In this paper,we investigate the global complexity bound for the inexact Levenberg–Marquardt method,where the Jacobian may be perturbed and the solution is possibly not exact.Under reasonable assumptions,we show that...In this paper,we investigate the global complexity bound for the inexact Levenberg–Marquardt method,where the Jacobian may be perturbed and the solution is possibly not exact.Under reasonable assumptions,we show that the global complexity bound is O(ε^(−2)),which is the same as the exact case.We also show that it can be reduced to O(lgε^(−1))under some regularity assumption.展开更多
It is reported that two kinds of specific mass spectrometric fragmentations are generated from dissociations of the intermediates of both the ion-neutral complex and the proton-bound complex. Collision-induced dissoci...It is reported that two kinds of specific mass spectrometric fragmentations are generated from dissociations of the intermediates of both the ion-neutral complex and the proton-bound complex. Collision-induced dissociation, isotopic labelling, and semi-empirical AM1 calculations were used to investigate the formation mechanism of the ion of m/z 139 from ionized tetrahydroimidazole-substituted methylene beta-diketones and the unimolecular fragmentations pathway of 3-phenyl-1-butyn-3-ol upon electron impact.展开更多
We focus on the complexity of a special flow built over an irrational rotation of the unit circle and under a roof function on the unit circle.We construct a weak mixing minimal special flow with bounded topological c...We focus on the complexity of a special flow built over an irrational rotation of the unit circle and under a roof function on the unit circle.We construct a weak mixing minimal special flow with bounded topological complexity.We also prove that if the roof function is C^(∞),then the special flow has sub-polynomial topological complexity and the time one map meets the condition of Sarnak’s conjecture.展开更多
A k coloring(not necessarily proper) of vertices of a graph is called acyclic, if for every pair of distinct colors i and j the subgraph induced by the edges whose endpoints have colors i and j is acyclic. We consider...A k coloring(not necessarily proper) of vertices of a graph is called acyclic, if for every pair of distinct colors i and j the subgraph induced by the edges whose endpoints have colors i and j is acyclic. We consider some generalized acyclic k colorings, namely, we require that each color class induces an acyclic or bounded degree graph. Mainly we focus on graphs with maximum degree 5. We prove that any such graph has an acyclic 5 coloring such that each color class induces an acyclic graph with maximum degree at most 4. We prove that the problem of deciding whether a graph G has an acyclic 2 coloring in which each color class induces a graph with maximum degree at most 3 is NP complete, even for graphs with maximum degree 5. We also give a linear time algorithm for an acyclic t improper coloring of any graph with maximum degree d assuming that the number of colors is large enough.展开更多
In this paper we introduce two metrics:the max metric d_(n,q)and the mean metric d_(n,q).We give an equivalent characterization of rigid measure preserving systems by the two metrics.It turns out that an invariant mea...In this paper we introduce two metrics:the max metric d_(n,q)and the mean metric d_(n,q).We give an equivalent characterization of rigid measure preserving systems by the two metrics.It turns out that an invariant measureμon a topological dynamical system(X,T)has bounded complexity with respect to d_(n,q)if and only ifμhas bounded complexity with respect to d_(n,q)if and only if(X,B_X,μ,T)is rigid.We also obtain computation formulas of the measure-theoretic entropy of an ergodic measure preserving system(resp.the topological entropy of a topological dynamical system)by the two metrics dn,q and dn,q.展开更多
In this paper,we undertake further investigation to alleviate the issue of limit cycling behavior in training generative adversarial networks(GANs)through the proposed predictive centripetal acceleration algorithm(PCA...In this paper,we undertake further investigation to alleviate the issue of limit cycling behavior in training generative adversarial networks(GANs)through the proposed predictive centripetal acceleration algorithm(PCAA).Specifically,we first derive the upper and lower complexity bounds of PCAA for a general bilinear game,with the last-iterate convergence rate notably improving upon previous results.Then,we combine PCAA with the adaptive moment estimation algorithm(Adam)to propose PCAA-Adam,for practical training of GANs to enhance their generalization capability.Finally,we validate the effectiveness of the proposed algorithm through experiments conducted on bilinear games,multivariate Gaussian distributions,and the CelebA dataset,respectively.展开更多
In this paper,we present a primal-dual interior point algorithm for semidefinite optimization problems based on a new class of kernel functions.These functions constitute a combination of the classic kernel function a...In this paper,we present a primal-dual interior point algorithm for semidefinite optimization problems based on a new class of kernel functions.These functions constitute a combination of the classic kernel function and a barrier term.We derive the complexity bounds for large and small-update methods respectively.We show that the best result of iteration bounds for large and small-update methods can be achieved,namely O(q√n(log√n)^q+1/q logn/ε)for large-update methods and O(q^3/2(log√q)^q+1/q√nlogn/ε)for small-update methods.We test the efficiency and the validity of our algorithm by running some computational tests,then we compare our numerical results with results obtained by algorithms based on different kernel functions.展开更多
基金This work was partially supported by the National Natural Science Foundation of China(No.11571234).
文摘In this paper,we investigate the global complexity bound for the inexact Levenberg–Marquardt method,where the Jacobian may be perturbed and the solution is possibly not exact.Under reasonable assumptions,we show that the global complexity bound is O(ε^(−2)),which is the same as the exact case.We also show that it can be reduced to O(lgε^(−1))under some regularity assumption.
文摘It is reported that two kinds of specific mass spectrometric fragmentations are generated from dissociations of the intermediates of both the ion-neutral complex and the proton-bound complex. Collision-induced dissociation, isotopic labelling, and semi-empirical AM1 calculations were used to investigate the formation mechanism of the ion of m/z 139 from ionized tetrahydroimidazole-substituted methylene beta-diketones and the unimolecular fragmentations pathway of 3-phenyl-1-butyn-3-ol upon electron impact.
基金supported by NNSF of China(11431012,11731003)supported by NNSF of China(11801538,11871188).
文摘We focus on the complexity of a special flow built over an irrational rotation of the unit circle and under a roof function on the unit circle.We construct a weak mixing minimal special flow with bounded topological complexity.We also prove that if the roof function is C^(∞),then the special flow has sub-polynomial topological complexity and the time one map meets the condition of Sarnak’s conjecture.
基金supported by the Minister of Science and Higher Education of Poland (Grant No. JP2010009070)
文摘A k coloring(not necessarily proper) of vertices of a graph is called acyclic, if for every pair of distinct colors i and j the subgraph induced by the edges whose endpoints have colors i and j is acyclic. We consider some generalized acyclic k colorings, namely, we require that each color class induces an acyclic or bounded degree graph. Mainly we focus on graphs with maximum degree 5. We prove that any such graph has an acyclic 5 coloring such that each color class induces an acyclic graph with maximum degree at most 4. We prove that the problem of deciding whether a graph G has an acyclic 2 coloring in which each color class induces a graph with maximum degree at most 3 is NP complete, even for graphs with maximum degree 5. We also give a linear time algorithm for an acyclic t improper coloring of any graph with maximum degree d assuming that the number of colors is large enough.
基金Supported by NNSF of China(Grant Nos.11971455,11801538,11801193,11871188,11731003 and 12090012)supported by STU Scientific Research Foundation for Talents(Grant No.NTF19047)。
文摘In this paper we introduce two metrics:the max metric d_(n,q)and the mean metric d_(n,q).We give an equivalent characterization of rigid measure preserving systems by the two metrics.It turns out that an invariant measureμon a topological dynamical system(X,T)has bounded complexity with respect to d_(n,q)if and only ifμhas bounded complexity with respect to d_(n,q)if and only if(X,B_X,μ,T)is rigid.We also obtain computation formulas of the measure-theoretic entropy of an ergodic measure preserving system(resp.the topological entropy of a topological dynamical system)by the two metrics dn,q and dn,q.
基金supported by the Major Program of National Natural Science Foundation of China(Grant Nos.11991020 and 11991024)the Team Project of Innovation Leading Talent in Chongqing(Grant No.CQYC20210309536)+1 种基金NSFC-RGC(Hong Kong)Joint Research Program(Grant No.12261160365)the Scientific and Technological Research Program of Chongqing Municipal Education Commission(Grant No.KJQN202300528)。
文摘In this paper,we undertake further investigation to alleviate the issue of limit cycling behavior in training generative adversarial networks(GANs)through the proposed predictive centripetal acceleration algorithm(PCAA).Specifically,we first derive the upper and lower complexity bounds of PCAA for a general bilinear game,with the last-iterate convergence rate notably improving upon previous results.Then,we combine PCAA with the adaptive moment estimation algorithm(Adam)to propose PCAA-Adam,for practical training of GANs to enhance their generalization capability.Finally,we validate the effectiveness of the proposed algorithm through experiments conducted on bilinear games,multivariate Gaussian distributions,and the CelebA dataset,respectively.
文摘In this paper,we present a primal-dual interior point algorithm for semidefinite optimization problems based on a new class of kernel functions.These functions constitute a combination of the classic kernel function and a barrier term.We derive the complexity bounds for large and small-update methods respectively.We show that the best result of iteration bounds for large and small-update methods can be achieved,namely O(q√n(log√n)^q+1/q logn/ε)for large-update methods and O(q^3/2(log√q)^q+1/q√nlogn/ε)for small-update methods.We test the efficiency and the validity of our algorithm by running some computational tests,then we compare our numerical results with results obtained by algorithms based on different kernel functions.
