A multiaxial elastic potential with error-minimizing approximation to rubberlike elasticity

This study is concerned with a new,explicit approach by means of which forms of the large strain elastic potential for multiaxial rubberlike elasticity may be obtained based on data for a single deformation mode.As a departure from usual studies,here for the first time errors may be estimated and rendered minimal for all possible deformation modes and,furthermore,failure behavior may be incorporated.Numerical examples presented are in accurate agreement with Treloar＇s well-known data.

QUANTUM COMPLEXITY OF SOBOLEV IMBEDDINGS

Using a new reduction approach, we derive a lower bound of quantum com- plexity for the approximation of imbeddings from anisotropic Sobolev classes B （Wp^r （[0, 1]^d）） to anisotropic Sobolev space Wq^s（[0, 1]d） for all 1 ≤ p, q ≤ ∞. When p ≥ q, we show this bound is optimal by deriving the matching upper bound. In this case, the quantum al- gorithms are not significantly better than the classical deterministic or randomized ones. We conjecture that the bound is also optimal for the case p 〈 q. This conjecture was confirmed in the situation s = 0.

QUANTUM COMPLEXITY OF THE APPROXIMATION FOR THE CLASSES B(W_p^r([0,1]~d)) AND B(H_p^r([0,1]~d))

We study the approximation of functions from anisotropic Sobolev classes b（WpR（[0, 1]d）） and HSlder-Nikolskii classes B（HPr（[0, 1]d）） in the Lq （[0, 1]d） norm with q 〈 p in the quantum model of computation. We determine the quantum query complexity of this problem up to logarithmic factors. It shows that the quantum algorithms are significantly better than the classical deterministic or randomized algorithms.

Optimal sensor placement for structural response estimation

A methodology, termed estimation error minimization(EEM) method, was proposed to determine the optimal number and locations of sensors so as to better estimate the vibration response of the entire structure. Utilizing the limited sensor measurements, the entire structure response can be estimated based on the system equivalent reduction-expansion process(SEREP) method. In order to compare the capability of capturing the structural vibration response with other optimal sensor placement(OSP) methods, the effective independence(EI) method, modal kinetic energy(MKE) method and modal assurance criterion(MAC) method, were also investigated. A statistical criterion, root mean square error(RMSE), was employed to assess the magnitude of the estimation error between the real response and the estimated response. For investigating the effectiveness and accuracy of the above OSP methods, a 31-bar truss structure is introduced as a simulation example. The analysis results show that both the maximum and mean of the RMSE value obtained from the EEM method are smaller than those from other OSP methods, which indicates that the optimal sensor configuration obtained from the EEM method can provide a more accurate estimation of the entire structure response compared with the EI, MKE and MAC methods.

Optimal cooperative beamforming design schemes for AF MOMO two-way relay channels

In this paper,beamforming parameters in multiple input multiple output(MIMO) two-way relay channels(TWRCs) are designed.We investigate three communicating scenarios,in which,the source nodes are all equipped with multiple antennas.In the first scenario,one pair of source nodes are communicating with each other under the help of a single multi-antenna equipped relay.A centralized scheme is correspondingly developed where the optimal relay beamforming(RaB) is jointly designed with the transmit beamformings(TBs) and the receive beamformings(RcBs) at both source nodes to minimize the sum of mean square errors(SMSE).In the second scenario,one pair of users in the first scenario is extended to multi-pair of source nodes.We derive a general expression of the optimal RaB matrix of this scenario in the second scheme,and based on which,a RaB matrix is designed to cancel the inter-pair interference(IPI) and to minimize the intra-pair SMSE.At last,we consider a distributed scenario where multiple single-antenna equipped relays are helping the communication between one pair of source nodes.In the scheme associated with this scenario,beamformings are developed under relay total power constraint and relay individual power constraint,respectively.The simulation results reveal that beamformings at source and relay nodes significantly improve the performance in the sense of average bit error rate(BER).The proposed multi-pair scheme has made superior progress in BER performance because it not only can cancel the IPIs but also can balance the useful signal and the noise at each user.Moreover,in one-pair scenarios,the performance of the centralized scheme is better than the distributed one,but the latter is nevertheless much more practical.

Network traffic prediction method based on improved ABC algorithm optimized EM-ELM

In order to overcome the poor generalization ability and low accuracy of traditional network traffic prediction methods, a prediction method based on improved artificial bee colony （ABC） algorithm optimized error minimized extreme learning machine （EM-ELM） is proposed. EM-ELM has good generalization ability. But many useless neurons in EM-ELM have little influences on the final network output, and reduce the efficiency of the algorithm. Based on the EM-ELM, an improved ABC algorithm is introduced to optimize the parameters of the hidden layer nodes, decrease the number of useless neurons. Network complexity is reduced. The efficiency of the algorithm is improved. The stability and convergence property of the proposed prediction method are proved. The proposed prediction method is used in the prediction of network traffic. In the simulation, the actual collected network traffic is used as the research object. Compared with other prediction methods, the simulation results show that the proposed prediction method reduces the training time of the prediction model, decreases the number of hidden layer nodes. The proposed prediction method has higher prediction accuracy and reliable performance. At the same time, the performance indicators are improved.

Optimal query error of quantum approximation on some Sobolev classes

We study the approximation of the imbedding of functions from anisotropic and generalized Sobolev classes into L q ([0, 1]d) space in the quantum model of computation. Based on the quantum algorithms for approximation of finite imbedding from L p N to L q N , we develop quantum algorithms for approximating the imbedding from anisotropic Sobolev classes B(W p r ([0, 1] d )) to L q ([0, 1] d ) space for all 1 ? q,p ? ∞ and prove their optimality. Our results show that for p < q the quantum model of computation can bring a speedup roughly up to a squaring of the rate in the classical deterministic and randomized settings.

Multicopy quantum state discrimination

In this paper, we study the problem of multicopy quantum two-state discrimination. By exploring the quantum hypothesis testing, i.e., the probabilisfic quantum cloning, we derive the upper bounds of the minimal error discrimination （MED） and the optimal unambiguous discrimination （OUD）, which coincides with the Helstrom theorem and the JS limit. Furthermore, when prior probabilities are unknown, we derive the minimax MED and the minimax OUD. Based on the optimal NM probabilistic quantum cloning, we present the optimal strategies of collective measurements of the MED and the OUD. When the number of the copies is infinite, regardless of whether prior probabilities are known or not, the success probabilities of the MED and the OUD go to 100%, in accordance with the quantum measurement hypothesis that unknown quantum state can be determined if and only if infinite identical quantum state copies are given.

Lower Bound for Quantum Integration Error on Anisotropic Sobolev Classes

We study the approximation of the integration of multivariate functions in the quantum model of computation. Using a new reduction approach we obtain a lower bound of the n-th minimal query error on anisotropic Sobolev class R（Wpr（[0, 1]d）） （r R＋d）. Then combining this result with our previous one we determine the optimal bound of n-th minimal query error for anisotropic Hblder- Nikolskii class R（H∞r（[0,1]d）） and Sobolev class R（W∞r（[0,1]d））. The results show that for these two types of classes the quantum algorithms give significant speed up over classical deterministic and randomized algorithms.

Tile selection method based on error minimization for photomosaic image creation

Photomosaic images are composite images composed of many small images called tiles.In its overall visual effect,a photomosaic image is similar to the target image,and photomosaics are also called“montage art”.Noisy blocks and the loss of local information are the major obstacles in most methods or programs that create photomosaic images.To solve these problems and generate a photomosaic image in this study,we propose a tile selection method based on error minimization.A photomosaic image can be generated by partitioning the target image in a rectangular pattern,selecting appropriate tile images,and then adding them with a weight coefficient.Based on the principles of montage art,the quality of the generated photomosaic image can be evaluated by both global and local error.Under the proposed framework,via an error function analysis,the results show that selecting a tile image using a global minimum distance minimizes both the global error and the local error simultaneously.Moreover,the weight coefficient of the image superposition can be used to adjust the ratio of the global and local errors.Finally,to verify the proposed method,we built a new photomosaic creation dataset during this study.The experimental results show that the proposed method achieves a low mean absolute error and that the generated photomosaic images have a more artistic effect than do the existing approaches.