arXiv subjects

Xiaolin Gong

Publications and source records attributed to Xiaolin Gong.

4 recordsLinked to original sources

arXiv2026

Theory of uncertain probability: can we derive the probability density function of uncertain random experiments with continuously changing conditions?

This paper aims to explore the formation mechanism of probability distribution in situations where the differences among random experiments are distinguishable, and these differences continue to evolve along with the dynamic changes in conditions and their mechanisms of action. To this end, we are motivated to devise a new theoretical system -- theory of uncertain prob ability (TUP) with Kolmogorov's system and nonlinear theories as special cases. TUP develops a novel model that integrates probability and uncertainty as well as the known and unknown to more accurately depict numerous typical random phenomena under more realistic assumptions, and thus provides appropriate tools for greater variety of real needs. It also allows for pioneering interpretation of the causal mechanisms underlying many important distributional characteristics and incorporation of pathwise property to distribution model.

math.PR↗

arXiv2024

TSNet:A Two-stage Network for Image Dehazing with Multi-scale Fusion and Adaptive Learning

Image dehazing has been a popular topic of research for a long time. Previous deep learning-based image dehazing methods have failed to achieve satisfactory dehazing effects on both synthetic datasets and real-world datasets, exhibiting poor generalization. Moreover, single-stage networks often result in many regions with artifacts and color distortion in output images. To address these issues, this paper proposes a two-stage image dehazing network called TSNet, mainly consisting of the multi-scale fusion module (MSFM) and the adaptive learning module (ALM). Specifically, MSFM and ALM enhance the generalization of TSNet. The MSFM can obtain large receptive fields at multiple scales and integrate features at different frequencies to reduce the differences between inputs and learning objectives. The ALM can actively learn of regions of interest in images and restore texture details more effectively. Additionally, TSNet is designed as a two-stage network, where the first-stage network performs image dehazing, and the second-stage network is employed to improve issues such as artifacts and color distortion present in the results of the first-stage network. We also change the learning objective from ground truth images to opposite fog maps, which improves the learning efficiency of TSNet. Extensive experiments demonstrate that TSNet exhibits superior dehazing performance on both synthetic and real-world datasets compared to previous state-of-the-art methods.

cs.CV↗

arXiv2013

The Numerical Properties of G-heat equation and Related Application

In this paper, we consider the numerical convergence of G-heat equation which was first introduced by Peng. The G-heat equation extends the classical heat equation with uncertain volatility. For G-heat equation is nonlinear partial differential equation(PDE), we prove that the Newton iteration is convergence and the fully implicit discretization is monotone and stable. Then, we have the fully implicit discretization convergence to the viscosity solution of a G-heat equation.

math.NA↗

arXiv2013

A New Distribution-Random Limit Normal Distribution

This paper introduces a new distribution to improve tail risk modeling. Based on the classical normal distribution, we define a new distribution by a series of heat equations. Then, we use market data to verify our model.

math.ST↗