@article{KucharskiErgintavAhmadetal.2019,
  author    = {Kucharski, Maciej and Ergintav, Arzu and Ahmad, Wael Abdullah and Krstić, Miloš and Ng, Herman Jalli and Kissinger, Dietmar},
  title     = {A Scalable 79-GHz Radar Platform Based on Single-Channel Transceivers},
  series = {IEEE Transactions on Microwave Theory and Techniques},
  volume    = {67},
  journal   = {IEEE Transactions on Microwave Theory and Techniques},
  number    = {9},
  publisher = {Inst. of Electr. and Electronics Engineers},
  address   = {Piscataway},
  issn      = {0018-9480},
  doi       = {10.1109/TMTT.2019.2914104},
  pages     = {3882 -- 3896},
  year      = {2019},
  abstract  = {This paper presents a scalable E-band radar platform based on single-channel fully integrated transceivers (TRX) manufactured using 130-nm silicon-germanium (SiGe) BiCMOS technology. The TRX is suitable for flexible radar systems exploiting massive multiple-input-multipleoutput (MIMO) techniques for multidimensional sensing. A fully integrated fractional-N phase-locked loop (PLL) comprising a 39.5-GHz voltage-controlled oscillator is used to generate wideband frequency-modulated continuous-wave (FMCW) chirp for E-band radar front ends. The TRX is equipped with a vector modulator (VM) for high-speed carrier modulation and beam-forming techniques. A single TRX achieves 19.2-dBm maximum output power and 27.5-dB total conversion gain with input-referred 1-dB compression point of -10 dBm. It consumes 220 mA from 3.3-V supply and occupies 3.96 mm(2) silicon area. A two-channel radar platform based on full-custom TRXs and PLL was fabricated to demonstrate high-precision and high-resolution FMCW sensing. The radar enables up to 10-GHz frequency ramp generation in 74-84-GHz range, which results in 1.5-cm spatial resolution. Due to high output power, thus high signal-to-noise ratio (SNR), a ranging precision of 7.5 mu m for a target at 2 m was achieved. The proposed architecture supports scalable multichannel applications for automotive FMCW using a single local oscillator (LO).},
  language  = {en}
}
@article{SharmaHainzlZoelleretal.2020,
  author    = {Sharma, Shubham and Hainzl, Sebastian and Z{\"o}ller, Gert and Holschneider, Matthias},
  title     = {Is Coulomb stress the best choice for aftershock forecasting?},
  series = {Journal of geophysical research : Solid earth},
  volume    = {125},
  journal   = {Journal of geophysical research : Solid earth},
  number    = {9},
  publisher = {American Geophysical Union},
  address   = {Washington},
  issn      = {2169-9313},
  doi       = {10.1029/2020JB019553},
  pages     = {12},
  year      = {2020},
  abstract  = {The Coulomb failure stress (CFS) criterion is the most commonly used method for predicting spatial distributions of aftershocks following large earthquakes. However, large uncertainties are always associated with the calculation of Coulomb stress change. The uncertainties mainly arise due to nonunique slip inversions and unknown receiver faults; especially for the latter, results are highly dependent on the choice of the assumed receiver mechanism. Based on binary tests (aftershocks yes/no), recent studies suggest that alternative stress quantities, a distance-slip probabilistic model as well as deep neural network (DNN) approaches, all are superior to CFS with predefined receiver mechanism. To challenge this conclusion, which might have large implications, we use 289 slip inversions from SRCMOD database to calculate more realistic CFS values for a layered half-space and variable receiver mechanisms. We also analyze the effect of the magnitude cutoff, grid size variation, and aftershock duration to verify the use of receiver operating characteristic (ROC) analysis for the ranking of stress metrics. The observations suggest that introducing a layered half-space does not improve the stress maps and ROC curves. However, results significantly improve for larger aftershocks and shorter time periods but without changing the ranking. We also go beyond binary testing and apply alternative statistics to test the ability to estimate aftershock numbers, which confirm that simple stress metrics perform better than the classic Coulomb failure stress calculations and are also better than the distance-slip probabilistic model.},
  language  = {en}
}
@article{EngbertRabeKliegletal.2021,
  author    = {Engbert, Ralf and Rabe, Maximilian Michael and Kliegl, Reinhold and Reich, Sebastian},
  title     = {Sequential data assimilation of the stochastic SEIR epidemic model for regional COVID-19 dynamics},
  series = {Bulletin of mathematical biology : official journal of the Society for Mathematical Biology},
  volume    = {83},
  journal   = {Bulletin of mathematical biology : official journal of the Society for Mathematical Biology},
  number    = {1},
  publisher = {Springer},
  address   = {New York},
  issn      = {0092-8240},
  doi       = {10.1007/s11538-020-00834-8},
  pages     = {16},
  year      = {2021},
  abstract  = {Newly emerging pandemics like COVID-19 call for predictive models to implement precisely tuned responses to limit their deep impact on society. Standard epidemic models provide a theoretically well-founded dynamical description of disease incidence. For COVID-19 with infectiousness peaking before and at symptom onset, the SEIR model explains the hidden build-up of exposed individuals which creates challenges for containment strategies. However, spatial heterogeneity raises questions about the adequacy of modeling epidemic outbreaks on the level of a whole country. Here, we show that by applying sequential data assimilation to the stochastic SEIR epidemic model, we can capture the dynamic behavior of outbreaks on a regional level. Regional modeling, with relatively low numbers of infected and demographic noise, accounts for both spatial heterogeneity and stochasticity. Based on adapted models, short-term predictions can be achieved. Thus, with the help of these sequential data assimilation methods, more realistic epidemic models are within reach.},
  language  = {en}
}
@phdthesis{Sareeto2024,
  author    = {Sareeto, Apatsara},
  title     = {Algebraic properties of a subsemigroup of the symmetric inverse semigroup},
  school      = {Universit{\"a}t Potsdam},
  pages     = {92},
  year      = {2024},
  language  = {en}
}
@article{GerlachGlueck2017,
  author    = {Gerlach, Moritz Reinhardt and Gl{\"u}ck, Jochen},
  title     = {On a convergence theorem for semigroups of positive integral operators},
  series = {Comptes Rendus Mathematique},
  volume    = {355},
  journal   = {Comptes Rendus Mathematique},
  publisher = {Elsevier},
  address   = {Paris},
  issn      = {1631-073X},
  doi       = {10.1016/j.crma.2017.07.017},
  pages     = {973 -- 976},
  year      = {2017},
  abstract  = {We give a new and very short proof of a theorem of Greiner asserting that a positive and contractive -semigroup on an -space is strongly convergent in case it has a strictly positive fixed point and contains an integral operator. Our proof is a streamlined version of a much more general approach to the asymptotic theory of positive semigroups developed recently by the authors. Under the assumptions of Greiner's theorem, this approach becomes particularly elegant and simple. We also give an outlook on several generalisations of this result.},
  language  = {en}
}
@article{Gerlach2018,
  author    = {Gerlach, Moritz Reinhardt},
  title     = {Convergence of dynamics and the Perron-Frobenius operator},
  series = {Israel Journal of Mathematics},
  volume    = {225},
  journal   = {Israel Journal of Mathematics},
  number    = {1},
  publisher = {Hebrew univ magnes press},
  address   = {Jerusalem},
  issn      = {0021-2172},
  doi       = {10.1007/s11856-018-1671-7},
  pages     = {451 -- 463},
  year      = {2018},
  abstract  = {We complete the picture how the asymptotic behavior of a dynamical system is reflected by properties of the associated Perron-Frobenius operator. Our main result states that strong convergence of the powers of the Perron-Frobenius operator is equivalent to setwise convergence of the underlying dynamic in the measure algebra. This situation is furthermore characterized by uniform mixing-like properties of the system.},
  language  = {en}
}
@article{GerlachGlueck2019,
  author    = {Gerlach, Moritz Reinhardt and Gl{\"u}ck, Jochen},
  title     = {Convergence of positive operator semigroups},
  series = {Transactions of the American Mathematical Society},
  volume    = {372},
  journal   = {Transactions of the American Mathematical Society},
  number    = {9},
  publisher = {American Mathematical Soc.},
  address   = {Providence},
  issn      = {0002-9947},
  doi       = {10.1090/tran/7836},
  pages     = {6603 -- 6627},
  year      = {2019},
  abstract  = {We present new conditions for semigroups of positive operators to converge strongly as time tends to infinity. Our proofs are based on a novel approach combining the well-known splitting theorem by Jacobs, de Leeuw, and Glicksberg with a purely algebraic result about positive group representations. Thus, we obtain convergence theorems not only for one-parameter semigroups but also for a much larger class of semigroup representations. Our results allow for a unified treatment of various theorems from the literature that, under technical assumptions, a bounded positive C-0-semigroup containing or dominating a kernel operator converges strongly as t ->infinity. We gain new insights into the structure theoretical background of those theorems and generalize them in several respects; especially we drop any kind of continuity or regularity assumption with respect to the time parameter.},
  language  = {en}
}
@article{EdekoGerlachKuehner2019,
  author    = {Edeko, Nikolai and Gerlach, Moritz Reinhardt and K{\"u}hner, Viktoria},
  title     = {Measure-preserving semiflows and one-parameter Koopman semigroups},
  series = {Semigroup forum},
  volume    = {98},
  journal   = {Semigroup forum},
  number    = {1},
  publisher = {Springer},
  address   = {New York},
  issn      = {0037-1912},
  doi       = {10.1007/s00233-018-9960-3},
  pages     = {48 -- 63},
  year      = {2019},
  abstract  = {For a finite measure space X, we characterize strongly continuous Markov lattice semigroups on Lp(X) by showing that their generator A acts as a derivation on the dense subspace D(A)L(X). We then use this to characterize Koopman semigroups on Lp(X) if X is a standard probability space. In addition, we show that every measurable and measure-preserving flow on a standard probability space is isomorphic to a continuous flow on a compact Borel probability space.},
  language  = {en}
}
@article{GerlachGlueck2018,
  author    = {Gerlach, Moritz Reinhardt and Gl{\"u}ck, Jochen},
  title     = {Lower bounds and the asymptotic behaviour of positive operator semigroups},
  series = {Ergodic theory and dynamical systems},
  volume    = {38},
  journal   = {Ergodic theory and dynamical systems},
  publisher = {Cambridge Univ. Press},
  address   = {New York},
  issn      = {0143-3857},
  doi       = {10.1017/etds.2017.9},
  pages     = {3012 -- 3041},
  year      = {2018},
  abstract  = {If (T-t) is a semigroup of Markov operators on an L-1-space that admits a nontrivial lower bound, then a well-known theorem of Lasota and Yorke asserts that the semigroup is strongly convergent as t -> infinity. In this article we generalize and improve this result in several respects. First, we give a new and very simple proof for the fact that the same conclusion also holds if the semigroup is merely assumed to be bounded instead of Markov. As a main result, we then prove a version of this theorem for semigroups which only admit certain individual lower bounds. Moreover, we generalize a theorem of Ding on semigroups of Frobenius-Perron operators. We also demonstrate how our results can be adapted to the setting of general Banach lattices and we give some counterexamples to show optimality of our results. Our methods combine some rather concrete estimates and approximation arguments with abstract functional analytical tools. One of these tools is a theorem which relates the convergence of a time-continuous operator semigroup to the convergence of embedded discrete semigroups.},
  language  = {en}
}
@article{GerlachGlueck2019,
  author    = {Gerlach, Moritz Reinhardt and Gl{\"u}ck, Jochen},
  title     = {Mean ergodicity vs weak almost periodicity},
  series = {Studia mathematica},
  volume    = {248},
  journal   = {Studia mathematica},
  number    = {1},
  publisher = {Polska Akademia Nauk, Instytut Matematyczny},
  address   = {Warszawa},
  issn      = {0039-3223},
  doi       = {10.4064/sm170918-20-3},
  pages     = {45 -- 56},
  year      = {2019},
  abstract  = {We provide explicit examples of positive and power-bounded operators on c(0) and l(infinity) which are mean ergodic but not weakly almost periodic. As a consequence we prove that a countably order complete Banach lattice on which every positive and power-bounded mean ergodic operator is weakly almost periodic is necessarily a KB-space. This answers several open questions from the literature. Finally, we prove that if T is a positive mean ergodic operator with zero fixed space on an arbitrary Banach lattice, then so is every power of T .},
  language  = {en}
}