Cycle symmetry, limit theorems, and fluctuation theorems for diffusion processes on the circle

Cyclic structure and dynamics are of great interest in both the fields of stochastic processes and nonequilibrium statistical physics. In this paper, we find a new symmetry of the Brownian motion named as the quasi-time-reversal invariance. It turns out that such an invariance of the Brownian motion is the key to prove the cycle symmetry for diffusion processes on the circle, which says that the distributions of the forming times of the forward and backward cycles, given that the corresponding cycle is formed earlier than the other, are exactly the same. With the aid of the cycle symmetry, we prove the strong law of large numbers, functional central limit theorem, and large deviation principle for the sample circulations and net circulations of diffusion processes on the circle. The cycle symmetry is further applied to obtain various types of fluctuation theorems for the sample circulations, net circulation, and entropy production rate.Comment: 28 page

New insights into the mechanism of low high-density lipoprotein cholesterol in obesity

Obesity, a significant risk factor for various chronic diseases, is universally related to dyslipidemia mainly represented by decreasing high-density lipoprotein cholesterol (HDL-C), which plays an indispensible role in development of cardiovascular disease (CVD). However, the mechanisms underlying obesity and low HDL-C have not been fully elucidated. Previous studies have focused on the alteration of HDL catabolism in circulation following elevated triglyceride (TG). But recent findings suggested that liver and fat tissue played pivotal role in obesity related low HDL-C. Some new molecular pathways like microRNA have also been proposed in the regulation of HDL metabolism in obesity. This article will review recent advances in understanding of the potential mechanism of low HDL-C in obesity

Regret Bounds for Risk-sensitive Reinforcement Learning with Lipschitz Dynamic Risk Measures

We study finite episodic Markov decision processes incorporating dynamic risk measures to capture risk sensitivity. To this end, we present two model-based algorithms applied to \emph{Lipschitz} dynamic risk measures, a wide range of risk measures that subsumes spectral risk measure, optimized certainty equivalent, distortion risk measures among others. We establish both regret upper bounds and lower bounds. Notably, our upper bounds demonstrate optimal dependencies on the number of actions and episodes, while reflecting the inherent trade-off between risk sensitivity and sample complexity. Additionally, we substantiate our theoretical results through numerical experiments

An Image Based Visual Servo Method for Probe-and-Drogue Autonomous Aerial Refueling

With the high focus on autonomous aerial refueling recently, it becomes increasingly urgent to design efficient methods or algorithms to solve AAR problems in complicated aerial environments. Apart from the complex aerodynamic disturbance, another problem is the pose estimation error caused by the camera calibration error, installation error, or 3D object modeling error, which may not satisfy the highly accurate docking. The main objective of the effort described in this paper is the implementation of an image-based visual servo control method, which contains the establishment of an image-based visual servo model involving the receiver's dynamics and the design of the corresponding controller. Simulation results indicate that the proposed method can make the system dock successfully under complicated conditions and improve the robustness against pose estimation error

Empirical Analysis of Vehicle Tracking Algorithms for Extracting Integral Trajectories from Consecutive Videos

This study introduces a novel methodological frame-work for extracting integral vehicle trajectories from several consecutive pictures automatically. The frame-work contains camera observation, eliminating image distortions, video stabilising, stitching images, identify-ing vehicles and tracking vehicles. Observation videos of four sections in South Fengtai Road, Nanjing, Jiangsu Province, China are taken as a case study to validate the framework. As key points, six typical tracking algorithms, including boosting, CSRT, KCF, median flow, MIL and MOSSE, are compared in terms of tracking reliability, operational time, random access memory (RAM) usage and data accuracy. Main impact factors taken into con-sideration involve vehicle colours, zebra lines, lane lines, lamps, guide boards and image stitching seams. Based on empirical analysis, it is found that MOSSE requires the least operational time and RAM usage, whereas CSRT presents the best tracking reliability. In addition, all tracking algorithms produce reliable vehicle trajecto-ry and speed data if vehicles are tracked steadily