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

2-(4-Fluoro­phen­yl)-4-(4-meth­oxy­phen­yl)-5-(piperidin-1-ylmeth­yl)thia­zole

In the title compound, C22H23FN2OS, the piperidine ring shows chair confirmation and the two benzene rings make a dihedral angle of 17.0 (6)°. The thia­zole fragment is essentially planar with an r.m.s. deviation of 0.004 (2) Å and a maximum deviation of 0.006 (2) Å.. In the crystal, inter­molecular C—H⋯π inter­actions lead to the formation of a layer structure

Analysis of primary resistance mutations to HIV-1 entry inhibitors in therapy naive subtype C HIV-1 infected mother– infant pairs from Zambia

Background—Small molecular CCR5 inhibitors represent a new class of drugs for treating HIV-1 infection. The evaluation of the primary resistance mutations associated with entry inhibitors during HIV-1 perinatal transmission is required because they may have a profound impact on the clinical management in MTCT. Objectives—To evaluate the primary resistance mutations to maraviroc and vicriviroc during perinatal transmission and analyze the sensitivity of Env derived from mother–infant pairs to maraviroc. Study design—Nine MIPs infected by subtype C HIV-1 were recruited to analyze the prevalence and transmission of primary resistance mutations to maraviroc and vicriviroc. Moreover, Env derived from six MIPs were employed to construct provirus clones and to analyze the sensitivity to maraviroc. Results—Mutations A316T, conferring partial resistance to maraviroc, T307I and R315Q, both conferring partial resistance to vicriviroc are prevalent in mother and infant cohorts, indicating the transmission of primary resistance mutations during HIV-1 perinatal transmission. However, the mutations of acutely infected mothers seem to directly transmit to their corresponding infants, while some mutations at low frequency of chronically infected mothers would be lost during transmission. Moreover, provirus clones derived from acutely infected MIPs are less susceptible to maraviroc than those from chronically infected MIPs. Conclusions—Our study suggests that the transmission mode of primary resistance mutations and the sensitivity to maraviroc are dependent on infection status of MIPs either acutely or chronically infected. These results may indicate that higher dose of maraviroc could be needed for treatment of acutely infected MIPs compared to chronically infected MIPs

Analysis of primary resistance mutations to HIV-1 entry inhibitors in therapy naive subtype C HIV-1 infected mother– infant pairs from Zambia

Background—Small molecular CCR5 inhibitors represent a new class of drugs for treating HIV-1 infection. The evaluation of the primary resistance mutations associated with entry inhibitors during HIV-1 perinatal transmission is required because they may have a profound impact on the clinical management in MTCT. Objectives—To evaluate the primary resistance mutations to maraviroc and vicriviroc during perinatal transmission and analyze the sensitivity of Env derived from mother–infant pairs to maraviroc. Study design—Nine MIPs infected by subtype C HIV-1 were recruited to analyze the prevalence and transmission of primary resistance mutations to maraviroc and vicriviroc. Moreover, Env derived from six MIPs were employed to construct provirus clones and to analyze the sensitivity to maraviroc. Results—Mutations A316T, conferring partial resistance to maraviroc, T307I and R315Q, both conferring partial resistance to vicriviroc are prevalent in mother and infant cohorts, indicating the transmission of primary resistance mutations during HIV-1 perinatal transmission. However, the mutations of acutely infected mothers seem to directly transmit to their corresponding infants, while some mutations at low frequency of chronically infected mothers would be lost during transmission. Moreover, provirus clones derived from acutely infected MIPs are less susceptible to maraviroc than those from chronically infected MIPs. Conclusions—Our study suggests that the transmission mode of primary resistance mutations and the sensitivity to maraviroc are dependent on infection status of MIPs either acutely or chronically infected. These results may indicate that higher dose of maraviroc could be needed for treatment of acutely infected MIPs compared to chronically infected MIPs

Disease History and Life History Predict Behavioral Control of the COVID-19 Pandemic

202106 bcwhVersion of RecordRGC15608415Publishe

Three Kinds of Special Relativity via Inverse Wick Rotation

Since the special relativity can be viewed as the physics in an inverse Wick rotation of 4-d Euclid space, which is at almost equal footing with the 4-d Riemann/Lobachevski space, there should be important physics in the inverse Wick rotation of 4-d Riemann/Lobachevski space. Thus, there are three kinds of special relativity in de Sitter/Minkowski/anti-de Sitter space at almost equal footing, respectively. There is an instanton tunnelling scenario in the Riemann-de Sitter case that may explain why \La be positive and link with the multiverse.Comment: 3 pages, no figures, to appear in Chin. Phys. Let