TY  - JOUR
A1  - Kucharski, Maciej
A1  - Ergintav, Arzu
A1  - Ahmad, Wael Abdullah
A1  - Krstić, Miloš
A1  - Ng, Herman Jalli
A1  - Kissinger, Dietmar
T1  - A Scalable 79-GHz Radar Platform Based on Single-Channel Transceivers
JF  - IEEE Transactions on Microwave Theory and Techniques
N2  - 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).
KW  - Automotive
KW  - E-band
KW  - frequency-modulated continuous-wave (FMCW)
KW  - patch antenna
KW  - phase-locked loop (PLL)
KW  - power amplifier (PA)
KW  - radar
KW  - scalable
KW  - transceiver (TRX)
Y1  - 2019
U6  - https://doi.org/10.1109/TMTT.2019.2914104
SN  - 0018-9480
SN  - 1557-9670
VL  - 67
IS  - 9
SP  - 3882
EP  - 3896
PB  - Inst. of Electr. and Electronics Engineers
CY  - Piscataway
ER  - 
TY  - JOUR
A1  - Sharma, Shubham
A1  - Hainzl, Sebastian
A1  - Zöller, Gert
A1  - Holschneider, Matthias
T1  - Is Coulomb stress the best choice for aftershock forecasting?
JF  - Journal of geophysical research : Solid earth
N2  - 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.
Y1  - 2020
U6  - https://doi.org/10.1029/2020JB019553
SN  - 2169-9313
SN  - 2169-9356
VL  - 125
IS  - 9
PB  - American Geophysical Union
CY  - Washington
ER  - 
TY  - JOUR
A1  - Engbert, Ralf
A1  - Rabe, Maximilian Michael
A1  - Kliegl, Reinhold
A1  - Reich, Sebastian
T1  - Sequential data assimilation of the stochastic SEIR epidemic model for regional COVID-19 dynamics
JF  - Bulletin of mathematical biology : official journal of the Society for Mathematical Biology
N2  - 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.
KW  - Stochastic epidemic model
KW  - Sequential data assimilation
KW  - Ensemble Kalman
KW  - filter
KW  - COVID-19
Y1  - 2020
U6  - https://doi.org/10.1007/s11538-020-00834-8
SN  - 0092-8240
SN  - 1522-9602
VL  - 83
IS  - 1
PB  - Springer
CY  - New York
ER  - 
TY  - THES
A1  - Sareeto, Apatsara
T1  - Algebraic properties of a subsemigroup of the symmetric inverse semigroup
Y1  - 2024
ER  - 
TY  - JOUR
A1  - Gerlach, Moritz Reinhardt
A1  - Glück, Jochen
T1  - On a convergence theorem for semigroups of positive integral operators
JF  - Comptes Rendus Mathematique
N2  - 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.
Y1  - 2017
U6  - https://doi.org/10.1016/j.crma.2017.07.017
SN  - 1631-073X
SN  - 1778-3569
VL  - 355
SP  - 973
EP  - 976
PB  - Elsevier
CY  - Paris
ER  - 
TY  - JOUR
A1  - Gerlach, Moritz Reinhardt
T1  - Convergence of dynamics and the Perron-Frobenius operator
JF  - Israel Journal of Mathematics
N2  - 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.
Y1  - 2018
U6  - https://doi.org/10.1007/s11856-018-1671-7
SN  - 0021-2172
SN  - 1565-8511
VL  - 225
IS  - 1
SP  - 451
EP  - 463
PB  - Hebrew univ magnes press
CY  - Jerusalem
ER  - 
TY  - JOUR
A1  - Gerlach, Moritz Reinhardt
A1  - Glück, Jochen
T1  - Convergence of positive operator semigroups
JF  - Transactions of the American Mathematical Society
N2  - 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.
KW  - Positive semigroups
KW  - semigroup representations
KW  - asymptotic behavior
KW  - kernel operator
Y1  - 2019
U6  - https://doi.org/10.1090/tran/7836
SN  - 0002-9947
SN  - 1088-6850
VL  - 372
IS  - 9
SP  - 6603
EP  - 6627
PB  - American Mathematical Soc.
CY  - Providence
ER  - 
TY  - JOUR
A1  - Edeko, Nikolai
A1  - Gerlach, Moritz Reinhardt
A1  - Kühner, Viktoria
T1  - Measure-preserving semiflows and one-parameter Koopman semigroups
JF  - Semigroup forum
N2  - 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.
KW  - Measure-preserving semiflow
KW  - Koopman semigroup
KW  - Derivation
KW  - Topological model
Y1  - 2019
U6  - https://doi.org/10.1007/s00233-018-9960-3
SN  - 0037-1912
SN  - 1432-2137
VL  - 98
IS  - 1
SP  - 48
EP  - 63
PB  - Springer
CY  - New York
ER  - 
TY  - JOUR
A1  - Gerlach, Moritz Reinhardt
A1  - Glück, Jochen
T1  - Lower bounds and the asymptotic behaviour of positive operator semigroups
JF  - Ergodic theory and dynamical systems
N2  - 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.
Y1  - 2017
U6  - https://doi.org/10.1017/etds.2017.9
SN  - 0143-3857
SN  - 1469-4417
VL  - 38
SP  - 3012
EP  - 3041
PB  - Cambridge Univ. Press
CY  - New York
ER  - 
TY  - JOUR
A1  - Gerlach, Moritz Reinhardt
A1  - Glück, Jochen
T1  - Mean ergodicity vs weak almost periodicity
JF  - Studia mathematica
N2  - 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 .
KW  - positive operators
KW  - weakly almost periodic
KW  - order continuous norm
KW  - KB-space
KW  - mean ergodic
Y1  - 2019
U6  - https://doi.org/10.4064/sm170918-20-3
SN  - 0039-3223
SN  - 1730-6337
VL  - 248
IS  - 1
SP  - 45
EP  - 56
PB  - Polska Akademia Nauk, Instytut Matematyczny
CY  - Warszawa
ER  -