In differentiable search architecture search methods,a more efficient search space design can significantly improve the performance of the searched architecture,thus requiring people to carefully define the search spa...In differentiable search architecture search methods,a more efficient search space design can significantly improve the performance of the searched architecture,thus requiring people to carefully define the search space with different complexity according to various operations.Meanwhile rationalizing the search strategies to explore the well-defined search space will further improve the speed and efficiency of architecture search.With this in mind,we propose a faster and more efficient differentiable architecture search method,AllegroNAS.Firstly,we introduce a more efficient search space enriched by the introduction of two redefined convolution modules.Secondly,we utilize a more efficient architectural parameter regularization method,mitigating the overfitting problem during the search process and reducing the error brought about by gradient approximation.Meanwhile,we introduce a natural exponential cosine annealing method to make the learning rate of the neural network training process more suitable for the search procedure.Moreover,group convolution and data augmentation are employed to reduce the computational cost.Finally,through extensive experiments on several public datasets,we demonstrate that our method can more swiftly search for better-performing neural network architectures in a more efficient search space,thus validating the effectiveness of our approach.展开更多
A Riesz space K1 whose elements are pairs of convex-set collections is presented for the study on the calculus of generalized quasi-differentiable functions. The space K1 is constructed by introducing a well-defined e...A Riesz space K1 whose elements are pairs of convex-set collections is presented for the study on the calculus of generalized quasi-differentiable functions. The space K1 is constructed by introducing a well-defined equivalence relation among pairs of collections of convex sets. Some important properties on the norm and operations in K1 are given.展开更多
In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Su...In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Sub-differential. We extend the results on the characterizations of non-smooth convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the monotonicity of its sub-differentials to the lower semi-continuous pseudo-convex functions on real Banach spaces.展开更多
In the realm of large-scale machine learning,it is crucial to explore methods for reducing computational complexity and memory demands while maintaining generalization performance.Additionally,since the collected data...In the realm of large-scale machine learning,it is crucial to explore methods for reducing computational complexity and memory demands while maintaining generalization performance.Additionally,since the collected data may contain some sensitive information,it is also of great significance to study privacy-preserving machine learning algorithms.This paper focuses on the performance of the differentially private stochastic gradient descent(SGD)algorithm based on random features.To begin,the algorithm maps the original data into a lowdimensional space,thereby avoiding the traditional kernel method for large-scale data storage requirement.Subsequently,the algorithm iteratively optimizes parameters using the stochastic gradient descent approach.Lastly,the output perturbation mechanism is employed to introduce random noise,ensuring algorithmic privacy.We prove that the proposed algorithm satisfies the differential privacy while achieving fast convergence rates under some mild conditions.展开更多
Characterizations of differentiability are obtained for continuous convex functions defined on nonempty open convex sets of Banach spaces as a generalization and application of a mumber of mathematicians several years...Characterizations of differentiability are obtained for continuous convex functions defined on nonempty open convex sets of Banach spaces as a generalization and application of a mumber of mathematicians several years effort, and a characteristic theorem is given for Banach spaces which are (weak) Asplund spaces.展开更多
A locally convex space is said to be a Gateaux differentiability space (GDS) provided every continuous convex function defined on a nonempty convex open subset D of the space is densely Gateaux differentiable in .D.Th...A locally convex space is said to be a Gateaux differentiability space (GDS) provided every continuous convex function defined on a nonempty convex open subset D of the space is densely Gateaux differentiable in .D.This paper shows that the product of a GDS and a family of separable Prechet spaces is a GDS,and that the product of a GDS and an arbitrary locally convex space endowed with the weak topology is a GDS.展开更多
In this article, a new differential inverse variational inequality is introduced and studied in finite dimensional Euclidean spaces. Some results concerned with the linear growth of the solution set for the differenti...In this article, a new differential inverse variational inequality is introduced and studied in finite dimensional Euclidean spaces. Some results concerned with the linear growth of the solution set for the differential inverse variational inequalities are obtained under different conditions. Some existence theorems of Caratheodory weak solutions for the differential inverse variational inequality are also established under suitable conditions. An application to the time-dependent spatial price equilibrium control problem is also given.展开更多
We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applic...We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applications, we also give estimates of the es- sential norms of weighted composition operators between weighted Banach space of analytic functions and Bloch-type spaces.展开更多
The parapharyngeal space(PPS) is an inverted pyramid-shaped deep space in the head and neck region, and a variety of tumors, such as salivary gland tumors, neurogenic tumors, nasopharyngeal carcinomas with parapharyng...The parapharyngeal space(PPS) is an inverted pyramid-shaped deep space in the head and neck region, and a variety of tumors, such as salivary gland tumors, neurogenic tumors, nasopharyngeal carcinomas with parapharyngeal invasion, and lymphomas, can be found in this space. The differential diagnosis of PPS tumors remains challenging for radiologists. This study aimed to develop and test a modified method for locating PPS tumors on magnetic resonance(MR) images to improve preoperative differential diagnosis. The new protocol divided the PPS into three compartments: a prestyloid compartment, the carotid sheath, and the areas outside the carotid sheath. PPS tumors were located in these compartments according to the displacements of the tensor veli palatini muscle and the styloid process, with or without blood vessel separations and medial pterygoid invasion. This protocol, as well as a more conventional protocol that is based on displacements of the internal carotid artery(ICA), was used to assess MR images captured from a series of 58 PPS tumors. The consequent distributions of PPS tumor locations determined by both methods were compared. Of all 58 tumors, our new method determined that 57 could be assigned to precise PPS compartments. Nearly all(13/14; 93%) tumors that were located in the pre-styloid compartment were salivary gland tumors. All 15 tumors within the carotid sheath were neurogenic tumors. The vast majority(18/20; 90%) of trans-spatial lesions were malignancies. However, according to the ICA-based method, 28 tumors were located in the pre-styloid compartment, and 24 were located in the post-styloid compartment, leaving 6 tumors that were difficult to locate. Lesions located in both the pre-styloid and the post-styloid compartments comprised various types of tumors. Compared with the conventional ICA-based method, our new method can help radiologists to narrow the differential diagnosis of PPS tumors to specific compartments.展开更多
Let T be the singular integral operator with variable kernel, T* be the adjoint of T and T# be the pseudo-adjoint of T. Let TIT2 be the product of T1 and T2, T1 o T2 be the pseudo product of T1 and T2. In this paper,...Let T be the singular integral operator with variable kernel, T* be the adjoint of T and T# be the pseudo-adjoint of T. Let TIT2 be the product of T1 and T2, T1 o T2 be the pseudo product of T1 and T2. In this paper, we establish the boundedness for commutators of these operators and the fractional differentiation operator D^γ on the weighted Morrey spaces.展开更多
We characterize boundedness and compactness of products of differentiation op- erators and weighted composition operators between weighted Banach spaces of analytic functions and weighted Zygmund spaces or weighted Bl...We characterize boundedness and compactness of products of differentiation op- erators and weighted composition operators between weighted Banach spaces of analytic functions and weighted Zygmund spaces or weighted Bloch spaces with general weights.展开更多
We introduce a novel numerical method for solving two-sided space fractional partial differential equations in two-dimensional case.The approximation of the space fractional Riemann-Liouville derivative is based on th...We introduce a novel numerical method for solving two-sided space fractional partial differential equations in two-dimensional case.The approximation of the space fractional Riemann-Liouville derivative is based on the approximation of the Hadamard finite-part integral which has the convergence order O(h^3-a),where h is the space step size and α∈(1,2)is the order of Riemann-Liouville fractional derivative.Based on this scheme,we introduce a shifted finite difference method for solving space fractional partial differential equations.We obtained the error estimates with the convergence orders O(τ+h^3-a+h^β),where τ is the time step size and β>0 is a parameter which measures the smoothness of the fractional derivatives of the solution of the equation.Unlike the numerical methods for solving space fractional partial differential equations constructed using the standard shifted Griinwald-Letnikov formula or higher order Lubich's methods which require the solution of the equation to satisfy the homogeneous Dirichlet boundary condition to get the firstorder convergence,the numerical method for solving the space fractional partial differential equation constructed using the Hadamard finite-part integral approach does not require the solution of the equation to satisfy the Dirichlet homogeneous boundary condition.Numerical results show that the experimentally determined convergence order obtained using the Hadamard finite-part integral approach for solving the space fractional partial differential equation with non-homogeneous Dirichlet boundary conditions is indeed higher than the convergence order obtained using the numerical methods constructed with the standard shifted Griinwald-Letnikov formula or Lubich's higher order approximation schemes.展开更多
In this paper, the fluid flow differential equation based on the homogenous reservoirs model is first reviewed. Then a theorem about the formal similarity of solutions in the Laplace space with outer boundary conditio...In this paper, the fluid flow differential equation based on the homogenous reservoirs model is first reviewed. Then a theorem about the formal similarity of solutions in the Laplace space with outer boundary conditions and inner boundary condition is presented and proved. Lastly, a corollary of our theorem is given particularly on inner boundary. The obtained results are very helpful for understanding inherent laws of relevant engineering science and designing practical analysis software.展开更多
Phase space reconstruction is the first step of recognizing the chaotic time series.On the basis of differential entropy ratio method,the embedding dimension opt m and time delay t are optimal for the state space reco...Phase space reconstruction is the first step of recognizing the chaotic time series.On the basis of differential entropy ratio method,the embedding dimension opt m and time delay t are optimal for the state space reconstruction could be determined.But they are not the optimal parameters accepted for prediction.This study proposes an improved method based on the differential entropy ratio and Radial Basis Function(RBF)neural network to estimate the embedding dimension m and the time delay t,which have both optimal characteristics of the state space reconstruction and the prediction.Simulating experiments of Lorenz system and Doffing system show that the original phase space could be reconstructed from the time series effectively,and both the prediction accuracy and prediction length are improved greatly.展开更多
Differential space-time coding was proposed recently in the literature for multi-antenna systems, where neither the transmitter nor the receiver knows the fading coefficients. Among existing schemes, double differenti...Differential space-time coding was proposed recently in the literature for multi-antenna systems, where neither the transmitter nor the receiver knows the fading coefficients. Among existing schemes, double differential space-time (DDST) coding is of special interest because it is applicable to continuous fast time-varying channels. However, it is less effective in fre- quency-selective fading channels. This paper’s authors derived a novel time-frequency double differential space-time (TF-DDST) coding scheme for multi-antenna orthogonal frequency division multiplexing (OFDM) systems in a time-varying fre- quency-selective fading environment, where double differential space-time coding is introduced into both time domain and fre- quency domain. Our proposed TF-DDST-OFDM system has a low-complexity non-coherent decoding scheme and is robust for time- and frequency-selective Rayleigh fading. In this paper, we also propose the use of state-of-the-art low-density parity-check (LDPC) code in serial concatenation with our TF-DDST scheme as a channel code. Simulations revealed that the LDPC based TF-DDST OFDM system has low decoding complexity and relatively better performance.展开更多
The aim of this work is to study the existence of a periodic solution for some neutral partial functional differential equations. Our approach is based on the R-boundedness of linear operators Lp-multipliers and UMD-s...The aim of this work is to study the existence of a periodic solution for some neutral partial functional differential equations. Our approach is based on the R-boundedness of linear operators Lp-multipliers and UMD-spaces.展开更多
This paper investigates the maximal and minimal solutions of initial value problems for second order nonlinear integro-differential equations of Volterra type on a finite interval in a Banach space by establishing a c...This paper investigates the maximal and minimal solutions of initial value problems for second order nonlinear integro-differential equations of Volterra type on a finite interval in a Banach space by establishing a comparison result and using the monotone iterative technique.展开更多
基金This work was supported in part by the National Natural Science Foundation of China under Grant 61305001the Natural Science Foundation of Heilongjiang Province of China under Grant F201222.
文摘In differentiable search architecture search methods,a more efficient search space design can significantly improve the performance of the searched architecture,thus requiring people to carefully define the search space with different complexity according to various operations.Meanwhile rationalizing the search strategies to explore the well-defined search space will further improve the speed and efficiency of architecture search.With this in mind,we propose a faster and more efficient differentiable architecture search method,AllegroNAS.Firstly,we introduce a more efficient search space enriched by the introduction of two redefined convolution modules.Secondly,we utilize a more efficient architectural parameter regularization method,mitigating the overfitting problem during the search process and reducing the error brought about by gradient approximation.Meanwhile,we introduce a natural exponential cosine annealing method to make the learning rate of the neural network training process more suitable for the search procedure.Moreover,group convolution and data augmentation are employed to reduce the computational cost.Finally,through extensive experiments on several public datasets,we demonstrate that our method can more swiftly search for better-performing neural network architectures in a more efficient search space,thus validating the effectiveness of our approach.
文摘A Riesz space K1 whose elements are pairs of convex-set collections is presented for the study on the calculus of generalized quasi-differentiable functions. The space K1 is constructed by introducing a well-defined equivalence relation among pairs of collections of convex sets. Some important properties on the norm and operations in K1 are given.
文摘In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Sub-differential. We extend the results on the characterizations of non-smooth convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the monotonicity of its sub-differentials to the lower semi-continuous pseudo-convex functions on real Banach spaces.
基金supported by Zhejiang Provincial Natural Science Foundation of China(LR20A010001)National Natural Science Foundation of China(12271473 and U21A20426)。
文摘In the realm of large-scale machine learning,it is crucial to explore methods for reducing computational complexity and memory demands while maintaining generalization performance.Additionally,since the collected data may contain some sensitive information,it is also of great significance to study privacy-preserving machine learning algorithms.This paper focuses on the performance of the differentially private stochastic gradient descent(SGD)algorithm based on random features.To begin,the algorithm maps the original data into a lowdimensional space,thereby avoiding the traditional kernel method for large-scale data storage requirement.Subsequently,the algorithm iteratively optimizes parameters using the stochastic gradient descent approach.Lastly,the output perturbation mechanism is employed to introduce random noise,ensuring algorithmic privacy.We prove that the proposed algorithm satisfies the differential privacy while achieving fast convergence rates under some mild conditions.
文摘Characterizations of differentiability are obtained for continuous convex functions defined on nonempty open convex sets of Banach spaces as a generalization and application of a mumber of mathematicians several years effort, and a characteristic theorem is given for Banach spaces which are (weak) Asplund spaces.
基金Supported by the NSF of China (10071063 and 10471114)
文摘A locally convex space is said to be a Gateaux differentiability space (GDS) provided every continuous convex function defined on a nonempty convex open subset D of the space is densely Gateaux differentiable in .D.This paper shows that the product of a GDS and a family of separable Prechet spaces is a GDS,and that the product of a GDS and an arbitrary locally convex space endowed with the weak topology is a GDS.
基金supported by the National Natural Science Foundation of China(11301359,11171237)the Key Program of NSFC(70831005)
文摘In this article, a new differential inverse variational inequality is introduced and studied in finite dimensional Euclidean spaces. Some results concerned with the linear growth of the solution set for the differential inverse variational inequalities are obtained under different conditions. Some existence theorems of Caratheodory weak solutions for the differential inverse variational inequality are also established under suitable conditions. An application to the time-dependent spatial price equilibrium control problem is also given.
文摘We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applications, we also give estimates of the es- sential norms of weighted composition operators between weighted Banach space of analytic functions and Bloch-type spaces.
文摘The parapharyngeal space(PPS) is an inverted pyramid-shaped deep space in the head and neck region, and a variety of tumors, such as salivary gland tumors, neurogenic tumors, nasopharyngeal carcinomas with parapharyngeal invasion, and lymphomas, can be found in this space. The differential diagnosis of PPS tumors remains challenging for radiologists. This study aimed to develop and test a modified method for locating PPS tumors on magnetic resonance(MR) images to improve preoperative differential diagnosis. The new protocol divided the PPS into three compartments: a prestyloid compartment, the carotid sheath, and the areas outside the carotid sheath. PPS tumors were located in these compartments according to the displacements of the tensor veli palatini muscle and the styloid process, with or without blood vessel separations and medial pterygoid invasion. This protocol, as well as a more conventional protocol that is based on displacements of the internal carotid artery(ICA), was used to assess MR images captured from a series of 58 PPS tumors. The consequent distributions of PPS tumor locations determined by both methods were compared. Of all 58 tumors, our new method determined that 57 could be assigned to precise PPS compartments. Nearly all(13/14; 93%) tumors that were located in the pre-styloid compartment were salivary gland tumors. All 15 tumors within the carotid sheath were neurogenic tumors. The vast majority(18/20; 90%) of trans-spatial lesions were malignancies. However, according to the ICA-based method, 28 tumors were located in the pre-styloid compartment, and 24 were located in the post-styloid compartment, leaving 6 tumors that were difficult to locate. Lesions located in both the pre-styloid and the post-styloid compartments comprised various types of tumors. Compared with the conventional ICA-based method, our new method can help radiologists to narrow the differential diagnosis of PPS tumors to specific compartments.
基金supported by NSF of China (Grant No. 11471033)NCET of China (Grant No. NCET-11-0574)the Fundamental Research Funds for the Central Universities (FRF-TP-12-006B)
文摘Let T be the singular integral operator with variable kernel, T* be the adjoint of T and T# be the pseudo-adjoint of T. Let TIT2 be the product of T1 and T2, T1 o T2 be the pseudo product of T1 and T2. In this paper, we establish the boundedness for commutators of these operators and the fractional differentiation operator D^γ on the weighted Morrey spaces.
基金supported by SQU Grant No.IG/SCI/DOMS/16/12The second author was partially supported by NSFC(11720101003)the Project of International Science and Technology Cooperation Innovation Platform in Universities in Guangdong Province(2014KGJHZ007)
文摘We characterize boundedness and compactness of products of differentiation op- erators and weighted composition operators between weighted Banach spaces of analytic functions and weighted Zygmund spaces or weighted Bloch spaces with general weights.
基金Y.Wang's research was supported by the Natural Science Foundation of Luliang University(XN201510).
文摘We introduce a novel numerical method for solving two-sided space fractional partial differential equations in two-dimensional case.The approximation of the space fractional Riemann-Liouville derivative is based on the approximation of the Hadamard finite-part integral which has the convergence order O(h^3-a),where h is the space step size and α∈(1,2)is the order of Riemann-Liouville fractional derivative.Based on this scheme,we introduce a shifted finite difference method for solving space fractional partial differential equations.We obtained the error estimates with the convergence orders O(τ+h^3-a+h^β),where τ is the time step size and β>0 is a parameter which measures the smoothness of the fractional derivatives of the solution of the equation.Unlike the numerical methods for solving space fractional partial differential equations constructed using the standard shifted Griinwald-Letnikov formula or higher order Lubich's methods which require the solution of the equation to satisfy the homogeneous Dirichlet boundary condition to get the firstorder convergence,the numerical method for solving the space fractional partial differential equation constructed using the Hadamard finite-part integral approach does not require the solution of the equation to satisfy the Dirichlet homogeneous boundary condition.Numerical results show that the experimentally determined convergence order obtained using the Hadamard finite-part integral approach for solving the space fractional partial differential equation with non-homogeneous Dirichlet boundary conditions is indeed higher than the convergence order obtained using the numerical methods constructed with the standard shifted Griinwald-Letnikov formula or Lubich's higher order approximation schemes.
文摘In this paper, the fluid flow differential equation based on the homogenous reservoirs model is first reviewed. Then a theorem about the formal similarity of solutions in the Laplace space with outer boundary conditions and inner boundary condition is presented and proved. Lastly, a corollary of our theorem is given particularly on inner boundary. The obtained results are very helpful for understanding inherent laws of relevant engineering science and designing practical analysis software.
基金Supported by the Key Program of National Natural Science Foundation of China(Nos.61077071,51075349)Program of National Natural Science Foundation of Hebei Province(Nos.F2011203207,F2010001312)
文摘Phase space reconstruction is the first step of recognizing the chaotic time series.On the basis of differential entropy ratio method,the embedding dimension opt m and time delay t are optimal for the state space reconstruction could be determined.But they are not the optimal parameters accepted for prediction.This study proposes an improved method based on the differential entropy ratio and Radial Basis Function(RBF)neural network to estimate the embedding dimension m and the time delay t,which have both optimal characteristics of the state space reconstruction and the prediction.Simulating experiments of Lorenz system and Doffing system show that the original phase space could be reconstructed from the time series effectively,and both the prediction accuracy and prediction length are improved greatly.
基金Project supported by the Hi-Tech Research and Development Pro-gram (863) of China (No. 2003AA123310) and the National Natural Science Foundation of China (No. 60272079)
文摘Differential space-time coding was proposed recently in the literature for multi-antenna systems, where neither the transmitter nor the receiver knows the fading coefficients. Among existing schemes, double differential space-time (DDST) coding is of special interest because it is applicable to continuous fast time-varying channels. However, it is less effective in fre- quency-selective fading channels. This paper’s authors derived a novel time-frequency double differential space-time (TF-DDST) coding scheme for multi-antenna orthogonal frequency division multiplexing (OFDM) systems in a time-varying fre- quency-selective fading environment, where double differential space-time coding is introduced into both time domain and fre- quency domain. Our proposed TF-DDST-OFDM system has a low-complexity non-coherent decoding scheme and is robust for time- and frequency-selective Rayleigh fading. In this paper, we also propose the use of state-of-the-art low-density parity-check (LDPC) code in serial concatenation with our TF-DDST scheme as a channel code. Simulations revealed that the LDPC based TF-DDST OFDM system has low decoding complexity and relatively better performance.
文摘The aim of this work is to study the existence of a periodic solution for some neutral partial functional differential equations. Our approach is based on the R-boundedness of linear operators Lp-multipliers and UMD-spaces.
文摘This paper investigates the maximal and minimal solutions of initial value problems for second order nonlinear integro-differential equations of Volterra type on a finite interval in a Banach space by establishing a comparison result and using the monotone iterative technique.