The noncompact Schauder fixed point theorem in random normed modules

Random normed modules ($RN$ modules) are a random generalization of ordinary normed spaces, which are usually endowed with the two kinds of topologies -- the $(\varepsilon,\lambda)$-topology and the locally $L^0$-convex topology. The purpose of this paper is to give a noncompact generalization of the classical Schauder fixed point theorem for the development and financial applications of $RN$ modules. Motivated by the randomized version of the classical Bolzano-Weierstrauss theorem, we first introduce the two notions of a random sequentially compact set and a random sequentially continuous mapping under the $(\varepsilon,\lambda)$-topology and further establish their corresponding characterizations under the locally $L^0$-convex topology so that we can treat the fixed point problems under the two kinds of topologies in an unified way. Then we prove our desired Schauder fixed point theorem that in a $\sigma$-stable $RN$ module every continuous (under either topology) $\sigma$-stable mapping $T$ from a random sequentially compact closed $L^0$-convex subset $G$ to $G$ has a fixed point. The whole idea to prove the fixed point theorem is to find an approximate fixed point of $T$, but, since $G$ is not compact in general, realizing such an idea in the random setting forces us to construct the corresponding Schauder projection in a subtle way and carry out countably many decompositions for $T$ so that we can first obtain an approximate fixed point for each decomposition and eventually one for $T$ by the countable concatenation skill. Besides, the new fixed point theorem not only includes as a special case Bharucha-Reid and Mukherjea's famous random version of the classical Schauder fixed point theorem but also implies the corresponding Krasnoselskii fixed point theorem in $RN$ modules.Comment: 37 page

The Framework for the Prediction of the Critical Turning Period for Outbreak of COVID-19 Spread in China based on the iSEIR Model

The goal of this study is to establish a general framework for predicting the so-called critical Turning Period in an infectious disease epidemic such as the COVID-19 outbreak in China early this year. This framework enabled a timely prediction of the turning period when applied to Wuhan COVID-19 epidemic and informed the relevant authority for taking appropriate and timely actions to control the epidemic. It is expected to provide insightful information on turning period for the world's current battle against the COVID-19 pandemic. The underlying mathematical model in our framework is the individual Susceptible-Exposed- Infective-Removed (iSEIR) model, which is a set of differential equations extending the classic SEIR model. We used the observed daily cases of COVID-19 in Wuhan from February 6 to 10, 2020 as the input to the iSEIR model and were able to generate the trajectory of COVID-19 cases dynamics for the following days at midnight of February 10 based on the updated model, from which we predicted that the turning period of CIVID-19 outbreak in Wuhan would arrive within one week after February 14. This prediction turned to be timely and accurate, providing adequate time for the government, hospitals, essential industry sectors and services to meet peak demands and to prepare aftermath planning. Our study also supports the observed effectiveness on flatting the epidemic curve by decisively imposing the Lockdown and Isolation Control Program in Wuhan since January 23, 2020. The Wuhan experience provides an exemplary lesson for the whole world to learn in combating COVID-19.Comment: 24 paages, 9 figures, 10 table

CasFusionNet: A Cascaded Network for Point Cloud Semantic Scene Completion by Dense Feature Fusion

Semantic scene completion (SSC) aims to complete a partial 3D scene and predict its semantics simultaneously. Most existing works adopt the voxel representations, thus suffering from the growth of memory and computation cost as the voxel resolution increases. Though a few works attempt to solve SSC from the perspective of 3D point clouds, they have not fully exploited the correlation and complementarity between the two tasks of scene completion and semantic segmentation. In our work, we present CasFusionNet, a novel cascaded network for point cloud semantic scene completion by dense feature fusion. Specifically, we design (i) a global completion module (GCM) to produce an upsampled and completed but coarse point set, (ii) a semantic segmentation module (SSM) to predict the per-point semantic labels of the completed points generated by GCM, and (iii) a local refinement module (LRM) to further refine the coarse completed points and the associated labels from a local perspective. We organize the above three modules via dense feature fusion in each level, and cascade a total of four levels, where we also employ feature fusion between each level for sufficient information usage. Both quantitative and qualitative results on our compiled two point-based datasets validate the effectiveness and superiority of our CasFusionNet compared to state-of-the-art methods in terms of both scene completion and semantic segmentation. The codes and datasets are available at: https://github.com/JinfengX/CasFusionNet

Mechanistic study of visible light-driven CdS or g-C₃N₄-catalyzed C–H direct trifluoromethylation of (hetero)arenes using CF₃SO₂Na as the trifluoromethyl source

The mild and sustainable methods for C–H direct trifluoromethylation of (hetero)arenes without any base or strong oxidants are in extremely high demand. Here, we report that the photo-generated electron-hole pairs of classical semiconductors (CdS or g-C3N4) under visible light excitation are effective to drive C–H trifluoromethylation of (hetero)arenes with stable and inexpensive CF3SO2Na as the trifluoromethyl (TFM) source via radical pathway. Either CdS or g-C3N4 propagated reaction can efficiently transform CF3SO2Na to [rad]CF3 radical and further afford the desired benzotrifluoride derivatives in moderate to good yields. After visible light initiated photocatalytic process, the key elements (such as F, S and C) derived from the starting TFM source of CF3SO2Na exhibited differential chemical forms as compared to those in other oxidative reactions. The photogenerated electron was trapped by chemisorbed O2 on photocatalysts to form superoxide radical anion (O2[rad]−) which will further attack [rad]CF3 radical with the generation of inorganic product F− and CO2. This resulted in a low utilization efficiency of [rad]CF3 (&lt;50%). When nitro aromatic compounds and CF3SO2Na served as the starting materials in inert atmosphere, the photoexcited electrons can be directed to reduce the nitro group to amino group rather than being trapped by O2. Meanwhile, the photogenerated holes oxidize SO2CF3− into [rad]CF3. Both the photogenerated electrons and holes were engaged in reductive and oxidative paths, respectively. The desired product, trifluoromethylated aniline, was obtained successfully via one-pot free-radical synthesis.</p

Oxidative Stress Activated by Sorafenib Alters the Temozolomide Sensitivity of Human Glioma Cells Through Autophagy and JAK2/STAT3-AIF Axis

The development of temozolomide (TMZ) resistance in glioma leads to poor patient prognosis. Sorafenib, a novel diaryl urea compound and multikinase inhibitor, has the ability to effectively cross the blood-brain barrier. However, the effect of sorafenib on glioma cells and the molecular mechanism underlying the ability of sorafenib to enhance the antitumor effects of TMZ remain elusive. Here, we found that sorafenib could enhance the cytotoxic effects of TMZ in glioma cells in vitro and in vivo. Mechanistically, the combination of sorafenib and TMZ induced mitochondrial depolarization and apoptosis inducing factor (AIF) translocation from mitochondria to nuclei, and this process was dependent on STAT3 inhibition. Moreover, the combination of sorafenib and TMZ inhibited JAK2/STAT3 phosphorylation and STAT3 translocation to mitochondria. Inhibition of STAT3 activation promoted the autophagy-associated apoptosis induced by the combination of sorafenib and TMZ. Furthermore, the combined sorafenib and TMZ treatment induced oxidative stress while reactive oxygen species (ROS) clearance reversed the treatment-induced inhibition of JAK2/STAT3. The results indicate that sorafenib enhanced the temozolomide sensitivity of human glioma cells by inducing oxidative stress-mediated autophagy and JAK2/STAT3-AIF axis

Radiomic Features From Multi-Parameter MRI Combined With Clinical Parameters Predict Molecular Subgroups in Patients With Medulloblastoma

The 2016 WHO classification of central nervous system tumors has included four molecular subgroups under medulloblastoma (MB) as sonic hedgehog (SHH), wingless (WNT), Grade 3, and Group 4. We aimed to develop machine learning models for predicting MB molecular subgroups based on multi-parameter magnetic resonance imaging (MRI) radiomics, tumor locations, and clinical factors. A total of 122 MB patients were enrolled retrospectively. After selecting robust, non-redundant, and relevant features from 5,529 extracted radiomics features, a random forest model was constructed based on a training cohort (n= 92) and evaluated on a testing cohort (n= 30). By combining radiographic features and clinical parameters, two combined prediction models were also built. The subgroup can be classified using an 11-feature radiomics model with a high area under the curve (AUC) of 0.8264 for WNT and modest AUCs of 0.6683, 0.6004, and 0.6979 for SHH, Group 3, and Group 4 in the testing cohort, respectively. Incorporating location and hydrocephalus into the radiomics model resulted in improved AUCs of 0.8403 and 0.8317 for WNT and SHH, respectively. After adding gender and age, the AUCs for WNT and SHH were further improved to 0.9097 and 0.8654, while the accuracies were 70 and 86.67% for Group 3 and Group 4, respectively. Prediction performance was excellent for WNT and SHH, while that for Group 3 and Group 4 needs further improvements. Machine learning algorithms offer potentials to non-invasively predict the molecular subgroups of MB.</p

Construction of a cross-species cell landscape at single-cell level.

Individual cells are basic units of life. Despite extensive efforts to characterize the cellular heterogeneity of different organisms, cross-species comparisons of landscape dynamics have not been achieved. Here, we applied single-cell RNA sequencing (scRNA-seq) to map organism-level cell landscapes at multiple life stages for mice, zebrafish and Drosophila. By integrating the comprehensive dataset of > 2.6 million single cells, we constructed a cross-species cell landscape and identified signatures and common pathways that changed throughout the life span. We identified structural inflammation and mitochondrial dysfunction as the most common hallmarks of organism aging, and found that pharmacological activation of mitochondrial metabolism alleviated aging phenotypes in mice. The cross-species cell landscape with other published datasets were stored in an integrated online portal-Cell Landscape. Our work provides a valuable resource for studying lineage development, maturation and aging