Mean field limits for nonlinear spatially extended Hawkes processes with exponential memory kernels

We consider spatially extended systems of interacting nonlinear Hawkes processes modeling large systems of neurons placed in ${\mathbb{R}}^d$ and study the associated mean field limits. As the total number of neurons tends to infinity, we prove that the evolution of a typical neuron, attached to a given spatial position, can be described by a nonlinear limit differential equation driven by a Poisson random measure. The limit process is described by a neural field equation. As a consequence, we provide a rigorous derivation of the neural field equation based on a thorough mean field analysis.     

Effect of variation in signal amplitude and transit time on reliability analysis of ultrasonic time of flight diffraction characterization of vertical and inclined cracks

The variation of amplitude and transit time of the diffracted signal from the crack-tip in complex geometry components and their resulting effect on the probability of detection (POD) and probability of sizing (POS) was studied. The diffracted signal amplitude has been evaluated from the standard expressions for diffraction coefficient, spatial attenuation and the transit time from the respective mathematical models for both vertical and inclined cracks. The same parameters namely the signal amplitude and the transit time have been measured through experiments conducted on simulated test specimens. It has been observed that the analytical and experimental results compare well with each other. Based on this result the trend and shape (width of the transition zone) of the POD/POS curves can be predicted.     

Facile preparation of MgAl2O4/CeO2/Mn3O4 heterojunction photocatalyst and enhanced photocatalytic activity

Novel Mn₃O₄-promoted double p?n junction MgAl₂O₄/CeO₂/Mn₃O₄ heterojunction photocatalyst was constructed by one-step synthesis method and two-step synthesis method. The X-ray powder diffraction, Fourier transform infrared spectrum, X-ray photoelectron spectroscopy, optical and photoluminescence demonstrated that the MgAl₂O₄/CeO₂/Mn₃O₄ heterojunction photocatalyst was synthesized by the two-step synthesis method comprehends a high crystallinity, charge carrier migration and separation efficiency, and relatively low optical absorption coefficient. The MgAl₂O₄/CeO₂/Mn₃O₄ heterojunction photocatalysts were efficiently used as simulated sunlight-driven n-n and p-n double junction photocatalyst for the simultaneous degradation of methylene blue (MB) dye. The continuous double p?n junction MgAl₂O₄/CeO₂/Mn₃O₄ heterojunctions strengthened the function of single n-n or p-n junction and guided the charge carrier migration and separation direction; thus, the oxidation and reduction reactions occur at the active site of spatial separation and prevent the recombination of electrons and holes. The results suggest that the continuous double p?n junction MgAl₂O₄/CeO₂/Mn₃O₄ heterojunctions are very promising candidate material for enhancing the photocatalytic activity in the photocatalytic degradation of MB dye.     

Steering spatially separated dual sites on nano-TiO2 through SMSI and lattice matching for robust photocatalytic hydrogen evolution

Spatial isolation of different functional sites at the nanoscale in multifunctional catalysts for steering reaction sequence and paths remains a major challenge. Herein, we reported the spatial separation of dual-site Au and RuO₂ on the nanosurface of TiO₂ (Au/TiO₂/RuO₂) through the strong metal-support interaction (SMSI) and the lattice matching (LM) for robust photocatalytic hydrogen evolution. The SMSI between Au and TiO₂ induced the encapsulation of Au nanoparticles by an impermeable TiO_x overlayer, which can function as a physical separation barrier to the permeation of the second precursor. The LM between RuO₂ and rutile-TiO₂ can increase the stability of RuO₂/TiO₂ interface and thus prevent the aggregation of dual-site Au and RuO₂ in the calcination process of removing TiO_x overlayer of Au. The photocatalytic hydrogen production is used as a model reaction to evaluate the performance of spatially separated dual-site Au/TiO₂/RuO₂ catalysts. The rate of hydrogen production of the Au/TiO₂/RuO₂ is as high as 84 μmol h⁻¹ g⁻¹ under solar light irradiation without sacrificial agents, which is 2.5 times higher than the reference Au/TiO₂ and non-separated Au/RuO₂/TiO₂ samples. Systematic characterizations verify that the spatially separated dual-site Au and RuO₂ on the nanosurface of TiO₂ can effectively separate the photo-generated carriers and lower the height of the Schottky barrier, respectively, under UV and visible light irradiation. This study provides new inspiration for the precise construction of different sites in multifunctional catalysts.     

CORSICA: correction of structured noise in fMRI by automatic identification of ICA components

When applied to functional magnetic resonance imaging (fMRI) data, spatial independent component analysis (sICA), a data-driven technique that addresses the blind source separation problem, seems able to extract components specifically related to physiological noise and brain movements. These components should be removed from the data to achieve structured noise reduction and improve any subsequent detection and analysis of signal fluctuations related to neural activity. We propose a new automatic method called CORSICA (CORrection of Structured noise using spatial Independent Component Analysis) to identify the components related to physiological noise, using prior information on the spatial localization of the main physiological fluctuations in fMRI data. As opposed to existing spectral priors, which may be subject to aliasing effects for long-TR data sets (typically acquired with TR >1 s), such spatial priors can be applied to fMRI data, regardless of the TR of the acquisitions. By comparing the proposed automatic selection to a manual selection performed visually by a human operator, we first show that CORSICA is able to identify the noise-related components for long-TR data with a high sensitivity and a specificity of 1. On short-TR data sets, we validate that the proposed method of noise reduction allows a substantial improvement of the signal-to-noise ratio evaluated at the cardiac and respiratory frequencies, even in the gray matter, while preserving the main fluctuations related to neural activity.     

基于光楔阵列产生光学涡旋阵列的研究

在研究光楔衍射法产生单涡旋的基础上,基于长条形光楔阵列,提出了利用光束阵列衍射产生涡旋阵列的方法.该方法要求光束阵列在平行于光楔边缘方向上的光束间距等于光束直径的整数倍.利用超精密机床采用一体化加工法加工了光楔阵列元件,验证了该方法的可行性.利用空间光调制器快速灵活调整光束阵列的优点,搭建了借助空间光调制器加载达曼光栅衍射产生所需光束阵列的实验光学系统.针对光束阵列与光楔阵列的匹配问题,研究了达曼光栅掩模图基本单元对光束阵列的调控,获得了可调结构的光束阵列.实验产生了拓扑荷一致的光学涡旋阵列,与仿真结果相一致,证明所提方法的有效性.     

On the Relation between Prediction and Imputation Accuracy under Missing Covariates

Missing covariates in regression or classification problems can prohibit the direct use of advanced tools for further analysis. Recent research has realized an increasing trend towards the use of modern Machine-Learning algorithms for imputation. This originates from their capability of showing favorable prediction accuracy in different learning problems. In this work, we analyze through simulation the interaction between imputation accuracy and prediction accuracy in regression learning problems with missing covariates when Machine-Learning-based methods for both imputation and prediction are used. We see that even a slight decrease in imputation accuracy can seriously affect the prediction accuracy. In addition, we explore imputation performance when using statistical inference procedures in prediction settings, such as the coverage rates of (valid) prediction intervals. Our analysis is based on empirical datasets provided by the UCI Machine Learning repository and an extensive simulation study.     

激光大气等离子体的电子密度空间分布特性研究

利用Nd∶YAG激光器产生的1.06 μm激光束(脉冲能量为500 mJ,脉冲宽度为10 ns, 重复频率30 Hz)聚焦击穿大气形成长约为8 cm、最大直径为5 cm的激光大气等离子体柱,用光谱测量的方法,分别沿平行于激光束方向和垂直于激光束方向探测该等离子体柱的空间分辨光谱,并由此反演得出电子密度空间分布特性。实验结果表明,激光大气等离子体中各种离子和电子呈橄榄形分布,沿激光束方向不对称,而垂直激光束方向对称分布,最大电子密度为1018 cm-3。文章还探讨了激光大气等离子体中处在不同状态的各种原子、分子和离子在空间的分布特性,为进一步揭示激光大气等离子体的微观空间分布规律提供了实验依据。     

用极值频率法分析数字全息的记录条件

根据全息理论,通过分析全息图光栅结构的极值频率,利用抽样定理以及频谱分离条件,分析了离轴菲涅耳全息的记录条件,得到了不同于以往文献的最小记录距离及参考光源设置表达式,并做了计算机模拟验证.结果表明：用该方法推得的离轴菲涅耳全息最小记录距离和参考光设置表达式是正确的.只有同时满足抽样条件和频谱分离条件,才能得到高质量的再现像.