We study the entanglement dynamics of the three-qubit Dicke model by means of the adiabatic approximation and the exact diagonalization in the parameter regime where the qubit transition frequencies are far off-resonance with the radiation field and the interaction strengths reach the ultrastrong-coupling regime. The single-mode field is prepared in the coherent state and two typical states GHZ and W are chosen as the initial three-qubit states. In the process of evolution, the interaction between the quantized field and three-qubit system leads to the generation of entanglement between the field and qubits, as well as between different parties in the three-qubit system, i.e. the pairwise entanglement of two qubits and the tripartite entanglement, which are of ongoing interest in quantum information process. The generalized concurrence and negativity are adopted to quantify different kinds of entanglement. The qubit-field entanglement never reaches the maximum and no sudden death occurs in the the tripartite entanglement for GHZ state, but it is exactly the opposite for W state. This reflects that the tripartite entanglement of the GHZ state is more robust than W sate, which is the same as in the rotating wave approximation. The results beyond the rotating wave approximation show that the pairwise entanglement gradually decreases and vanishes in the evolution of both initial states, with the tripartite entanglement periodically reaching relatively high level. This means that the interaction in system supports the tripartite entanglement at the cost of pairwise entanglement. The conclusions provide theoretical reference for the robustness of entanglement state and quantum information processing using Dicke model.
The hybrid composite materials are a new type of composite material. Due to their complex microscopic structures, it is very challenging to predict the equivalent thermal conductivities of hybrid composites. In this paper, an innovative hybrid wavelet-based learning method assisted multiscale analysis is developed to predict the effective thermal conductivities of hybrid composite materials with heterogeneous conductivity by the asymptotic homogenization method, wavelet transform method, and machine learning method. This innovative approach mainly includes two parts: off-line multi-scale modeling and on-line machine learning. Firstly, the material database about thermal transfer performance of hybrid composites is established by the asymptotic homogenization method and off-line multi-scale modeling, and then the off-line material database is preprocessed by the wavelet transform method. Secondly, the artificial neural network and support vector regression method are employed to establish the on-line machine learning model for predicting the equivalent heat conduction properties of hybrid composites. Finally, the effectiveness of the proposed hybrid wavelet-based learning method is verified by numerical experiments on the periodic and random hybrid composites. The numerical results show that the hybrid wavelet-based artificial neural network method owns the optimal capability of parameter prediction and anti-noise. Furthermore, it should be emphasized that the hybrid wavelet-based learning method can not only extract the important features of off-line material database for random hybrid composites with high-dimensional large-scale data features, but also significantly reduce the quantity of input data for ensuring the successful on-line supervised learning and improve the training efficiency and anti-noise performance of the machine learning model. The established hybrid wavelet-based learning method in this paper can not only be used to evaluate the equivalent thermal conductivities of hybrid composite materials, but also further extend to the predicting of the equivalent physical and mechanical properties of composite materials.
Compressed sensing is a revolutionary signal processing technique, which allows the signals of interest to be acquired at a sub-Nyquist rate, meanwhile still permitting the signals from highly incomplete measurements to be reconstructed perfectly. As is well known, the construction of sensing matrix is one of the key technologies to promote compressed sensing from theory to application. Because the Toeplitz sensing matrix can support fast algorithm and corresponds to discrete convolution operation, it has essential research significance. However, the conventional random Toeplitz sensing matrix, due to the uncertainty of its elements, is subject to many limitations in practical applications, such as high memory consumption and difficulty of hardware implementation. To avoid these limitations, we propose a bipolar Toeplitz block-based chaotic sensing matrix (Bi-TpCM) by combining the intrinsic advantages of Toeplitz matrix and bipolar chaotic sequence. Firstly, the generation of bipolar chaotic sequence is introduced and its statistical characteristics are analyzed, showing that the generated bipolar chaotic sequence is an independent and identically distributed Rademacher sequence, which makes it possible to construct the sensing matrix. Secondly, the proposed Bi-TpCM is constructed, and it is proved that Bi-TpCM has almost optimal theoretical guarantees in terms of the coherence, and also satisfies the restricted isometry condition. Finally, the measurement performances on one-dimensional signals and images by using the proposed Bi-TpCM are investigated and compared with those of its counterparts, including random matrix, random Toeplitz matrix, real-valued chaotic matrix, and chaotic circulant sensing matrix. The results show that Bi-TpCM not only has better performance for these testing signals, but also possesses considerable advantages in terms of the memory cost, computational complexity, and hardware realization. In particular, the proposed Bi-TpCM is extremely suitable for the compressed sensing measurement of linear time-invariant (LTI) systems with multiple inputs and single output, such as the joint parameter and time-delay estimation for finite impulse response. Moreover, the construction framework of the proposed Bi-TpCM can be extended to different chaotic systems, such as Logistic or Cat chaotic systems, and it is also possible for the proposed Bi-TpCM to derive the Hankel blocks, additional stacking of blocks, partial circulant blocks sensing matrices. With these block-based sensing architectures, we can more easily implement compressed sensing for various compressed measurement problems of LTI systems.
Electrocardiogram (ECG) diagnosis is based on the waveform, duration and amplitude of characteristic wave, which are required to have a high accuracy for ECG signal reconstruction. As an effective nonlinear signal processing method, empirical mode decomposition (EMD) has been widely used for diagnosing and reconstructing the ECG signal, but there are two problems arising here. One is the mode mixing, and the other is that the mode components used in reconstruction are identified by experience. Therefore, the method of reconstruction is not adaptive and universal, and reconstructed ECG signal loses accuracy. Firstly, we propose an improved EMD method, which is called integral mean mode decomposition (IMMD). The analysis of 5000 samples of Gaussian white noise shows that IMMD has better multi-resolution analysis ability than EMD, and it can effectively alleviate mode mixing consequently. Secondly, based on the inherent physical characteristics of ECG signal, cardiac cycle or heart rate (HR), it has practical physical significance to identify the mode components used in ECG signal reconstruction. The cardiac cycle feature acts as the intrinsic mode function (IMF) component through two modes. 1) For the low-order IMF that belongs to the ECG signal, the cardiac cycle feature acts as the amplitude modulation. The envelope of the IMF component has the characteristics of the cardiac cycle, and the frequency corresponding to the maximum amplitude in the spectrum of the envelope is equal to HR. 2) For the high-order IMF that belongs to the ECG signal, the cardiac cycle feature acts as frequency modulation. Those IMF components have the harmonic characteristics of periodic heartbeats, and the maximum amplitude in the spectrum corresponds to an integral multiple of HR (usually 1－3 times). The noise attributed to IMF component cannot show the above two cardiac cycle characteristics. Thus the proposed method is adaptive and universal. The 47 ECG signals with baseline drift and muscle artifact noise are tested. The results show that the proposed method is more effective than the variational mode decomposition (VMD), Haar wavelet with soft threshold, ensemble empirical mode decomposition (EEMD) and EMD. Among the 47 correlation coefficients between reconstructed and original ECG signals, the proposed method has 31 better than VMD, 33 better than Haar wavelet, 42 better than EEMD and 45 better than EMD. The mean of 47 correlation coefficients from the proposed method is 0.8904, and the variance is 0.0071, which shows that the proposed method has good performance and stability.