This paper establishes a theoretical framework for the uniform convergence of smoothly activated deep neural network (DNN) estimators. While standard ReLU networks achieve minimax-optimal rates in the L^2(P) norm for various nonparametric regression tasks, we establish a theoretical lower bound demonstrating that least-squares ReLU estimators can suffer from the curse of dimensionality in their uniform convergence behavior. Motivated by the need for reliable uniform guarantees in downstream tasks requiring worst-case reliability, we address this limitation by analyzing smoothly activated DNNs (smooth DNNs), encompassing both feedforward and residual structures. We establish novel pseudo-dimension bounds, non-asymptotic approximation guarantees, and Hölder-norm bounds for the approximators of these models. Leveraging these results, we derive non-asymptotic uniform convergence rates for smooth DNN estimators across multiple statistical contexts, including Huber, least-squares, quantile, and logistic regression. We prove that smooth DNNs can mitigate the curse of dimensionality in uniform convergence by adaptively exploiting the low-dimensional hierarchical composition structure of the target function. Supported by both simulation studies and a real-world application, our results position smooth DNNs as a theoretically grounded and practically viable alternative to ReLU networks for statistical learning tasks requiring uniform guarantees.

In this paper, we propose a nonparametric independence test based on mutual information. Distinguished from the existing works, we estimate the mutual information in a conditional density form, whose dimension could be reduced to 1 with projection pursuit. The optimal projection direction is estimated by maximizing a penalized mutual information. Based on the optimal projection, we construct an independence test via the projected mutual information, which is insensitive to the dimensions of random vectors. The test is consistent against global alternatives, and can detect local alternatives at a fast rate as if the variables were univariate. Numerical results indicate that the test is more powerful compared with other existing independence tests, especially when the sample size is small or the dimension is large. We also apply the method to a stock portfolio performance data and show the superior performance of the new test.

Distributed statistical modeling is a powerful tool for dealing with large-scale datasets while maintaining data privacy. In this study, we propose a data-driven weighted aggregation procedure that leverages model prediction performance and is adaptable to heterogeneous distributed environments. The proposed procedures utilize the squared prediction error matrix as the main transmitted quantity, with its dimension being the square of the number of workers, ensuring communication efficiency. We show that the proposed estimates have asymptotical optimal weights in terms of quadratic loss and corresponding risk. The limits of data-driven weights are also derived. We also study the minimax property of the proposed nonparametric function estimates. To examine the finite sample performance of the proposed procedure, we conduct Monte Carlo simulation studies. Furthermore, we illustrate the proposed methodology via an empirical analysis of a real-world dataset on heart rate prediction.

This study addresses the challenges in estimating mean vectors and autocovariance matrices in modern data settings, which are often affected by three key issues: high-dimensionality, heavy-tailed distributions, and temporal dependence. These salient features lead to reduced performance of many existing methods. To tackle these challenges, we introduce a computationally efficient framework centered around the median-of-means. In particular, we study the non-asymptotic properties of median-of-means estimators for mean vectors and autocovariance matrices for high-dimensional, heavy-tailed dependent data. Extensive simulations demonstrate the finite sample and computational advantages of the proposed estimators. The effectiveness of our approach is further validated through its application in analyzing the autocovariance patterns of S&P 500 daily returns over the past two decades.

Parameter transfer aims to improve parameter estimation accuracy by leveraging knowledge from related sources. This paper studies the parameter transfer problem from heterogeneous sources for high-dimensional M-estimators. Specifically, we propose a novel one-step estimator with a fused-regularizer and a target-data-oriented constraint, which can robustly capture parameter knowledge from source data in the presence of different types of data distribution shifts. Nonasymptotic bound is provided for the estimation error of target parameter, showing the proposed estimator could achieve effective parameter transfer under distribution shifts, and is guaranteed to perform no worse than any estimators learned only from the target data. We further show that the proposed estimator can achieve the minimax-optimal rate under much weaker conditions than existing methods. In addition, we extend the method to a distributed setting, requiring just one round of communication with source parameter estimators, while retaining the estimation accuracy of the centralized version. Extensive simulations and real data analysis further verify the effectiveness of the method.

Comparing K-sample distributions is a fundamental problem in data science that arises in a wide variety of fields and applications. In this article, we introduce a maximum-of-differences approach to make such comparisons. Specifically, we first calculate the pairwise distances from the pooled observations of the K samples. We then define the two observations as connected if their distance is less than a pre-specified threshold value. For each observation, we next calculate the “within" and the “between" probabilities associated with these two types of connections for the given observation, i.e., with other observations within the same sample and between the given observation and the observations in other samples. Subsequently, we propose a maximum-of-differences (MOD) test that finds the maximum value among the standardized squared differences between the “within" and the “between" probabilities of all observations. Accordingly, the proposed test is not only applicable to multivariate data with K samples, but can also be extended to multivariate regression models. Furthermore, we obtain the covariance-adjusted (CA) version of the MOD (CA-MOD) test, which converges to the Type I extreme value distribution under some conditions. Moreover, we demonstrate the asymptotic properties of the two tests under both the null and alternative hypotheses. The performance and usefulness of the tests are illustrated via simulation studies and real examples.

Platelets have been increasingly recognized as versatile regulators of ageing, immunity, and cancer, yet their functional heterogeneity has remained poorly defined. We performed the first large-scale single-cell RNA sequencing of 28,192 platelets from healthy, aged, metastatic, and treated mice using the BD Rhapsody platform. Our analysis revealed four conserved and functionally distinct platelet transcriptional states: haemostatic platelet (HP), neural gene-enriched platelet (NEP), platelet-leukocyte aggregate (PLA) and platelet-erythrocyte aggregate (PEA). Among these states, Tpm2-high HP is linked to ageing-associated lung metastasis and is characterized by cytoskeletal remodelling gene signatures. The PLA state was predicted to be a signalling hub for immunothrombosis, with a PLA-Bridge subpopulation coordinating immune-adherent platelets via the Ppbp-Cxcr2 and Thbs1-Cd47 checkpoint axes. Strikingly, AAV-mPf4 gene therapy was associated with a NEP-associated transcriptional program, which mitigates age-related functional decline. This study provides a single-cell transcriptomic atlas of murine platelets under ageing and metastasis conditions and reveals transcriptional state-specific heterogeneity. This study also proposes PF4-based interventions and cytoskeletal candidates for diagnosis and therapy.

In this paper, we study the autocovariance matrix estimation and inference problems under heavy-tailedness, high-dimensionality, general nonlinear temporal dependence, and potentially nonstationarity of time series. We consider two types of tail-robust autocovariance matrix estimation methods: the element-wise Huber's M-estimator and a computationally more efficient element-wise truncated estimator. Both estimators are designed to achieve sharp error bounds in matrix max-norm. The nonasymptotic properties of these estimators are proved based on new variants of Bernstein-type inequalities under functional dependence for the potentially nonstationary processes which may be of independent interest. Moreover, we prove a high-dimensional Gaussian approximation result, as a limiting distribution, for our element-wise truncated autocovariance estimator. A Gaussian multiplier bootstrap result is also given to facilitate the practicality. Our theoretical results are nonasymptotic, which gives explicit error bounds in terms of the sample size, dimensionality, moments, and the strength of temporal dependence. Numerical evidence is provided to support our theoretical results. Finally, we illustrate the benefits of the proposed methodology for detecting change points in monthly macroeconomic data.

High-frequency death counts are now widely available and contain timely information about intra-year mortality dynamics, but most stochastic mortality models are still estimated on annual data and therefore update only when annual totals are released. We propose a mixed-frequency state-space (MF–SS) extension of the Lee–Carter framework that jointly uses annual mortality rates and monthly death counts. The two series are linked through a shared latent monthly mortality factor, with the annual period factor defined as the intra-year average of the monthly factors. The latent monthly factor follows a seasonal ARIMA process, and parameters are estimated by maximum likelihood using an EM algorithm with Kalman filtering and smoothing. This setup enables real-time intra-year updates of the latent state and forecasts as new monthly observations arrive without re-estimating model parameters. Using U.S. data for ages 20–90 over 1999–2019, we evaluate intra-year annual nowcasts and one- to five-year-ahead forecasts. The MF–SS model produces both a direct annual forecast and an annual forecast implied by aggregating monthly projections. In our application, the aggregated monthly forecast is typically more accurate. Incorporating monthly information substantially improves intra-year annual nowcasts, especially after the first few months of the year. As a benchmark, we also fit separate annual and monthly Lee–Carter models and combine their forecasts using temporal reconciliation. Reconciliation improves these independent forecasts but adds little to MF–SS forecasts, consistent with MF–SS pooling information across frequencies during estimation. The MF–SS aggregated monthly forecasts generally outperform both unreconciled and temporally reconciled Lee–Carter forecasts and produce more cautious predictive intervals than the reconciled Lee–Carter approach.

While deep reinforcement learning has achieved tremendous successes in various applications, most existing works only focus on maximizing the expected value of total return and thus ignore its inherent stochasticity. Such stochasticity is also known as the aleatoric uncertainty and is closely related to the notion of risk. In this work, we make the first attempt to study risk-sensitive deep reinforcement learning under the average reward setting with the variance risk criteria. In particular, we focus on a variance-constrained policy optimization problem where the goal is to find a policy that maximizes the expected value of the long-run average reward, subject to a constraint that the long-run variance of the average reward is upper bounded by a threshold. Utilizing Lagrangian and Fenchel dualities, we transform the original problem into an unconstrained saddle-point policy optimization problem, and propose an actor-critic algorithm that iteratively and efficiently updates the policy, the Lagrange multiplier, and the Fenchel dual variable. When both the value and policy functions are represented by multi-layer overparameterized neural networks, we prove that our actor-critic algorithm generates a sequence of policies that finds a globally optimal policy at a sublinear rate. Further, We provide numerical studies of the proposed method using two real datasets to back up the theoretical results.

This paper aims to derive asymptotical distributions of the spiked eigenvalues of the large-dimensional spiked Fisher matrices without Gaussian assumption and the restrictive assumptions on covariance matrices. We first establish invariance principle for the spiked eigenvalues of the Fisher matrix. That is, we show that the limiting distributions of the spiked eigenvalues are invariant over a large class of population distributions satisfying certain conditions. Using the invariance principle, we further established a central limit theorem (CLT) for the spiked eigenvalues. As some interesting applications, we use the CLT to derive the power functions of Roy Maximum root test for linear hypothesis in linear models and the test in signal detection. We conduct some Monte Carlo simulation to compare the proposed test with existing ones.

Background:The results of three modern randomized controlled trials have proved sublobar resection as an effective procedure for early-stage non-small cell lung cancer (NSCLC) up to 2 cm. We aimed to examine whether sublobar resection is oncologically feasible and what constitutes adequate lymph node assessment for hypermetabolic clinical stage IA (cIA) NSCLC. Methods:A single-center retrospective study was conducted in 589 patients who underwent lobectomy (n=526) or sublobar resection (n=63) for hypermetabolic cIA NSCLC [maximum standardized uptake value (SUVmax) ≥2.6 g/dL]. The primary outcomes (lung cancer-specific death and tumor recurrence) were compared in a competing risks framework for all patients and the propensity score matched pairs. Random forests were used to examine the variable importance for lung cancer-specific survival and tumor recurrence. Factors affecting pathological upstaging and recurrence-free survival were assessed by logistic regression analysis and Cox regression analysis, respectively. Results:Sublobar resection had significantly higher lung cancer-specific cumulative incidence of death (LC-CID) and cumulative incidence of recurrence (CIR) than lobectomy after matching (5-year LC-CID, 20.8% vs. 6.5%, P<0.001; 5-year CIR, 37.9% vs. 14.8%, P<0.001). Wedge resection was an independent risk factor for both lung-cancer specific death [hazard ratio (HR) =4.17; 95% confidence interval (CI): 2.07-8.36; P<0.001] and recurrence (HR =3.48; 95% CI: 1.91-6.33; P<0.001). Lymphadenectomy that failed to meet the lobe-specific nodal dissection (LSND) criteria correlated with decreased odds of pathological nodal upstaging [odds ratio (OR) =0.55; 95% CI: 0.34-0.87; P=0.01]. While patients with LSND had lower LC-CIR and CIR, there was no additional prognostic benefit of systemic nodal dissection (SND) over LSND. Conclusions:Lobectomy was oncologically superior to sublobar resection as a curative-intent procedure for hypermetabolic cIA NSCLC. Lobectomy plus lobe-specific lymphadenectomy should be considered as the minimum standards of curative resection for hypermetabolic early-stage NSCLC in order to achieve more accurate pathological N staging and better cancer control.

Light-sheet fluorescence microscopy (LSFM) provides an ideal tool for long-term observation of live specimens due to its low photodamage and fast volumetric imaging speed. The wavefront distortions in the illumination path of LSFM will reduce the intensity and broaden the light-sheet thickness, thereby degrading the image quality. We propose to use the wavefront shaping technique to reduce the scattering effect and shrink the light-sheet thickness. Scanning the refocused laser beam to generate LS improves both the fluorescence intensity and the axial resolution. The axial resolution can be further enhanced by subtracting the two images captured via double scanning the samples with the refocused beam and the uncorrected scattered beam for each slice. The axial resolution is improved from 2.2 ± 0.3 to 1.5 ± 0.2 μm across the field of view of 270 μm × 270 μm. The effectiveness of the wavefront shaping subtraction method is demonstrated by imaging fluorescent beads and Aspergillus conidiophores behind a scattering medium.

Covariance regression analysis is an approach to linking the covariance of responses to a set of explanatory variables X, where X can be a vector, matrix, or tensor. Most of the literature on this topic focuses on the "Fixed-X" setting and treats X as nonrandom. By contrast, treating explanatory variables X as random, namely the "Random-X" setting, is often more realistic in practice. This article aims to fill this gap in the literature on the estimation and model assessment theory for Random-X covariance regression models. Specifically, we construct a new theoretical framework for studying the covariance estimators under the Random-X setting, and we demonstrate that the quasi-maximum likelihood estimator and the weighted least squares estimator are both consistent and asymptotically normal. In addition, we develop pioneering work on the model assessment theory of covariance regression. In particular, we obtain the bias-variance decompositions for the expected test errors under both the Fixed-X and Random-X settings. We show that moving from a Fixed-X to a Random-X setting can increase both the bias and the variance in expected test errors. Subsequently, we propose estimators of the expected test errors under the Fixed-X and Random-X settings, which can be used to assess the performance of the competing covariance regression models. The proposed estimation and model assessment approaches are illustrated via extensive simulation experiments and an empirical study of stock returns in the US market.

Surface thermal damage in a difficult-to-process metal precision grinding workpiece has emerged as a technical bottleneck restricting machining quality. As an alternative to traditional pouring cooling, a green clean minimum-quantity lubrication technology still has defects, such as insufficient heat dissipation. The use of cryogenic air instead of normal temperature air, that is, the supply of low-temperature energized lubricant, can effectively improve oil film heat transfer and lubrication performance in a grinding area. Under the premise of ensuring the effective flow of lubricating oil in a grinding zone, the thickness of a liquid film in the wedge zone of a grinding wheel or workpiece is the key factor for determining its performance. However, the dynamic mechanism of droplet formation and distribution of liquid film thickness are still unclear. Hence, the mechanism by which nozzle orientation influences the effective region of a liquid film was analyzed, and the range of nozzle inclination that helps to atomize droplets and enables them to enter the grinding zone was revealed. Then, the dynamic mechanism of atomized droplet film formation was analyzed, and the influence of normal and tangential momentum sources generated by gas impingement perturbation flow and droplet impingement steady flow on the driving effect of liquid film flow was revealed. The thickness distribution model of a liquid film in the impact zone of gas-liquid two-phase flow under different cryogenic air temperatures was established. The model results under different working conditions were obtained by numerical analysis, and validation experiments were carried out. Results show that the measured values agree with the theoretical values. At 0.4 MPa air pressure, the thickness of the liquid film in the impact zone of the atomized droplets increases with decreasing cryogenic air temperature. At −10 and −50 °C, the thickness of the liquid film is 0.92 and 1.26 mm, respectively. Further, on the basis of the surface topography model of cubic boron nitride grinding wheel, the pose relationship of any three adjacent abrasive particles was analyzed, and the theoretical model of abrasive clearance volume was established. The dynamic variation of abrasive clearance volume distribution domain is [70.46, 78.72] mm3, and the total volume distribution domain is [140.84, 155.67] mm3. The research will provide a theoretical basis for the application of cryogenic air minimum quantity lubrication technology to hard metal grinding.

In this work, Yb3+, Ho3+, and Pr3+ co-doped Ca3NbGa3Si2O14 (Yb:Ho:Pr:CNGS) single crystal was grown by the Czochralski (Cz) method. The properties of the crystal are regulated by doping of rare earth elements. Powder Xray diffraction (PXRD) was exhibited and the cell parameters were calculated. The dielectric, elastic compliance, and piezoelectric constants were measured and calculated at room temperature, the good performance parameters such as epsilon ij/epsilon 0, d11, and s 11 were presented. In addition, the temperature dependence of the full set of electroelastic properties in the range of 25 degrees C-700 degrees C was provided, and the high temperature stability were also presented. The temperature stability of epsilon 11 / epsilon 0 , k12, d 11 and s 11 in the range of 25 degrees C-700 degrees C were 3.37 %, 10.97 %, 21.08 % and 11.43 %, respectively. The binding energy of metal-oxygen bond in the crystal was characterized by X-ray photoelectron spectroscopy (XPS). It is also confirmed that the crystal has good optical properties, the fluorescence emission spectrum of 2 mu m is obtained, and this crystal could be a potential multifunctional material for the applications of high temperature piezoelectric sensors and flowmeters.

Lung cancer brain metastasis (LCBM) is a major contributor to cancer-related mortality, with a median survival of 8–16 months following diagnosis, despite advances in therapeutic strategies. The development of clinically relevant animal models is crucial for understanding the metastatic cascade and assessing therapies that can penetrate the blood–brain barrier (BBB). This review critically evaluates five primary LCBM modeling approaches—orthotopic implantation, intracardiac injection, stereotactic intracranial injection, carotid artery injection, and tail vein injection—focusing on their clinical applicability. We systematically compare their ability to replicate human metastatic pathophysiology and highlight emerging technologies for personalized therapy screening. Additionally, we analyze breakthrough strategies in central nervous system (CNS)-targeted drug delivery, including microparticle targeted delivery systems designed to enhance brain accumulation. By incorporating advances in single-cell omics and AI-driven metastasis prediction, this work provides a roadmap for the next generation of LCBM models, aimed at bridging preclinical and clinical research.

This paper proposes an innovative double power-enhanced testing procedure for inference on high-dimensional linear hypotheses in high-dimensional regression models. Through a projection approach that aims to separate useful inferential information from the nuisance one, our proposed test accurately accounts for the impact of high-dimensional nuisance parameters. We discover that with a carefully-designed projection matrix, the projection procedure enables us to transform the problem of interest into a test on moment conditions, from which we construct a U -statistic-based test that is applicable in simultaneous inference on a diverging number of linear hypotheses. We prove that under regularity conditions, the plug-in test statistic converges to its oracle counterpart, acting as well as if the nuisance parameters were known in advance. Moreover, we introduce an implementation-friendly version to tackle the computational challenge. Asymptotic null normality is established to provide convenient tools for statistical inference, accompanied by rigorous power analysis. To further strengthen the testing power, we develop two power enhancement techniques to boost the power from two distinct aspects respectively, and integrate them into one powerful testing procedure to achieve double power enhancement. The finite-sample performance is demonstrated using simulation studies, and an empirical analysis of a real data example.