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13
On topography and functionality
 in the BD rings of cephalostatin cytotoxins. Bioorganic & Medicinal Chemistry Letters 9
, 1999
"... A serious problem limiting the applicability of the fuzzy neural networks is the “curse of dimensionality”, especially for general continuous functions. A way to deal with this problem is to construct a dynamic hierarchical fuzzy neural network. In this paper, we propose a twostage genetic algor ..."
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Cited by 46 (1 self)
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A serious problem limiting the applicability of the fuzzy neural networks is the “curse of dimensionality”, especially for general continuous functions. A way to deal with this problem is to construct a dynamic hierarchical fuzzy neural network. In this paper, we propose a twostage genetic algorithm to intelligently construct the dynamic hierarchical fuzzy neural network (HFNN) based on the mergedFNN for general continuous functions. First, we use a genetic algorithm which is popular for flowshop scheduling problems (GA_FSP) to construct the HFNN. Then, a reducedform genetic algorithm (RGA) optimizes the HFNN constructed by GA_FSP. For a realworld application, the presented method is used to approximate the Taiwanese stock market.
On the Numerical Evaluation of Distributions in Random Matrix Theory: A Review
, 2010
"... In this paper we review and compare the numerical evaluation of those probability distributions in random matrix theory that are analytically represented in terms of Painlevé transcendents or Fredholm determinants. Concrete examples for the Gaussian and Laguerre (Wishart) βensembles and their var ..."
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Cited by 36 (4 self)
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In this paper we review and compare the numerical evaluation of those probability distributions in random matrix theory that are analytically represented in terms of Painlevé transcendents or Fredholm determinants. Concrete examples for the Gaussian and Laguerre (Wishart) βensembles and their various scaling limits are discussed. We argue that the numerical approximation of Fredholm determinants is the conceptually more simple and efficient of the two approaches, easily generalized to the computation of joint probabilities and correlations. Having the means for extensive numerical explorations at hand, we discovered new and surprising determinantal formulae for the kth largest (or smallest) level in the edge scaling limits of the Orthogonal and Symplectic Ensembles; formulae that in turn led to improved numerical evaluations. The paper comes with a toolbox of Matlab functions that facilitates further mathematical experiments by the reader.
THE EXPONENTIALLY CONVERGENT TRAPEZOIDAL RULE
"... Abstract. It is well known that the trapezoidal rule converges geometrically when applied to analytic functions on periodic intervals or the real line. The mathematics and history of this phenomenon are reviewed and it is shown that far from being a curiosity, it is linked with computational methods ..."
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Cited by 17 (3 self)
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Abstract. It is well known that the trapezoidal rule converges geometrically when applied to analytic functions on periodic intervals or the real line. The mathematics and history of this phenomenon are reviewed and it is shown that far from being a curiosity, it is linked with computational methods all across scientific computing, including algorithms related to inverse Laplace transforms, special functions, complex analysis, rational approximation, integral equations, and the computation of functions and eigenvalues of matrices and operators.
A fast algorithm for simulating vesicle flows in three dimensions
, 2010
"... Vesicles are locallyinextensible fluid membranes that can sustain bending. In this paper, we extend “A numerical method for simulating the dynamics of 3D axisymmetric vesicles suspended in viscous flows”, Veerapaneni et al. Journal of Computational Physics, 228(19), 2009 to general nonaxisymmetric ..."
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Cited by 14 (1 self)
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Vesicles are locallyinextensible fluid membranes that can sustain bending. In this paper, we extend “A numerical method for simulating the dynamics of 3D axisymmetric vesicles suspended in viscous flows”, Veerapaneni et al. Journal of Computational Physics, 228(19), 2009 to general nonaxisymmetric vesicle flows in three dimensions. Although the main components of the algorithm are similar in spirit to the axisymmetric case (spectral approximation in space, semiimplicit timestepping scheme), important new elements need to be introduced for a full 3D method. In particular, spatial quantities are discretized using spherical harmonics, and quadrature rules for singular surface integrals need to be adapted to this case; an algorithm for surface reparameterization is neeed to ensure sufficient of the timestepping scheme, and spectral filtering is introduced to maintain reasonable accuracy while minimizing computational costs. To characterize the stability of the scheme and to construct preconditioners for the iterative linear system solvers used in the semiimplicit timestepping scheme, we perform a spectral analysis of the evolution operator on the unit sphere. By introducing these algorithmic components, we obtain a timestepping scheme that, in our numerical experiments, is unconditionally stable. We present results to analyze the cost and convergence rates of the overall scheme. To illustrate the applicability of the new method, we consider a few vesicleflow interaction problems: a single vesicle in relaxation, sedimentation, shear flows, and manyvesicle flows. 1
Numerical computation of convolutions in free probability theory. arXiv:1203.1958
, 2012
"... Abstract. We develop a numerical approach for computing the additive, multiplicative and compressive convolution operations from free probability theory. We utilize the regularity properties of free convolution to identify (pairs of) ‘admissible ’ measures whose convolution results in a socalled ‘ ..."
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Cited by 5 (1 self)
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Abstract. We develop a numerical approach for computing the additive, multiplicative and compressive convolution operations from free probability theory. We utilize the regularity properties of free convolution to identify (pairs of) ‘admissible ’ measures whose convolution results in a socalled ‘invertible measure ’ which is either a smoothlydecaying measure supported on the entire real line (such as the Gaussian) or squareroot decaying measure supported on a compact interval (such as the semicircle). This class of measures is important because these measures along with their Cauchy transforms can be accurately represented via a Fourier or Chebyshev series expansion, respectively. Thus, knowledge of the functional inverse of their Cauchy transform suffices for numerically recovering the invertible measure via a nonstandard yet wellbehaved Vandermonde system of equations. We describe explicit algorithms for computing the inverse Cauchy transform alluded to and recovering the associated measure with spectral accuracy. Convergence is guaranteed under broad assumptions on the input measures. 1.
NUMERICAL ALGORITHMS BASED ON ANALYTIC FUNCTION VALUES AT ROOTS OF UNITY ∗
"... Abstract. Let f(z) be an analytic or meromorphic function in the closed unit disk sampled at the nth roots of unity. Based on these data, how can we approximately evaluate f(z) or f (m) (z) at a point z in the disk? How can we calculate the zeros or poles of f in the disk? These questions exhibit in ..."
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Cited by 4 (1 self)
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Abstract. Let f(z) be an analytic or meromorphic function in the closed unit disk sampled at the nth roots of unity. Based on these data, how can we approximately evaluate f(z) or f (m) (z) at a point z in the disk? How can we calculate the zeros or poles of f in the disk? These questions exhibit in the purest form certain algorithmic issues that arise across computational science in areas including integral equations, partial differential equations, and largescale linear algebra. We analyze the possibilities and emphasize a basic distinction between algorithms based on polynomial or rational interpolation and those based on trapezoidal rule approximations of Cauchy integrals. We then show how these developments apply to the problem of computing the eigenvalues in the disk of a matrix of large dimension.
Joint distribution of the first and second eigenvalues at the soft edge of unitary ensembles
, 2013
"... The density function for the joint distribution of the first and second eigenvalues at the soft edge of unitary ensembles is found in terms of a Painleve ́ II transcendent and its associated isomonodromic system. As a corollary, the density function for the spacing between these two eigenvalues is s ..."
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Cited by 2 (1 self)
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The density function for the joint distribution of the first and second eigenvalues at the soft edge of unitary ensembles is found in terms of a Painleve ́ II transcendent and its associated isomonodromic system. As a corollary, the density function for the spacing between these two eigenvalues is similarly characterized.The particular solution of Painleve ́ II that arises is a double shifted Bäcklund transformation of the Hastings–McLeod solution, which applies in the case of the distribution of the largest eigenvalue at the soft edge. Our deductions are made by employing the hardtosoft edge transition, involving the limit as the repulsion strength at the hard edge a → ∞, to existing results for the joint distribution of the first and second eigenvalue at the hard edge (Forrester and Witte 2007 Kyushu J. Math. 61 457–526). In addition recursions under a → a + 1 of quantities specifying the latter are obtained. A Fredholm determinant type characterization is used to provide accurate numerics for the distribution of the spacing between the two largest eigenvalues.
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"... You can submit your corrections online, via email or by fax. For online submission please insert your corrections in the online correction form. Always indicate the line number to which the correction refers. You can also insert your corrections in the proof PDF and email the annotated PDF. For fax ..."
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You can submit your corrections online, via email or by fax. For online submission please insert your corrections in the online correction form. Always indicate the line number to which the correction refers. You can also insert your corrections in the proof PDF and email the annotated PDF. For fax submission, please ensure that your corrections are clearly legible. Use a fine black pen and write the correction in the margin, not too close to the edge of the page. Remember to note the journal title, article number, and your name when sending your response via email or fax. Check the metadata sheet to make sure that the header information, especially author names and the corresponding affiliations are correctly shown. Check the questions that may have arisen during copy editing and insert your answers/ corrections. Check that the text is complete and that all figures, tables and their legends are included. Also check the accuracy of special characters, equations, and electronic supplementary material if applicable. If necessary refer to the Edited manuscript. The publication of inaccurate data such as dosages and units can have serious consequences. Please take particular care that all such details are correct. Please do not make changes that involve only matters of style. We have generally introduced forms that follow the journal’s style. Substantial changes in content, e.g., new results, corrected values, title and authorship are not allowed without the approval of the responsible editor. In such a case, please contact the Editorial Office and return his/her consent together with the proof. If we do not receive your corrections within 48 hours, we will send you a reminder. Your article will be published Online First approximately one week after receipt of your corrected proofs. This is the official first publication citable with the DOI. Further changes are, therefore, not possible. The printed version will follow in a forthcoming issue. Please note After online publication, subscribers (personal/institutional) to this journal will have access to the complete article via the DOI using the
unknown title
, 2010
"... Vesicles are locallyinextensible fluid membranes that can sustain bending. In this paper, we extend “A numerical method for simulating the dynamics of 3D axisymmetric vesicles suspended in viscous flows”, Veerapaneni et al. Journal of Computational Physics, 228(19), 2009 to general nonaxisymmetric ..."
Abstract
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Vesicles are locallyinextensible fluid membranes that can sustain bending. In this paper, we extend “A numerical method for simulating the dynamics of 3D axisymmetric vesicles suspended in viscous flows”, Veerapaneni et al. Journal of Computational Physics, 228(19), 2009 to general nonaxisymmetric vesicle flows in three dimensions. Although the main components of the algorithm are similar in spirit to the axisymmetric case (spectral approximation in space, semiimplicit timestepping scheme), important new elements need to be introduced for a full 3D method. In particular, spatial quantities are discretized using spherical harmonics, and quadrature rules for singular surface integrals need to be adapted to this case; an algorithm for surface reparameterization is neeed to ensure sufficient of the timestepping scheme, and spectral filtering is introduced to maintain reasonable accuracy while minimizing computational costs. To characterize the stability of the scheme and to construct preconditioners for the iterative linear system solvers used in the semiimplicit timestepping scheme, we perform a spectral analysis of the evolution operator on the unit sphere. By introducing these algorithmic components, we obtain a timestepping scheme that, in our numerical experiments, is unconditionally stable. We present results to analyze the cost and convergence rates of the overall scheme. To illustrate the applicability of the new method, we consider a few vesicleflow interaction problems: a single vesicle in relaxation, sedimentation, shear flows, and manyvesicle flows. 1