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Browsing by Author "Zhang, Jingwei"

Now showing 1 - 3 of 3
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    Algorithm XXX: SHEPPACK: Modified Shepard Algorithm for Interpolation of Scattered Multivariate Data
    Thacker, William I.; Zhang, Jingwei; Watson, Layne T.; Birch, Jeffrey B.; Iyer, Manjula A.; Berry, Michael W. (Department of Computer Science, Virginia Polytechnic Institute & State University, 2009)
    Scattered data interpolation problems arise in many applications. Shepard’s method for constructing a global interpolant by blending local interpolants using local-support weight functions usually creates reasonable approximations. SHEPPACK is a Fortran 95 package containing five versions of the modified Shepard algorithm: quadratic (Fortran 95 translations of Algorithms 660, 661, and 798), cubic (Fortran 95 translation of Algorithm 791), and linear variations of the original Shepard algorithm. An option to the linear Shepard code is a statistically robust fit, intended to be used when the data is known to contain outliers. SHEPPACK also includes a hybrid robust piecewise linear estimation algorithm RIPPLE (residual initiated polynomial-time piecewise linear estimation) intended for data from piecewise linear functions in arbitrary dimension m. The main goal of SHEPPACK is to provide users with a single consistent package containing most existing polynomial variations of Shepard’s algorithm. The algorithms target data of different dimensions. The linear Shepard algorithm, robust linear Shepard algorithm, and RIPPLE are the only algorithms in the package that are applicable to arbitrary dimensional data.
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    A Modified Uniformization Method for the Solution of the Chemical Master Equation
    Zhang, Jingwei; Watson, Layne T.; Cao, Yang (Department of Computer Science, Virginia Polytechnic Institute & State University, 2007)
    The chemical master equation is considered an accurate description of general chemical systems, and especially so for modeling cell cycle and gene regulatory networks. This paper proposes an efficient way of solving the chemical master equation for some prototypical problems in systems biology. A comparison between this new approach and some traditional approaches is also given.
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    Numerical Methods for the Chemical Master Equation
    Zhang, Jingwei (Virginia Tech, 2009-12-02)
    The chemical master equation, formulated on the Markov assumption of underlying chemical kinetics, offers an accurate stochastic description of general chemical reaction systems on the mesoscopic scale. The chemical master equation is especially useful when formulating mathematical models of gene regulatory networks and protein-protein interaction networks, where the numbers of molecules of most species are around tens or hundreds. However, solving the master equation directly suffers from the so called "curse of dimensionality" issue. This thesis first tries to study the numerical properties of the master equation using existing numerical methods and parallel machines. Next, approximation algorithms, namely the adaptive aggregation method and the radial basis function collocation method, are proposed as new paths to resolve the "curse of dimensionality". Several numerical results are presented to illustrate the promises and potential problems of these new algorithms. Comparisons with other numerical methods like Monte Carlo methods are also included. Development and analysis of the linear Shepard algorithm and its variants, all of which could be used for high dimensional scattered data interpolation problems, are also included here, as a candidate to help solve the master equation by building surrogate models in high dimensions.