Wellposedness of Cauchy problem for the Fourth Order Nonlinear Schr\"odinger Equations in Multi-dimensional Spaces

We study the wellposedness of Cauchy problem for the fourth order nonlinear Schr\"odinger equations i\partial_t u=-\eps\Delta u+\Delta^2 u+P((\partial_x^\alpha u)_{\abs{\alpha}\ls 2}, (\partial_x^\alpha \bar{u})_{\abs{\alpha}\ls 2}),\quad t\in \Real, x\in\Real^n, where \eps\in\{-1,0,1\}, n\gs 2 denotes the spatial dimension and $P(\cdot)$ is a polynomial excluding constant and linear terms.Comment: 28 page

Estimating Signal Timing of Actuated Signal Control Using Pattern Recognition under Connected Vehicle Environment

The Signal Phase and Timing (SPaT) message is an important input for research and applications of Connected Vehicles (CVs). However, the actuated signal controllers are not able to directly give the SPaT information since the SPaT is influenced by both signal control logic and real-time traffic demand. This study elaborates an estimation method which is proposed according to the idea that an actuated signal controller would provide similar signal timing for similar traffic states. Thus, the quantitative description of traffic states is important. The traffic flow at each approaching lane has been compared to fluids. The state of fluids can be indicated by state parameters, e.g. speed or height, and its energy, which includes kinetic energy and potential energy. Similar to the fluids, this paper has proposed an energy model for traffic flow, and it has also added the queue length as an additional state parameter. Based on that, the traffic state of intersections can be descripted. Then, a pattern recognition algorithm was developed to identify the most similar historical states and also their corresponding SPaTs, whose average is the estimated SPaT of this second. The result shows that the average error is 3.1 seconds

Diaqua­bis­{5-carb­oxy-2-[(1H-1,2,4-triazol-1-yl)meth­yl]-1H-imidazole-4-carboxyl­ato}zinc

In the title compound, [Zn(C8H6N5O4)2(H2O)2], the six-coordinate ZnII ion, which is located on an inversion center, has a distorted octa­hedral configuration. Each 5-carb­oxy-2-[(1H-1,2,4-triazol-1-yl)meth­yl]-1H-imidazole-4-carboxyl­ate ligand chelates to the ZnII ion through a triazole N atom and a carboxyl­ate O atom in the equatorial plane. The coordination sphere is completed by two water mol­ecules in axial positions. There is an intra­molecular O—H⋯O hydrogen bond in the ligand. In the crystal, mol­ecules are linked via inter­molecular O—H⋯O, O—H⋯N and N—H⋯N hydrogen bonds, forming a three-dimensional structure

Reading Alphabetic and Nonalphabetic Writing Systems: A Case Study of Bilingual Teachers\u27 Reading Processes through Eye Movement Miscue Analysis

This case study investigates the reading processes of two bilingual teachers who speak English as a second language and use different first languages—Mandarin Chinese and Korean. The two participants read researcher-selected digital texts in English and in their respective first language, retold the texts, and answered comprehension questions about the texts. Their reading aloud and eye movements were recorded for miscue and eye movement analysis. Using Eye Movement Miscue Analysis, the findings showcase the distinctive characteristics of their first-language and second-language reading processes. The cross-linguistic comparison between bilingual reading processes further shows the bilingual participants\u27 similarities and differences in terms of the use of language systems, eye movements, language variations, and image use. This study supports the understanding of non-Roman alphabetical language speakers\u27 reading process, adds to our understanding of the bilingual reading process, and provides teaching and research implications for bilingual teachers and educators

Mental health resources and awareness of anxiety and depressive disorders in general hospitals in China

Background: Mental health disorders are common in China. There is a lack of knowledge and resources of mental health in China. Objectives: To assess the levels of psychiatric resources and services in general hospitals in China. Methods: Data regarding psychiatric departments, wards and staff were collected from 57 general hospitals in four provinces of China (Hubei, Zhejiang, Heilongjiang and Yunnan) between April 2014 and June 2014. Questionnaires were distributed to 1,200 non-psychiatric clinicians. Results: Among the 57 hospitals, 50 provided mental health services, 36 had mental health wards, and seven had neither mental health clinics nor wards. The median number of mental health clinicians was six per hospital. The median number of specialized nurses was 42 per hospital. A total of 1,152 non-psychiatric clinicians with a career duration of 9.4 ± 8.9 years returned completed questionnaires. Only 6.9% reported a good understanding of the manifestation of anxiety and depressive disorders, 4.5% reported a good understanding of the diagnostic criteria, and 3.8% reported a good understanding of the treatment protocols. Discussion: There is inadequate awareness of anxiety and depressive disorders among non-psychiatric clinicians in general hospitals in China. This awareness/understanding increased with increasing hospital level

IB-UQ: Information bottleneck based uncertainty quantification for neural function regression and neural operator learning

We propose a novel framework for uncertainty quantification via information bottleneck (IB-UQ) for scientific machine learning tasks, including deep neural network (DNN) regression and neural operator learning (DeepONet). Specifically, we incorporate the bottleneck by a confidence-aware encoder, which encodes inputs into latent representations according to the confidence of the input data belonging to the region where training data is located, and utilize a Gaussian decoder to predict means and variances of outputs conditional on representation variables. Furthermore, we propose a data augmentation based information bottleneck objective which can enhance the quantification quality of the extrapolation uncertainty, and the encoder and decoder can be both trained by minimizing a tractable variational bound of the objective. In comparison to uncertainty quantification (UQ) methods for scientific learning tasks that rely on Bayesian neural networks with Hamiltonian Monte Carlo posterior estimators, the model we propose is computationally efficient, particularly when dealing with large-scale data sets. The effectiveness of the IB-UQ model has been demonstrated through several representative examples, such as regression for discontinuous functions, real-world data set regression, learning nonlinear operators for partial differential equations, and a large-scale climate model. The experimental results indicate that the IB-UQ model can handle noisy data, generate robust predictions, and provide confident uncertainty evaluation for out-of-distribution data.Comment: 27 pages, 22figure