimensional Kaluza-Klein theory holds.展开更多
文摘BACKGROUND Dysfunction of the glymphatic system in the brain in different stages of altered glucose metabolism and its influencing factors are not well characterized.AIM To investigate the function of the glymphatic system and its clinical correlates in patients with different glucose metabolism states,the present study employed diffusion tensor imaging along the perivascular space(DTI-ALPS)index.METHODS Sample size was calculated using the pwr package in R software.This crosssectional study enrolled 22 patients with normal glucose metabolism(NGM),20 patients with prediabetes,and 22 patients with type 2 diabetes mellitus(T2DM).A 3.0T magnetic resonance imaging was used to evaluate the function of the glymphatic system.The mini-mental state examination(MMSE)was used to assess general cognitive function.The DTI-ALPS index of bilateral basal ganglia and the mean DTI-ALPS index was calculated.Further,the correlation between DTI-ALPS and clinical features was assessed.RESULTS The left-side,right-side,and mean DTI-ALPS index in the T2DM group were significantly lower than that in the NGM group.The right-side DTI-ALPS and mean DTI-ALPS index in the T2DM group were significantly lower than those in the prediabetes group.DTI-ALPS index lateralization was not observed.The MMSE score in the T2DM group was significantly lower than that in the NGM and prediabetes group.After controlling for sex,the left-side DTI-ALPS and mean DTI-ALPS index in the prediabetes group were positively correlated with 2-hour postprandial blood glucose level;the left-side DTI-ALPS index was negatively correlated with total cholesterol and low-density lipoprotein level.The right-side DTI-ALPS and mean DTI-ALPS index were negatively correlated with the glycosylated hemoglobin level and waist-to-hip ratio in the prediabetes group.The left-side,right-side,and mean DTI-ALPS index in the T2DM group were positively correlated with height.The left-side and mean DTIALPS index in the T2DM group were negatively correlated with high-density lipoprotein levels.
基金the National Natural Science Foundation of China(NSFC)under Grant Nos.62073315,61074114,and 61273013。
文摘Nowadays the semi-tensor product(STP)approach to finite games has become a promising new direction.This paper provides a comprehensive survey on this prosperous field.After a brief introduction for STP and finite(networked)games,a description for the principle and fundamental technique of STP approach to finite games is presented.Then several problems and recent results about theory and applications of finite games via STP are presented.A brief comment about the potential use of STP to artificial intelligence is also proposed.
基金Supported by European Union-Next Generation EU,through the National Recovery and Resilience Plan of the Republic of Bulgaria,No.BG-RRP-2.004-0008.
文摘In this article,we comment on an original article published in a recent issue of the World Journal of Diabetes.That observational cross-sectional study focused on investigating the function of the glymphatic system and its clinical correlates in patients with different glucose metabolism states by using diffusion tensor imaging along the perivascular space(DTI-ALPS)index.It was shown that the cerebral glymphatic system may be dysfunctional in patients with type 2 diabetes.Various clinical variables affected the DTI-ALPS index in different glucose metabolism states.In conclusion,the study by Tian et al improves the under-standing of the pathophysiology of diabetes-associated brain damage and pro-vides insights for early diagnosis.
基金supported by the National Natural Science Foundation of China under Grant No.61673129the Key Programs in Shaanxi Province of China under Grant No.2021JZ-12Science and the Technology Bureau Project of Yulin under Grant Nos.2019-89-2 and 2019-89-4。
文摘The cross-dimensional dynamical systems have received increasing research attention in recent years.This paper characterizes the structure features of the cross-dimensional vector space.Specifically,it is proved that the completion of cross-dimensional vector space is an infinite-dimensional separable Hilbert space.Hence,it means that one can isometrically and linearly embed the crossdimensional vector space into theℓ^(2),which is known as the space of square summable sequences.This result will be helpful in the modeling and analyzing the dynamics of cross-dimensional dynamical systems.
基金National Natural Science Foundation of China (Nos. 61733018, 61333001, 61773371).
文摘A new matrix product, called the second semi-tensor product (STP-Ⅱ) of matrices is proposed. It is similar to the classical semi-tensor product (STP-I). First, its fundamental properties are presented. Then, the equivalence relation caused by STP-II is obtained. Using this equivalence, a quotient space is also obtained. Finally, the vector space structure, the metric and the metric topology, the projection and subspaces, etc. of the quotient space are investigated in detail.
基金supported by the National Natural Science Foundation of China(No.51875014)。
文摘It is a challenge to investigate the interrelationship between the geometric structure and performance of sensor networks due to the increasingly complex and diverse architecture of them.This paper presents two new formulations for the information space of sensor networks,including Lagrangian and energy–momentum tensor,which are expected to integrate sensor networks target tracking and performance evaluation from a unified perspective.The proposed method presents two geometric objects to represent the dynamic state and manifold structure of the information space of sensor networks.Based on that,the authors conduct the property analysis and target tracking of sensor networks.To the best of our knowledge,it is the first time to investigate and analyze the information energy-momentum tensor of sensor networks and evaluate the performance of sensor networks in the context of target tracking.Simulations and examples confirm the competitive performance of the proposed method.
基金supported by the National Natural Science Foundation of China(61573288)the Key Programs in Shaanxi Province of China(2021JZ-12)and the Yulin Science and Technology Bureau project(2019-89-2).
文摘The kernel function method in support vector machine(SVM)is an excellent tool for nonlinear classification.How to design a kernel function is difficult for an SVM nonlinear classification problem,even for the polynomial kernel function.In this paper,we propose a new kind of polynomial kernel functions,called semi-tensor product kernel(STP-kernel),for an SVM nonlinear classification problem by semi-tensor product of matrix(STP)theory.We have shown the existence of the STP-kernel function and verified that it is just a polynomial kernel.In addition,we have shown the existence of the reproducing kernel Hilbert space(RKHS)associated with the STP-kernel function.Compared to the existing methods,it is much easier to construct the nonlinear feature mapping for an SVM nonlinear classification problem via an STP operator.
文摘Let φ be an Orlicz function that has a complementary function φ＊ and let lφ be an Orlicz sequence space. We prove a similar version of Rearrangement Inequality and Chebyshev＇s Sum Inequality in lφ FX, the Fremlin projective tensor product of lφ with a Banach lattice X, and in lφ iX, the Wittstock injective tensor product of lφ with a Banach lattice X.
文摘It was noted earlier that the general relativity field equations for static systems with spherical symmetry can be put into a linear form when the source energy density equals radial stress. These linear equations lead to a delta function energymomentum tensor for a point mass source for the Schwarzschild field that has vanishing self-stress, and whose integral therefore transforms properly under a Lorentz transformation, as though the particle is in the flat space-time of special relativity (SR). These findings were later extended to n spatial dimensions. Consistent with this SR-like result for the source tensor, Nordstrom and independently, Schrodinger, found for three spatial dimensions that the Einstein gravitational energy-momentum pseudo-tensor vanished in proper quasi-rectangular coordinates. The present work shows that this vanishing holds for the pseudo-tensor when extended to n spatial dimensions. Two additional consequences of this work are: 1) the dependency of the Einstein gravitational coupling constant κ on spatial dimensionality employed earlier is further justified;2) the Tolman expression for the mass of a static, isolated system is generalized to take into account the dimensionality of space for n ≥ 3.
文摘Einstein theorized that Gravity is not a force derived from a potential that acts across a distance. It is a distortion of space and time in which we live by masses and energy. Consistent with Einstein’s theory, a model of space-time curvature modes and associated curvature quanta in slightly warped space-time generated by a light Photon is derived. Both a Schr<span style="white-space:nowrap;">?</span>dinger and a Second Quantized representation of the space-time curvature mode quanta are calculated and are fourth rank tensors. The eigenvalues of these equations are radii of curvature, not energy. The Eigenfunctions are linear functions of the components of the tensor that describes the curvature of space-time.
文摘The theory of general relativity is related to the concept of curvature of space- time induced by the presence of the massive objects. We will see through this paper that the general relativity can be linked with linear Algebra and Vector Analysis without the need for concept of space-time. This is important for the unification of general relativity with quantum mechanics, gravity with electromagnetic, and a better understanding of the universe, gravity, black holes. The most important is the separation between the space-time and the big bang theory, which prove the existence of space-time before that, which leads to the existence of the creator of the universe.
基金Shanghai Development Fund for SciencesTechnology and by Shanghai Higher-Education Institution Development Fund for Sciences and Technology
文摘The author considers relations between Yang-Baxter operators and tensor transformations, and proves that all tensor transform at ions over the category of modules of a Yang-space form a group.
文摘It is proved that the action of the higher-dimensional gravity in Weitzenb(?)ck space reduces to the sum of the action of gravity in four-dimensional space-time and that of gauge fields. In this sense we conclude that in Weitzenb(?)ck space the higher-dimensional Kaluza-Klein theory holds.
