In this work,we study the performance of one shot and concatenated deleting machines(DMs).We show that the output state of one shot DMs are mixed inseparable,and do not violate Bell's inequality but can be used as...In this work,we study the performance of one shot and concatenated deleting machines(DMs).We show that the output state of one shot DMs are mixed inseparable,and do not violate Bell's inequality but can be used as a teleportation channel for all values of the input state parameters.On the other hand,we observe in the concatenation of different DMs that the output states are mixed inseparable and do not violate Bell's inequality,and cannot be used as a teleportation channel.Further,some important attributes such as inseparability,violation of Bell's inequality,and teleportation fidelity of the DMs remain unchanged under the order of concatenation.In this context of a teleportation channel,one shot DMs are useful when compared to concatenated DMs.展开更多
In robust regression we often have to decide how many are the unusualobservations, which should be removed from the sample in order to obtain better fitting for the restof the observations. Generally, we use the basic...In robust regression we often have to decide how many are the unusualobservations, which should be removed from the sample in order to obtain better fitting for the restof the observations. Generally, we use the basic principle of LTS, which is to fit the majority ofthe data, identifying as outliers those points that cause the biggest damage to the robust fit.However, in the LTS regression method the choice of default values for high break down-point affectsseriously the efficiency of the estimator. In the proposed approach we introduce penalty cost fordiscarding an outlier, consequently, the best fit for the majority of the data is obtained bydiscarding only catastrophic observations. This penalty cost is based on robust design weights andhigh break down-point residual scale taken from the LTS estimator. The robust estimation is obtainedby solving a convex quadratic mixed integer programming problem, where in the objective functionthe sum of the squared residuals and penalties for discarding observations is minimized. Theproposed mathematical programming formula is suitable for small-sample data. Moreover, we conduct asimulation study to compare other robust estimators with our approach in terms of their efficiencyand robustness.展开更多
In this paper, we introduce some new definitions such as the U＊L＊ condition to describe the zero-divisor graph G = F（P） of a poser P, and give a new and quick proof to a main result in [2, 4]. By deleting a typica...In this paper, we introduce some new definitions such as the U＊L＊ condition to describe the zero-divisor graph G = F（P） of a poser P, and give a new and quick proof to a main result in [2, 4]. By deleting a typical vertex with least degree, we provide an algorithm for finding a maximum clique of a finite graph G. We study some properties of the zero-divisor graphs of posets concerning diameters and girths. We also provide stratified presentations of posets.展开更多
In conventional quantum mechanics,quantum no-deleting and no-cloning theorems indicate that two different and nonorthogonal states cannot be perfectly and deterministically deleted and cloned,respectively.Here,we inve...In conventional quantum mechanics,quantum no-deleting and no-cloning theorems indicate that two different and nonorthogonal states cannot be perfectly and deterministically deleted and cloned,respectively.Here,we investigate the quantum deleting and cloning in a pseudo-unitary system.We first present a pseudo-Hermitian Hamiltonian with real eigenvalues in a two-qubit system.By using the pseudo-unitary operators generated from this pseudo-Hermitian Hamiltonian,we show that it is possible to delete and clone a class of two different and nonorthogonal states,and it can be generalized to arbitrary two different and nonorthogonal pure qubit states.Furthermore,state discrimination,which is strongly related to quantum no-cloning theorem,is also discussed.Last but not least,we simulate the pseudo-unitary operators in conventional quantum mechanics with post-selection,and obtain the success probability of simulations.Pseudo-unitary operators are implemented with a limited efficiency due to the post-selections.Thus,the success probabilities of deleting and cloning in the simulation by conventional quantum mechanics are less than unity,which maintain the quantum no-deleting and no-cloning theorems.展开更多
In order to discover the probability distribution feature of edge in aviation network adjacent matrix of China and on the basis of this feature to establish an algorithm of searching non-overlap community structure in...In order to discover the probability distribution feature of edge in aviation network adjacent matrix of China and on the basis of this feature to establish an algorithm of searching non-overlap community structure in network to reveal the inner principle of complex network with the feature of small world in aspect of adjacent matrix and community structure,aviation network adjacent matrix of China was transformed according to the node rank and the matrix was arranged on the basis of ascending node rank with the center point as original point.Adjacent probability from the original point to extension around in approximate area was calculated.Through fitting probability distribution curve,power function of probability distribution of edge in adjacent matrix arranged by ascending node rank was found.According to the feature of adjacent probability distribution,deleting step by step with node rank ascending algorithm was set up to search non-overlap community structure in network and the flow chart of algorithm was given.A non-overlap community structure with 10 different scale communities in aviation network of China was found by the computer program written on the basis of this algorithm.展开更多
文摘In this work,we study the performance of one shot and concatenated deleting machines(DMs).We show that the output state of one shot DMs are mixed inseparable,and do not violate Bell's inequality but can be used as a teleportation channel for all values of the input state parameters.On the other hand,we observe in the concatenation of different DMs that the output states are mixed inseparable and do not violate Bell's inequality,and cannot be used as a teleportation channel.Further,some important attributes such as inseparability,violation of Bell's inequality,and teleportation fidelity of the DMs remain unchanged under the order of concatenation.In this context of a teleportation channel,one shot DMs are useful when compared to concatenated DMs.
文摘In robust regression we often have to decide how many are the unusualobservations, which should be removed from the sample in order to obtain better fitting for the restof the observations. Generally, we use the basic principle of LTS, which is to fit the majority ofthe data, identifying as outliers those points that cause the biggest damage to the robust fit.However, in the LTS regression method the choice of default values for high break down-point affectsseriously the efficiency of the estimator. In the proposed approach we introduce penalty cost fordiscarding an outlier, consequently, the best fit for the majority of the data is obtained bydiscarding only catastrophic observations. This penalty cost is based on robust design weights andhigh break down-point residual scale taken from the LTS estimator. The robust estimation is obtainedby solving a convex quadratic mixed integer programming problem, where in the objective functionthe sum of the squared residuals and penalties for discarding observations is minimized. Theproposed mathematical programming formula is suitable for small-sample data. Moreover, we conduct asimulation study to compare other robust estimators with our approach in terms of their efficiencyand robustness.
基金Supported by the National Natural Science Foundation of China （11271250）.Acknowledgements. The authors express their sincere thanks to the referees for the careful reading and suggestions which improved the exposition of the paper.
文摘In this paper, we introduce some new definitions such as the U＊L＊ condition to describe the zero-divisor graph G = F（P） of a poser P, and give a new and quick proof to a main result in [2, 4]. By deleting a typical vertex with least degree, we provide an algorithm for finding a maximum clique of a finite graph G. We study some properties of the zero-divisor graphs of posets concerning diameters and girths. We also provide stratified presentations of posets.
基金This work was funded by the National Natural Science Foundation of China(Grant Nos.11734015,11474049,and 11674056)the K.C.Wong Magna Fund in Ningbo University,the financial support from Research Grants Council of Hong Kong(RGC,Hong Kong)(Grant No.538213)+1 种基金M.G.was supported by the National Youth Thousand Talents Program(Grant No.KJ2030000001)the USTC start-up funding(Grant No.KY2030000053).
文摘In conventional quantum mechanics,quantum no-deleting and no-cloning theorems indicate that two different and nonorthogonal states cannot be perfectly and deterministically deleted and cloned,respectively.Here,we investigate the quantum deleting and cloning in a pseudo-unitary system.We first present a pseudo-Hermitian Hamiltonian with real eigenvalues in a two-qubit system.By using the pseudo-unitary operators generated from this pseudo-Hermitian Hamiltonian,we show that it is possible to delete and clone a class of two different and nonorthogonal states,and it can be generalized to arbitrary two different and nonorthogonal pure qubit states.Furthermore,state discrimination,which is strongly related to quantum no-cloning theorem,is also discussed.Last but not least,we simulate the pseudo-unitary operators in conventional quantum mechanics with post-selection,and obtain the success probability of simulations.Pseudo-unitary operators are implemented with a limited efficiency due to the post-selections.Thus,the success probabilities of deleting and cloning in the simulation by conventional quantum mechanics are less than unity,which maintain the quantum no-deleting and no-cloning theorems.
基金National Natural Science Foundation of China(71971017).
文摘In order to discover the probability distribution feature of edge in aviation network adjacent matrix of China and on the basis of this feature to establish an algorithm of searching non-overlap community structure in network to reveal the inner principle of complex network with the feature of small world in aspect of adjacent matrix and community structure,aviation network adjacent matrix of China was transformed according to the node rank and the matrix was arranged on the basis of ascending node rank with the center point as original point.Adjacent probability from the original point to extension around in approximate area was calculated.Through fitting probability distribution curve,power function of probability distribution of edge in adjacent matrix arranged by ascending node rank was found.According to the feature of adjacent probability distribution,deleting step by step with node rank ascending algorithm was set up to search non-overlap community structure in network and the flow chart of algorithm was given.A non-overlap community structure with 10 different scale communities in aviation network of China was found by the computer program written on the basis of this algorithm.
