Isometric embedding via strongly symmetric positive systems

We give a new proof for the local existence of a smooth isometric embedding of a smooth $3$-dimensional Riemannian manifold with nonzero Riemannian curvature tensor into $6$-dimensional Euclidean space. Our proof avoids the sophisticated arguments via microlocal analysis used in earlier proofs. In Part 1, we introduce a new type of system of partial differential equations, which is not one of the standard types (elliptic, hyperbolic, parabolic) but satisfies a property called strong symmetric positivity. Such a PDE system is a generalization of and has properties similar to a system of ordinary differential equations with a regular singular point. A local existence theorem is then established by using a novel local-to-global-to-local approach. In Part 2, we apply this theorem to prove the local existence result for isometric embeddings.Comment: 39 page

Developing a Modern Infrastructure for Open Distance Education in China: The Implementation of the NCEC Project

The NCEC project was a joint venture between China and Europe to deliver Internet-based distance education in China. The project was proposed in 1995, sponsored by the European Union since 1998, and finally completed in 2002. This paper shows how the NCEC project was planned and developed, and the importance of its role in the history of Internet application development in China

Towards Automated Neural Interaction Discovery for Click-Through Rate Prediction

Click-Through Rate (CTR) prediction is one of the most important machine learning tasks in recommender systems, driving personalized experience for billions of consumers. Neural architecture search (NAS), as an emerging field, has demonstrated its capabilities in discovering powerful neural network architectures, which motivates us to explore its potential for CTR predictions. Due to 1) diverse unstructured feature interactions, 2) heterogeneous feature space, and 3) high data volume and intrinsic data randomness, it is challenging to construct, search, and compare different architectures effectively for recommendation models. To address these challenges, we propose an automated interaction architecture discovering framework for CTR prediction named AutoCTR. Via modularizing simple yet representative interactions as virtual building blocks and wiring them into a space of direct acyclic graphs, AutoCTR performs evolutionary architecture exploration with learning-to-rank guidance at the architecture level and achieves acceleration using low-fidelity model. Empirical analysis demonstrates the effectiveness of AutoCTR on different datasets comparing to human-crafted architectures. The discovered architecture also enjoys generalizability and transferability among different datasets

Photo-Otto engine with quantum correlations

We theoretically prose and investigate a photo-Otto engine that is working with a single-mode radiation field inside an optical cavity and alternatively driven by a hot and a cold reservoir, where the hot reservoir is realized by sending one of a pair of correlated two-level atoms to pass through the optical cavity, and the cold one is made of a collection of noninteracting boson modes. In terms of the quantum discord of the pair of atoms, we derive the analytical expressions for the performance parameters (power and efficiency) and stability measure (coefficient of variation for power). We show that quantum discord boosts the performance and efficiency of the quantum engine, and even may change the operation mode. We also demonstrate that quantum discord improves the stability of machine by decreasing the coefficient of variation for power which satisfies the generalized thermodynamic uncertainty relation. Finally, we find that these results can be transferred to another photo-Otto engine model, where the optical cavity is alternatively coupled to a hot thermal bosonic bath and to a beam of pairs of the two correlated atoms that play the role of a cold reservoir

Study on the spatial variation of sensitivity of soil nutrient system in Xinjiang, China

Previous studies have explored the long time series and large-scale cultivated land nutrient sensitivity and its spatial differentiation characteristics in arid zones from human activities in the context of climate change. This study is based on 10-year interval data on soil nutrient content of cultivated land in the oasis in Xinjiang, China, cultivated land use intensity (LUI) and climate data sets. Using sensitivity and GIS analysis methods, this paper studies soil nutrient sensitivities and their spatial distribution patterns in the context of LUI and climate change. The results showed significant response differences and spatial heterogeneity regarding the sensitivity of soil nutrient systems to LUI and climate change. Among them, soil nutrients were the most sensitive to temperature changes, followed by LUI, while precipitation was the weakest. Soil nutrient sensitivity showed a decreasing spatial distribution pattern from the northeast to the southwest. The soil nutrient system had a strong adaptability to LUI and climate change. However, there were differences in different sensitivity states. These results provide scientific guidance for the spatial selection and implementation of soil fertility enhancement and land remediation projects in similar arid areas

More complex encoder is not all you need

U-Net and its variants have been widely used in medical image segmentation. However, most current U-Net variants confine their improvement strategies to building more complex encoder, while leaving the decoder unchanged or adopting a simple symmetric structure. These approaches overlook the true functionality of the decoder: receiving low-resolution feature maps from the encoder and restoring feature map resolution and lost information through upsampling. As a result, the decoder, especially its upsampling component, plays a crucial role in enhancing segmentation outcomes. However, in 3D medical image segmentation, the commonly used transposed convolution can result in visual artifacts. This issue stems from the absence of direct relationship between adjacent pixels in the output feature map. Furthermore, plain encoder has already possessed sufficient feature extraction capability because downsampling operation leads to the gradual expansion of the receptive field, but the loss of information during downsampling process is unignorable. To address the gap in relevant research, we extend our focus beyond the encoder and introduce neU-Net (i.e., not complex encoder U-Net), which incorporates a novel Sub-pixel Convolution for upsampling to construct a powerful decoder. Additionally, we introduce multi-scale wavelet inputs module on the encoder side to provide additional information. Our model design achieves excellent results, surpassing other state-of-the-art methods on both the Synapse and ACDC datasets

Distribution of fast radio burst dispersion measures in CHIME/FRB Catalog 1: implications on the origin of FRBs

Recently, CHIME/FRB project published its first fast radio burst (FRB) catalog (hereafter, Catalog 1), which totally contains 536 unique bursts. With the help of the latest set of FRBs in this large-size catalog, we aim to investigate the dispersion measure (DM) or redshift ($z$) distribution of the FRB population, and solution of this problem could be used to clarify the question of FRB origin. In this study, we adopted the M\&E 2018 model, to fit the observed $z$ distribution of FRBs in Catalog 1. In the M\&E 2018 model, we are mostly interested in the $\Phi(z)$ function, i.e., number of bursts per proper time per comoving volume, which is represented by the star formation rate (SFR) with a power-law index $n$. Our estimated value of $n$ is $0.0_{-0.0}^{+0.6}$ ($0.0_{-0.0}^{+2.1}$) at the 68 (95) per cent confidence level, implying that the FRB population evolves with redshift consistent with, or faster than, the SFR. Specially, the consistency of the $n$ values estimated by this study and the SFR provides a potential support for the hypothesis of FRBs originating from young magnetars.Comment: 7 pages, 2 figures, accepted for publication in Astronomy Report

Retinal pigment epithelial cells secrete neurotrophic factors and synthesize dopamine: possible contribution to therapeutic effects of RPE cell transplantation in Parkinson's disease

<p>Abstract</p> <p>Background</p> <p>New strategies for the treatment of Parkinson's disease (PD) are shifted from dopamine (DA) replacement to regeneration or restoration of the nigro-striatal system. A cell therapy using human retinal pigment epithelial (RPE) cells as substitution for degenerated dopaminergic (DAergic) neurons has been developed and showed promising prospect in clinical treatment of PD, but the exact mechanism underlying this therapy is not fully elucidated. In the present study, we investigated whether the beneficial effects of this therapy are related to the trophic properties of RPE cells and their ability to synthesize DA.</p> <p>Methods</p> <p>We evaluated the protective effects of conditioned medium (CM) from cultured RPE cells on the DAergic cells against 6-hydroxydopamine (6-OHDA)- and rotenone-induced neurotoxicity and determined the levels of glial cell derived neurotrophic factor (GDNF) and brain derived neurotrophic factor (BDNF) released by RPE cells. We also measured the DA synthesis and release. Finally we transplanted microcarriers-RPE cells into 6-OHDA lesioned rats and observed the improvement in apomorphine-induced rotations (AIR).</p> <p>Results</p> <p>We report here: (1) CM from RPE cells can secret trophic factors GDNF and BDNF, and protect DAergic neurons against the 6-OHDA- and rotenone-induced cell injury; (2) cultured RPE cells express L-dopa decarboxylase (DDC) and synthesize DA; (3) RPE cells attached to microcarriers can survive in the host striatum and improve the AIR in 6-OHDA-lesioned animal model of PD; (4) GDNF and BDNF levels are found significantly higher in the RPE cell-grafted tissues.</p> <p>Conclusion</p> <p>These findings indicate the RPE cells have the ability to secret GDNF and BDNF, and synthesize DA, which probably contribute to the therapeutic effects of RPE cell transplantation in PD.</p