Principal component analysis for second-order stationary vector time series

We extend the principal component analysis (PCA) to second-order stationary vector time series in the sense that we seek for a contemporaneous linear transformation for a $p$-variate time series such that the transformed series is segmented into several lower-dimensional subseries, and those subseries are uncorrelated with each other both contemporaneously and serially. Therefore those lower-dimensional series can be analysed separately as far as the linear dynamic structure is concerned. Technically it boils down to an eigenanalysis for a positive definite matrix. When $p$ is large, an additional step is required to perform a permutation in terms of either maximum cross-correlations or FDR based on multiple tests. The asymptotic theory is established for both fixed $p$ and diverging $p$ when the sample size $n$ tends to infinity. Numerical experiments with both simulated and real data sets indicate that the proposed method is an effective initial step in analysing multiple time series data, which leads to substantial dimension reduction in modelling and forecasting high-dimensional linear dynamical structures. Unlike PCA for independent data, there is no guarantee that the required linear transformation exists. When it does not, the proposed method provides an approximate segmentation which leads to the advantages in, for example, forecasting for future values. The method can also be adapted to segment multiple volatility processes.Comment: The original title dated back to October 2014 is "Segmenting Multiple Time Series by Contemporaneous Linear Transformation: PCA for Time Series

High dimensional stochastic regression with latent factors, endogeneity and nonlinearity

We consider a multivariate time series model which represents a high dimensional vector process as a sum of three terms: a linear regression of some observed regressors, a linear combination of some latent and serially correlated factors, and a vector white noise. We investigate the inference without imposing stationary conditions on the target multivariate time series, the regressors and the underlying factors. Furthermore we deal with the endogeneity that there exist correlations between the observed regressors and the unobserved factors. We also consider the model with nonlinear regression term which can be approximated by a linear regression function with a large number of regressors. The convergence rates for the estimators of regression coefficients, the number of factors, factor loading space and factors are established under the settings when the dimension of time series and the number of regressors may both tend to infinity together with the sample size. The proposed method is illustrated with both simulated and real data examples

Analysis of the forming characteristics for Cu/Al bimetal tubes produced by the spinning process

Tube spinning technology represents a process with high forming precision and good flexibility and is increasingly being used in the manufacture of bimetal composite tubular structures. In the present study, a forming analysis of clad tube and base tube in spinning process was conducted through numerical simulations and experiments. There was an equivalent stress transition on the interface since the stress transmission was retarded from clad tube to base tube. The yield strength became a main consideration during a design bimetal composite tube. Meanwhile, the strain distributions in axial direction, tangential direction, and radial direction were also investigated to determine the deformation characteristics of each component. As the press amount increased, the strain of clad tube changed more than base tube. As the feed rate increased, the strain decreased in axial direction and tangential direction but almost unchanged in radial direction. Simultaneously, a method for controlling the wall thickness of the clad tube and the base tube is proposed. These results to guide the design of bimetal tube composite spinning process have the certain meanings

High-dimensional and banded vector autoregressions

We consider a class of vector autoregressive models with banded coefficient matrices. The setting represents a type of sparse structure for high-dimensional time series, though the implied autocovariance matrices are not banded. The structure is also practically meaningful when the order of component time series is arranged appropriately. The convergence rates for the estimated banded autoregressive coefficient matrices are established. We also propose a Bayesian information criterion for determining the width of the bands in the coefficient matrices, which is proved to be consistent. By exploring some approximate banded structure for the autocovariance functions of banded vector autoregressive processes, consistent estimators for the auto-covariance matrices are constructed

Relationship of Family Environment, Psychological Resilience, Campus Bullying with Tobacco Use among Preadolescents

Objective. To explore the relationship between family environment, psychological resilience, campus bullying and tobacco use in early adolescence. Methods. According to the principle of cluster sampling, 4,792 students from grade 4 to grade 6 in five primary schools in Baise City and county were selected from February to November 2018, including 2,522 males (52.63%), 2,236 females (46.66%)and 34 missing genders (0.71%); the average age was (11.8 ± 0.5) years; 2,721 students in urban areas (56.78%) and 2,071 students in county towns (43.22%); 4,313 Zhuang (90.00%), 365 Han (7.62%), 98 other ethnic groups (Yao, Miao, Yi, etc.) (2.05%). The General Family Environment Questionnaire, Adolescent Mental Resilience Scale, School Bullying Questionnaire, and Tobacco Use Questionnaire were used for evaluation, and logistic regression was used to analyze the effect relationship between the study variables. Results. 467 people tried to smoke, and the total detection rate was 9.75%. The number of smokers was 334, and the total detection rate was 6.97%. Boys’ tobacco attempt and smoking behavior were higher than girls (χ2 were 57.230 and 56.013, P < 0. 001). Multivariate logistic regression analysis showed that the risk of tobacco attempt of boys was 2.37 times thanthat of girls (OR = 0.468, 95% CI 0.377 ~ 0.582), the risk of smoking in boys is 2.5 times that in girls 32 times (OR = 0.422, 95% CI 0.324 ~ 0.551); older adolescents had more tobacco attempts (OR = 1.609, 95% CI 1.446 ~ 1.791)and smoking behavior (OR = 2.026, 95% CI 1.776 ~ 2.310); campus bullying increased the risk of smoking behavior among adolescents (OR = 1.106, 95% CI 1.073 ~ 1.140). Psychological resilience (personal strength), family intimacy and family rules can effectively reduce the risk of adolescent tobacco attempts (personal strength, OR = 0.964, 95% CI = 0.951 ~ 0.976; family intimacy, OR = 0.946, 95% CI 0.892 ~ 0.984; family rules, OR = 0.949, 95% CI 0.930 ~ 0.965) and smoking behavior (personal strength, OR = 0.962, 95% CI 0.947 ~ 0.977; family intimacy, OR = 0.937, 95% CI 0.885 ~ 0.992; family rules, OR = 0.952, 95% CI 0.932 ~ 0.973). Conclusion. Campus bullying increases the risk of smoking behavior among adolescents. Psychological resilience (personal strength), family intimacy and family rules can effectively reduce teenagers’ tobacco attempts and smoking behavior

Label-free photoacoustic tomography of whole mouse brain structures ex vivo

Capitalizing on endogenous hemoglobin contrast, photoacoustic-computed tomography (PACT), a deep-tissue high-resolution imaging modality, has drawn increasing interest in neuroimaging. However, most existing studies are limited to functional imaging on the cortical surface and the deep brain structural imaging capability of PACT has never been demonstrated. Here, we explicitly studied the limiting factors of deep brain PACT imaging. We found that the skull distorted the acoustic signal and blood suppressed the structural contrast from other chromophores. When the two effects are mitigated, PACT can potentially provide high-resolution label-free imaging of structures in the entire mouse brain. With 100-μm in-plane resolution, we can clearly identify major structures of the brain, which complements magnetic resonance microscopy for imaging small-animal brain structures. Spectral PACT studies indicate that structural contrasts mainly originate from cytochrome distribution and that the presence of lipid sharpens the image contrast; brain histology results provide further validation. The feasibility of imaging the structure of the brain in vivo is also discussed. Our results demonstrate that PACT is a promising modality for both structural and functional brain imaging

A Simple and Low-Cost Strategy to Improve Conidial Yield and Stress Resistance of Trichoderma guizhouense through Optimizing Illumination Conditions

Light is perceived by photoreceptors in fungi and further integrated into the stress-activated MAPK HOG pathway, and thereby potentially activates the expression of genes for stress responses. This indicates that the precise control of light conditions can likely improve the conidial yield and stress resistance to guarantee the low cost and long shelf life of Trichoderma-based biocontrol agents and biofertilizers. In this study, effects of wavelengths and intensities of light on conidial yield and stress tolerance to osmotic, oxidative and pH stresses in Trichoderma guizhouense were investigated. We found that 2 μmol photons/(m$^{2}$ × s) of blue light increased the conidial yield more than 1000 folds as compared to dark condition and simultaneously enhanced conidial stress resistance. The enhanced conidial stress resistance is probably due to the upregulated stress-related genes in blue light, which is under the control of the blue light receptor BLR1 and the MAP kinase HOG1

10-qubit entanglement and parallel logic operations with a superconducting circuit

Here we report on the production and tomography of genuinely entangled Greenberger-Horne-Zeilinger states with up to 10 qubits connecting to a bus resonator in a superconducting circuit, where the resonator-mediated qubit-qubit interactions are used to controllably entangle multiple qubits and to operate on different pairs of qubits in parallel. The resulting 10-qubit density matrix is unambiguously probed, with a fidelity of $0.668 \pm 0.025$. Our results demonstrate the largest entanglement created so far in solid-state architectures, and pave the way to large-scale quantum computation.Comment: Revised version with 16 pages, 13 figures, and 2 table