@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} } @phdthesis{Maier2021, author = {Maier, Corinna}, title = {Bayesian data assimilation and reinforcement learning for model-informed precision dosing in oncology}, doi = {10.25932/publishup-51587}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-515870}, school = {Universit{\"a}t Potsdam}, pages = {x, 138}, year = {2021}, abstract = {While patients are known to respond differently to drug therapies, current clinical practice often still follows a standardized dosage regimen for all patients. For drugs with a narrow range of both effective and safe concentrations, this approach may lead to a high incidence of adverse events or subtherapeutic dosing in the presence of high patient variability. Model-informedprecision dosing (MIPD) is a quantitative approach towards dose individualization based on mathematical modeling of dose-response relationships integrating therapeutic drug/biomarker monitoring (TDM) data. MIPD may considerably improve the efficacy and safety of many drug therapies. Current MIPD approaches, however, rely either on pre-calculated dosing tables or on simple point predictions of the therapy outcome. These approaches lack a quantification of uncertainties and the ability to account for effects that are delayed. In addition, the underlying models are not improved while applied to patient data. Therefore, current approaches are not well suited for informed clinical decision-making based on a differentiated understanding of the individually predicted therapy outcome. The objective of this thesis is to develop mathematical approaches for MIPD, which (i) provide efficient fully Bayesian forecasting of the individual therapy outcome including associated uncertainties, (ii) integrate Markov decision processes via reinforcement learning (RL) for a comprehensive decision framework for dose individualization, (iii) allow for continuous learning across patients and hospitals. Cytotoxic anticancer chemotherapy with its major dose-limiting toxicity, neutropenia, serves as a therapeutically relevant application example. For more comprehensive therapy forecasting, we apply Bayesian data assimilation (DA) approaches, integrating patient-specific TDM data into mathematical models of chemotherapy-induced neutropenia that build on prior population analyses. The value of uncertainty quantification is demonstrated as it allows reliable computation of the patient-specific probabilities of relevant clinical quantities, e.g., the neutropenia grade. In view of novel home monitoring devices that increase the amount of TDM data available, the data processing of sequential DA methods proves to be more efficient and facilitates handling of the variability between dosing events. By transferring concepts from DA and RL we develop novel approaches for MIPD. While DA-guided dosing integrates individualized uncertainties into dose selection, RL-guided dosing provides a framework to consider delayed effects of dose selections. The combined DA-RL approach takes into account both aspects simultaneously and thus represents a holistic approach towards MIPD. Additionally, we show that RL can be used to gain insights into important patient characteristics for dose selection. The novel dosing strategies substantially reduce the occurrence of both subtherapeutic and life-threatening neutropenia grades in a simulation study based on a recent clinical study (CEPAC-TDM trial) compared to currently used MIPD approaches. If MIPD is to be implemented in routine clinical practice, a certain model bias with respect to the underlying model is inevitable, as the models are typically based on data from comparably small clinical trials that reflect only to a limited extent the diversity in real-world patient populations. We propose a sequential hierarchical Bayesian inference framework that enables continuous cross-patient learning to learn the underlying model parameters of the target patient population. It is important to note that the approach only requires summary information of the individual patient data to update the model. This separation of the individual inference from population inference enables implementation across different centers of care. The proposed approaches substantially improve current MIPD approaches, taking into account new trends in health care and aspects of practical applicability. They enable progress towards more informed clinical decision-making, ultimately increasing patient benefits beyond the current practice.}, language = {en} } @article{MicheletBindelliniMelinetal.2023, author = {Michelet, Robin and Bindellini, Davide and Melin, Johanna and Neumann, Uta and Blankenstein, Oliver and Huisinga, Wilhelm and Johnson, Trevor N. and Whitaker, Martin J. and Ross, Richard and Kloft, Charlotte}, title = {Insights in the maturational processes influencing hydrocortisone pharmacokinetics in congenital adrenal hyperplasia patients using a middle-out approach}, series = {Frontiers in Pharmacology}, volume = {13}, journal = {Frontiers in Pharmacology}, publisher = {Frontiers Media}, address = {Lausanne}, issn = {1663-9812}, doi = {10.3389/fphar.2022.1090554}, pages = {14}, year = {2023}, abstract = {Introduction: Hydrocortisone is the standard of care in cortisol replacement therapy for congenital adrenal hyperplasia patients. Challenges in mimicking cortisol circadian rhythm and dosing individualization can be overcome by the support of mathematical modelling. Previously, a non-linear mixed-effects (NLME) model was developed based on clinical hydrocortisone pharmacokinetic (PK) pediatric and adult data. Additionally, a physiologically-based pharmacokinetic (PBPK) model was developed for adults and a pediatric model was obtained using maturation functions for relevant processes. In this work, a middle-out approach was applied. The aim was to investigate whether PBPK-derived maturation functions could provide a better description of hydrocortisone PK inter-individual variability when implemented in the NLME framework, with the goal of providing better individual predictions towards precision dosing at the patient level. Methods: Hydrocortisone PK data from 24 adrenal insufficiency pediatric patients and 30 adult healthy volunteers were used for NLME model development, while the PBPK model and maturation functions of clearance and cortisol binding globulin (CBG) were developed based on previous studies published in the literature. Results: Clearance (CL) estimates from both approaches were similar for children older than 1 year (CL/F increasing from around 150 L/h to 500 L/h), while CBG concentrations differed across the whole age range (CBG(NLME) stable around 0.5 mu M vs. steady increase from 0.35 to 0.8 mu M for CBG (PBPK)). PBPK-derived maturation functions were subsequently included in the NLME model. After inclusion of the maturation functions, none, a part of, or all parameters were re-estimated. However, the inclusion of CL and/or CBG maturation functions in the NLME model did not result in improved model performance for the CL maturation function (\& UDelta;OFV > -15.36) and the re-estimation of parameters using the CBG maturation function most often led to unstable models or individual CL prediction bias. Discussion: Three explanations for the observed discrepancies could be postulated, i) non-considered maturation of processes such as absorption or first-pass effect, ii) lack of patients between 1 and 12 months, iii) lack of correction of PBPK CL maturation functions derived from urinary concentration ratio data for the renal function relative to adults. These should be investigated in the future to determine how NLME and PBPK methods can work towards deriving insights into pediatric hydrocortisone PK.}, language = {en} } @article{KrippendorffOyarzunHuisinga2012, author = {Krippendorff, Ben-Fillippo and Oyarz{\´u}n, Diego A. and Huisinga, Wilhelm}, title = {Predicting the F(ab)-mediated effect of monoclonal antibodies in vivo by combining cell-level kinetic and pharmacokinetic modelling}, series = {Journal of pharmacokinetics and pharmacodynamics}, volume = {39}, journal = {Journal of pharmacokinetics and pharmacodynamics}, number = {2}, publisher = {Springer}, address = {New York}, issn = {1567-567X}, doi = {10.1007/s10928-012-9243-7}, pages = {125 -- 139}, year = {2012}, abstract = {Cell-level kinetic models for therapeutically relevant processes increasingly benefit the early stages of drug development. Later stages of the drug development processes, however, rely on pharmacokinetic compartment models while cell-level dynamics are typically neglected. We here present a systematic approach to integrate cell-level kinetic models and pharmacokinetic compartment models. Incorporating target dynamics into pharmacokinetic models is especially useful for the development of therapeutic antibodies because their effect and pharmacokinetics are inherently interdependent. The approach is illustrated by analysing the F(ab)-mediated inhibitory effect of therapeutic antibodies targeting the epidermal growth factor receptor. We build a multi-level model for anti-EGFR antibodies by combining a systems biology model with in vitro determined parameters and a pharmacokinetic model based on in vivo pharmacokinetic data. Using this model, we investigated in silico the impact of biochemical properties of anti-EGFR antibodies on their F(ab)-mediated inhibitory effect. The multi-level model suggests that the F(ab)-mediated inhibitory effect saturates with increasing drug-receptor affinity, thereby limiting the impact of increasing antibody affinity on improving the effect. This indicates that observed differences in the therapeutic effects of high affinity antibodies in the market and in clinical development may result mainly from Fc-mediated indirect mechanisms such as antibody-dependent cell cytotoxicity.}, language = {en} } @article{WeissHuisinga2011, author = {Weiss, Andrea Y. and Huisinga, Wilhelm}, title = {Error-controlled global sensitivity analysis of ordinary differential equations}, series = {Journal of computational physics}, volume = {230}, journal = {Journal of computational physics}, number = {17}, publisher = {Elsevier}, address = {San Diego}, issn = {0021-9991}, doi = {10.1016/j.jcp.2011.05.011}, pages = {6824 -- 6842}, year = {2011}, abstract = {We propose a novel strategy for global sensitivity analysis of ordinary differential equations. It is based on an error-controlled solution of the partial differential equation (PDE) that describes the evolution of the probability density function associated with the input uncertainty/variability. The density yields a more accurate estimate of the output uncertainty/variability, where not only some observables (such as mean and variance) but also structural properties (e.g., skewness, heavy tails, bi-modality) can be resolved up to a selected accuracy. For the adaptive solution of the PDE Cauchy problem we use the Rothe method with multiplicative error correction, which was originally developed for the solution of parabolic PDEs. We show that, unlike in parabolic problems, conservation properties necessitate a coupling of temporal and spatial accuracy to avoid accumulation of spatial approximation errors over time. We provide convergence conditions for the numerical scheme and suggest an implementation using approximate approximations for spatial discretization to efficiently resolve the coupling of temporal and spatial accuracy. The performance of the method is studied by means of low-dimensional case studies. The favorable properties of the spatial discretization technique suggest that this may be the starting point for an error-controlled sensitivity analysis in higher dimensions.}, language = {en} } @article{WeisseMiddletonHuisinga2010, author = {Weiße, Andrea Y. and Middleton, Richard H. and Huisinga, Wilhelm}, title = {Quantifying uncertainty, variability and likelihood for ordinary differential equation models}, issn = {1752-0509}, doi = {10.1186/1752-0509-4-144}, year = {2010}, abstract = {Background: In many applications, ordinary differential equation (ODE) models are subject to uncertainty or variability in initial conditions and parameters. Both, uncertainty and variability can be quantified in terms of a probability density function on the state and parameter space. Results: The partial differential equation that describes the evolution of this probability density function has a form that is particularly amenable to application of the well- known method of characteristics. The value of the density at some point in time is directly accessible by the solution of the original ODE extended by a single extra dimension (for the value of the density). This leads to simple methods for studying uncertainty, variability and likelihood, with significant advantages over more traditional Monte Carlo and related approaches especially when studying regions with low probability. Conclusions: While such approaches based on the method of characteristics are common practice in other disciplines, their advantages for the study of biological systems have so far remained unrecognized. Several examples illustrate performance and accuracy of the approach and its limitations.}, language = {en} } @article{PilariPreusseHuisinga2011, author = {Pilari, Sabine and Preusse, Cornelia and Huisinga, Wilhelm}, title = {Gestational influences on the pharmacokinetics of gestagenic drugs a combined in silico, in vitro and in vivo analysis}, series = {European journal of pharmaceutical sciences : official journal of the European Federation for Pharmaceutical Sciences, EUFEPS}, volume = {42}, journal = {European journal of pharmaceutical sciences : official journal of the European Federation for Pharmaceutical Sciences, EUFEPS}, number = {4}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0928-0987}, doi = {10.1016/j.ejps.2010.12.003}, pages = {318 -- 331}, year = {2011}, abstract = {During preclinical development of a gestagenic drug, a significant increase of the total plasma concentration was observed after multiple dosing in pregnant rabbits, but not in (non-pregnant) rats or monkeys. We used a PBPK modeling approach in combination with in vitro and in vivo data to address the question to what extent the pharmacologically active free drug concentration is affected by pregnancy induced processes. In human, a significant increase in sex hormone binding globulin (SHBG), and an induction of hepatic CYP3A4 as well as plasma esterases is observed during pregnancy. We find that the observed increase in total plasma trough levels in rabbits can be explained as a combined result of (i) drug accumulation due to multiple dosing, (ii) increase of the binding protein SHBG, and (iii) clearance induction. For human, we predict that free drug concentrations in plasma would not increase during pregnancy above the steady state trough level for non-pregnant women.}, language = {en} } @article{vonKleistMenzStockeretal.2011, author = {von Kleist, Max and Menz, Stephan and Stocker, Hartmut and Arasteh, Keikawus and Schuette, Christof and Huisinga, Wilhelm}, title = {HIV quasispecies dynamics during pro-active treatment switching impact on multi-drug resistance and resistance archiving in latent reservoirs}, series = {PLoS one}, volume = {6}, journal = {PLoS one}, number = {3}, publisher = {PLoS}, address = {San Fransisco}, issn = {1932-6203}, doi = {10.1371/journal.pone.0018204}, pages = {12}, year = {2011}, abstract = {The human immunodeficiency virus (HIV) can be suppressed by highly active anti-retroviral therapy (HAART) in the majority of infected patients. Nevertheless, treatment interruptions inevitably result in viral rebounds from persistent, latently infected cells, necessitating lifelong treatment. Virological failure due to resistance development is a frequent event and the major threat to treatment success. Currently, it is recommended to change treatment after the confirmation of virological failure. However, at the moment virological failure is detected, drug resistant mutants already replicate in great numbers. They infect numerous cells, many of which will turn into latently infected cells. This pool of cells represents an archive of resistance, which has the potential of limiting future treatment options. The objective of this study was to design a treatment strategy for treatment-naive patients that decreases the likelihood of early treatment failure and preserves future treatment options. We propose to apply a single, pro-active treatment switch, following a period of treatment with an induction regimen. The main goal of the induction regimen is to decrease the abundance of randomly generated mutants that confer resistance to the maintenance regimen, thereby increasing subsequent treatment success. Treatment is switched before the overgrowth and archiving of mutant strains that carry resistance against the induction regimen and would limit its future re-use. In silico modelling shows that an optimal trade-off is achieved by switching treatment at \& 80 days after the initiation of antiviral therapy. Evaluation of the proposed treatment strategy demonstrated significant improvements in terms of resistance archiving and virological response, as compared to conventional HAART. While continuous pro-active treatment alternation improved the clinical outcome in a randomized trial, our results indicate that a similar improvement might also be reached after a single pro-active treatment switch. The clinical validity of this finding, however, remains to be shown by a corresponding trial.}, language = {en} } @inproceedings{SteenholdtEdlundAinsworthetal.2015, author = {Steenholdt, Casper and Edlund, Helena and Ainsworth, Mark A. and Brynskov, Jorn and Thomsen, Ole Ostergaard and Huisinga, Wilhelm and Kloft, Charlotte}, title = {Relationship between measures of infliximab exposure and clinical outcome of infliximab intensification at therapeutic failure in Crohn's disease}, series = {JOURNAL OF CROHNS \& COLITIS}, volume = {9}, booktitle = {JOURNAL OF CROHNS \& COLITIS}, publisher = {Oxford Univ. Press}, address = {Oxford}, issn = {1873-9946}, pages = {S330 -- S330}, year = {2015}, language = {en} } @article{MenzLatorreSchuetteetal.2012, author = {Menz, Stephan and Latorre, Juan C. and Sch{\"u}tte, Christof and Huisinga, Wilhelm}, title = {Hybrid stochastic-deterministic solution of the chemical master equation}, series = {Multiscale modeling \& simulation : a SIAM interdisciplinary journal}, volume = {10}, journal = {Multiscale modeling \& simulation : a SIAM interdisciplinary journal}, number = {4}, publisher = {Society for Industrial and Applied Mathematics}, address = {Philadelphia}, issn = {1540-3459}, doi = {10.1137/110825716}, pages = {1232 -- 1262}, year = {2012}, abstract = {The chemical master equation (CME) is the fundamental evolution equation of the stochastic description of biochemical reaction kinetics. In most applications it is impossible to solve the CME directly due to its high dimensionality. Instead, indirect approaches based on realizations of the underlying Markov jump process are used, such as the stochastic simulation algorithm (SSA). In the SSA, however, every reaction event has to be resolved explicitly such that it becomes numerically inefficient when the system's dynamics include fast reaction processes or species with high population levels. In many hybrid approaches, such fast reactions are approximated as continuous processes or replaced by quasi-stationary distributions in either a stochastic or a deterministic context. Current hybrid approaches, however, almost exclusively rely on the computation of ensembles of stochastic realizations. We present a novel hybrid stochastic-deterministic approach to solve the CME directly. Our starting point is a partitioning of the molecular species into discrete and continuous species that induces a partitioning of the reactions into discrete-stochastic and continuous-deterministic processes. The approach is based on a WKB (Wentzel-Kramers-Brillouin) ansatz for the conditional probability distribution function (PDF) of the continuous species (given a discrete state) in combination with Laplace's method of integral approximation. The resulting hybrid stochastic-deterministic evolution equations comprise a CME with averaged propensities for the PDF of the discrete species that is coupled to an evolution equation of the related expected levels of the continuous species for each discrete state. In contrast to indirect hybrid methods, the impact of the evolution of discrete species on the dynamics of the continuous species has to be taken into account explicitly. The proposed approach is efficient whenever the number of discrete molecular species is small. We illustrate the performance of the new hybrid stochastic-deterministic approach in an application to model systems of biological interest.}, language = {en} } @inproceedings{AnderssonKeuneckeEseretal.2014, author = {Andersson, H. and Keunecke, A. and Eser, A. and Huisinga, Wilhelm and Reinisch, W. and Kloft, Charlotte}, title = {Pharmacokinetic considerations for optimising dosing regimens of a potsdam univ infliximab in patients with Crohn's disease}, series = {JOURNAL OF CROHNS \& COLITIS}, volume = {8}, booktitle = {JOURNAL OF CROHNS \& COLITIS}, publisher = {Oxford Univ. Press}, address = {Oxford}, issn = {1873-9946}, doi = {10.1016/S1873-9946(14)60086-6}, pages = {S44 -- S44}, year = {2014}, language = {en} } @article{KaminskiSchlagenhaufRappetal.2018, author = {Kaminski, Jakob A. and Schlagenhauf, Florian and Rapp, Michael A. and Awasthi, Swapnil and Ruggeri, Barbara and Deserno, Lorenz and Banaschewski, Tobias and Bokde, Arun L. W. and Bromberg, Uli and B{\"u}chel, Christian and Quinlan, Erin Burke and Desrivieres, Sylvane and Flor, Herta and Frouin, Vincent and Garavan, Hugh and Gowland, Penny and Ittermann, Bernd and Martinot, Jean-Luc and Martinot, Marie-Laure Paillere and Nees, Frauke and Orfanos, Dimitri Papadopoulos and Paus, Tomas and Poustka, Luise and Smolka, Michael N. and Fr{\"o}hner, Juliane H. and Walter, Henrik and Whelan, Robert and Ripke, Stephan and Schumann, Gunter and Heinz, Andreas}, title = {Epigenetic variance in dopamine D2 receptor}, series = {Translational Psychiatry}, volume = {8}, journal = {Translational Psychiatry}, publisher = {Nature Publ. Group}, address = {New York}, organization = {IMAGEN Consortium}, issn = {2158-3188}, doi = {10.1038/s41398-018-0222-7}, pages = {11}, year = {2018}, abstract = {Genetic and environmental factors both contribute to cognitive test performance. A substantial increase in average intelligence test results in the second half of the previous century within one generation is unlikely to be explained by genetic changes. One possible explanation for the strong malleability of cognitive performance measure is that environmental factors modify gene expression via epigenetic mechanisms. Epigenetic factors may help to understand the recent observations of an association between dopamine-dependent encoding of reward prediction errors and cognitive capacity, which was modulated by adverse life events. The possible manifestation of malleable biomarkers contributing to variance in cognitive test performance, and thus possibly contributing to the "missing heritability" between estimates from twin studies and variance explained by genetic markers, is still unclear. Here we show in 1475 healthy adolescents from the IMaging and GENetics (IMAGEN) sample that general IQ (gIQ) is associated with (1) polygenic scores for intelligence, (2) epigenetic modification of DRD2 gene, (3) gray matter density in striatum, and (4) functional striatal activation elicited by temporarily surprising reward-predicting cues. Comparing the relative importance for the prediction of gIQ in an overlapping subsample, our results demonstrate neurobiological correlates of the malleability of gIQ and point to equal importance of genetic variance, epigenetic modification of DRD2 receptor gene, as well as functional striatal activation, known to influence dopamine neurotransmission. Peripheral epigenetic markers are in need of confirmation in the central nervous system and should be tested in longitudinal settings specifically assessing individual and environmental factors that modify epigenetic structure.}, language = {en} } @article{GerlachGlueckKunze2023, author = {Gerlach, Moritz and Gl{\"u}ck, Jochen and Kunze, Markus}, title = {Stability of transition semigroups and applications to parabolic equations}, series = {Transactions of the American Mathematical Society}, volume = {376}, journal = {Transactions of the American Mathematical Society}, number = {1}, publisher = {American Mathematical Soc.}, address = {Providence}, issn = {0002-9947}, doi = {10.1090/tran/8620}, pages = {153 -- 180}, year = {2023}, abstract = {This paper deals with the long-term behavior of positive operator semigroups on spaces of bounded functions and of signed measures, which have applications to parabolic equations with unbounded coefficients and to stochas-tic analysis. The main results are a Tauberian type theorem characterizing the convergence to equilibrium of strongly Feller semigroups and a generalization of a classical convergence theorem of Doob. None of these results requires any kind of time regularity of the semigroup.}, language = {en} } @article{DimitrovaKoppitz2022, author = {Dimitrova, Ilinka and Koppitz, J{\"o}rg}, title = {On relative ranks of the semigroup of orientation-preserving transformations on infinite chain with restricted range}, series = {Communications in algebra}, volume = {50}, journal = {Communications in algebra}, number = {5}, publisher = {Taylor \& Francis Group}, address = {Philadelphia}, issn = {0092-7872}, doi = {10.1080/00927872.2021.2000998}, pages = {2157 -- 2168}, year = {2022}, abstract = {Let X be an infinite linearly ordered set and let Y be a nonempty subset of X. We calculate the relative rank of the semigroup OP(X,Y) of all orientation-preserving transformations on X with restricted range Y modulo the semigroup O(X,Y) of all order-preserving transformations on X with restricted range Y. For Y = X, we characterize the relative generating sets of minimal size.}, language = {en} } @article{DimitrovaKoppitz2020, author = {Dimitrova, Ilinka and Koppitz, J{\"o}rg}, title = {On relative ranks of the semigroup of orientation-preserving transformations on infinite chains}, series = {Asian-European journal of mathematics}, volume = {14}, journal = {Asian-European journal of mathematics}, number = {08}, publisher = {World Scientific}, address = {Singapore}, issn = {1793-5571}, doi = {10.1142/S1793557121501461}, pages = {15}, year = {2020}, abstract = {In this paper, we determine the relative rank of the semigroup OP(X) of all orientation-preserving transformations on infinite chains modulo the semigroup O(X) of all order-preserving transformations.}, language = {en} } @article{SharmaHainzlZoeller2023, author = {Sharma, Shubham and Hainzl, Sebastian and Z{\"o}ller, Gert}, title = {Seismicity parameters dependence on main shock-induced co-seismic stress}, series = {Geophysical journal international}, volume = {235}, journal = {Geophysical journal international}, number = {1}, publisher = {Oxford Univ. Press}, address = {Oxford}, issn = {0956-540X}, doi = {10.1093/gji/ggad201}, pages = {509 -- 517}, year = {2023}, abstract = {The Gutenberg-Richter (GR) and the Omori-Utsu (OU) law describe the earthquakes' energy release and temporal clustering and are thus of great importance for seismic hazard assessment. Motivated by experimental results, which indicate stress-dependent parameters, we consider a combined global data set of 127 main shock-aftershock sequences and perform a systematic study of the relationship between main shock-induced stress changes and associated seismicity patterns. For this purpose, we calculate space-dependent Coulomb Stress (\& UDelta;CFS) and alternative receiver-independent stress metrics in the surrounding of the main shocks. Our results indicate a clear positive correlation between the GR b-value and the induced stress, contrasting expectations from laboratory experiments and suggesting a crucial role of structural heterogeneity and strength variations. Furthermore, we demonstrate that the aftershock productivity increases nonlinearly with stress, while the OU parameters c and p systematically decrease for increasing stress changes. Our partly unexpected findings can have an important impact on future estimations of the aftershock hazard.}, 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} } @article{LilienkampvonSpechtWeatherilletal.2022, author = {Lilienkamp, Henning and von Specht, Sebastian and Weatherill, Graeme and Caire, Giuseppe and Cotton, Fabrice}, title = {Ground-Motion modeling as an image processing task}, series = {Bulletin of the Seismological Society of America}, volume = {112}, journal = {Bulletin of the Seismological Society of America}, number = {3}, publisher = {Seismological Society of America}, address = {Albany}, issn = {0037-1106}, doi = {10.1785/0120220008}, pages = {1565 -- 1582}, year = {2022}, abstract = {We construct and examine the prototype of a deep learning-based ground-motion model (GMM) that is both fully data driven and nonergodic. We formulate ground-motion modeling as an image processing task, in which a specific type of neural network, the U-Net, relates continuous, horizontal maps of earthquake predictive parameters to sparse observations of a ground-motion intensity measure (IM). The processing of map-shaped data allows the natural incorporation of absolute earthquake source and observation site coordinates, and is, therefore, well suited to include site-, source-, and path-specific amplification effects in a nonergodic GMM. Data-driven interpolation of the IM between observation points is an inherent feature of the U-Net and requires no a priori assumptions. We evaluate our model using both a synthetic dataset and a subset of observations from the KiK-net strong motion network in the Kanto basin in Japan. We find that the U-Net model is capable of learning the magnitude???distance scaling, as well as site-, source-, and path-specific amplification effects from a strong motion dataset. The interpolation scheme is evaluated using a fivefold cross validation and is found to provide on average unbiased predictions. The magnitude???distance scaling as well as the site amplification of response spectral acceleration at a period of 1 s obtained for the Kanto basin are comparable to previous regional studies.}, language = {en} } @article{JulienMatthiasSaynischWagneretal.2022, author = {Julien, B{\"a}renzung and Matthias, Holschneider and Saynisch-Wagner, Jan and Thomas, Maik}, title = {Kalmag: a high spatio-temporal model of the geomagnetic field}, series = {Earth, planets and space}, volume = {74}, journal = {Earth, planets and space}, number = {1}, publisher = {Springer}, address = {New York}, issn = {1880-5981}, doi = {10.1186/s40623-022-01692-5}, pages = {22}, year = {2022}, abstract = {We present the extension of the Kalmag model, proposed as a candidate for IGRF-13, to the twentieth century. The dataset serving its derivation has been complemented by new measurements coming from satellites, ground-based observatories and land, marine and airborne surveys. As its predecessor, this version is derived from a combination of a Kalman filter and a smoothing algorithm, providing mean models and associated uncertainties. These quantities permit a precise estimation of locations where mean solutions can be considered as reliable or not. The temporal resolution of the core field and the secular variation was set to 0.1 year over the 122 years the model is spanning. Nevertheless, it can be shown through ensembles a posteriori sampled, that this resolution can be effectively achieved only by a limited amount of spatial scales and during certain time periods. Unsurprisingly, highest accuracy in both space and time of the core field and the secular variation is achieved during the CHAMP and Swarm era. In this version of Kalmag, a particular effort was made for resolving the small-scale lithospheric field. Under specific statistical assumptions, the latter was modeled up to spherical harmonic degree and order 1000, and signal from both satellite and survey measurements contributed to its development. External and induced fields were jointly estimated with the rest of the model. We show that their large scales could be accurately extracted from direct measurements whenever the latter exhibit a sufficiently high temporal coverage. Temporally resolving these fields down to 3 hours during the CHAMP and Swarm missions, gave us access to the link between induced and magnetospheric fields. In particular, the period dependence of the driving signal on the induced one could be directly observed. The model is available through various physical and statistical quantities on a dedicated website at https://ionocovar.agnld.uni-potsdam.de/Kalmag/.}, language = {en} } @misc{Reimann2024, type = {Master Thesis}, author = {Reimann, Hans}, title = {Towards robust inference for Bayesian filtering of linear Gaussian dynamical systems subject to additive change}, doi = {10.25932/publishup-64946}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-649469}, school = {Universit{\"a}t Potsdam}, pages = {ix, 156}, year = {2024}, abstract = {State space models enjoy wide popularity in mathematical and statistical modelling across disciplines and research fields. Frequent solutions to problems of estimation and forecasting of a latent signal such as the celebrated Kalman filter hereby rely on a set of strong assumptions such as linearity of system dynamics and Gaussianity of noise terms. We investigate fallacy in mis-specification of the noise terms, that is signal noise and observation noise, regarding heavy tailedness in that the true dynamic frequently produces observation outliers or abrupt jumps of the signal state due to realizations of these heavy tails not considered by the model. We propose a formalisation of observation noise mis-specification in terms of Huber's ε-contamination as well as a computationally cheap solution via generalised Bayesian posteriors with a diffusion Stein divergence loss resulting in the diffusion score matching Kalman filter - a modified algorithm akin in complexity to the regular Kalman filter. For this new filter interpretations of novel terms, stability and an ensemble variant are discussed. Regarding signal noise mis-specification, we propose a formalisation in the frame work of change point detection and join ideas from the popular CUSUM algo- rithm with ideas from Bayesian online change point detection to combine frequent reliability constraints and online inference resulting in a Gaussian mixture model variant of multiple Kalman filters. We hereby exploit open-end sequential probability ratio tests on the evidence of Kalman filters on observation sub-sequences for aggregated inference under notions of plausibility. Both proposed methods are combined to investigate the double mis-specification problem and discussed regarding their capabilities in reliable and well-tuned uncertainty quantification. Each section provides an introduction to required terminology and tools as well as simulation experiments on the popular target tracking task and the non-linear, chaotic Lorenz-63 system to showcase practical performance of theoretical considerations.}, language = {en} } @article{HanischStrohmaierWaters2022, author = {Hanisch, Florian and Strohmaier, Alexander and Waters, Alden}, title = {A relative trace formula for obstacle scattering}, series = {Duke mathematical journal}, volume = {171}, journal = {Duke mathematical journal}, number = {11}, publisher = {Duke Univ. Press}, address = {Durham, NC}, issn = {0012-7094}, doi = {10.1215/00127094-2022-0053}, pages = {2233 -- 2274}, year = {2022}, abstract = {We consider the case of scattering by several obstacles in Rd for d ≥ 2. In this setting, the absolutely continuous part of the Laplace operator Δ with Dirichlet boundary conditions and the free Laplace operator Δ0 are unitarily equivalent. For suitable functions that decay sufficiently fast, we have that the difference g(Δ) - g(Δ0) is a trace-class operator and its trace is described by the Krein spectral shift function. In this article, we study the contribution to the trace (and hence the Krein spectral shift function) that arises from assembling several obstacles relative to a setting where the obstacles are completely separated. In the case of two obstacles, we consider the Laplace operators Δ1 and Δ2 obtained by imposing Dirichlet boundary conditions only on one of the objects. Our main result in this case states that then g(Δ) - g(Δ1) - g(Δ2) C g(Δ0) is a trace-class operator for a much larger class of functions (including functions of polynomial growth) and that this trace may still be computed by a modification of the Birman-Krein formula. In case g(x) D x 2 , 1 the relative trace has a physical meaning as the vacuum energy of the massless scalar field and is expressible as an integral involving boundary layer operators. Such integrals have been derived in the physics literature using nonrigorous path integral derivations and our formula provides both a rigorous justification as well as a generalization.}, language = {en} } @article{MaoutsaOpper2022, author = {Maoutsa, Dimitra Despoina and Opper, Manfred}, title = {Deterministic particle flows for constraining stochastic nonlinear systems}, series = {Physical Review Research / American Physical Society}, volume = {4}, journal = {Physical Review Research / American Physical Society}, number = {4}, publisher = {American Physical Society}, address = {College Park}, issn = {2643-1564}, doi = {10.1103/PhysRevResearch.4.043035}, pages = {17}, year = {2022}, abstract = {Devising optimal interventions for constraining stochastic systems is a challenging endeavor that has to confront the interplay between randomness and dynamical nonlinearity. Existing intervention methods that employ stochastic path sampling scale poorly with increasing system dimension and are slow to converge. Here we propose a generally applicable and practically feasible methodology that computes the optimal interventions in a noniterative scheme. We formulate the optimal dynamical adjustments in terms of deterministically sampled probability flows approximated by an interacting particle system. Applied to several biologically inspired models, we demonstrate that our method provides the necessary optimal controls in settings with terminal, transient, or generalized collective state constraints and arbitrary system dynamics.}, language = {en} } @article{FischerKeller2021, author = {Fischer, Florian and Keller, Matthias}, title = {Riesz decompositions for Schr{\"o}dinger operators on graphs}, series = {Journal of mathematical analysis and applications}, volume = {495}, journal = {Journal of mathematical analysis and applications}, number = {1}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0022-247X}, doi = {10.1016/j.jmaa.2020.124674}, pages = {22}, year = {2021}, abstract = {We study superharmonic functions for Schrodinger operators on general weighted graphs. Specifically, we prove two decompositions which both go under the name Riesz decomposition in the literature. The first one decomposes a superharmonic function into a harmonic and a potential part. The second one decomposes a superharmonic function into a sum of superharmonic functions with certain upper bounds given by prescribed superharmonic functions. As application we show a Brelot type theorem.}, language = {en} } @phdthesis{Fischer2024, author = {Fischer, Florian}, title = {Hardy inequalities on graphs}, doi = {10.25932/publishup-64773}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-647730}, school = {Universit{\"a}t Potsdam}, pages = {vi, 160}, year = {2024}, abstract = {Die Dissertation befasst sich mit einer zentralen Ungleichung der nicht-linearen Potentialtheorie, der Hardy-Ungleichung. Sie besagt, dass das nicht-lineare Energiefunktional von unten durch eine p-te Potenz einer gewichteten p-Norm abgesch{\"a}tzt werden kann, p>1. Das Energiefunktional besteht dabei aus einem Divergenz- und einem beliebigen Potentialteil. Als zugrundeliegender Raum wurden hier lokal summierbare unendliche Graphen gew{\"a}hlt. Bisherige Ver{\"o}ffentlichungen zu Hardy-Ungleichungen auf Graphen haben vor allem den Spezialfall p=2 betrachtet, oder lokal endliche Graphen ohne Potentialteil. Zwei grundlegende Fragestellungen ergeben sich nun ganz nat{\"u}rlich: F{\"u}r welche Graphen gibt {\"u}berhaupt es eine Hardy-Ungleichung? Und, wenn es sie gibt, gibt es einen Weg um ein optimales Gewicht zu erhalten? Antworten auf diese Fragen werden in Theorem 10.1 und Theorem 12.1 gegeben. Theorem 10.1 gibt eine Reihe an Charakterisierungen an; unter anderem gibt es eine Hardy-Ungleichung auf einem Graphen genau dann, wenn es eine Greensche Funktion gibt. Theorem 12.1 gibt eine explizite Formel an, um optimale Hardy-Gewichte f{\"u}r lokal endliche Graphen unter einigen technischen Zusatzannahmen zu berechnen. In Beispielen wird gezeigt, dass Greensche Funktionen gute Kandidaten sind um in die Formel eingesetzt zu werden. Um diese beiden Theoreme beweisen zu k{\"o}nnen, m{\"u}ssen eine Vielzahl an Techniken erarbeitet werden, welche in den ersten Kapiteln behandelt werden. Dabei sind eine Verallgemeinerung der Grundzustandstransformation (Theorem 4.1), ein Agmon-Allegretto-Piepenbrink-artiges Resultat (Theorem 6.1) und das Vergleichsprinzip (Proposition 7.3) besonders hervorzuheben, da diese Resultate sehr h{\"a}ufig angewendet werden und somit das Fundament der Dissertation bilden. Es wird zudem darauf Wert gelegt die Theorie durch Beispiele zu veranschaulichen. Hierbei wird der Fokus auf die nat{\"u}rlichen Zahlen, Euklidische Gitter, B{\"a}ume und Sterne gelegt. Als Abschluss werden noch eine nicht-lineare Version der Heisenbergschen Unsch{\"a}rferelation und eine Rellich-Ungleichung aus der Hardy-Ungleichung geschlussfolgert.}, language = {en} }