@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{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} } @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{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{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{FalkenhagenKnoechelKloftetal.2023, author = {Falkenhagen, Undine and Kn{\"o}chel, Jane and Kloft, Charlotte and Huisinga, Wilhelm}, title = {Deriving mechanism-based pharmacodynamic models by reducing quantitative systems pharmacology models}, series = {CPT: Pharmacometrics \& Systems Pharmacology}, volume = {12}, journal = {CPT: Pharmacometrics \& Systems Pharmacology}, number = {4}, publisher = {Wiley}, address = {Hoboken}, issn = {2163-8306}, doi = {10.1002/psp4.12903}, pages = {432 -- 443}, year = {2023}, abstract = {Quantitative systems pharmacology (QSP) models integrate comprehensive qualitative and quantitative knowledge about pharmacologically relevant processes. We previously proposed a first approach to leverage the knowledge in QSP models to derive simpler, mechanism-based pharmacodynamic (PD) models. Their complexity, however, is typically still too large to be used in the population analysis of clinical data. Here, we extend the approach beyond state reduction to also include the simplification of reaction rates, elimination of reactions, and analytic solutions. We additionally ensure that the reduced model maintains a prespecified approximation quality not only for a reference individual but also for a diverse virtual population. We illustrate the extended approach for the warfarin effect on blood coagulation. Using the model-reduction approach, we derive a novel small-scale warfarin/international normalized ratio model and demonstrate its suitability for biomarker identification. Due to the systematic nature of the approach in comparison with empirical model building, the proposed model-reduction algorithm provides an improved rationale to build PD models also from QSP models in other applications.}, language = {en} }