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Xiaojuan Li

Publications and source records attributed to Xiaojuan Li.

29 records · Page 2Linked to original sources
arXiv2022

Relationship between MP and DPP for stochastic recursive optimal control problem under volatility uncertainty

In this paper, we study the relationship between maximum principle (MP) and dynamic programming principle (DPP) for stochastic recursive optimal control problem driven by $G$-Brownian motion. Under the smooth assumption for the value function, we obtain the connection between MP and DPP under a reference probability $P_{t,x}^{\ast}$. Within the framework of viscosity solution, we establish the relation between the first-order super-jet, sub-jet of the value function and the solution to the adjoint equation respectively.

math.OC↗
arXiv2022

G-capacity under degenerate case and its application

In this paper, we first find a type of viscosity solution of $G$-heat equation under degenerate case, and then obtain the related $G$-capacity $c(\{B_{T}\in A\})$ for any Borel set $A$. Furthermore, we prove that $I_{A}(B_{T})$ has no quasi-continuous version when it is not a constant function.

math.AP↗
arXiv2022

Maximum principle for discrete-time stochastic optimal control problem under distribution uncertainty

In this paper, we study a discrete-time stochastic optimal control problem under distribution uncertainty with convex control domain. By weak convergence method and Sion's minimax theorem, we obtain the variational inequality for cost functional under a reference probability $P^{\ast}$. Moreover, under the square integrability condition for noise and control, we establish the discrete-time stochastic maximum principle under $P^{\ast}$. Finally, we introduce a backward algorithm to calculate the reference probability $P^{\ast}$ and the optimal control $u^{\ast}$.

math.OC↗
arXiv2022

Quantifying Wetting Dynamics with Triboelectrification

Wetting is often perceived as an intrinsic surface property of materials, but determining its evolution is complicated by its complex dependence on roughness across the scales. The Wenzel state, where liquids have intimate contact with the rough substrate, and the Cassie-Baxter state, where liquids sit onto air pockets formed between asperities, are only two states among the plethora of wetting behaviors. Furthermore, transitions from the Cassie-Baxter to the Wenzel state dictate completely different surface performance, such as anti-contamination, anti-icing, drag reduction etc.; however, little is known about how transition occurs during time between the several wetting modes. In this paper, we show that wetting dynamics can be accurately quantified and tracked using solid-liquid triboelectrification. Theoretical underpinning reveals how surface micro-/nano-geometries regulate stability/infiltration, also demonstrating the generality of our theoretical approach in understanding wetting transitions.

cond-mat.soft↗
arXiv2021

Dynamic programming principle and Hamilton-Jacobi-Bellman equation under nonlinear expectation

In this paper, we study a stochastic recursive optimal control problem in which the value functional is defined by the solution of a backward stochastic differential equation (BSDE) under $\tilde{G}$-expectation. Under standard assumptions, we establish the comparison theorem for this kind of BSDE and give a novel and simple method to obtain the dynamic programming principle. Finally, we prove that the value function is the unique viscosity solution of a type of fully nonlinear HJB equation.

math.OC↗
arXiv2020

Local Indicator of Colocation Quotient with a Statistical Significance Test: Examining Spatial Association of Crime and Facilities

Most existing point-based colocation methods are global measures (e.g., join count statistic, cross K function, and global colocation quotient). Most recently, a local indicator such as the local colocation quotient is proposed to capture the variability of colocation across areas. Our research advances this line of work by developing a simulation-based statistic test for the local indicator of colocation quotient (LCLQ). The study applies the indicator to examine the association of land use facilities with crime patterns. Moreover, we use the street network distance in addition to the traditional Euclidean distance in defining neighbors since human activities (including facilities and crimes) usually occur along a street network. The method is applied to analyze the colocation of three types of crimes and three categories of facilities in a city in Jiangsu Province, China. The findings demonstrate the value of the proposed method in colocation analysis of crime and facilities, and in general colocation analysis of point data.

stat.AP↗
arXiv2020

The International Workshop on Osteoarthritis Imaging Knee MRI Segmentation Challenge: A Multi-Institute Evaluation and Analysis Framework on a Standardized Dataset

Purpose: To organize a knee MRI segmentation challenge for characterizing the semantic and clinical efficacy of automatic segmentation methods relevant for monitoring osteoarthritis progression. Methods: A dataset partition consisting of 3D knee MRI from 88 subjects at two timepoints with ground-truth articular (femoral, tibial, patellar) cartilage and meniscus segmentations was standardized. Challenge submissions and a majority-vote ensemble were evaluated using Dice score, average symmetric surface distance, volumetric overlap error, and coefficient of variation on a hold-out test set. Similarities in network segmentations were evaluated using pairwise Dice correlations. Articular cartilage thickness was computed per-scan and longitudinally. Correlation between thickness error and segmentation metrics was measured using Pearson's coefficient. Two empirical upper bounds for ensemble performance were computed using combinations of model outputs that consolidated true positives and true negatives. Results: Six teams (T1-T6) submitted entries for the challenge. No significant differences were observed across all segmentation metrics for all tissues (p=1.0) among the four top-performing networks (T2, T3, T4, T6). Dice correlations between network pairs were high (>0.85). Per-scan thickness errors were negligible among T1-T4 (p=0.99) and longitudinal changes showed minimal bias (<0.03mm). Low correlations (<0.41) were observed between segmentation metrics and thickness error. The majority-vote ensemble was comparable to top performing networks (p=1.0). Empirical upper bound performances were similar for both combinations (p=1.0). Conclusion: Diverse networks learned to segment the knee similarly where high segmentation accuracy did not correlate to cartilage thickness accuracy. Voting ensembles did not outperform individual networks but may help regularize individual models.

eess.IV↗
arXiv2019

3-Lie-Rinehart Algebras

In this paper, we define a class of 3-algebras which are called 3-Lie-Rinehart algebras. A 3-Lie-Rinehart algebra is a triple $(L, A, ρ)$, where $A$ is a commutative associative algebra, $L$ is an $A$-module, $(A, ρ)$ is a 3-Lie algebra $L$-module and $ρ(L, L)\subseteq Der(A)$. We discuss the basic structures, actions and crossed modules of 3-Lie-Rinehart algebras and construct 3-Lie-Rinehart algebras from given algebras, we also study the derivations from 3-Lie-Rinehart algebras to 3-Lie $A$-algebras. From the study, we see that there is much difference between 3-Lie algebras and 3-Lie-Rinehart algebras.

math.RA↗