Hassan E. Abdalla, Felix A. Aharonian, F. Ait Benkhali, Ekrem Oǧuzhan Angüner, M. Arakawa, C. Arcaro, C. Armand, M. Arrieta, M. Backes, M. Barnard, Y. Becherini, J. Becker Tjus, D. Berge, S. Bernhard, K. Bernloehr, R. Blackwell, M. Bottcher, C. Boisson, J. Bolmont, S. Bonnefoy, Pol Bordas, J. Bregeon, F. Brun, P. Brun, M. Bryan, M. Buechele, T. Bulik, T. Bylund, M. Capasso, S. Caroff, A. Carosi, M. Cerruti, N. Chakraborty, S. Chandra, R. C. G. Chaves, A. Chen, S. Colafrancesco, B. Condon, I. D. Davids, C. Deil, J. Devin, P. deWilt, L. Dirson, A. Djannati-Atai, A. Dmytriiev, A. Donath, V Doroshenko, J. Dyks, Kathrin Egberts, G. Emery, J-P Ernenwein, S. Eschbach, S. Fegan, A. Fiasson, G. Fontaine, S. Funk, M. Fuessling, S. Gabici, Y. A. Gallant, F. Gate, G. Giavitto, D. Glawion, J. F. Glicenstein, D. Gottschall, M-H Grondin, J. Hahn, M. Haupt, G. Heinzelmann, G. Henri, G. Hermann, James Anthony Hinton, W. Hofmann, Clemens Hoischen, Tim Lukas Holch, M. Holler, D. Horns, D. Huber, H. Iwasaki, A. Jacholkowska, M. Jamrozy, D. Jankowsky, F. Jankowsky, L. Jouvin, I Jung-Richardt, M. A. Kastendieck, K. Katarzynski, M. Katsuragawa, U. Katz, D. Kerszberg, D. Khangulyan, B. Khelifi, J. King, S. Klepser, W. Kluzniak, Nu Komin, K. Kosack, S. Krakau, M. Kraus, P. P. Kruger, G. Lamanna, J. Lau, J. Lefaucheur, A. Lemiere, M. Lemoine-Goumard, J-P Lenain, Eva Leser, T. Lohse, M. Lorentz, R. Lopez-Coto, I Lypova, D. Malyshev, V Marandon, A. Marcowith, C. Mariaud, G. Marti-Devesa, R. Marx, G. Maurin, P. J. Meintjes, A. M. W. Mitchell, R. Moderski, M. Mohamed, L. Mohrmann, E. Moulin, T. Murach, S. Nakashima, M. de Naurois, H. Ndiyavala, F. Niederwanger, J. Niemiec, L. Oakes, H. Odaka, S. Ohm, M. Ostrowski, I Oya, M. Padovani, M. Panter, R. D. Parsons, C. Perennes, P-O Petrucci, B. Peyaud, Q. Piel, S. Pita, V Poireau, A. Priyana Noel, D. Prokhorov, H. Prokoph, G. Puehlhofer, M. Punch, A. Quirrenbach, S. Raab, R. Rauth, A. Reimer, O. Reimer, M. Renaud, F. Rieger, L. Rinchiuso, C. Romoli, G. Rowell, B. Rudak, E. Ruiz-Velasco, V Sahakian, S. Saito, David M. Sanchez, A. Santangelo, M. Sasaki, R. Schlickeiser, F. Schussler, A. Schulz, U. Schwanke, S. Schwemmer, M. Seglar-Arroyo, M. Senniappan, A. S. Seyffert, N. Shafi, I Shilon, K. Shiningayamwe, R. Simoni, A. Sinha, H. Sol, F. Spanier, A. Specovius, M. Spir-Jacob, L. Stawarz, R. Steenkamp, Christian Stegmann, Constantin Beverly Steppa, T. Takahashi, J-P Tavernet, T. Tavernier, A. M. Taylor, R. Terrier, L. Tibaldo, D. Tiziani, M. Tluczykont, C. Trichard, M. Tsirou, N. Tsuji, R. Tuffs, Y. Uchiyama, D. J. van der Walt, C. van Eldik, C. van Rensburg, B. van Soelen, G. Vasileiadis, J. Veh, C. Venter, P. Vincent, J. Vink, F. Voisin, H. J. Voelk, T. Vuillaume, Z. Wadiasingh, S. J. Wagner, R. M. Wagner, R. White, A. Wierzcholska, R. Yang, D. Zaborov, M. Zacharias, R. Zanin, A. A. Zdziarski, Alraune Zech, F. Zefi, A. Ziegler, J. Zorn, N. Zywucka

• The blazar Mrk 501 (z = 0.034) was observed at very-high-energy (VHE, E greater than or similar to 100 GeV) gamma-ray wavelengths during a bright flare on the night of 2014 June 23-24 (MJD 56832) with the H.E.S.S. phase-II array of Cherenkov telescopes. Data taken that night by H.E.S.S. at large zenith angle reveal an exceptional number of gamma-ray photons at multi-TeV energies, with rapid flux variability and an energy coverage extending significantly up to 20 TeV. This data set is used to constrain Lorentz invariance violation (LIV) using two independent channels: a temporal approach considers the possibility of an energy dependence in the arrival time of gamma-rays, whereas a spectral approach considers the possibility of modifications to the interaction of VHE gamma-rays with extragalactic background light (EBL) photons. The non-detection of energy-dependent time delays and the non-observation of deviations between the measured spectrum and that of a supposed power-law intrinsic spectrum with standard EBL attenuation are usedThe blazar Mrk 501 (z = 0.034) was observed at very-high-energy (VHE, E greater than or similar to 100 GeV) gamma-ray wavelengths during a bright flare on the night of 2014 June 23-24 (MJD 56832) with the H.E.S.S. phase-II array of Cherenkov telescopes. Data taken that night by H.E.S.S. at large zenith angle reveal an exceptional number of gamma-ray photons at multi-TeV energies, with rapid flux variability and an energy coverage extending significantly up to 20 TeV. This data set is used to constrain Lorentz invariance violation (LIV) using two independent channels: a temporal approach considers the possibility of an energy dependence in the arrival time of gamma-rays, whereas a spectral approach considers the possibility of modifications to the interaction of VHE gamma-rays with extragalactic background light (EBL) photons. The non-detection of energy-dependent time delays and the non-observation of deviations between the measured spectrum and that of a supposed power-law intrinsic spectrum with standard EBL attenuation are used independently to derive strong constraints on the energy scale of LIV (E-QG) in the subluminal scenario for linear and quadratic perturbations in the dispersion relation of photons. For the case of linear perturbations, the 95% confidence level limits obtained are E-QG,E-1 > 3.6 x 10(17) GeV using the temporal approach and E-QG,E-1 > 2.6 x 10(19) GeV using the spectral approach. For the case of quadratic perturbations, the limits obtained are E-QG,E-2 > 8.5 x 10(10) GeV using the temporal approach and E-QG,E-2 > 7.8 x 10(11) GeV using the spectral approach.…