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  1. Book ; Online: A dual number formulation to efficiently compute higher order directional derivatives

    Peón-Escalante, R. / Cantún-Avila, K. B. / Carvente, O. / Espinosa-Romero, A. / Peñuñuri, F.

    2023  

    Abstract: This contribution proposes a new formulation to efficiently compute directional derivatives of order one to fourth. The formulation is based on automatic differentiation implemented with dual numbers. Directional derivatives are particular cases of ... ...

    Abstract This contribution proposes a new formulation to efficiently compute directional derivatives of order one to fourth. The formulation is based on automatic differentiation implemented with dual numbers. Directional derivatives are particular cases of symmetric multilinear forms; therefore, using their symmetric properties and their coordinate representation, we implement functions to calculate mixed partial derivatives. Moreover, with directional derivatives, we deduce concise formulas for the velocity, acceleration, jerk, and jounce/snap vectors. The utility of our formulation is proved with three examples. The first example presents a comparison against the forward mode of finite differences to compute the fourth-order directional derivative of a scalar function. To this end, we have coded the finite differences method to calculate partial derivatives until the fourth order, to any order of approximation. The second example presents efficient computations of the velocity, acceleration, jerk, and jounce/snap. Finally, the third example is related to the computation of some partial derivatives. The implemented code of the proposed formulation and the finite differences method is proportioned as additional material to this article.
    Keywords Mathematics - Numerical Analysis ; Computer Science - Computational Engineering ; Finance ; and Science
    Subject code 510
    Publishing date 2023-06-13
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  2. Article ; Online: Measurement of Lepton-Jet Correlation in Deep-Inelastic Scattering with the H1 Detector Using Machine Learning for Unfolding.

    Andreev, V / Arratia, M / Baghdasaryan, A / Baty, A / Begzsuren, K / Belousov, A / Bolz, A / Boudry, V / Brandt, G / Britzger, D / Buniatyan, A / Bystritskaya, L / Campbell, A J / Cantun Avila, K B / Cerny, K / Chekelian, V / Chen, Z / Contreras, J G / Cunqueiro Mendez, L /
    Cvach, J / Dainton, J B / Daum, K / Deshpande, A / Diaconu, C / Eckerlin, G / Egli, S / Elsen, E / Favart, L / Fedotov, A / Feltesse, J / Fleischer, M / Fomenko, A / Gal, C / Gayler, J / Goerlich, L / Gogitidze, N / Gouzevitch, M / Grab, C / Greenshaw, T / Grindhammer, G / Haidt, D / Henderson, R C W / Hessler, J / Hladký, J / Hoffmann, D / Horisberger, R / Hreus, T / Huber, F / Jacobs, P M / Jacquet, M / Janssen, T / Jung, A W / Jung, H / Kapichine, M / Katzy, J / Kiesling, C / Klein, M / Kleinwort, C / Klest, H T / Kogler, R / Kostka, P / Kretzschmar, J / Krücker, D / Krüger, K / Landon, M P J / Lange, W / Laycock, P / Lee, S H / Levonian, S / Li, W / Lin, J / Lipka, K / List, B / List, J / Lobodzinski, B / Malinovski, E / Martyn, H-U / Maxfield, S J / Mehta, A / Meyer, A B / Meyer, J / Mikocki, S / Mondal, M M / Morozov, A / Müller, K / Nachman, B / Naumann, Th / Newman, P R / Niebuhr, C / Nowak, G / Olsson, J E / Ozerov, D / Park, S / Pascaud, C / Patel, G D / Perez, E / Petrukhin, A / Picuric, I / Pitzl, D / Polifka, R / Preins, S / Radescu, V / Raicevic, N / Ravdandorj, T / Reimer, P / Rizvi, E / Robmann, P / Roosen, R / Rostovtsev, A / Rotaru, M / Sankey, D P C / Sauter, M / Sauvan, E / Schmitt, S / Schmookler, B A / Schoeffel, L / Schöning, A / Sefkow, F / Shushkevich, S / Soloviev, Y / Sopicki, P / South, D / Spaskov, V / Specka, A / Steder, M / Stella, B / Straumann, U / Sun, C / Sykora, T / Thompson, P D / Traynor, D / Tseepeldorj, B / Tu, Z / Valkárová, A / Vallée, C / Van Mechelen, P / Wegener, D / Wünsch, E / Žáček, J / Zhang, J / Zhang, Z / Žlebčík, R / Zohrabyan, H / Zomer, F

    Physical review letters

    2022  Volume 128, Issue 13, Page(s) 132002

    Abstract: The first measurement of lepton-jet momentum imbalance and azimuthal correlation in lepton-proton scattering at high momentum transfer is presented. These data, taken with the H1 detector at HERA, are corrected for detector effects using an unbinned ... ...

    Abstract The first measurement of lepton-jet momentum imbalance and azimuthal correlation in lepton-proton scattering at high momentum transfer is presented. These data, taken with the H1 detector at HERA, are corrected for detector effects using an unbinned machine learning algorithm (multifold), which considers eight observables simultaneously in this first application. The unfolded cross sections are compared with calculations performed within the context of collinear or transverse-momentum-dependent factorization in quantum chromodynamics as well as Monte Carlo event generators.
    Language English
    Publishing date 2022-01-18
    Publishing country United States
    Document type Journal Article
    ZDB-ID 208853-8
    ISSN 1079-7114 ; 0031-9007
    ISSN (online) 1079-7114
    ISSN 0031-9007
    DOI 10.1103/PhysRevLett.128.132002
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  3. Article: Determination of the strong coupling constant

    Andreev, V / Baghdasaryan, A / Begzsuren, K / Belousov, A / Bertone, V / Bolz, A / Boudry, V / Brandt, G / Brisson, V / Britzger, D / Buniatyan, A / Bylinkin, A / Bystritskaya, L / Campbell, A J / Cantun Avila, K B / Cerny, K / Chekelian, V / Contreras, J G / Cvach, J /
    Currie, J / Dainton, J B / Daum, K / Diaconu, C / Dobre, M / Dodonov, V / Eckerlin, G / Egli, S / Elsen, E / Favart, L / Fedotov, A / Feltesse, J / Fleischer, M / Fomenko, A / Gabathuler, E / Gayler, J / Gehrmann, T / Ghazaryan, S / Goerlich, L / Gogitidze, N / Gouzevitch, M / Grab, C / Grebenyuk, A / Greenshaw, T / Grindhammer, G / Gwenlan, C / Haidt, D / Henderson, R C W / Hladkỳ, J / Hoffmann, D / Horisberger, R / Hreus, T / Huber, F / Huss, A / Jacquet, M / Janssen, X / Jung, A W / Jung, H / Kapichine, M / Katzy, J / Kiesling, C / Klein, M / Kleinwort, C / Kogler, R / Kostka, P / Kretzschmar, J / Krücker, D / Krüger, K / Landon, M P J / Lange, W / Laycock, P / Lebedev, A / Levonian, S / Lipka, K / List, B / List, J / Lobodzinski, B / Malinovski, E / Martyn, H-U / Maxfield, S J / Mehta, A / Meyer, A B / Meyer, H / Meyer, J / Mikocki, S / Morozov, A / Müller, K / Naumann, Th / Newman, P R / Niebuhr, C / Niehues, J / Nowak, G / Olsson, J E / Ozerov, D / Pascaud, C / Patel, G D / Perez, E / Petrukhin, A / Picuric, I / Pirumov, H / Pitzl, D / Plačakytė, R / Polifka, R / Rabbertz, K / Radescu, V / Raicevic, N / Ravdandorj, T / Reimer, P / Rizvi, E / Robmann, P / Roosen, R / Rostovtsev, A / Rotaru, M / Šálek, D / Sankey, D P C / Sauter, M / Sauvan, E / Schmitt, S / Schoeffel, L / Schöning, A / Sefkow, F / Shushkevich, S / Soloviev, Y / Sopicki, P / South, D / Spaskov, V / Specka, A / Steder, M / Stella, B / Straumann, U / Sutton, M R / Sykora, T / Thompson, P D / Traynor, D / Truöl, P / Tsakov, I / Tseepeldorj, B / Valkárová, A / Vallée, C / Van Mechelen, P / Vazdik, Y / Wegener, D / Wünsch, E / Žáček, J / Zhang, Z / Žlebčík, R / Zohrabyan, H / Zomer, F

    The European physical journal. C, Particles and fields

    2017  Volume 77, Issue 11, Page(s) 791

    Abstract: The strong coupling ... ...

    Abstract The strong coupling constant
    Language English
    Publishing date 2017-11-22
    Publishing country France
    Document type Journal Article
    ZDB-ID 1459069-4
    ISSN 1434-6052 ; 1434-6044
    ISSN (online) 1434-6052
    ISSN 1434-6044
    DOI 10.1140/epjc/s10052-017-5314-7
    Database MEDical Literature Analysis and Retrieval System OnLINE

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