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

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

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

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

Evolution of Maximum Bending Strain on Poisson's Ratio Distribution

In recent years, new flexible functional materials have attracted increasing interest, but there is a lack of the designing mechanisms of flexibility design with superstructures. In traditional engineering mechanics, the maximum bending strain (MBS) was considered universal for describing the bendable properties of a given material, leading to the universal designing method of lowering the dimension such as thin membranes designed flexible functional materials.In this work, the MBS was found only applicable for materials with uniformly distributed Poisson's ratio, while the MBS increases with the thickness of the given material in case there is a variation Poisson's ratio in different areas. This means the MBS can be enhanced by certain Poisson's ratio design in the future to achieve better flexibility of thick materials. Here, the inorganic freestanding nanofiber membranes, which have a nonconstant Poisson's ratio response on stress/strain for creating nonuniformly distributed Poisson's ratio were proven applicable for designing larger MBS and lower Young's modulus for thicker samples

Design, synthesis and pharmacological evaluation of tricyclic derivatives as selective RXFP4 agonists

Relaxin family peptide receptors (RXFPs) are the potential therapeutic targets for neurological, cardiovascular, and metabolic indications. Among them, RXFP3 and RXFP4 (formerly known as GPR100 or GPCR142) are homologous class A G protein-coupled receptors with short N-terminal domain. Ligands of RXFP3 or RXFP4 are only limited to endogenous peptides and their analogues, and no natural product or synthetic agonists have been reported to date except for a scaffold of indole-containing derivatives as dual agonists of RXFP3 and RXFP4. In this study, a new scaffold of tricyclic derivatives represented by compound 7a was disclosed as a selective RXFP4 agonist after a high-throughput screening campaign against a diverse library of 52,000 synthetic and natural compounds. Two rounds of structural modification around this scaffold were performed focusing on three parts: 2-chlorophenyl group, 4-hydroxylphenyl group and its skeleton including cyclohexane-1,3-dione and 1,2,4-triazole group. Compound 14b with a new skeleton of 7,9-dihydro-4H-thiopyrano[3,4-d][1,2,4]triazolo[1,5-a]pyrimidin-8(5H)-one was thus obtained. The enantiomers of 7a and 14b were also resolved with their 9-(S)-conformer favoring RXFP4 agonism. Compared with 7a, compound 9-(S)-14b exhibited 2.3-fold higher efficacy and better selectivity for RXFP4 (selective ratio of RXFP4 vs. RXFP3 for 9-(S)-14b and 7a were 26.9 and 13.9, respectively)