Browsing by Author "Li, Q"

Now showing 1 - 8 of 8
  • Thumbnail Image
    ItemOpen Access
    A convergent method for linear half-space kinetic equations
    (2017-04-23) Li, Q; Lu, J; Sun, W
    We give a unified proof for the well-posedness of a class of linear half-space equations with general incoming data and construct a Galerkin method to numerically resolve this type of equations in a systematic way. Our main strategy in both analysis and numerics includes three steps: adding damping terms to the original half-space equation, using an inf-sup argument and even-odd decomposition to establish the well-posedness of the damped equation, and then recovering solutions to the original half-space equation. The proposed numerical methods for the damped equation is shown to be quasi-optimal and the numerical error of approximations to the original equation is controlled by that of the damped equation. This efficient solution to the half-space problem is useful for kinetic-fluid coupling simulations.
  • Thumbnail Image
    ItemOpen Access
    An asymptotic preserving method for transport equations with oscillatory scattering coefficients
    (2017-04-26) Li, Q; Lu, J
    We design a numerical scheme for transport equations with oscillatory periodic scattering coefficients. The scheme is asymptotic preserving in the diffusion limit as Knudsen number goes to zero. It also captures the homogenization limit as the length scale of the scattering coefficient goes to zero. The proposed method is based on the construction of multiscale finite element basis and a Galerkin projection based on the even-odd decomposition. The method is analyzed in the asymptotic regime, as well as validated numerically.
  • Thumbnail Image
    ItemOpen Access
    Diffusion approximations and domain decomposition method of linear transport equations: Asymptotics and numerics
    (Journal of Computational Physics, 2015-07-01) Li, Q; Lu, J; Sun, W
    © 2015 Elsevier Inc.In this paper we construct numerical schemes to approximate linear transport equations with slab geometry by diffusion equations. We treat both the case of pure diffusive scaling and the case where kinetic and diffusive scalings coexist. The diffusion equations and their data are derived from asymptotic and layer analysis which allows general scattering kernels and general data. We apply the half-space solver in [20] to resolve the boundary layer equation and obtain the boundary data for the diffusion equation. The algorithms are validated by numerical experiments and also by error analysis for the pure diffusive scaling case.
  • Thumbnail Image
    ItemOpen Access
    Genetic variants in the TEP1 gene are associated with prostate cancer risk and recurrence.
    (Prostate Cancer Prostatic Dis, 2015-12) Gu, C; Li, Q; Zhu, Y; Qu, Y; Zhang, G; Wang, M; Yang, Y; Wang, J; Jin, L; Wei, Q; Ye, D
    BACKGROUND: Telomere-related genes play an important role in carcinogenesis and progression of prostate cancer (PCa). It is not fully understood whether genetic variations in telomere-related genes are associated with development and progression in PCa patients. METHODS: Six potentially functional single-nucleotide polymorphisms (SNPs) of three key telomere-related genes were evaluated in 1015 PCa cases and 1052 cancer-free controls, to test their associations with risk of PCa. Among 426 PCa patients who underwent radical prostatectomy (RP), the prognostic significance of the studied SNPs on biochemical recurrence (BCR) was also assessed using the Kaplan-Meier analysis and Cox proportional hazards regression model. The relative telomere lengths (RTLs) were measured in peripheral blood leukocytes using real-time PCR in the RP patients. RESULTS: TEP1 rs1760904 AG/AA genotypes were significantly associated with a decreased risk of PCa (odds ratio (OR): 0.77, 95% confidence interval (CI): 0.64-0.93, P=0.005) compared with the GG genotype. By using median RTL as a cutoff level, RP patients with TEP1 rs1760904 AG/AA genotypes tended to have a longer RTL than those with the GG genotype (OR: 1.55, 95% CI: 1.04-2.30, P=0.031). A significant interaction between TEP1 rs1713418 and age in modifying PCa risk was observed (P=0.005). After adjustment for clinicopathologic risk factors, the presence of heterozygotes or rare homozygotes of TEP1 rs1760904 and TNKS2 rs1539042 were associated with BCR in the RP cohorts (hazard ratio: 0.53, 95% CI: 0.36-0.79, P=0.002 and hazard ratio: 1.67, 95% CI: 1.07-2.48, P=0.017, respectively). CONCLUSIONS: These data suggest that genetic variations in the TEP1 gene may be biomarkers for risk of PCa and BCR after RP.
  • Thumbnail Image
    ItemOpen Access
    Half-space kinetic equations with general boundary conditions
    (Mathematics of Computation, 2017-01-01) Li, Q; Lu, J; Sun, W
    © 2016 American Mathematical Society.We study half-space linear kinetic equations with general boundary conditions that consist of both given incoming data and various types of reflections, extending our previous work on half-space equations with incoming boundary conditions. As in our previous work, the main technique is a damping adding-removing procedure. We establish the well-posedness of linear (or linearized) half-space equations with general boundary conditions and quasioptimality of the numerical scheme. The numerical method is validated by examples including a two-species transport equation, a multi-frequency transport equation, and the linearized BGK equation in 2D velocity space.
  • Thumbnail Image
    ItemOpen Access
    Randomized sampling for basis functions construction in generalized finite element methods
    (2018-02-14) Chen, K; Li, Q; Lu, J; Wright, SJ
    In the context of generalized finite element methods for elliptic equations with rough coefficients $a(x)$, efficiency and accuracy of the numerical method depend critically on the use of appropriate basis functions. This work explores several random sampling strategies for construction of basis functions, and proposes a quantitative criterion to analyze and compare these sampling strategies. Numerical evidence shows that the optimal basis functions can be well approximated by a random projection of generalized eigenvalue problem onto subspace of $a$-harmonic functions.
  • Thumbnail Image
    ItemOpen Access
    The autism brain imaging data exchange: towards a large-scale evaluation of the intrinsic brain architecture in autism.
    (Molecular psychiatry, 2014-06) Di Martino, A; Yan, C-G; Li, Q; Denio, E; Castellanos, FX; Alaerts, K; Anderson, JS; Assaf, M; Bookheimer, SY; Dapretto, M; Deen, B; Delmonte, S; Dinstein, I; Ertl-Wagner, B; Fair, DA; Gallagher, L; Kennedy, DP; Keown, CL; Keysers, C; Lainhart, JE; Lord, C; Luna, B; Menon, V; Minshew, NJ; Monk, CS; Mueller, S; Müller, R-A; Nebel, MB; Nigg, JT; O'Hearn, K; Pelphrey, KA; Peltier, SJ; Rudie, JD; Sunaert, S; Thioux, M; Tyszka, JM; Uddin, LQ; Verhoeven, JS; Wenderoth, N; Wiggins, JL; Mostofsky, SH; Milham, MP
    Autism spectrum disorders (ASDs) represent a formidable challenge for psychiatry and neuroscience because of their high prevalence, lifelong nature, complexity and substantial heterogeneity. Facing these obstacles requires large-scale multidisciplinary efforts. Although the field of genetics has pioneered data sharing for these reasons, neuroimaging had not kept pace. In response, we introduce the Autism Brain Imaging Data Exchange (ABIDE)-a grassroots consortium aggregating and openly sharing 1112 existing resting-state functional magnetic resonance imaging (R-fMRI) data sets with corresponding structural MRI and phenotypic information from 539 individuals with ASDs and 573 age-matched typical controls (TCs; 7-64 years) (http://fcon_1000.projects.nitrc.org/indi/abide/). Here, we present this resource and demonstrate its suitability for advancing knowledge of ASD neurobiology based on analyses of 360 male subjects with ASDs and 403 male age-matched TCs. We focused on whole-brain intrinsic functional connectivity and also survey a range of voxel-wise measures of intrinsic functional brain architecture. Whole-brain analyses reconciled seemingly disparate themes of both hypo- and hyperconnectivity in the ASD literature; both were detected, although hypoconnectivity dominated, particularly for corticocortical and interhemispheric functional connectivity. Exploratory analyses using an array of regional metrics of intrinsic brain function converged on common loci of dysfunction in ASDs (mid- and posterior insula and posterior cingulate cortex), and highlighted less commonly explored regions such as the thalamus. The survey of the ABIDE R-fMRI data sets provides unprecedented demonstrations of both replication and novel discovery. By pooling multiple international data sets, ABIDE is expected to accelerate the pace of discovery setting the stage for the next generation of ASD studies.
  • Thumbnail Image
    ItemOpen Access
    Validity and Regularization of Classical Half-Space Equations
    (Journal of Statistical Physics, 2017-01-01) Li, Q; Lu, J; Sun, W
    © 2016, Springer Science+Business Media New York.Recent result (Wu and Guo in Commun Math Phys 336(3):1473–1553, 2015) has shown that over the 2D unit disk, the classical half-space equation (CHS) for the neutron transport does not capture the correct boundary layer behaviour as long believed. In this paper we develop a regularization technique for CHS to any arbitrary order and use its first-order regularization to show that in the case of the 2D unit disk, although CHS misrepresents the boundary layer behaviour, it does give the correct boundary condition for the interior macroscopic (Laplace) equation. Therefore CHS is still a valid equation to recover the correct boundary condition for the interior Laplace equation over the 2D unit disk.