Mixture Models

Sofroniou, Nick

doi:10.4135/9781446251119.n58

Cited by 7 publications

(9 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For the translation of the Mathematica expressions to Fortran77 functions we use the package Format.m [71]. The subdirectories basesv5.1 and Cuba-2.1 contain the libraries for the numerical integration, taken from [69] and [70], respectively.…”

Section: Structure Of the Programmentioning

confidence: 99%

SecDec: A general program for sector decomposition

Carter

Heinrich

2011

Computer Physics Communications

138

146

View full text Add to dashboard Cite

We present a program for the numerical evaluation of multi-dimensional polynomial parameter integrals. Singularities regulated by dimensional regularisation are extracted using iterated sector decomposition. The program evaluates the coefficients of a Laurent series in the regularisation parameter. It can be applied to multi-loop integrals in Euclidean space as well as other parametric integrals, e.g. phase space integrals. Nature of problem:Extraction of ultraviolet and infrared singularities from parametric integrals appearing in higher order perturbative calculations in gauge theories, e.g. multi-loop Feynman integrals, Wilson loops, phase space integrals. Solution method:Algebraic extraction of singularities in dimensional regularisation using iterated sector decomposition. This leads to a Laurent series in the dimensional regularisation parameter ǫ, where the coefficients are finite integrals over the unit-hypercube. Those integrals are evaluated numerically by Monte Carlo integration.Restrictions: Depending on the complexity of the problem, limited by memory and CPU time. Multi-scale integrals can only be evaluated at Euclidean points. Running time:Between a few minutes and several days, depending on the complexity of the problem.

show abstract

Section: Structure Of the Programmentioning

confidence: 99%

SecDec: A general program for sector decomposition

Carter

Heinrich

2011

Computer Physics Communications

138

146

View full text Add to dashboard Cite

show abstract

“…The Mathematica source files are located in the subdirectories src/deco: files used for the decomposition, src/subexp: files used for the pole subtraction and expansion in ǫ, src/util: miscellaneous useful functions. For the translation of the Mathematica expressions to Fortran77 functions we use the package Format.m [71]. The subdirectories basesv5.1 and Cuba-2.1 contain the libraries for the numerical integration, taken from [69] and [70], respectively.…”

Section: Structure Of the Programmentioning

confidence: 99%

SecDec: A general program for sector decomposition

Carter,

Heinrich

2010

Preprint

View full text Add to dashboard Cite

show abstract

“…These libraries were built using the symbolic manipulation features of Mathematica 75 and the FortranAssign utility in Format.m. 76 In addition to factoring out a 2 and symbolically eliminating elements that are zero by symmetry, the resulting code does not encumber loop overheads and fully exploits floating-point multiply-add parallelism ͑a factor of 2 on the IBM RS6000s͒.…”

Section: A the Two-center Multipole Expansion In Real Arithmeticmentioning

confidence: 99%

Linear scaling computation of the Fock matrix

Challacombe¹,

Schwegler²

1997

The Journal of Chemical Physics

201

155

View full text Add to dashboard Cite

Computation of the Fock matrix is currently the limiting factor in the application of Hartree-Fock and hybrid Hartree-Fock/density functional theories to larger systems. Computation of the Fock matrix is dominated by calculation of the Coulomb and exchange matrices. With conventional Gaussian-based methods, computation of the Fock matrix typically scales as ϳN 2.7 , where N is the number of basis functions. A hierarchical multipole method is developed for fast computation of the Coulomb matrix. This method, together with a recently described approach to computing the Hartree-Fock exchange matrix of insulators ͓J. Chem. Phys. 105, 2726 ͑1900͔͒, leads to a linear scaling algorithm for calculation of the Fock matrix. Linear scaling computation the Fock matrix is demonstrated for a sequence of water clusters at the restricted Hartree-Fock/3-21G level of theory, and corresponding accuracies in converged total energies are shown to be comparable with those obtained from standard quantum chemistry programs. Restricted Hartree-Fock/3-21G calculations on several proteins of current interest are documented, including endothelin, charybdotoxin, and the tetramerization monomer of P53. The P53 calculation, involving 698 atoms and 3836 basis functions, may be the largest Hartree-Fock calculation to date. The electrostatic potentials of charybdotoxin and the tetramerization monomer of P53 are visualized and the results are related to molecular function.

show abstract

Mixture Models

Cited by 7 publications

References 0 publications

SecDec: A general program for sector decomposition

SecDec: A general program for sector decomposition

SecDec: A general program for sector decomposition

Linear scaling computation of the Fock matrix

Contact Info

Product

Resources

About