For multivariate functional data, it is quite challenging to model the cross-covariance structure which consists of dual aspects of multivariate and functional features. To simplify the cross-covariance analysis, the assumption of partial separability is widely used to decompose the data into an additive form of multivariate random variables and functional components. In this article, we propose hypothesis testing procedures to examine the validity of partial separability. We study the asymptotic properties of the l2 and l infinity norm of the test statistic, resulting in a chi-square type mixture test and a high-dimensional test that are suitable to finite-or high-dimensional multivariate functional data with diverse multivariate dependence. We assess the empirical performance of the proposed tests through two simulation studies for multivariate functional data and graphical functional data, followed by two corresponding real examples: multichannel tonnage data and electroencephalography data.

Introduction: Toll-like receptor 4 (TLR4) has emerged as a crucial factor in the pathogenesis of various kidney disease including diabetic kidney disease (DKD), whereas its intricate role in the complex pathophysiology of DKD and associated diabetic podocyte injury remains inadequately elucidated. Objectives: In this study we aimed to investigate the regulatory role and mechanism of TLR4 dysregulation in diabetic podocyte injury. Results: Upregulation of TLR4 was demonstrated in high glucose (HG)-challenged podocytes and in streptozocin (STZ)-induced diabetic renal tissue. Mechanistically, TLR4 signaling activation upon hyperglycemia stimulation, mediated by its adaptor protein myeloid differentiation factor 88 (MyD88), initiated a downstream protein kinase C delta (PKCδ)/Src homology-2 domain-containing phosphatase-1 (SHP-1) signaling cascade. This cascade subsequently triggered endoplasmic reticulum (ER) stress and release of the inflammatory chemokine monocyte chemotactic protein 1 (MCP-1), which exacerbated damage to slit diaphragm (SD) proteins and disrupted cytoskeletal structure, enhanced cell motility, and promoted inflammation in podocytes. Podocyte-specific deletion of TLR4 was able to alleviate diabetic podocyte injury and proteinuria by interrupting these abnormalities, and thereby to reinstate the integrity of the SD, rectify the effacement of foot processes (FPs), and reduce proteinuria, confirming a pivotal role of the TLR4/MyD88/PKCδ/SHP-1 axis in vivo. Conclusions: These findings elucidated the involvement of the TLR4/MyD88/PKCδ/SHP-1 signaling cascade in diabetic podocyte injury and inflammation, provided evidence for the renal protective and therapeutic potential of podocyte-specific targeting TLR4 in the challenge of DKD and might shed light on therapeutic strategies in proteinuric diseases.

In this paper, we consider multivariate functional time series with a two-way dependence structure: a serial dependence across time points and a graphical interaction among the multiple functions within each time point. We develop the notion of dynamic weak separability, a more general condition than those assumed in literature, and use it to characterize the two-way structure in multivariate functional time series. Based on the proposed weak separability, we develop a unified framework for functional graphical models and dynamic principal component analysis, and further extend it to optimally reconstruct signals from contaminated functional data using graphical-level information. We investigate asymptotic properties of the resulting estimators and illustrate the effectiveness of our proposed approach through extensive simulations. We apply our method to hourly air pollution data that were collected from a monitoring network in China.

In many applications involving data streams, the sequences of data arise from highly dynamic and often unstable real-life processes, rendering untenable the standard assumption that current and future data come from the same distribution. In response, new methodologies, such as dynamic online learning, have been proposed in order to account for the nonstationary features in the data-generating process. Motivated by the stability and statistical efficiency of the notable stochastic approximation method, average stochastic gradient descent (ASGD) in time-invariant systems, the authors propose an exponentially weighted moving average (EWMA)-based stochastic gradient descent (SGD) which accommodates the dynamic structure by introducing a forgetting factor and replacing the simple averaging step in ASGD with an EWMA step. Provided that the dynamic drift is Lipschitz continuous, the mean squared tracking error rate of the proposed method achieves the optimal rate in the nonparametric statistical paradigm. The proposed framework also allows us to derive the dynamic regret bound and asymptotic normality with a path variation constraint in a natural manner. Numerical analysis has been conducted to verify the performance of the proposed method. In particular, the proposed method is much more robust to the selection of learning rates compared with the ordinary SGD method.

This paper establishes the asymptotic independence between the quadratic form and maximum of a sequence of independent random variables. Based on this theoretical result, we find the asymptotic joint distribution for the quadratic form and maximum, which can be applied into the high-dimensional testing problems. By combining the sum-type test and the max-type test, we propose the Fisher's combination tests for the one-sample mean test and two-sample mean test. Under this novel general framework, several strong assumptions in existing literature have been relaxed. Monte Carlo simulation has been done which shows that our proposed tests are strongly robust to both sparse and dense data.

Many existing methodologies for analyzing spatiotemporal point patterns are developed based on the assumption of stationarity in both space and time for the second-order intensity or pair correlation. In practice, however, such an assumption often lacks validity or proves to be unrealistic. In this paper, we propose a novel and flexible nonparametric approach for estimating the second-order characteristics of spatiotemporal point processes, accommodating non-stationary temporal correlations. Our proposed method employs kernel smoothing and effectively accounts for spatial and temporal correlations differently. Under a spatially increasing-domain asymptotic framework, we establish consistency of the proposed estimators, which can be constructed using different first-order intensity estimators to enhance practicality. Simulation results reveal that our method, in comparison with existing approaches, significantly improves statistical efficiency. An application to a COVID-19 dataset further illustrates the flexibility and interpretability of our procedure.

For spatially dependent functional data, a generalized Karhunen-Loève expansion is commonly used to decompose data into an additive form of temporal components and spatially correlated coefficients. This structure provides a convenient model to investigate the space-time interactions, but may not hold for complex spatio-temporal processes. In this work, we introduce the concept of weak separability, and propose a formal test to examine its validity for non-replicated spatially stationary functional field. The asymptotic distribution of the test statistic that adapts to potentially diverging ranks is derived by constructing lag covariance estimation, which is easy to compute for practical implementation. We demonstrate the efficacy of the proposed test via simulations and illustrate its usefulness in two real examples: China PM 2.5 data and Harvard Forest data. Supplementary materials for this article are available online.

Inadequate trophoblastic invasion is considered as one of hallmarks of preeclampsia (PE), which is characterized by newly onset of hypertension (>140/90 mmHg) and proteinuria (>300 mg in a 24-h urine) after 20 weeks of gestation. Accumulating evidence has indicated that long noncoding RNAs are aberrantly expressed in PE, whereas detailed mechanisms are unknown. In the present study, we showed that lncRNA Taurine upregulated 1 (TUG1) were downregulated in preeclamptic placenta and in HTR8/SVneo cells under hypoxic conditions, together with reduced enhancer of zeste homolog2 (EZH2) and embryonic ectoderm development (EED) expression, major components of polycomb repressive complex 2 (PRC2), as well as activation of Nodal/ALK7 signalling pathway. Mechanistically, we found that TUG1 bound to PRC2 (EZH2/EED) in HTR8/SVneo cells and weakened TUG1/PRC2 interplay was correlated with upregulation of Nodal expression via decreasing H3K27me3 mark at the promoter region of Nodal gene under hypoxic conditions. And activation of Nodal signalling prohibited trophoblast invasion via reducing MMP2 levels. Overexpression of TUG1 or EZH2 significantly attenuated hypoxia-induced reduction of trophoblastic invasiveness via negative modulating Nodal/ALK7 signalling and rescuing expression of its downstream target MMP2. These investigations might provide some evidence for novel mechanisms responsible for inadequate trophoblastic invasion and might shed some light on identifying future therapeutic targets for PE.

Severe air pollution affects billions of people around the world, particularly in developing countries such as China. Effective emission control policies rely primarily on a proper assessment of air pollutants and accurate spatial clustering outcomes. Unfortunately, emission patterns are difficult to observe as they are highly confounded by many meteorological and geographical factors. In this study, we propose a novel approach for modeling and clustering PM2.5 concentrations across China. We model observed concentrations from monitoring stations as spatially dependent functional data and assume latent emission processes originate from a functional mixture model with each component as a spatio-temporal process. Cluster memberships of monitoring stations are modeled as a Markov random field, in which confounding effects are controlled through energy functions. The superior performance of our approach is demonstrated using extensive simulation studies. Our method is effective in dividing China and the Beijing-Tianjin-Hebei region into several regions based on PM2.5 concentrations, suggesting that separate local emission control policies are needed. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

Severe air pollution affects billions of people around the world, particularly in developing countries such as China. Effective emission control policies rely primarily on a proper assessment of air pollutants and accurate spatial clustering outcomes. Unfortunately, emission patterns are difficult to observe as they are highly confounded by many meteorological and geographical factors. In this study, we propose a novel approach for modeling and clustering PM2.5 concentrations across China. We model observed concentrations from monitoring stations as spatially dependent functional data and assume latent emission processes originate from a functional mixture model with each component as a spatio-temporal process. Cluster memberships of monitoring stations are modeled as a Markov random field, in which confounding effects are controlled through energy functions. The superior performance of our approach is demonstrated using extensive simulation studies. Our method is effective in dividing China and the Beijing-Tianjin-Hebei region into several regions based on PM2.5 concentrations, suggesting that separate local emission control policies are needed.

The purpose of this study was to assess the value of echocardiography for intraoperative guidance during closure of perimembranous ventricular septal defects (pmVSD) and to assess outcomes of these patients. We identified and assessed 78 patients who underwent 2- and 3-dimensional echocardiography-guided mini-invasive per-atrial closure of pmVSD in the cardiac surgery department of our institution, from February 2016 to August 2018, and 76 patients who underwent transcatheter closure of VSD guided by fluoroscopy at the pediatric department (percutaneous control group). All the patients underwent echocardiography. Their clinical data were retrospectively reviewed and analyzed. All patients were followed up using transthoracic echocardiography (TTE) for a maximum of 24 months after the closure. All patients underwent successful device implantation. Echocardiography showed that the major immediate complications included residual shunt, pericardial effusion, and tricuspid regurgitation in the per-atrial group. During the mid-term follow-up period, TTE revealed that the most common complication was tricuspid regurgitation (non-preexisting). There were no cases of VSD recurrence, device displacement, valvular injury, malignant arrhythmias, hemolysis, or death. Moreover, according to the TTE data, the intracardiac structure of the patients were improved. Compared to the control group, the intracardiac manipulation time was shorter and the number of patients with residual shunts, redeployment of devices, or immediate new tricuspid regurgitations was fewer when using 2- and 3-dimensional echocardiography. However, the procedure time in the per-atrial group was slightly longer than that in the control group. Two- and 3-dimensional echocardiography are feasible monitoring tools during mini-invasive per-atrial VSD closure. The short- and mid-term follow-up showed satisfactory results compared to fluoroscopy.