Xuesong Fu | Searcharxiv

arXiv2025

Disconnection probability of Brownian motion on an annulus

We derive an exact formula for the probability that a Brownian path on an annulus does not disconnect the two boundary components of the annulus. The leading asymptotic behavior of this probability is governed by the disconnection exponent obtained by Lawler-Schramm-Werner (2001) using the connection to Schramm-Loewner evolution (SLE). The derivation of our formula is based on this connection and the coupling with Liouville quantum gravity (LQG). As byproducts of our proof, we obtain a precise relation between Brownian motion on a disk stopped upon hitting the boundary and the SLE$_{8/3}$ loop measure on the disk; we also obtain a detailed description of the LQG surfaces cut by the outer boundary of stopped Brownian motion on a $\sqrt{8/3}$-LQG disk.

math.PR↗

arXiv2019

DC-SPP-YOLO: Dense Connection and Spatial Pyramid Pooling Based YOLO for Object Detection

Although the YOLOv2 method is extremely fast on object detection, its detection accuracy is restricted due to the low performance of its backbone network and the underutilization of multi-scale region features. Therefore, a dense connection (DC) and spatial pyramid pooling (SPP) based YOLO (DC-SPP-YOLO) method for ameliorating the object detection accuracy of YOLOv2 is proposed in this paper. Specifically, the dense connection of convolution layers is employed in the backbone network of YOLOv2 to strengthen the feature extraction and alleviate the vanishing-gradient problem. Moreover, an improved spatial pyramid pooling is introduced to pool and concatenate the multi-scale region features, so that the network can learn the object features more comprehensively. The DC-SPP-YOLO model is established and trained based on a new loss function composed of MSE (mean square error) loss and cross-entropy loss. The experimental results indicated that the mAP (mean Average Precision) of DC-SPP-YOLO is higher than that of YOLOv2 on the PASCAL VOC datasets and the UA-DETRAC datasets. The effectiveness of DC-SPP-YOLO method proposed is demonstrated.

cs.CV↗