arXiv subjects

Jiaying Feng

Publications and source records attributed to Jiaying Feng.

4 recordsLinked to original sources

arXiv2026

An hp-version time stepping spectral Monte Carlo method for semi-linear parabolic equations

In this paper, we present an $hp$-version time-stepping spectral Monte Carlo method for solving semi-linear parabolic equations. The key innovation lies in constructing an exponentially accurate stochastic algorithm that integrates a residual iteration scheme on Gauss-type nodes in both temporal and spatial directions with a reconstruction strategy rooted in spectral methods. To address the long-time simulations and initial singularities that are often challenging for traditional stochastic algorithms (e.g., walk-on-spheres method), we further develop an $hp$-version time-stepping framework that employs multiple time steps and, respectively, geometric time partitions with linearly increasing polynomial degrees to handle these difficulties. Notably, the proposed algorithm bypasses the need to solve linear systems required by traditional spectral methods and remarkably supports parallel computation at both temporal and spatial grid points. We rigorously establish exponential convergence rates for the multistep method within a finite number of iterations. Extensive numerical experiments are conducted to demonstrate the spectral accuracy and computational efficiency of the proposed method in long-time simulations, problems with initial singularities, and a five-dimensional problem, thereby validating the theoretical results.

math.NA↗

arXiv2025

Exponentially accurate spectral Monte Carlo method for linear PDEs and their error estimates

This paper introduces a spectral Monte Carlo iterative method (SMC) for solving linear Poisson and parabolic equations driven by $\alpha$-stable L\'evy process with $\alpha\in (0,2)$, which was initially proposed and developed by Gobet and Maire in their pioneering works (Monte Carlo Methods Appl 10(3-4), 275--285, 2004, and SIAM J Numer Anal 43(3), 1256--1275, 2005) for the case $\alpha=2$. The novel method effectively integrates multiple computational techniques, including the interpolation based on generalized Jacobi functions (GJFs), space-time spectral methods, control variates techniques, and a novel walk-on-sphere method (WOS). The exponential convergence of the error bounds is rigorously established through finite iterations for both Poisson and parabolic equations involving the integral fractional Laplacian operator. Remarkably, the proposed space-time spectral Monte Carlo method (ST-SMC) for the parabolic equation is unified for both $\alpha\in(0,2)$ and $\alpha=2$. Extensive numerical results are provided to demonstrate the spectral accuracy and efficiency of the proposed method, thereby validating the theoretical findings.

math.NA↗

arXiv2022

Dark patterns in e-commerce: a dataset and its baseline evaluations

Dark patterns, which are user interface designs in online services, induce users to take unintended actions. Recently, dark patterns have been raised as an issue of privacy and fairness. Thus, a wide range of research on detecting dark patterns is eagerly awaited. In this work, we constructed a dataset for dark pattern detection and prepared its baseline detection performance with state-of-the-art machine learning methods. The original dataset was obtained from Mathur et al.'s study in 2019, which consists of 1,818 dark pattern texts from shopping sites. Then, we added negative samples, i.e., non-dark pattern texts, by retrieving texts from the same websites as Mathur et al.'s dataset. We also applied state-of-the-art machine learning methods to show the automatic detection accuracy as baselines, including BERT, RoBERTa, ALBERT, and XLNet. As a result of 5-fold cross-validation, we achieved the highest accuracy of 0.975 with RoBERTa. The dataset and baseline source codes are available at https://github.com/yamanalab/ec-darkpattern.

cs.LG↗

arXiv2017

MapSQ: A MapReduce-based Framework for SPARQL Queries on GPU

In this paper, we present a MapReduce-based framework for evaluating SPARQL queries on GPU (named MapSQ) to large-scale RDF datesets efficiently by applying both high performance. Firstly, we develop a MapReduce-based Join algorithm to handle SPARQL queries in a parallel way. Secondly, we present a coprocessing strategy to manage the process of evaluating queries where CPU is used to assigns subqueries and GPU is used to compute the join of subqueries. Finally, we implement our proposed framework and evaluate our proposal by comparing with two popular and latest SPARQL query engines gStore and gStoreD on the LUBM benchmark. The experiments demonstrate that our proposal MapSQ is highly efficient and effective (up to 50% speedup).

cs.DB↗