Interdisciplinary applications of mathematical modeling

We demonstrate applications of numerical integration and visualization algorithms in diverse fields including psychological modeling (biometrics); in high energy physics for the study of collisions of elementary particles; and in medical physics for regulating the dosage of proton beam radiation therapy. We discuss the problems and solution methods, as supported by numerical results.

[1]  Shujun Li,et al.  Distributed Adaptive Multivariate Function Visualization , 2006, Int. J. Comput. Intell. Appl..

[2]  Elise de Doncker,et al.  A subroutine package for automatic integration. Part II: special purpose quadrature , 1977 .

[3]  H Edwin Romeijn,et al.  A fourier analysis on the maximum acceptable grid size for discrete proton beam dose calculation. , 2006, Medical physics.

[4]  Robert Piessens,et al.  Quadpack: A Subroutine Package for Automatic Integration , 2011 .

[5]  Elise de Doncker,et al.  Numerical Computation of a Non-Planar Two-Loop Vertex Diagram , 2006 .

[6]  J. Fujimoto,et al.  Numerical Evaluation of Feynman Integrals by a Direct Computation Method , 2008 .

[7]  Fukuko Yuasa.  Precise Numerical Results of IR-vertex and box integration with Extrapolation Method , 2009 .

[8]  Shujun Li,et al.  Regularization and Extrapolation Methods for Infrared Divergent Loop Integrals , 2005, International Conference on Computational Science.

[9]  Shujun Li,et al.  A Fast Integration Method and Its Application in a Medical Physics Problem , 2006, ICCSA.

[10]  Terje O. Espelid,et al.  Algorithm 698: DCUHRE: an adaptive multidemensional integration routine for a vector of integrals , 1991, TOMS.

[11]  L. Thurstone.  A law of comparative judgment. , 1994 .

[12]  J. Fujimoto,et al.  Status reports from the GRACE Group , 2007, 0710.2957.

[13]  Elise de Doncker,et al.  Error distribution for iterated integrals , 2006 .

[14]  Elise de Doncker,et al.  Computation of loop integrals using extrapolation , 2004 .

[15]  S. Li,et al.  Grid-based numerical integration and visualization , 2005, Sixth International Conference on Computational Intelligence and Multimedia Applications (ICCIMA'05).

[16]  Elise de Doncker,et al.  Methods for enhancing numerical integration , 2003 .

[17]  Shujun Li,et al.  On Iterated Numerical Integration , 2005, International Conference on Computational Science.

[18]  Elise de Doncker,et al.  The Integration of the Multivariate Normal Density Function for the Triangular Method , 1987 .

[19]  K Mullen,et al.  Models for the duo-trio and triangular methods. , 1988, Biometrics.

[20]  Elise de Doncker,et al.  Online support for multivariate integration , 2005 .

[21]  J. Van Voorst,et al.  Loop integration results using numerical extrapolation for a non-scalar integral , 2004 .

[22]  Alan Genz,et al.  An adaptive algorithm for numerical integration over an n-dimensional rectangular region , 1980 .

[23]  Elise de Doncker,et al.  On a Numerical Evaluation of Loop Integrals , 2003 .