@article{GonzalezDornerBretzetal.2019, author = {Gonz{\´a}lez, Mar{\´i}a Magdalena and Dorner, Daniela and Bretz, Thomas and Garc{\´i}a-Gonz{\´a}lez, Jos{\´e} Andr{\´e}s}, title = {Unbiased long-term monitoring at TeV energies}, series = {Galaxies}, volume = {7}, journal = {Galaxies}, number = {2}, issn = {2075-4434}, doi = {10.3390/galaxies7020051}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-197389}, year = {2019}, abstract = {For the understanding of the variable, transient and non-thermal universe, unbiased long-term monitoring is crucial. To constrain the emission mechanisms at the highest energies, it is important to characterize the very high energy emission and its correlation with observations at other wavelengths. At very high energies, only a limited number of instruments is available. This article reviews the current status of monitoring of the extra-galactic sky at TeV energies.}, language = {en} } @article{RoelofsBlackburnLindahletal.2023, author = {Roelofs, Freek and Blackburn, Lindy and Lindahl, Greg and Doeleman, Sheperd S. and Johnson, Michael D. and Arras, Philipp and Chatterjee, Koushik and Emami, Razieh and Fromm, Christian and Fuentes, Antonio and Knollm{\"u}ller, Jakob and Kosogorov, Nikita and M{\"u}ller, Hendrik and Patel, Nimesh and Raymond, Alexander and Tiede, Paul and Traianou, Efthalia and Vega, Justin}, title = {The ngEHT analysis challenges}, series = {Galaxies}, volume = {11}, journal = {Galaxies}, number = {1}, issn = {2075-4434}, doi = {10.3390/galaxies11010012}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-304976}, year = {2023}, abstract = {The next-generation Event Horizon Telescope (ngEHT) will be a significant enhancement of the Event Horizon Telescope (EHT) array, with ∼10 new antennas and instrumental upgrades of existing antennas. The increased uv-coverage, sensitivity, and frequency coverage allow a wide range of new science opportunities to be explored. The ngEHT Analysis Challenges have been launched to inform the development of the ngEHT array design, science objectives, and analysis pathways. For each challenge, synthetic EHT and ngEHT datasets are generated from theoretical source models and released to the challenge participants, who analyze the datasets using image reconstruction and other methods. The submitted analysis results are evaluated with quantitative metrics. In this work, we report on the first two ngEHT Analysis Challenges. These have focused on static and dynamical models of M87* and Sgr A* and shown that high-quality movies of the extended jet structure of M87* and near-horizon hourly timescale variability of Sgr A* can be reconstructed by the reference ngEHT array in realistic observing conditions using current analysis algorithms. We identify areas where there is still room for improvement of these algorithms and analysis strategies. Other science cases and arrays will be explored in future challenges.}, language = {en} } @article{DashkovskiySlynko2022, author = {Dashkovskiy, Sergey and Slynko, Vitalii}, title = {Stability conditions for impulsive dynamical systems}, series = {Mathematics of Control, Signals, and Systems}, volume = {34}, journal = {Mathematics of Control, Signals, and Systems}, number = {1}, issn = {1435-568X}, doi = {10.1007/s00498-021-00305-y}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-268390}, pages = {95-128}, year = {2022}, abstract = {In this work, we consider impulsive dynamical systems evolving on an infinite-dimensional space and subjected to external perturbations. We look for stability conditions that guarantee the input-to-state stability for such systems. Our new dwell-time conditions allow the situation, where both continuous and discrete dynamics can be unstable simultaneously. Lyapunov like methods are developed for this purpose. Illustrative finite and infinite dimensional examples are provided to demonstrate the application of the main results. These examples cannot be treated by any other published approach and demonstrate the effectiveness of our results.}, language = {en} } @article{WangLiuXiaoetal.2023, author = {Wang, Xiaoliang and Liu, Xuan and Xiao, Yun and Mao, Yue and Wang, Nan and Wang, Wei and Wu, Shufan and Song, Xiaoyong and Wang, Dengfeng and Zhong, Xingwang and Zhu, Zhu and Schilling, Klaus and Damaren, Christopher}, title = {On-orbit verification of RL-based APC calibrations for micrometre level microwave ranging system}, series = {Mathematics}, volume = {11}, journal = {Mathematics}, number = {4}, issn = {2227-7390}, doi = {10.3390/math11040942}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-303970}, year = {2023}, abstract = {Micrometre level ranging accuracy between satellites on-orbit relies on the high-precision calibration of the antenna phase center (APC), which is accomplished through properly designed calibration maneuvers batch estimation algorithms currently. However, the unmodeled perturbations of the space dynamic and sensor-induced uncertainty complicated the situation in reality; ranging accuracy especially deteriorated outside the antenna main-lobe when maneuvers performed. This paper proposes an on-orbit APC calibration method that uses a reinforcement learning (RL) process, aiming to provide the high accuracy ranging datum for onboard instruments with micrometre level. The RL process used here is an improved Temporal Difference advantage actor critic algorithm (TDAAC), which mainly focuses on two neural networks (NN) for critic and actor function. The output of the TDAAC algorithm will autonomously balance the APC calibration maneuvers amplitude and APC-observed sensitivity with an object of maximal APC estimation accuracy. The RL-based APC calibration method proposed here is fully tested in software and on-ground experiments, with an APC calibration accuracy of less than 2 mrad, and the on-orbit maneuver data from 11-12 April 2022, which achieved 1-1.5 mrad calibration accuracy after RL training. The proposed RL-based APC algorithm may extend to prove mass calibration scenes with actions feedback to attitude determination and control system (ADCS), showing flexibility of spacecraft payload applications in the future.}, language = {en} } @article{RenautFreiNuechter2023, author = {Renaut, L{\´e}o and Frei, Heike and N{\"u}chter, Andreas}, title = {Lidar pose tracking of a tumbling spacecraft using the smoothed normal distribution transform}, series = {Remote Sensing}, volume = {15}, journal = {Remote Sensing}, number = {9}, issn = {2072-4292}, doi = {10.3390/rs15092286}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-313738}, year = {2023}, abstract = {Lidar sensors enable precise pose estimation of an uncooperative spacecraft in close range. In this context, the iterative closest point (ICP) is usually employed as a tracking method. However, when the size of the point clouds increases, the required computation time of the ICP can become a limiting factor. The normal distribution transform (NDT) is an alternative algorithm which can be more efficient than the ICP, but suffers from robustness issues. In addition, lidar sensors are also subject to motion blur effects when tracking a spacecraft tumbling with a high angular velocity, leading to a loss of precision in the relative pose estimation. This work introduces a smoothed formulation of the NDT to improve the algorithm's robustness while maintaining its efficiency. Additionally, two strategies are investigated to mitigate the effects of motion blur. The first consists in un-distorting the point cloud, while the second is a continuous-time formulation of the NDT. Hardware-in-the-loop tests at the European Proximity Operations Simulator demonstrate the capability of the proposed methods to precisely track an uncooperative spacecraft under realistic conditions within tens of milliseconds, even when the spacecraft tumbles with a significant angular rate.}, language = {en} } @article{AdrianMartinezAgeronAharonianetal.2016, author = {Adri{\´a}n-Mart{\´i}nez, S. and Ageron, M. and Aharonian, F. and Aiello, S. and Albert, A. and Ameli, F. and Annasontzis, E. and Andre, M. and Androulakis, G. and Anghinolfi, M. and Anton, G. and Ardid, M. and Avgitas, T. and Barbarino, G. and Baret, B. and Barrios-Mart{\´i}, J. and Belhorma, B. and Belias, A. and Berbee, A. and van den Berg, A. and Bertin, V. and Beurthey, S. and van Beeveren, V. and Beverini, N. and Biagi, S. and Biagioni, A. and Billault, M. and Bond{\`i}, M. and Bormuth, R. and Bouhadef, B. and Bourlis, G. and Bourret, S. and Boutonnet, C. and Bouwhuis, M. and Bozza, C. and Bruijn, R. and Brunner, J. and Buis, E. and Busto, J. and Cacopardo, G. and Caillat, L. and Calmai, M. and Calvo, D. and Capone, A. and Caramete, L. and Cecchini, S. and Celli, S. and Champion, C. and Cherkaoui El Moursli, R. and Cherubini, S. and Chiarusi, T. and Circella, M. and Classen, L. and Cocimano, R. and Coelho, J. A. B. and Coleiro, A. and Colonges, S. and Coniglione, R. and Cordelli, M. and Cosquer, A. and Coyle, P. and Creusot, A. and Cuttone, G. and D'Amico, A. and De Bonis, G. and De Rosa, G. and De Sio, C. and Di Capua, F. and Di Palma, I. and D{\´i}az Garc{\´i}a, A. F. and Distefano, C. and Donzaud, C. and Dornic, D. and Dorosti-Hasankiadeh, Q. and Drakopoulou, E. and Drouhin, D. and Drury, L. and Durocher, M. and Eberl, T. and Eichie, S. and van Eijk, D. and El Bojaddaini, I. and El Khayati, N. and Elsaesser, D. and Enzenh{\"o}fer, A. and Fassi, F. and Favali, P. and Fermani, P. and Ferrara, G. and Filippidis, C. and Frascadore, G. and Fusco, L. A. and Gal, T. and Galat{\`a}, S. and Garufi, F. and Gay, P. and Gebyehu, M. and Giordano, V. and Gizani, N. and Gracia, R. and Graf, K. and Gr{\´e}goire, T. and Grella, G. and Habel, R. and Hallmann, S. and van Haren, H. and Harissopulos, S. and Heid, T. and Heijboer, A. and Heine, E. and Henry, S. and Hern{\´a}ndez-Rey, J. J. and Hevinga, M. and Hofest{\"a}dt, J. and Hugon, C. M. F. and Illuminati, G. and James, C. W. and Jansweijer, P. and Jongen, M. and de Jong, M. and Kadler, M. and Kalekin, O. and Kappes, A. and Katz, U. F. and Keller, P. and Kieft, G. and Kießling, D. and Koffeman, E. N. and Kooijman, P. and Kouchner, A. and Kulikovskiy, V. and Lahmann, R. and Lamare, P. and Leisos, A. and Leonora, E. and Lindsey Clark, M. and Liolios, A. and Llorenz Alvarez, C. D. and Lo Presti, D. and L{\"o}hner, H. and Lonardo, A. and Lotze, M. and Loucatos, S. and Maccioni, E. and Mannheim, K. and Margiotta, A. and Marinelli, A. and Mari{\c{s}}, O. and Markou, C. and Mart{\´i}nez-Mora, J. A. and Martini, A. and Mele, R. and Melis, K. W. and Michael, T. and Migliozzi, P. and Migneco, E. and Mijakowski, P. and Miraglia, A. and Mollo, C. M. and Mongelli, M. and Morganti, M. and Moussa, A. and Musico, P. and Musumeci, M. and Navas, S. and Nicoleau, C. A. and Olcina, I. and Olivetto, C. and Orlando, A. and Papaikonomou, A. and Papaleo, R. and Păvăla{\c{s}}, G. E. and Peek, H. and Pellegrino, C. and Perrina, C. and Pfutzner, M. and Piattelli, P. and Pikounis, K. and Poma, G. E. and Popa, V. and Pradier, T. and Pratolongo, F. and P{\"u}hlhofer, G. and Pulvirenti, S. and Quinn, L. and Racca, C. and Raffaelli, F. and Randazzo, N. and Rapidis, P. and Razis, P. and Real, D. and Resvanis, L. and Reubelt, J. and Riccobene, G. and Rossi, C. and Rovelli, A. and Salda{\~n}a, M. and Salvadori, I. and Samtleben, D. F. E. and S{\´a}nchez Garc{\´i}a, A. and S{\´a}nchez Losa, A. and Sanguineti, M. and Santangelo, A. and Santonocito, D. and Sapienza, P. and Schimmel, F. and Schmelling, J. and Sciacca, V. and Sedita, M. and Seitz, T. and Sgura, I. and Simeone, F. and Siotis, I. and Sipala, V. and Spisso, B. and Spurio, M. and Stavropoulos, G. and Steijger, J. and Stellacci, S. M. and Stransky, D. and Taiuti, M. and Tayalati, Y. and T{\´e}zier, D. and Theraube, S. and Thompson, L. and Timmer, P. and T{\"o}nnis, C. and Trasatti, L. and Trovato, A. and Tsirigotis, A. and Tzamarias, S. and Tzamariudaki, E. and Vallage, B. and Van Elewyk, V. and Vermeulen, J. and Vicini, P. and Viola, S. and Vivolo, D. and Volkert, M. and Voulgaris, G. and Wiggers, L. and Wilms, J. and de Wolf, E. and Zachariadou, K. and Zornoza, J. D. and Z{\´u}{\~n}iga, J.}, title = {Letter of intent for KM3NeT 2.0}, series = {Journal of Physics G-Nuclear and Particle Physics}, volume = {43}, journal = {Journal of Physics G-Nuclear and Particle Physics}, number = {8}, doi = {10.1088/0954-3899/43/8/084001}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-188050}, pages = {84001}, year = {2016}, abstract = {The main objectives of the KM3NeT Collaboration are (i) the discovery and subsequent observation of high-energy neutrino sources in the Universe and (ii) the determination of the mass hierarchy of neutrinos. These objectives are strongly motivated by two recent important discoveries, namely: (1) the high-energy astrophysical neutrino signal reported by IceCube and (2) the sizable contribution of electron neutrinos to the third neutrino mass eigenstate as reported by Daya Bay, Reno and others. To meet these objectives, the KM3NeT Collaboration plans to build a new Research Infrastructure consisting of a network of deep-sea neutrino telescopes in the Mediterranean Sea. A phased and distributed implementation is pursued which maximises the access to regional funds, the availability of human resources and the synergistic opportunities for the Earth and sea sciences community. Three suitable deep-sea sites are selected, namely off-shore Toulon (France), Capo Passero (Sicily, Italy) and Pylos (Peloponnese, Greece). The infrastructure will consist of three so-called building blocks. A building block comprises 115 strings, each string comprises 18 optical modules and each optical module comprises 31 photo-multiplier tubes. Each building block thus constitutes a three-dimensional array of photo sensors that can be used to detect the Cherenkov light produced by relativistic particles emerging from neutrino interactions. Two building blocks will be sparsely configured to fully explore the IceCube signal with similar instrumented volume, different methodology, improved resolution and}, language = {en} } @article{JohnsonAkiyamaBlackburnetal.2023, author = {Johnson, Michael D. and Akiyama, Kazunori and Blackburn, Lindy and Bouman, Katherine L. and Broderick, Avery E. and Cardoso, Vitor and Fender, Rob P. and Fromm, Christian M. and Galison, Peter and G{\´o}mez, Jos{\´e} L. and Haggard, Daryl and Lister, Matthew L. and Lobanov, Andrei P. and Markoff, Sera and Narayan, Ramesh and Natarajan, Priyamvada and Nichols, Tiffany and Pesce, Dominic W. and Younsi, Ziri and Chael, Andrew and Chatterjee, Koushik and Chaves, Ryan and Doboszewski, Juliusz and Dodson, Richard and Doeleman, Sheperd S. and Elder, Jamee and Fitzpatrick, Garret and Haworth, Kari and Houston, Janice and Issaoun, Sara and Kovalev, Yuri Y. and Levis, Aviad and Lico, Rocco and Marcoci, Alexandru and Martens, Niels C. M. and Nagar, Neil M. and Oppenheimer, Aaron and Palumbo, Daniel C. M. and Ricarte, Angelo and Rioja, Mar{\´i}a  J. and Roelofs, Freek and Thresher, Ann C. and Tiede, Paul and Weintroub, Jonathan and Wielgus, Maciek}, title = {Key science goals for the next-generation Event Horizon Telescope}, series = {Galaxies}, volume = {11}, journal = {Galaxies}, number = {3}, issn = {2075-4434}, doi = {10.3390/galaxies11030061}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-313525}, year = {2023}, abstract = {The Event Horizon Telescope (EHT) has led to the first images of a supermassive black hole, revealing the central compact objects in the elliptical galaxy M87 and the Milky Way. Proposed upgrades to this array through the next-generation EHT (ngEHT) program would sharply improve the angular resolution, dynamic range, and temporal coverage of the existing EHT observations. These improvements will uniquely enable a wealth of transformative new discoveries related to black hole science, extending from event-horizon-scale studies of strong gravity to studies of explosive transients to the cosmological growth and influence of supermassive black holes. Here, we present the key science goals for the ngEHT and their associated instrument requirements, both of which have been formulated through a multi-year international effort involving hundreds of scientists worldwide.}, language = {en} } @article{GedalinDroege2013, author = {Gedalin, Michael and Dr{\"o}ge, Wolfgang}, title = {Ion dynamics in quasi-perpendicular collisionless interplanetary shocks: a case study}, series = {Frontiers in Physics}, volume = {1}, journal = {Frontiers in Physics}, issn = {2296-424X}, doi = {10.3389/fphy.2013.00029}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-189407}, pages = {29}, year = {2013}, abstract = {Interplanetary shocks are believed to play an important role in the acceleration of charged particles in the heliosphere. While the acceleration to high energies proceeds via the diffusive mechanism at the scales exceeding by far the shock width, the initial stage (injection) should occur at the shock itself. Numerical tracing of ions is done in a model quasi-perpendicular shock front with a typical interplanetary shock parameters (Mach number, upstream ion temperature). The analysis of the distribution of the transmitted solar wind is used to adjust the cross-shock potential which is not directly measured. It is found that, for typical upstream ion temperatures, acceleration of the ions from the tail of the solar wind distribution is unlikely. Pickup ions with a shell distribution are found to be effectively energized and may be injected into further diffusive acceleration regime. Pre-accelerated ions are efficiently upscaled in energies. A part of these ions is returned to the upstream region where they can further be diffusively accelerated.}, language = {en} } @article{DornerMostafaSatalecka2021, author = {Dorner, Daniela and Mostaf{\´a}, Miguel and Satalecka, Konstancja}, title = {High-energy alerts in the multi-messenger era}, series = {Universe}, volume = {7}, journal = {Universe}, number = {11}, issn = {2218-1997}, doi = {10.3390/universe7110393}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-248496}, year = {2021}, abstract = {The observation of electromagnetic counterparts to both high energy neutrinos and gravitational waves marked the beginning of a new era in astrophysics. The multi-messenger approach allows us to gain new insights into the most energetic events in the Universe such as gamma-ray bursts, supernovas, and black hole mergers. Real-time multi-messenger alerts are the key component of the observational strategies to unravel the transient signals expected from astrophysical sources. Focusing on the high-energy regime, we present a historical perspective of multi-messenger observations, the detectors and observational techniques used to study them, the status of the multi-messenger alerts and the most significant results, together with an overview of the future prospects in the field.}, language = {en} } @article{MoraisPasechnikPorod2021, author = {Morais, Ant{\´o}nio P. and Pasechnik, Roman and Porod, Werner}, title = {Grand Unified origin of gauge interactions and families replication in the Standard Model}, series = {Universe}, volume = {7}, journal = {Universe}, number = {12}, issn = {2218-1997}, doi = {10.3390/universe7120461}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-250237}, year = {2021}, abstract = {The tremendous phenomenological success of the Standard Model (SM) suggests that its flavor structure and gauge interactions may not be arbitrary but should have a fundamental first-principle explanation. In this work, we explore how the basic distinctive properties of the SM dynamically emerge from a unified New Physics framework tying together both flavor physics and Grand Unified Theory (GUT) concepts. This framework is suggested by a novel anomaly-free supersymmetric chiral E\(_6\)×SU(2)\(_F\)×U(1)\(_F\) GUT containing the SM. Among the most appealing emergent properties of this theory is the Higgs-matter unification with a highly-constrained massless chiral sector featuring two universal Yukawa couplings close to the GUT scale. At the electroweak scale, the minimal SM-like effective field theory limit of this GUT represents a specific flavored three-Higgs doublet model consistent with the observed large hierarchies in the quark mass spectra and mixing already at tree level.}, language = {en} } @article{RomoliChakrabortyDorneretal.2018, author = {Romoli, Carlo and Chakraborty, Nachiketa and Dorner, Daniela and Taylor, Andrew and Blank, Michael}, title = {Flux Distribution of Gamma-Ray Emission in Blazars: The Example of Mrk 501}, series = {Galaxies}, volume = {6}, journal = {Galaxies}, number = {4}, organization = {FACT and H.E.S.S. Collaborations}, issn = {2075-4434}, doi = {10.3390/galaxies6040135}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-197580}, year = {2018}, abstract = {Flux distribution is an important tool to understand the variability processes in activegalactic nuclei. We now have available a great deal of observational evidences pointing towards thepresence of log-normal components in the high energy light curves, and different models have beenproposed to explain these data. Here, we collect some of the recent developments on this topic usingthe well-known blazar Mrk 501 as example of complex and interesting aspects coming from its fluxdistribution in different energy ranges and at different timescales. The observational data we refer toare those collected in a complementary manner by Fermi-LAT over multiple years, and by the FirstG-APD Cherenkov Telescope (FACT) telescope and the H.E.S.S. array in correspondence of the brightflare of June 2014}, language = {en} } @article{ChatterjeeChaelTiedeetal.2023, author = {Chatterjee, Koushik and Chael, Andrew and Tiede, Paul and Mizuno, Yosuke and Emami, Razieh and Fromm, Christian and Ricarte, Angelo and Blackburn, Lindy and Roelofs, Freek and Johnson, Michael D. and Doeleman, Sheperd S. and Arras, Philipp and Fuentes, Antonio and Knollm{\"u}ller, Jakob and Kosogorov, Nikita and Lindahl, Greg and M{\"u}ller, Hendrik and Patel, Nimesh and Raymond, Alexander and Traianou, Efthalia and Vega, Justin}, title = {Accretion flow morphology in numerical simulations of black holes from the ngEHT model library: the impact of radiation physics}, series = {Galaxies}, volume = {11}, journal = {Galaxies}, number = {2}, issn = {2075-4434}, doi = {10.3390/galaxies11020038}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-304084}, year = {2023}, abstract = {In the past few years, the Event Horizon Telescope (EHT) has provided the first-ever event horizon-scale images of the supermassive black holes (BHs) M87* and Sagittarius A* (Sgr A*). The next-generation EHT project is an extension of the EHT array that promises larger angular resolution and higher sensitivity to the dim, extended flux around the central ring-like structure, possibly connecting the accretion flow and the jet. The ngEHT Analysis Challenges aim to understand the science extractability from synthetic images and movies to inform the ngEHT array design and analysis algorithm development. In this work, we compare the accretion flow structure and dynamics in numerical fluid simulations that specifically target M87* and Sgr A*, and were used to construct the source models in the challenge set. We consider (1) a steady-state axisymmetric radiatively inefficient accretion flow model with a time-dependent shearing hotspot, (2) two time-dependent single fluid general relativistic magnetohydrodynamic (GRMHD) simulations from the H-AMR code, (3) a two-temperature GRMHD simulation from the BHAC code, and (4) a two-temperature radiative GRMHD simulation from the KORAL code. We find that the different models exhibit remarkably similar temporal and spatial properties, except for the electron temperature, since radiative losses substantially cool down electrons near the BH and the jet sheath, signaling the importance of radiative cooling even for slowly accreting BHs such as M87*. We restrict ourselves to standard torus accretion flows, and leave larger explorations of alternate accretion models to future work.}, language = {en} } @article{KrausMouchaRoth2022, author = {Kraus, Daniela and Moucha, Annika and Roth, Oliver}, title = {A sharp Bernstein-type inequality and application to the Carleson embedding theorem with matrix weights}, series = {Analysis and Mathematical Physics}, volume = {12}, journal = {Analysis and Mathematical Physics}, number = {1}, issn = {1664-235X}, doi = {10.1007/s13324-021-00639-5}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-270485}, year = {2022}, abstract = {We prove a sharp Bernstein-type inequality for complex polynomials which are positive and satisfy a polynomial growth condition on the positive real axis. This leads to an improved upper estimate in the recent work of Culiuc and Treil (Int. Math. Res. Not. 2019: 3301-3312, 2019) on the weighted martingale Carleson embedding theorem with matrix weights. In the scalar case this new upper bound is optimal.}, language = {en} }