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Vitaly Magerya - One of the best experts on this subject based on the ideXlab platform.
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Fuchsia a tool for reducing differential equations for feynman master integrals to epsilon form
Computer Physics Communications, 2017Co-Authors: Oleksandr Gituliar, Vitaly MageryaAbstract:Abstract We present Fuchsia — an implementation of the Lee algorithm, which for a given system of ordinary differential equations with rational coefficients ∂ x J ( x , ϵ ) = A ( x , ϵ ) J ( x , ϵ ) finds a basis transformation T ( x , ϵ ) , i.e., J ( x , ϵ ) = T ( x , ϵ ) J ′ ( x , ϵ ) , such that the system turns into the epsilon form : ∂ x J ′ ( x , ϵ ) = ϵ S ( x ) J ′ ( x , ϵ ) , where S ( x ) is a Fuchsian matrix. A system of this form can be trivially solved in terms of polylogarithms as a Laurent series in the dimensional regulator ϵ . That makes the construction of the transformation T ( x , ϵ ) crucial for obtaining solutions of the initial system. In principle, Fuchsia can deal with any regular systems, however its primary task is to reduce differential equations for Feynman master integrals. It ensures that solutions contain only regular singularities due to the properties of Feynman integrals. Program summary Program Title: Fuchsia Program Files doi: http://dx.doi.org/10.17632/zj6zn9vfkh.1 Licensing provisions: MIT Programming language: Python 2.7 Nature of problem: Feynman master integrals may be calculated from solutions of a linear system of differential equations with rational coefficients. Such a system can be easily solved as an ϵ -series when its epsilon form is known. Hence, a tool which is able to find the epsilon form transformations can be used to evaluate Feynman master integrals. Solution method: The solution method is based on the Lee algorithm (Lee, 2015) which consists of three main steps: fuchsification, normalization, and factorization . During the fuchsification step a given system of differential equations is transformed into the Fuchsian form with the help of the Moser method (Moser, 1959). Next, during the normalization step the system is transformed to the form where eigenvalues of all residues are proportional to the dimensional regulator ϵ . Finally, the system is factorized to the epsilon form by finding an unknown transformation which satisfies a system of linear equations . Additional comments including Restrictions and Unusual features: Systems of single-variable differential equations are considered. A system needs to be reducible to Fuchsian form and eigenvalues of its residues must be of the form n + m ϵ , where n is integer. Performance depends upon the input matrix, its size, number of singular points and their degrees. It takes around an hour to reduce an example 74 × 74 matrix with 20 singular points on a PC with a 1.7 GHz Intel Core i5 CPU. An additional slowdown is to be expected for matrices with complex and/or irrational singular point locations, as these are particularly difficult for symbolic algebra software to handle.
P R Narayanan - One of the best experts on this subject based on the ideXlab platform.
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comparison of variants of carbol fuchsin solution in ziehl neelsen for detection of acid fast bacilli
International Journal of Tuberculosis and Lung Disease, 2005Co-Authors: N Selvakumar, Fathima Rahman, Gomathi M Sekar, A Syamsunder, M Duraipandian, Fraser Wares, P R NarayananAbstract:To evaluate Ziehl-Neelsen (ZN) staining using variants of carbol-fuchsin solution, duplicate smears from 416 samples were stained with ZN, one set with 1% basic fuchsin and the other 0.3%. Another set of duplicate smears from 398 samples were stained with ZN, one with 1% basic fuchsin and the other 0.1%. The coded smears were read and discrepancies resolved. All samples underwent mycobacterial culture. The sensitivity of ZN using 0.3% (65%) and 1% basic fuchsin (62%) was comparable, while it was reduced using 0.1% (74%) compared to 1% basic fuchsin (83%). Reducing the concentration of basic fuchsin below 0.3% in ZN staining was found to significantly reduce its sensitivity.
Oleksandr Gituliar - One of the best experts on this subject based on the ideXlab platform.
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Fuchsia a tool for reducing differential equations for feynman master integrals to epsilon form
Computer Physics Communications, 2017Co-Authors: Oleksandr Gituliar, Vitaly MageryaAbstract:Abstract We present Fuchsia — an implementation of the Lee algorithm, which for a given system of ordinary differential equations with rational coefficients ∂ x J ( x , ϵ ) = A ( x , ϵ ) J ( x , ϵ ) finds a basis transformation T ( x , ϵ ) , i.e., J ( x , ϵ ) = T ( x , ϵ ) J ′ ( x , ϵ ) , such that the system turns into the epsilon form : ∂ x J ′ ( x , ϵ ) = ϵ S ( x ) J ′ ( x , ϵ ) , where S ( x ) is a Fuchsian matrix. A system of this form can be trivially solved in terms of polylogarithms as a Laurent series in the dimensional regulator ϵ . That makes the construction of the transformation T ( x , ϵ ) crucial for obtaining solutions of the initial system. In principle, Fuchsia can deal with any regular systems, however its primary task is to reduce differential equations for Feynman master integrals. It ensures that solutions contain only regular singularities due to the properties of Feynman integrals. Program summary Program Title: Fuchsia Program Files doi: http://dx.doi.org/10.17632/zj6zn9vfkh.1 Licensing provisions: MIT Programming language: Python 2.7 Nature of problem: Feynman master integrals may be calculated from solutions of a linear system of differential equations with rational coefficients. Such a system can be easily solved as an ϵ -series when its epsilon form is known. Hence, a tool which is able to find the epsilon form transformations can be used to evaluate Feynman master integrals. Solution method: The solution method is based on the Lee algorithm (Lee, 2015) which consists of three main steps: fuchsification, normalization, and factorization . During the fuchsification step a given system of differential equations is transformed into the Fuchsian form with the help of the Moser method (Moser, 1959). Next, during the normalization step the system is transformed to the form where eigenvalues of all residues are proportional to the dimensional regulator ϵ . Finally, the system is factorized to the epsilon form by finding an unknown transformation which satisfies a system of linear equations . Additional comments including Restrictions and Unusual features: Systems of single-variable differential equations are considered. A system needs to be reducible to Fuchsian form and eigenvalues of its residues must be of the form n + m ϵ , where n is integer. Performance depends upon the input matrix, its size, number of singular points and their degrees. It takes around an hour to reduce an example 74 × 74 matrix with 20 singular points on a PC with a 1.7 GHz Intel Core i5 CPU. An additional slowdown is to be expected for matrices with complex and/or irrational singular point locations, as these are particularly difficult for symbolic algebra software to handle.
Claude Labrecque - One of the best experts on this subject based on the ideXlab platform.
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Delphastus catalinae and Coleomegilla maculata lengi (Coleoptera: Coccinellidae) as biological control agents of the greenhouse whitefly, Trialeurodes vaporariorum (Homoptera: Aleyrodidae)
Pest management science, 2004Co-Authors: Éric Lucas, Claude LabrecqueAbstract:Predation efficacy and compatibility of the predatory lady beetles Coleomegilla maculata lengi Timberlake and Delphastus catalinae (Horn) against the greenhouse whitefly, Trialeurodes vaporariorum (Westwood) were studied in laboratory on glabrous Fuchsia (Fuchsia hybrida Voss cv Lena Corolla) and pubescent poinsettia plants (Euphorbia pulcherrima Willd ex Klotzch cv Dark Red Annette Hegg). On glabrous plants (Fuchsia), fourth-instar and adults of C maculata were the most efficient, both against whitefly eggs and pupae. On pubescent plants (poinsettia), the larger stages of C maculata were negatively affected and less efficient than adults of D catalinae. The presence of plant structure did not affect the voracity of either predator species. Finally, the simultaneous use of both predator species generated inter-specific competition. These results provide recommendations for biological control of whitefly in horticultural greenhouses.
David Y Graham - One of the best experts on this subject based on the ideXlab platform.
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a new triple stain for helicobacter pylori suitable for the autostainer carbol fuchsin alcian blue hematoxylin eosin
Archives of Pathology & Laboratory Medicine, 1998Co-Authors: Hala M T Elzimaity, H Ota, S Scott, D E Killen, David Y GrahamAbstract:OBJECTIVE To develop an inexpensive stain to simultaneously visualize gastric morphology and Helicobacter pylori. METHODS Gastric biopsies were stained with Genta stain using manual methods, and with carbol fuchsin/Alcian blue/hematoxylin-eosin using an automatic slide stainer (Sakura DRS-601). Slides were then coded and interpreted by 2 pathologists. Helicobacter pylori was scored using a visual scale (0 [none] to 5 [maximum]). RESULTS One hundred slides were scored; H pylori was present in 64%. Carbol fuchsin/Alcian blue/hematoxylin-eosin stain gave excellent demonstration of gastric morphology. All positive cases (score > or =2) were correctly interpreted. Thirty-six slides had a score of 1 (< or =2 bacteria per entire slide). Of these, 10 were scored negative by Genta stain and 12 were scored negative by the carbol fuchsin/Alcian blue/hematoxylin-eosin stain (P = not significant). Hematoxylin-eosin was significantly less accurate than either of the other 2 stains (P < .02). CONCLUSION The carbol fuchsin/Alcian blue/hematoxylin-eosin (El-Zimaity) stain is an economical stain suitable for simultaneous visualization of H pylori infection and gastric morphology.
