A fast numerical solver for local barycentric coordinates

The local barycentric coordinates (LBC), proposed in Zhang et al (2014), demonstrate good locality and can be used for local control on function value interpolation and shape deformation. However, it has no closed- form expression and must be computed by solving an optimization problem, which can be time-consuming especially for high-resolution models. In this paper, we propose a new technique to compute LBC efficiently. The new solver is developed based on two key insights. First, we prove that the non-negativity constraints in the original LBC formulation is not necessary, and can be removed without affecting the solution of the optimization problem. Furthermore, the removal of this constraint allows us to reformulate the computation of LBC as a convex constrained optimization for its gradients, followed by a fast integration to recover the coordinate values. The reformulated gradient optimization problem can be solved using ADMM, where each step is trivially parallelizable and does not involve global linear system solving, making it much more scalable and efficient than the original LBC solver. Numerical experiments verify the effectiveness of our technique on a large variety of models

Genomic Discovery of recurrent CD44-SLC1A2 Gene Fusion in Gastric Cancer

Ph.DDOCTOR OF PHILOSOPH

Average Symmetry Protected Higher-order Topological Amorphous Insulators

While topological phases have been extensively studied in amorphous systems in recent years, it remains unclear whether the random nature of amorphous materials can give rise to higher-order topological phases that have no crystalline counterparts. Here we theoretically demonstrate the existence of higher-order topological insulators in two-dimensional amorphous systems that can host more than six corner modes, such as eight or twelve corner modes. Although individual sample configuration lacks crystalline symmetry, we find that an ensemble of all configurations exhibits an average crystalline symmetry that provides protection for the new topological phases. To characterize the topological phases, we construct two topological invariants. Even though the bulk energy gap in the topological phase vanishes in the thermodynamic limit, we show that the bulk states near zero energy are localized, as supported by the level-spacing statistics. Our findings open an avenue for exploring average symmetry protected higher-order topological phases in amorphous systems without crystalline counterparts.Comment: 8 pages, 6 figure

No association between XRCC1 gene Arg194Trp polymorphism and risk of lung cancer: evidence based on an updated cumulative meta-analysis

X-ray repair cross-complementing group 1 (XRCC1) gene Arg194Trp polymorphism has been reported to be associated with risk of lung cancer in many published studies. Nevertheless, the research results were inconclusive and conflicting. To reach conclusive results, several meta-analysis studies were conducted by combining results from literature reports through pooling analysis. However, these previous meta-analysis studies were still not consistent. Hence, we used an updated and cumulative meta-analysis to get a more comprehensive and precise result from 25 case–control studies searching through the PubMed database up to September 1, 2013. The meta-analysis was carried out by the Comprehensive Meta-Analysis software and the odds ratio (OR) with 95 % confidence interval (CI) was used to estimate the pooled effect. The result involving 8,876 lung cancer patients and 11,210 controls revealed that XRCC1 Arg194Trp polymorphism was not associated with lung cancer risk [(OR = 0.97, 95 %CI = 0.92–1.03) for Trp vs. Arg; (OR = 0.92, 95 % CI = 0.85–0.98) for ArgTrp vs. ArgArg; (OR = 1.07, 95 % CI = 0.92–1.23) for TrpTrp vs. ArgArg; (OR = 0.93, 95 % CI = 0.87–1.00) for (TrpTrp + ArgTrp) vs. ArgArg; and (OR = 1.08, 95 % CI = 0.94–1.25) for TrpTrp vs. (ArgTrp + ArgArg)]. The cumulative meta-analysis showed that the results maintained the same, while the ORs with 95 % CI were more stable with the accumulation of case–control studies. The sensitivity and subgroups analyses showed that the results were robust and not affected by any single study with no publication bias. Relevant studies might not be needed for supporting these results

Higher-order Topological Insulators and Semimetals in Three Dimensions without Crystalline Counterparts

Quasicrystals allow for symmetries that are impossible in crystalline materials, such as eight-fold rotational symmetry, enabling the existence of novel higher-order topological insulators in two dimensions without crystalline counterparts. However, it remains an open question whether three-dimensional higher-order topological insulators and Weyl-like semimetals without crystalline counterparts can exist. Here, we demonstrate the existence of a second-order topological insulator by constructing and exploring a three-dimensional model Hamiltonian in a stack of Ammann-Beenker tiling quasicrystalline lattices. The topological phase has eight chiral hinge modes that lead to quantized longitudinal conductances of $4 e^2/h$. We show that the topological phase is characterized by the winding number of the quadrupole moment. We further establish the existence of a second-order topological insulator with time-reversal symmetry, characterized by a $\mathbb{Z}_2$ topological invariant. Finally, we propose a model that exhibits a higher-order Weyl-like semimetal phase, demonstrating both hinge and surface Fermi arcs. Our findings highlight that quasicrystals in three dimensions can give rise to higher-order topological insulators and semimetal phases that are unattainable in crystals.Comment: 7 pages, 6 figure

Nonmonotone globalization for Anderson acceleration via adaptive regularization

Anderson acceleration (AA) is a popular method for accelerating fixed-point iterations, but may suffer from instability and stagnation. We propose a globalization method for AA to improve stability and achieve unified global and local convergence. Unlike existing AA globalization approaches that rely on safeguarding operations and might hinder fast local convergence, we adopt a nonmonotone trust-region framework and introduce an adaptive quadratic regularization together with a tailored acceptance mechanism. We prove global convergence and show that our algorithm attains the same local convergence as AA under appropriate assumptions. The effectiveness of our method is demonstrated in several numerical experiments

Parallel and scalable heat methods for geodesic distance computation

In this paper, we propose a parallel and scalable approach for geodesic distance computation on triangle meshes. Our key observation is that the recovery of geodesic distance with the heat method from [Crane et al. 2013] can be reformulated as optimization of its gradients subject to integrability, which can be solved using an efficient first-order method that requires no linear system solving and converges quickly. Afterward, the geodesic distance is efficiently recovered by parallel integration of the optimized gradients in breadth-first order. Moreover, we employ a similar breadth-first strategy to derive a parallel Gauss-Seidel solver for the diffusion step in the heat method. To further lower the memory consumption from gradient optimization on faces, we also propose a formulation that optimizes the projected gradients on edges, which reduces the memory footprint by about 50%. Our approach is trivially parallelizable, with a low memory footprint that grows linearly with respect to the model size. This makes it particularly suitable for handling large models. Experimental results show that it can efficiently compute geodesic distance on meshes with more than 200 million vertices on a desktop PC with 128GB RAM, outperforming the original heat method and other state-of-the-art geodesic distance solvers