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Abstract Based on the vertical Total Electron Content (TEC) data observed by the Global Navigation Satellite System in the northern hemisphere, a large area of low plasma density during summer at high latitudes, termed decreased TEC region, was investigated statistically between 2014 and 2024. Compared with the classical depleted structures that usually occur in the nighttime F region at high latitudes during winter, decreased TEC region is usually found in the sunlit polar cap ionosphere during summer. The decreased TEC region is predominantly located in regions above 70° magnetic latitude for moderate and high solar activity. The lower‐TEC region is biased towards the dawn and midnight sectors. Along the 18:25–06:25 Magnetic Local Time meridian, the depth of the decreased TEC region reached 7.6TECu in 2014. The decreased TEC region is deeper for higher Kp (Kp > 2) than for low Kp (Kp ≤ 2). 

Abstract We prove the closure ordering conjecture on the local 𝐿-parameters of representations in local Arthur packets of ${\mathrm{G}}_n={\mathrm{Sp}}_{2n},{\mathrm{SO}}_{2n+1}$ \mathrm{G}_{n}=\mathrm{Sp}_{2n},\mathrm{SO}_{2n+1}over a non-Archimedean local field of characteristic zero.Precisely, given any representation 𝜋 in a local Arthur packet ${\mathrm{\Pi }}_{\psi }$ \Pi_{\psi}, the closure of the local 𝐿-parameter of 𝜋 in the Vogan variety must contain the local 𝐿-parameter corresponding to 𝜓.This conjecture reveals a geometric nature of local Arthur packets and is inspired by the work of Adams, Barbasch and Vogan, and the work of Cunningham, Fiori, Moussaoui, Mracek and Xu, on ABV-packets.As an application, for general quasi-split connected reductive groups, we show that the closure ordering conjecture implies the enhanced Shahidi conjecture, under certain reasonable assumptions.This provides a framework towards the enhanced Shahidi conjecture in general.We verify these assumptions for ${\mathrm{G}}_n$ \mathrm{G}_{n}, hence give a new proof of the enhanced Shahidi conjecture.Finally, we show that local Arthur packets cannot be fully contained in other ones, which is in contrast to the situation over Archimedean local fields and is of independent interest. 

Using the Early Childhood Longitudinal Study - Kindergarten Cohort 2011, we examine (i) whether more preschool attendees in a kindergarten classroom relate to higher academic and social skills for children who did not go to preschool, (ii) whether more preschool attendees in the classroom moderate the benefits of preschool attendance (child N = 11,360; class N = 2,460; 67% White; 51% males; M_age= 5.6 years), and (iii) whether more preschool attendees in the classroom relate to teachers’ perceptions of children’s skills and their instructional content. In contrast to prior analyses using the 1998 cohort of the ECLS-K, we found no evidence of an association between the classroom percentage of preschool-attending peers and children’s academic, executive function, and behavioral and prosocial skills. However, we found that the percentage of preschool peers was associated with teachers’ perceptions of children’s reading skills and teachers’ instructional time spent on advanced reading content. 

This article is devoted to classification of stochastic systems given by stochastic differential equations in continuous time. We develop two novel approaches. The first one is based on the use of a deep neural network (NN), whereas the second one uses hypothesis test-based methods. The idea of deep learning method focuses on treating the given stochastic system models by generating Monte Carlo sample paths. These samples are used to train a deep neutral network. A least square error is used as the loss function for network training. Then, the resulting weights are applied to out of sample Monte Carlo paths for testing. The underlying problem is then converted to a stochastic optimization task. Recursive stochastic algorithms are developed; convergence of the algorithm and rate of convergence are fully analyzed. Such deep NN approach compares favorably to the hypothesis test approaches. Then mean reversion models are studied to show the adaptiveness and power of our deep NN method. An advantage of the deep NN approach is real data can be used directly to train the deep NN. Therefore, model calibration can be bypassed all together. 

Using administrative data of center-based child care providers in North Carolina from 2005 to 2018, we provide the first direct evidence on the effects of competition on provider quality and student outcomes in the context of early care and education, taking advantage of quality measures from the state’s Quality Rating and Improvement System (QRIS). We found that competition was associated with higher quality ratings and a higher probability to achieve a five-star rating—the highest tier in the QRIS. More competition increased providers’ probability to improve their rating and reduced the time to improve. Compared to public schools, private providers were responsive to competition. However, we did not find any effects of competition on district-level student third-grade academic performance. 

Abstract Supramolecular chirality typically originates from either chiral molecular building blocks or external chiral stimuli. Generating chirality in achiral systems in the absence of a chiral input, however, is non-trivial and necessitates spontaneous mirror symmetry breaking. Achiral nematic lyotropic chromonic liquid crystals have been reported to break mirror symmetry under strong surface or geometric constraints. Here we describe a previously unrecognised mechanism for creating chiral structures by subjecting the material to a pressure-driven flow in a microfluidic cell. The chirality arises from a periodic double-twist configuration of the liquid crystal and manifests as a striking stripe pattern. We show that the mirror symmetry breaking is triggered at regions of flow-induced biaxial-splay configurations of the director field, which are unstable to small perturbations and evolve into lower energy structures. The simplicity of this unique pathway to mirror symmetry breaking can shed light on the requirements for forming macroscopic chiral structures. 

Supramolecular chirality typically originates from either chiral molecular building blocks or external chiral stimuli. Generating chirality in achiral systems in the absence of a chiral input, however, is non-trivial and necessitates spontaneous mirror symmetry breaking. Achiral nematic lyotropic chromonic liquid crystals have been reported to break mirror symmetry under strong surface or geometric constraints. Here we describe a previously unrecognised mechanism for creating chiral structures by subjecting the material to a pressure-driven flow in a microfluidic cell. The chirality arises from a periodic double-twist configuration of the liquid crystal and manifests as a striking stripe pattern. We show that the mirror symmetry breaking is triggered at regions of flow-induced biaxial-splay configurations of the director field, which are unstable to small perturbations and evolve into lower energy structures. The simplicity of this unique pathway to mirror symmetry breaking can shed light on the requirements for forming macroscopic chiral structures.