CHINESE ANNALS OF MATHEMATICS SERIES B Volume 35 · 2014 TOTAL CONTENTS

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保结构算法的相位误差分析及其修正

辛算法和保能量算法是应用最为广泛的两种保结构算法.本文从相位误差的角度给出了他们的比较结果.我们针对线性动力系统,分别分析了基于Pade对角逼近给出的辛算法和基于平均向量场法得到的能量守恒算法的相位误差,并通过数值验证了分析结果.文章还给出了保结构算法相位误差的改进方法,并通过数值例子验证了方法的有效性.     

Any component of moduli of polarized hyperkähler manifolds is dense in its deformation space

Let M be a compact hyperkähler manifold, and W the coarse moduli of complex deformations of M. Every positive integer class v   in H²(M)$H^2(M)$ defines a divisor _Dv$D_v$ in W consisting of all algebraic manifolds polarized by v. We prove that every connected component of this divisor is dense in W.     

Asymptotic behavior of solutions for nonlinear elliptic problems with the fractional Laplacian

In this paper we study the asymptotic behavior of least energy solutions and the existence of multiple bubbling solutions of nonlinear elliptic equations involving the fractional Laplacians and the critical exponents. This work can be seen as a nonlocal analog of the results of Han (1991) [24] and Rey (1990) [35].     

Convergence of nonlocal diffusion models on lattices

In this paper we look at models of nonlocal (or anomalous) diffusion which are defined on subsets of the lattice ?Zⁿ$?{\mathbb{Z}}^n$, for some ?>0$?>0$, and ask if they can be approximated by continuum models. The answer is given by an operator semigroup convergence theorem. As an application, we establish hypotheses under which a discrete model of nonlocal diffusion satisfying an absorbing boundary condition has a continuum limit which is conservative.     

Unbounded quantum graphs with unbounded boundary conditions

We consider metric graphs with a uniform lower bound on the edge lengths but no further restrictions. We discuss how to describe every local self‐adjoint Laplace operator on such graphs by boundary conditions in the vertices given by projections and self‐adjoint operators. We then characterize the lower bounded self‐adjoint Laplacians and determine their associated quadratic form in terms of the operator families encoding the boundary conditions.     

Grid‐based molecular footprint comparison method for docking and de novo design: Application to HIVgp41

Scoring functions are a critically important component of computer‐aided screening methods for the identification of lead compounds during early stages of drug discovery. Here, we present a new multigrid implementation of the footprint similarity (FPS) scoring function that was recently developed in our laboratory which has proven useful for identification of compounds which bind to a protein on a per‐residue basis in a way that resembles a known reference. The grid‐based FPS method is much faster than its Cartesian‐space counterpart, which makes it computationally tractable for on‐the‐fly docking, virtual screening, or de novo design. In this work, we establish that: (i) relatively few grids can be used to accurately approximate Cartesian space footprint similarity, (ii) the method yields improved success over the standard DOCK energy function for pose identification across a large test set of experimental co‐crystal structures, for crossdocking, and for database enrichment, and (iii) grid‐based FPS scoring can be used to tailor construction of new molecules to have specific properties, as demonstrated in a series of test cases targeting the viral protein HIVgp41. The method is available in the program DOCK6. © 2013 Wiley Periodicals, Inc.