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Gumbel convergence of the maximum of convoluted half-normally distributed random variables [article]

Markus Bibinger
2021 arXiv   pre-print
It turns out that the Gumbel convergence for all such distributions can be proved following similar steps. We illustrate the results in Monte Carlo simulations.  ...  In this note, we establish the convergence in distribution of the maxima of i.i.d. random variables to the Gumbel distribution with the associated normalizing sequences for several examples that are related  ...  The black line gives the density of the Gumbel limit distribution.dard Gumbel limit distribution, including normalized versions of M , whose empirical distributions are quite different as shown in the  ... 
arXiv:2103.14525v1 fatcat:apm7f7iynndo5n32bean4imtgy

Polar mesospheric clouds formed from space shuttle exhaust

Michael H. Stevens, Jörg Gumbel, Christoph R. Englert, Klaus U. Grossmann, Markus Rapp, Paul Hartogh
2003 Geophysical Research Letters  
Acknowledgments: The authors are grateful to Jörg Gumbel, Klaus Grossmann, Paul Hartogh, Markus Rapp, Robert Meier, Xinzhao Chu, Matthew DeLand, and John Plane for providing data and model results in valuable  ... 
doi:10.1029/2003gl017249 fatcat:scbz3cnmgvazboskf23e5c2g3e

The simplicity of metazoan cell lineages

Ricardo B. R. Azevedo, Rolf Lohaus, Volker Braun, Markus Gumbel, Muralikrishna Umamaheshwar, Paul-Michael Agapow, Wouter Houthoofd, Ute Platzer, Gaëtan Borgonie, Hans-Peter Meinzer, Armand M. Leroi
2005 Nature  
characterize many carnivorous non-mammalian synapsids 24 . The molariform teeth at the back of the dentition of Repenomamus are small with blunt crowns; they probably played a minor role in food processing. Although mammals are considered definitive chewers within amniotes 25 , the dental morphology and large pieces of prey in the stomach of Repenomamus suggest that chewing as a derived feature in mammals was probably not present in Repenomamus. It is not easy to assess whether Repenomamus was
more » ... predator or scavenger. Scavengers are relatively rare among mammals-among extant carnivorous mammals, only two species of hyenas are habitual scavengers 12,26 . Compared to their hunting cousins, these hyenas have smaller second upper incisors and less jaw muscle leverage, which probably reflect their inability to capture and handle live prey. In contrast, the enlarged incisors and strong jaw muscles of Repenomamus are well shaped for catching prey, favouring it as a predator rather than a scavenger. For fossil mammals, body size is one of the most important factors influencing life history strategy 27 . Early mammals or their close relatives, such as morganocodontids and kuehneotheriids in the Late Triassic to Early Jurassic periods, were small and considered to be nocturnal insectivores 2,3 ; the same is true of most later Mesozoic mammals 28 (Fig. 4) . The reason for the very small size of Mesozoic mammals is uncertain 5 , but it has often been hypothesized that well-established larger (and presumably diurnal) reptilian carnivores and herbivores, particularly dinosaurs, prevented mammals from invading those niches 29 . Repenomamus extend significantly the upper limit of body size of Mesozoic mammals (Fig. 4) and are actually larger than several small dinosaurs, particularly dromaeosaurid dinosaurs, from the same fauna 11 . Larger animals can live longer and move faster, but they also need a larger food supply and broader home range 30 . Judging from their body size, R. giganticus could feed on larger prey and forage a wider area for food. These large Mesozoic mammals were probably carnivores that competed with dinosaurs for food and territory. A
doi:10.1038/nature03178 pmid:15650738 fatcat:34oul26odneqfcgvtc2slahjqi

Computational Analysis of Genetic Code Variations Optimized for the Robustness against Point Mutations with Wobble-like Effects

Elena Fimmel, Markus Gumbel, Martin Starman, Lutz Strüngmann
2021 Life  
It is believed that the codon–amino acid assignments of the standard genetic code (SGC) help to minimize the negative effects caused by point mutations. All possible point mutations of the genetic code can be represented as a weighted graph with weights that correspond to the probabilities of these mutations. The robustness of a code against point mutations can be described then by means of the so-called conductance measure. This paper quantifies the wobble effect, which was investigated
more » ... sly by applying the weighted graph approach, and seeks optimal weights using an evolutionary optimization algorithm to maximize the code's robustness. One result of our study is that the robustness of the genetic code is least influenced by mutations in the third position—like with the wobble effect. Moreover, the results clearly demonstrate that point mutations in the first, and even more importantly, in the second base of a codon have a very large influence on the robustness of the genetic code. These results were compared to single nucleotide variants (SNV) in coding sequences which support our findings. Additionally, it was analyzed which structure of a genetic code evolves from random code tables when the robustness is maximized. Our calculations show that the resulting code tables are very close to the standard genetic code. In conclusion, the results illustrate that the robustness against point mutations seems to be an important factor in the evolution of the standard genetic code.
doi:10.3390/life11121338 pmid:34947869 pmcid:PMC8707135 fatcat:isly2z5dc5d23eju7tgwmvrkom

X-ray Based Visualization of the Electrolyte Filling Process of Lithium Ion Batteries

Antje Schilling, Philip Gümbel, Markus Möller, Fatih Kalkan, Franz Dietrich, Klaus Dröder
2018 Journal of the Electrochemical Society  
The electrolyte filling process constitutes the interface between cell assembly and formation of lithium ion batteries. Electrolyte filling is known as a quality critical and also time consuming process step. To avoid limitations in battery quality a homogeneous electrolyte distribution is necessary. Therefore, especially large sized cells are stored for hours. To accelerate filling and wetting processes the effect of materials-and process parameters on electrolyte distribution needs to be
more » ... tigated. Unfortunately, in situ methods to characterize the filling and wetting state are still rare, limited in availability or even time-consuming in preparation. To overcome these drawbacks this paper introduces X-ray as an innovative method to visualize the electrolyte filling process in large scaled lithium ion batteries. Therefore, an experimental setup was developed to enable in situ X-ray measurements during the filling process of large scaled cells. Additionally, an evaluation process for the optical data was proposed. Based on these images the suitability of X-ray as visualization method is shown considering three exemplary filling parameters.
doi:10.1149/2.0251903jes fatcat:7f42tgtnsvg4rmtuyjyztxje7q

Combination of Lidar and Model Data for Studying Deep Gravity Wave Propagation

Benedikt Ehard, Peggy Achtert, Andreas Dörnbrack, Sonja Gisinger, Jörg Gumbel, Mikhail Khaplanov, Markus Rapp, Johannes Wagner
2016 Monthly Weather Review  
2 , Markus Rapp 1,4 and Johannes Wagner 1.5 Critical horizontal wavelength 1 Deutsches Zentrum für Luft-und Raumfahrt (DLR), Institut für Physik der Atmosphäre, Oberpfaffenhofen, Germany 2 Department  ...  Fig. 3b) Horizontal structure Combination of lidar and model data for studying deep gravity wave propagation Benedikt Ehard 1,2 , Peggy Achtert 2,3 , Andreas Dörnbrack 1 , Sonja Gisinger 1 , Jörg Gumbel  ... 
doi:10.1175/mwr-d-14-00405.1 fatcat:g24bwan4vvddpprrplsxkb6sdq

Atmospheric band fitting coefficients derived from a self-consistent rocket-borne experiment

Mykhaylo Grygalashvyly, Martin Eberhart, Jonas Hedin, Boris Strelnikov, Franz-Josef Lübken, Markus Rapp, Stefan Löhle, Stefanos Fasoulas, Mikhail Khaplanov, Jörg Gumbel, Ekaterina Vorobeva
2019 Atmospheric Chemistry and Physics  
<p><strong>Abstract.</strong> Based on self-consistent rocket-borne measurements of temperature, the densities of atomic oxygen and neutral air, and the volume emission of the atmospheric band (762<span class="thinspace"></span>nm), we examined the one-step and two-step excitation mechanism of <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1" display="inline" overflow="scroll" dspmath="mathml"><mrow><mrow class="chem"><msub><mi mathvariant="normal">O</mi><mn
more » ... athvariant="normal">2</mn></msub></mrow><mfenced close=")" open="("><mrow><msup><mi>b</mi><mn mathvariant="normal">1</mn></msup><msubsup><mi mathvariant="normal">Σ</mi><mi>g</mi><mo>+</mo></msubsup></mrow></mfenced></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="54pt" height="22pt" class="svg-formula" dspmath="mathimg" md5hash="8501444005187b3419b2cfeb981bdaf0"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-19-1207-2019-ie00001.svg" width="54pt" height="22pt" src="acp-19-1207-2019-ie00001.png"/></svg:svg></span></span> for nighttime conditions. Following McDade et al. (1986), we derived the empirical fitting coefficients, which parameterize the atmospheric band emission <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M2" display="inline" overflow="scroll" dspmath="mathml"><mrow><mrow class="chem"><msub><mi mathvariant="normal">O</mi><mn mathvariant="normal">2</mn></msub></mrow><mfenced close=")" open="("><mrow><msup><mi>b</mi><mn mathvariant="normal">1</mn></msup><msubsup><mi mathvariant="normal">Σ</mi><mi>g</mi><mo>+</mo></msubsup><mo>-</mo><msup><mi>X</mi><mn mathvariant="normal">3</mn></msup><msubsup><mi mathvariant="normal">Σ</mi><mi>g</mi><mo>-</mo></msubsup></mrow></mfenced><mfenced close=")" open="("><mrow><mn mathvariant="normal">0</mn><mo>,</mo><mn mathvariant="normal">0</mn></mrow></mfenced></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="117pt" height="22pt" class="svg-formula" dspmath="mathimg" md5hash="02f40fbcac4d1696b0544259b8712360"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-19-1207-2019-ie00002.svg" width="117pt" height="22pt" src="acp-19-1207-2019-ie00002.png"/></svg:svg></span></span>. This allows us to derive the atomic oxygen concentration from nighttime observations of atmospheric band emission <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M3" display="inline" overflow="scroll" dspmath="mathml"><mrow><mrow class="chem"><msub><mi mathvariant="normal">O</mi><mn mathvariant="normal">2</mn></msub></mrow><mfenced close=")" open="("><mrow><msup><mi>b</mi><mn mathvariant="normal">1</mn></msup><msubsup><mi mathvariant="normal">Σ</mi><mi>g</mi><mo>+</mo></msubsup><mo>-</mo><msup><mi>X</mi><mn mathvariant="normal">3</mn></msup><msubsup><mi mathvariant="normal">Σ</mi><mi>g</mi><mo>-</mo></msubsup></mrow></mfenced><mfenced close=")" open="("><mrow><mn mathvariant="normal">0</mn><mo>,</mo><mspace width="0.125em" linebreak="nobreak"/><mn mathvariant="normal">0</mn></mrow></mfenced></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="118pt" height="22pt" class="svg-formula" dspmath="mathimg" md5hash="1bba52d5e65e55fd0c192313ca591cdb"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-19-1207-2019-ie00003.svg" width="118pt" height="22pt" src="acp-19-1207-2019-ie00003.png"/></svg:svg></span></span>. The derived empirical parameters can also be utilized for atmospheric band modeling. Additionally, we derived the fit function and corresponding coefficients for the combined (one- and two-step) mechanism. The simultaneous common volume measurements of all the parameters involved in the theoretical calculation of the observed <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M4" display="inline" overflow="scroll" dspmath="mathml"><mrow><mrow class="chem"><msub><mi mathvariant="normal">O</mi><mn mathvariant="normal">2</mn></msub></mrow><mfenced close=")" open="("><mrow><msup><mi>b</mi><mn mathvariant="normal">1</mn></msup><msubsup><mi mathvariant="normal">Σ</mi><mi>g</mi><mo>+</mo></msubsup><mo>-</mo><msup><mi>X</mi><mn mathvariant="normal">3</mn></msup><msubsup><mi mathvariant="normal">Σ</mi><mi>g</mi><mo>-</mo></msubsup></mrow></mfenced><mfenced close=")" open="("><mrow><mn mathvariant="normal">0</mn><mo>,</mo><mspace width="0.125em" linebreak="nobreak"/><mn mathvariant="normal">0</mn></mrow></mfenced></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="118pt" height="22pt" class="svg-formula" dspmath="mathimg" md5hash="bfd2ab4f84219a19d95d236846513063"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="acp-19-1207-2019-ie00004.svg" width="118pt" height="22pt" src="acp-19-1207-2019-ie00004.png"/></svg:svg></span></span> emission, i.e., temperature and density of the background air, atomic oxygen density, and volume emission rate, is the novelty and the advantage of this work.</p>
doi:10.5194/acp-19-1207-2019 fatcat:loqyp6xrfveurax3gkpobpyiay

Atomic oxygen number densities in the MLT region measured by solid electrolyte sensors on WADIS-2

Martin Eberhart, Stefan Löhle, Boris Strelnikov, Jonas Hedin, Mikhail Khaplanov, Stefanos Fasoulas, Jörg Gumbel, Franz-Josef Lübken, Markus Rapp
2018 Atmospheric Measurement Techniques Discussions  
<p><strong>Abstract.</strong> Absolute profiles of atomic oxygen number densities with high vertical resolution have been determined in the MLT region from <i>in-situ</i> measurements by several rocket-borne solid electrolyte sensors. The amperometric sensors were operated in both controlled and uncontrolled modes and with various orientations on the fore and aft deck of the payload. Calibration was based on mass spectrometry in a molecular beam containing atomic oxygen produced in a microwave
more » ... ischarge. The sensor signal is proportional to the number flux onto the electrodes and the mass flow rate in the molecular beam was measured additionally to derive this quantity from the spectrometer reading. Numerical simulations provided aerodynamic correction factors to derive the atmospheric number density of atomic oxygen from the sensor data. The flight results indicate a preferable orientation of the electrode surface perpendicular to the rocket axis. While unstable during the upleg, the density profiles measured by these sensors show an excellent agreement with the atmospheric models and photometer results during the downleg of the trajectory. The high spatial resolution of the measurements allows the identification of small-scaled variations in the atomic oxygen concentration.</p>
doi:10.5194/amt-2018-341 fatcat:bfgp6vyfiref7lcipmtgazux7e

Atomic oxygen number densities in the mesosphere–lower thermosphere region measured by solid electrolyte sensors on WADIS-2

Martin Eberhart, Stefan Löhle, Boris Strelnikov, Jonas Hedin, Mikhail Khaplanov, Stefanos Fasoulas, Jörg Gumbel, Franz-Josef Lübken, Markus Rapp
2019 Atmospheric Measurement Techniques  
<p><strong>Abstract.</strong> Absolute profiles of atomic oxygen number densities with high vertical resolution have been determined in the mesosphere–lower thermosphere (MLT) region from in situ measurements by several rocket-borne solid electrolyte sensors. The amperometric sensors were operated in both controlled and uncontrolled modes and with various orientations on the foredeck and aft deck of the payload. Calibration was based on mass spectrometry in a molecular beam containing atomic
more » ... gen produced in a microwave discharge. The sensor signal is proportional to the number flux onto the electrodes, and the mass flow rate in the molecular beam was additionally measured to derive this quantity from the spectrometer reading. Numerical simulations provided aerodynamic correction factors to derive the atmospheric number density of atomic oxygen from the sensor data. The flight results indicate a preferable orientation of the electrode surface perpendicular to the rocket axis. While unstable during the upleg, the density profiles measured by these sensors show an excellent agreement with the atmospheric models and photometer results during the downleg of the trajectory. The high spatial resolution of the measurements allows for the identification of small-scale variations in the atomic oxygen concentration.</p>
doi:10.5194/amt-12-2445-2019 fatcat:veazw7doinbgtbybjrcjjc52b4

Spatial and temporal variability in MLT turbulence inferred from in situ and ground-based observations during the WADIS-1 sounding rocket campaign

Boris Strelnikov, Artur Szewczyk, Irina Strelnikova, Ralph Latteck, Gerd Baumgarten, Franz-Josef Lübken, Markus Rapp, Stefanos Fasoulas, Stefan Löhle, Martin Eberhart, Ulf-Peter Hoppe, Tim Dunker (+5 others)
2017 Annales Geophysicae  
<p><strong>Abstract.</strong> In summer 2013 the WADIS-1 sounding rocket campaign was conducted at the Andøya Space Center (ACS) in northern Norway (69°<span class="thinspace"></span>N, 16°<span class="thinspace"></span>E). Among other things, it addressed the question of the variability in mesosphere/lower thermosphere (MLT) turbulence, both in time and space. A unique feature of the <span style="" class="text">WADIS</span> project was multi-point turbulence sounding applying different
more » ... ent techniques including rocket-borne ionization gauges, VHF MAARSY radar, and VHF <span style="" class="text">EISCAT</span> radar near Tromsø. This allowed for horizontal variability to be observed in the turbulence field in the MLT at scales from a few to 100<span class="thinspace"></span>km. We found that the turbulence dissipation rate, <i>ε</i> varied in space in a wavelike manner both horizontally and in the vertical direction. This wavelike modulation reveals the same vertical wavelengths as those seen in gravity waves. We also found that the vertical mean value of radar observations of <i>ε</i> agrees reasonably with rocket-borne measurements. In this way defined 〈<i>ε</i><sub>radar</sub>〉 value reveals clear tidal modulation and results in variation by up to 2 orders of magnitude with periods of 24<span class="thinspace"></span>h. The 〈<i>ε</i><sub>radar</sub>〉 value also shows 12<span class="thinspace"></span>h and shorter (1 to a few hours) modulations resulting in one decade of variation in 〈<i>ε</i><sub>radar</sub>〉 magnitude. The 24<span class="thinspace"></span>h modulation appeared to be in phase with tidal change of horizontal wind observed by SAURA-MF radar. Such wavelike and, in particular, tidal modulation of the turbulence dissipation field in the MLT region inferred from our analysis is a new finding of this work.</p>
doi:10.5194/angeo-35-547-2017 fatcat:56tpx64te5cxjfx25y7c5ufvvu

Community-driven development for computational biology at Sprints, Hackathons and Codefests

Steffen Möller, Enis Afgan, Michael Banck, Raoul JP Bonnal, Timothy Booth, John Chilton, Peter JA Cock, Markus Gumbel, Nomi Harris, Richard Holland, Matúš Kalaš, László Kaján (+16 others)
2014 BMC Bioinformatics  
Computational biology comprises a wide range of technologies and approaches. Multiple technologies can be combined to create more powerful workflows if the individuals contributing the data or providing tools for its interpretation can find mutual understanding and consensus. Much conversation and joint investigation are required in order to identify and implement the best approaches. Traditionally, scientific conferences feature talks presenting novel technologies or insights, followed up by
more » ... formal discussions during coffee breaks. In multi-institution collaborations, in order to reach agreement on implementation details or to transfer deeper insights in a technology and practical skills, a representative of one group typically visits the other. However, this does not scale well when the number of technologies or research groups is large. Conferences have responded to this issue by introducing Birds-of-a-Feather (BoF) sessions, which offer an opportunity for individuals with common interests to intensify their interaction. However, parallel BoF sessions often make it hard for participants to join multiple BoFs and find common ground between the different technologies, and BoFs are generally too short to allow time for participants to program together. Results: This report summarises our experience with computational biology Codefests, Hackathons and Sprints, which are interactive developer meetings. They are structured to reduce the limitations of traditional scientific meetings described above by strengthening the interaction among peers and letting the participants determine the schedule and topics. These meetings are commonly run as loosely scheduled "unconferences" (self-organized identification of participants and topics for meetings) over at least two days, with early introductory talks to welcome and organize contributors, followed by intensive collaborative coding sessions. We summarise some prominent achievements of those meetings and describe differences in how these are organised, how their audience is addressed, and their outreach to their respective communities. Conclusions: Hackathons, Codefests and Sprints share a stimulating atmosphere that encourages participants to jointly brainstorm and tackle problems of shared interest in a self-driven proactive environment, as well as providing an opportunity for new participants to get involved in collaborative projects.
doi:10.1186/1471-2105-15-s14-s7 pmid:25472764 pmcid:PMC4255748 fatcat:p7jbtuipnbdafo3zauaqrhu5sq

Simultaneous in situ measurements of small-scale structures in neutral, plasma, and atomic oxygen densities during WADIS sounding rocket project

Boris Strelnikov, Martin Eberhart, Martin Friedrich, Jonas Hedin, Mikhail Khaplanov, Gerd Baumgarten, Bifford P. Williams, Tristan Staszak, Heiner Asmus, Irina Strelnikova, Ralph Latteck, Mykhaylo Grygalashvyly (+10 others)
2019 Atmospheric Chemistry and Physics Discussions  
<p><strong>Abstract.</strong> In this paper we present an overview of measurements conducted during the WADIS-2 rocket campaign. We investigate the effect of small-scale processes like gravity waves and turbulence on the distribution of atomic oxygen and other species in the MLT region. Our analysis suggests that density fluctuations of atomic oxygen are coupled to fluctuations of other constituents, i.e., plasma and neutrals. Our measurements show that all measured quantities, including winds,
more » ... densities, and temperatures, reveal signatures of both waves and turbulence. We show observations of gravity wave saturation and breakdown together with simultaneous measurements of generated turbulence. Atomic oxygen inside turbulence layers shows two different spectral behaviors, which might imply change of its diffusion properties.</p>
doi:10.5194/acp-2018-1043 fatcat:squdgd6cijhivgdxuynncny43y

Simultaneous in situ measurements of small-scale structures in neutral, plasma, and atomic oxygen densities during the WADIS sounding rocket project

Boris Strelnikov, Martin Eberhart, Martin Friedrich, Jonas Hedin, Mikhail Khaplanov, Gerd Baumgarten, Bifford P. Williams, Tristan Staszak, Heiner Asmus, Irina Strelnikova, Ralph Latteck, Mykhaylo Grygalashvyly (+10 others)
2019 Atmospheric Chemistry and Physics  
We also note that because of the supersonic rocket velocity the measurement results of most instruments onboard sounding rockets require an aerodynamic correction Gumbel, 2001; Rapp et al., 2001; Hedin  ... 
doi:10.5194/acp-19-11443-2019 fatcat:dcoy36pqarcgrd4m6lr67wijve

Uncertainty quantification in brain tumor segmentation using CRFs and random perturbation models

Esther Alberts, Markus Rempfler, Georgina Alber, Thomas Huber, Jan Kirschke, Claus Zimmer, Bjoern H. Menze
2016 2016 IEEE 13th International Symposium on Biomedical Imaging (ISBI)  
drawn IDD from a Gumbel distribution with zero mean for the full state table of y.  ...  Right: range of Gumbel samples compared to the non-perturbed unary potentials. Fig. 6 . 6 Uncertainty in brain tumor volumetry.  ... 
doi:10.1109/isbi.2016.7493299 dblp:conf/isbi/AlbertsRAHKZM16 fatcat:ylvjuxdom5bhnhobeuy7xawe6m

Estimação de nível de retorno da precipitação máxima diária na cidade de Jataí-GO

Elias Silva de Medeiros, Marcos Antônio Alves, Sidnei Azevedo de Souza
2019 Ciência e Natura  
Distribuição Gumbel. Desastres ambientais.  ...  For the likelihood ratio test, it was noted that the Gumbel distribution is preferable against the GEV to model precipitation data.  ...  De acordo com os dados do Instituto Nacional de Meteorologia (INMET), o clima tropical mesotérmico da região, segundo a classificação de Köppen (KOTTEK, MARKUS; GRIESER et al., 2006) , possui duas estações  ... 
doi:10.5902/2179460x35639 fatcat:fwlymdjqnzgcvhahgc4xflhl74
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