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The stochastic gradient descent (SGD) algorithm has been widely used in statistical estimation for large-scale data due to its computational and memory efficiency. While most existing works focus on the convergence of the objective function or the error of the obtained solution, we investigate the problem of statistical inference of true model parameters based on SGD when the population loss function is strongly convex and satisfies certain smoothness conditions. Our main contributions are twofold. First, in the fixed dimension setup, we propose two consistent estimators of the asymptotic covariance of the average iterate from SGD: (1) a plug-in estimator, and (2) a batch-means estimator, which is computationally more efficient and only uses the iterates from SGD. Both proposed estimators allow us to construct asymptotically exact confidence intervals and hypothesis tests. Second, for high-dimensional linear regression, using a variant of the SGD algorithm, we construct a debiased estimator of each regression coefficient that is asymptotically normal. This gives a one-pass algorithm for computing both the sparse regression coefficients and confidence intervals, which is computationally attractive and applicable to online data.

Ensemble Kalman filter (EnKF) is an important data assimilation method for high-dimensional geophysical systems. Efficient implementation of EnKF in practice often involves the localization technique, which updates each component using only information within a local radius. This paper rigorously analyzes the local EnKF (LEnKF) for linear systems and shows that the filter error can be dominated by the ensemble covariance, as long as (1) the sample size exceeds the logarithmic of state dimension and a constant that depends only on the local radius; (2) the forecast covariance matrix admits a stable localized structure. In particular, this indicates that with small system and observation noises, the filter error will be accurate in long time even if the initialization is not. The analysis also reveals an intrinsic inconsistency caused by the localization technique, and a stable localized structure is necessary to control this inconsistency. While this structure is usually taken for granted for the operation of LEnKF, it can also be rigorously proved for linear systems with sparse local observations and weak local interactions. These theoretical results are also validated by numerical implementation of LEnKF on a simple stochastic turbulence in two dynamical regimes.

The ensemble Kalman filter and ensemble square root filters are data assimilation methods used to combine high-dimensional, nonlinear dynamical models with observed data. Ensemble methods are indispensable tools in science and engineering and have enjoyed great success in geophysical sciences, because they allow for computationally cheap low-ensemble-state approximation for extremely high-dimensional turbulent forecast models. From a theoretical perspective, the dynamical properties of these methods are poorly understood. One of the central mysteries is the numerical phenomenon known as catastrophic filter divergence, whereby ensemble-state estimates explode to machine infinity, despite the true state remaining in a bounded region. In this article we provide a breakthrough insight into the phenomenon, by introducing a simple and natural forecast model that transparently exhibits catastrophic filter divergence under all ensemble methods and a large set of initializations. For this model, catastrophic filter divergence is not an artifact of numerical instability, but rather a true dynamical property of the filter. The divergence is not only validated numerically but also proven rigorously. The model cleanly illustrates mechanisms that give rise to catastrophic divergence and confirms intuitive accounts of the phenomena given in past literature.

Nature-inspired swarm-based algorithms are increasingly applied to tackle high-dimensional and complex optimization problems across disciplines. They are general purpose optimization algorithms, easy to implement and assumption-free. Some common drawbacks of these algorithms are their premature convergence and the solution found may not be a global optimum. We propose a general, simple and effective strategy, called heterogeneous Perturbation–Projection (HPP), to enhance an algorithm’s exploration capability so that our sufficient convergence conditions are guaranteed to hold and the algorithm converges almost surely to a global optimum. In summary, HPP applies stochastic perturbation on half of the swarm agents and then project all agents onto the set of feasible solutions. We illustrate this approach using three widely used nature-inspired swarm-based optimization algorithms: particle swarm optimization (PSO), bat algorithm (BAT) and Ant Colony Optimization for continuous domains (ACO). Extensive numerical experiments show that the three algorithms with the HPP strategy outperform the original versions with 60–80% the times with significant margins.

When implementing Markov Chain Monte Carlo (MCMC) algorithms, perturbation caused by numerical errors is sometimes inevitable. This paper studies how the perturbation of MCMC affects the convergence speed and approximation accuracy. Our results show that when the original Markov chain converges to stationarity fast enough and the perturbed transition kernel is a good approximation to the original transition kernel, the corresponding perturbed sampler has fast convergence speed and high approximation accuracy as well. Our convergence analysis is conducted under either the Wasserstein metric or the $\\chi^2$ metric, both are widely used in the literature. The results can be extended to obtain non-asymptotic error bounds for MCMC estimators. We demonstrate how to apply our convergence and approximation results to the analysis of specific sampling algorithms, including Random walk Metropolis, Metropolis adjusted Langevin algorithm with perturbed target densities, and parallel tempering Monte Carlo with perturbed densities. Finally, we present some simple numerical examples to verify our theoretical claims.

High brightness, high charge electron beams are critical for a number of advanced accelerator applications. The initial emittance of the electron beam, which is determined by the mean transverse energy (MTE) and laser spot size, is one of the most important parameters determining the beam quality. The bialkali photocathodes illuminated by a visible laser have the advantages of high quantum efficiency (QE) and low MTE. Furthermore, Superconducting Radio Frequency (SRF) guns can operate in the continuous wave (CW) mode at high accelerating gradients, e.g. with significant reduction of the laser spot size at the photocathode. Combining the bialkali photocathode with the SRF gun enables generation of high charge, high brightness, and possibly high average current electron beams. However, integrating the high QE semiconductor photocathode into the SRF guns has been challenging. In this article, we report on the development of bialkali photocathodes for successful operation in the SRF gun with months-long lifetime while delivering CW beams with nano-coulomb charge per bunch. This achievement opens a new era for high charge, high brightness CW electron beams.

The recovery of a random turbulent velocity field using Lagrangian tracers that move with the fluid flow is a practically important problem. This paper studies the filtering skill of L -noisy Lagrangian tracers in recovering random rotating compressible flows that are a linear combination of random incompressible geostrophically balanced (GB) flow and random rotating compressible gravity waves. The idealized random fields are defined through forced damped random amplitudes of Fourier eigenmodes of the rotating shallow-water equations with the rotation rate measured by the Rossby number ε . In many realistic geophysical flows, there is fast rotation so ε satisfies ε ≪ 1 and the random rotating shallow-water equations become a slow–fast system where often the primary practical objective is the recovery of the GB component from the Lagrangian tracer observations. Unfortunately, the L -noisy Lagrangian tracer observations are highly nonlinear and mix the slow GB modes and the fast gravity modes. Despite this inherent nonlinearity, it is shown here that there are closed analytical formulas for the optimal filter for recovering these random rotating compressible flows for any ε involving Ricatti equations with random coefficients. The performance of the optimal filter is compared and contrasted through mathematical theorems and concise numerical experiments with the performance of the optimal filter for the incompressible GB random flow with L -noisy Lagrangian tracers involving only the GB part of the flow. In addition, a sub-optimal filter is defined for recovering the GB flow alone through observing the L -noisy random compressible Lagrangian trajectories, so the effect of the gravity wave dynamics is unresolved but effects the tracer observations. Rigorous theorems proved below through suitable stochastic fast-wave averaging techniques and explicit formulas rigorously demonstrate that all these filters have comparable skill in recovering the slow GB flow in the limit ε → 0 for any bounded time interval. Concise numerical experiments confirm the mathematical theory and elucidate various new features of filter performance as the Rossby number ε , the number of tracers L and the tracer noise variance change.

This study aimed to explore the role of sleep quality as a mediator in the activities of daily living (ADLs) and depression. Participants (N=645; age≥60) were included in six nursing homes in Weifang, Shandong Province, using convenience sampling. Participants completed questionnaires to assess sleep quality, ADLs, and depression. Depression condition was assessed by the Patient Health Questionnaire (PHQ-9), ADLs was assessed by the Barthel Index (BI), and sleep quality was measured by the Pittsburgh Sleep Quality Index (PSQI). Mediation analysis was carried out by SPSS PROCESS. ADLs ( =0.449, <0.01) and sleep quality ( =0.450, <0.01) were found to be positively associated with depression among the elderly. Sleep quality plays a significant mediating role in the influence of ADLs on depression in the elderly in nursing homes (Bootstrap 95% [0.076, 0.139]), The pathway from ADLs to sleep quality to depression yielded a medium effect size of 20.23%. ADLs help to explain how sleep quality partly mediates depression among the elderly in nursing homes. It is therefore recommended that timely detection and efficient interventions should focus on promoting physical function and improving sleep quality among the elderly in nursing homes.

Guselkumab is a highly effective biologic agent for treating psoriasis. This study aimed to explore potential transcription factors involved in psoriasis pathogenesis and response to guselkumab treatment, aiming to provide new therapeutic strategies for psoriasis. We analyzed gene expression and single-cell RNA-seq data from the Gene Expression Omnibus (GEO) database. Differentially expressed genes (DEGs) that upregulated in psoriasis and downregulated after guselkumab treatment were subjected to enrichment analyses. Single-cell regulatory network inference and clustering (SENIC) and regulon module analyses identified different regulon activities between the lesion and non-lesion skin of psoriasis. Cell-cell communication analysis revealed interactions among specific cell clusters. Transcription factor (TF) regulons were identified from the guselkumab-specific regulon network. Gene set enrichment analysis (GSEA) confirmed the IRF7 regulon in the validation cohort. Finally, the expression level of IRF7 was identified in plaque psoriasis before and after 12 weeks of guselkumab therapy by immunohistochemical experiment. 799 DEGs were downregulated after guselkumab treatment. Enrichment analyses highlighted the interleukin-17 (IL-17) pathway in this gene set. The M2 module exhibited the primary difference in regulon activity. Strong cell-cell interactions were observed between keratinocytes and immune cells. IRF7 regulon had significant roles in psoriasis and treatment response, as validated by GSEA analysis using the IL-17 signaling pathway as a reference. The immunohistochemical analysis unveiled substantial differences in the expression levels of IRF7 in psoriatic skin samples before and after 12 weeks of guselkumab treatment. IRF7 may be the key player in psoriasis pathogenesis and the therapeutic process involving guselkumab. Targeting IRF7 might offer new therapeutic strategies for psoriasis.

The propellant tank is a vital structure for the liquid rocket, and the analysis of influence factors to the propellant tank stress can provide a significant reference to design the propellant tank. Through establishing the ellipsoid cylindrical tank model, the meridian stress and hoop stress distributions of tank roof, cylinder and bottom are analysed. And then the equivalent stress is defined based on the material strength theory. According to the parameters of a certain type tank, the equivalent stresses of tank roof, cylinder and bottom are worked out with different ellipsoidal norms, overload factors, tank radiuses and internal pressurizations, the effects of these influence factors on the tank stress are analysed, and the change laws of tank roof, cylinder and bottom equivalent stresses are determined to provide a reference for the design of propellant tank.