Positive Scalar Curvature Meets Ricci Limit Spaces

We investigate how the positive scalar curvature controls the size of a Ricci limit space when it comes from a sequence of $n$-manifolds with non-negative Ricci curvature and strictly positive scalar curvature lower bound. We prove such a limit space can split off $\mathbb{R}^{n-2}$ at most, and when the maximal splitting happens, the other non-splitting factor has an explicit uniform diameter upper bound. Besides, we study some other consequences of having positive scalar curvature for manifolds using Ricci limit spaces techniques, for instance volume gap estimates and volume growth order estimates.Comment: 22 pages. Some conditions added to the theorem 1.1 due to a gap in the original proof, and the proof is slightly changed accordingly. A corollary about the first Betti number is adde

LIO-GVM: an Accurate, Tightly-Coupled Lidar-Inertial Odometry with Gaussian Voxel Map

This letter presents an accurate and robust Lidar Inertial Odometry framework. We fuse LiDAR scans with IMU data using a tightly-coupled iterative error state Kalman filter for robust and fast localization. To achieve robust correspondence matching, we represent the points as a set of Gaussian distributions and evaluate the divergence in variance for outlier rejection. Based on the fitted distributions, a new residual metric is proposed for the filter-based Lidar inertial odometry, which demonstrates an improvement from merely quantifying distance to incorporating variance disparity, further enriching the comprehensiveness and accuracy of the residual metric. Due to the strategic design of the residual metric, we propose a simple yet effective voxel-solely mapping scheme, which only necessities the maintenance of one centroid and one covariance matrix for each voxel. Experiments on different datasets demonstrate the robustness and accuracy of our framework for various data inputs and environments. To the benefit of the robotics society, we open source the code at https://github.com/Ji1Xingyu/lio_gvm

Task-Robust Pre-Training for Worst-Case Downstream Adaptation

Pre-training has achieved remarkable success when transferred to downstream tasks. In machine learning, we care about not only the good performance of a model but also its behavior under reasonable shifts of condition. The same philosophy holds when pre-training a foundation model. However, the foundation model may not uniformly behave well for a series of related downstream tasks. This happens, for example, when conducting mask recovery regression where the recovery ability or the training instances diverge like pattern features are extracted dominantly on pre-training, but semantic features are also required on a downstream task. This paper considers pre-training a model that guarantees a uniformly good performance over the downstream tasks. We call this goal as $\textit{downstream-task robustness}$. Our method first separates the upstream task into several representative ones and applies a simple minimax loss for pre-training. We then design an efficient algorithm to solve the minimax loss and prove its convergence in the convex setting. In the experiments, we show both on large-scale natural language processing and computer vision datasets our method increases the metrics on worse-case downstream tasks. Additionally, some theoretical explanations for why our loss is beneficial are provided. Specifically, we show fewer samples are inherently required for the most challenging downstream task in some cases

Digital Loop-Mediated Isothermal Amplification on a Commercial Membrane

In this work, we report digital loop-mediated isothermal amplification (LAMP) or reverse-transcription LAMP (RT-LAMP) on a commercial membrane, without the need for complex chip fabrication or use of specialized equipment. Due to the pore size distribution, the theoretical error for digital LAMP on these membranes was analyzed, using a combination of Random Distribution Model and Multi-volume Theory. A facile peel-off process was developed for effective droplets formation on the commercial track-etched polycarbonate (PCTE) membrane. Each pore functions as an individual nanoreactor for single DNA amplification. Absolute quantification of bacteria genomic DNA was realized with a dynamic range from 11 to 1.1 105 copies/µL. One-step digital RT-LAMP was also successfully performed on the membrane for the quantification of MS2 virus in wastewater. With the introduction of new probes, the positive pores can be easily distinguished from negative ones with 100 times difference in fluorescence intensities. Finally, the cost of a disposable membrane is less than $0.1/piece, which, to the best of our knowledge, is the most inexpensive way to perform digital LAMP. The membrane system offers opportunities for point-of-care users or common laboratories to perform digital quantification, single cell analysis, or other bioassays in an inexpensive, flexible and simplified way

Social exclusion and suicide intention in Chinese college students: a moderated mediation model

Given the growing incidence rates of suicide among college students and the potential lifelong consequences of suicide, it is imperative to better understand the factors that reduce the rates at which college students in a clinical sample engage in suicide. This study examines the relationship between social exclusion and suicide intention, the mediating effect of depression, and the moderating effect of meaning in life. Two hundred and ninety-nine Chinese college students, aged from 18 to 22 years (56.86% female, M age = 20.14, SD = 1.27) completed questionnaires assessing their social exclusion, suicide intention, depression, and meaning in life. The result revealed that social exclusion was positively associated with suicide intention, and depression mediated this relationship. In addition, this mediating effect of depression was moderated by meaning in life. That is, the mediation effect was stronger for students with a higher level of meaning in life. These findings provide educational suggestions for preventing and intervening in suicide intention among college students