@article{BoeckmannBrueckner2001, author = {B{\"o}ckmann, Christine and Br{\"u}ckner, Axel}, title = {100 years of the Runge-Kutta method : a brief editing for schools}, issn = {0268-3679}, year = {2001}, abstract = {This paper reports on the historical development of the Runge-Kutta methods beginning with the simple Euler method up to an embedded 13-stage method. Moreover, the design and the use of those methods under error order, stability and computation time conditions is edited for students of numerical analysis at undergraduate level. The second part presents applications in natural sciences, compares different methods and illustrates some of the difficulties of numerical solutions.}, language = {en} } @article{DzhunushalievSchmidt1999, author = {Dzhunushaliev, Vladimir and Schmidt, Hans-J{\"u}rgen}, title = {2+2-decomposable solutions of weyl gravity}, year = {1999}, language = {en} } @article{GonzalesDiazKasperRainer1998, author = {Gonz{\´a}les-Diaz, P. F. and Kasper, Uwe and Rainer, Martin}, title = {2-Dimensional dilatonic gravity from multidimensional Einstein gravity}, year = {1998}, language = {en} } @book{GonzalesDiazKasperRainer1997, author = {Gonz{\´a}les-Diaz, P. F. and Kasper, Uwe and Rainer, Martin}, title = {2-Dimensional dilatonic gravity from multidimensional Einstein gravity}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, volume = {1997, 22}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, publisher = {Univ.}, address = {Potsdam}, pages = {14 Bl.}, year = {1997}, language = {en} } @article{Schmidt1998, author = {Schmidt, Hans-J{\"u}rgen}, title = {2-dimensional representations of 4-dimensional gravitational waves}, year = {1998}, language = {en} } @article{HoehnkeJohnson1995, author = {Hoehnke, Hans-J{\"u}rgen and Johnson, K. W.}, title = {3-characters are sufficient for the group determinant}, year = {1995}, language = {en} } @article{DzhunushalievSchmidt1999, author = {Dzhunushaliev, Vladimir and Schmidt, Hans-J{\"u}rgen}, title = {4D wormhole with signature change in the presence of extra dimensions}, series = {General relativity and quantum cosmology : preprints gr-qc}, volume = {9908076}, journal = {General relativity and quantum cosmology : preprints gr-qc}, year = {1999}, language = {en} } @article{MariucciRaySzabo2020, author = {Mariucci, Ester and Ray, Kolyan and Szabo, Botond}, title = {A Bayesian nonparametric approach to log-concave density estimation}, series = {Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability}, volume = {26}, journal = {Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability}, number = {2}, publisher = {International Statistical Institute}, address = {The Hague}, issn = {1350-7265}, doi = {10.3150/19-BEJ1139}, pages = {1070 -- 1097}, year = {2020}, abstract = {The estimation of a log-concave density on R is a canonical problem in the area of shape-constrained nonparametric inference. We present a Bayesian nonparametric approach to this problem based on an exponentiated Dirichlet process mixture prior and show that the posterior distribution converges to the log-concave truth at the (near-) minimax rate in Hellinger distance. Our proof proceeds by establishing a general contraction result based on the log-concave maximum likelihood estimator that prevents the need for further metric entropy calculations. We further present computationally more feasible approximations and both an empirical and hierarchical Bayes approach. All priors are illustrated numerically via simulations.}, language = {en} } @article{Hoehnke1996, author = {Hoehnke, Hans-J{\"u}rgen}, title = {A Birkhoff theorem for partial algebras via completion}, year = {1996}, language = {en} } @book{AizenbergTarchanov1999, author = {Aizenberg, Lev A. and Tarchanov, Nikolaj N.}, title = {A Bohr phenomenon for elliptic equations}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {24 S.}, year = {1999}, language = {en} } @book{Witt2002, author = {Witt, Ingo}, title = {A calculus for a class of finitely degenerate pseudodifferential operators}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {27 S.}, year = {2002}, language = {en} } @book{RabinovichSchulzeTarchanov1997, author = {Rabinovich, Vladimir and Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.}, title = {A calculus of boundary value problems in domains with Non-Lipschitz singular points}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, volume = {1997, 09}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, publisher = {Univ.}, address = {Potsdam}, pages = {54 S.}, year = {1997}, language = {en} } @article{Ly2020, author = {Ly, Ibrahim}, title = {A Cauchy problem for the Cauchy-Riemann operator}, series = {Afrika Matematika}, volume = {32}, journal = {Afrika Matematika}, number = {1-2}, publisher = {Springer}, address = {Heidelberg}, issn = {1012-9405}, doi = {10.1007/s13370-020-00810-4}, pages = {69 -- 76}, year = {2020}, abstract = {We study the Cauchy problem for a nonlinear elliptic equation with data on a piece S of the boundary surface partial derivative X. By the Cauchy problem is meant any boundary value problem for an unknown function u in a domain X with the property that the data on S, if combined with the differential equations in X, allows one to determine all derivatives of u on S by means of functional equations. In the case of real analytic data of the Cauchy problem, the existence of a local solution near S is guaranteed by the Cauchy-Kovalevskaya theorem. We discuss a variational setting of the Cauchy problem which always possesses a generalized solution.}, language = {en} } @article{DeneckeWismath2004, author = {Denecke, Klaus-Dieter and Wismath, Shelly}, title = {A characterization of k-normal varieties}, issn = {0002-5240}, year = {2004}, abstract = {Let v be a valuation of terms of type tau, assigning to each term t of type tau a value v(t) greater than or equal to 0. Let k greater than or equal to 1 be a natural number. An identity s approximate to t of type tau is called k- normal if either s = t or both s and t have value greater than or equal to k, and otherwise is called non-k-normal. A variety V of type tau is said to be k-normal if all its identities are k-normal, and non-k-normal otherwise. In the latter case, there is a unique smallest k-normal variety N-k(A) (V) to contain V , called the k-normalization of V. Inthe case k = 1, for the usual depth valuation of terms, these notions coincide with the well-known concepts of normal identity, normal variety, and normalization of a variety. I. Chajda has characterized the normalization of a variety by means of choice algebras. In this paper we generalize his results to a characterization of the k-normalization of a variety, using k-choice algebras. We also introduce the concept of a k-inflation algebra, and for the case that v is the usual depth valuation of terms, we prove that a variety V is k-normal iff it is closed under the formation of k- inflations, and that the k-normalization of V consists precisely of all homomorphic images of k-inflations of algebras in V}, language = {en} } @article{DeneckeKoppitz1999, author = {Denecke, Klaus-Dieter and Koppitz, J{\"o}rg}, title = {A characterization of M-solid varieties of semigroups}, year = {1999}, language = {en} } @unpublished{FedchenkoTarkhanov2013, author = {Fedchenko, Dmitry and Tarkhanov, Nikolai Nikolaevich}, title = {A Class of Toeplitz Operators in Several Variables}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-68932}, year = {2013}, abstract = {We introduce the concept of Toeplitz operator associated with the Laplace-Beltrami operator on a compact Riemannian manifold with boundary. We characterise those Toeplitz operators which are Fredholm, thus initiating the index theory.}, language = {en} } @article{FedchenkoTarkhanov2015, author = {Fedchenko, Dmitry and Tarkhanov, Nikolai Nikolaevich}, title = {A Class of Toeplitz Operators in Several Variables}, series = {Advances in applied Clifford algebras}, volume = {25}, journal = {Advances in applied Clifford algebras}, number = {4}, publisher = {Springer}, address = {Basel}, issn = {0188-7009}, doi = {10.1007/s00006-015-0546-9}, pages = {811 -- 828}, year = {2015}, abstract = {We introduce the concept of Toeplitz operator associated with the Laplace-Beltrami operator on a compact Riemannian manifold with boundary. We characterise those Toeplitz operators which are Fredholm, thus initiating the index theory.}, language = {en} } @article{AkhmatskayaBouRabeeReich2009, author = {Akhmatskaya, Elena and Bou-Rabee, Nawaf and Reich, Sebastian}, title = {A comparison of generalized hybrid Monte Carlo methods with and without momentum flip}, issn = {0021-9991}, doi = {10.1016/j.jcp.2008.12.014}, year = {2009}, abstract = {The generalized hybrid Monte Carlo (GHMC) method combines Metropolis corrected constant energy simulations with a partial random refreshment step in the particle momenta. The standard detailed balance condition requires that momenta are negated upon rejection of a molecular dynamics proposal step. The implication is a trajectory reversal upon rejection, which is undesirable when interpreting GHMC as thermostated molecular dynamics. We show that a modified detailed balance condition can be used to implement GHMC without momentum flips. The same modification can be applied to the generalized shadow hybrid Monte Carlo (GSHMC) method. Numerical results indicate that GHMC/GSHMC implementations with momentum flip display a favorable behavior in terms of sampling efficiency, i.e., the traditional GHMC/GSHMC implementations with momentum flip got the advantage of a higher acceptance rate and faster decorrelation of Monte Carlo samples. The difference is more pronounced for GHMC. We also numerically investigate the behavior of the GHMC method as a Langevin-type thermostat. We find that the GHMC method without momentum flip interferes less with the underlying stochastic molecular dynamics in terms of autocorrelation functions and it to be preferred over the GHMC method with momentum flip. The same finding applies to GSHMC.}, language = {en} } @article{MuehlenbruchKuxhausPencinaetal.2015, author = {M{\"u}hlenbruch, Kristin and Kuxhaus, Olga and Pencina, Michael J. and Boeing, Heiner and Liero, Hannelore and Schulze, Matthias Bernd}, title = {A confidence ellipse for the Net Reclassification Improvement}, series = {European journal of epidemiology}, volume = {30}, journal = {European journal of epidemiology}, number = {4}, publisher = {Springer}, address = {Dordrecht}, issn = {0393-2990}, doi = {10.1007/s10654-015-0001-1}, pages = {299 -- 304}, year = {2015}, abstract = {The Net Reclassification Improvement (NRI) has become a popular metric for evaluating improvement in disease prediction models through the past years. The concept is relatively straightforward but usage and interpretation has been different across studies. While no thresholds exist for evaluating the degree of improvement, many studies have relied solely on the significance of the NRI estimate. However, recent studies recommend that statistical testing with the NRI should be avoided. We propose using confidence ellipses around the estimated values of event and non-event NRIs which might provide the best measure of variability around the point estimates. Our developments are illustrated using practical examples from EPIC-Potsdam study.}, language = {en} } @article{MaierWiljesHartungetal.2022, author = {Maier, Corinna Sabrina and Wiljes, Jana de and Hartung, Niklas and Kloft, Charlotte and Huisinga, Wilhelm}, title = {A continued learning approach for model-informed precision dosing}, series = {CPT: pharmacometrics \& systems pharmacology}, volume = {11}, journal = {CPT: pharmacometrics \& systems pharmacology}, number = {2}, publisher = {London}, address = {Nature Publ. Group}, issn = {2163-8306}, doi = {10.1002/psp4.12745}, pages = {185 -- 198}, year = {2022}, abstract = {Model-informed precision dosing (MIPD) is a quantitative dosing framework that combines prior knowledge on the drug-disease-patient system with patient data from therapeutic drug/ biomarker monitoring (TDM) to support individualized dosing in ongoing treatment. Structural models and prior parameter distributions used in MIPD approaches typically build on prior clinical trials that involve only a limited number of patients selected according to some exclusion/inclusion criteria. Compared to the prior clinical trial population, the patient population in clinical practice can be expected to also include altered behavior and/or increased interindividual variability, the extent of which, however, is typically unknown. Here, we address the question of how to adapt and refine models on the level of the model parameters to better reflect this real-world diversity. We propose an approach for continued learning across patients during MIPD using a sequential hierarchical Bayesian framework. The approach builds on two stages to separate the update of the individual patient parameters from updating the population parameters. Consequently, it enables continued learning across hospitals or study centers, because only summary patient data (on the level of model parameters) need to be shared, but no individual TDM data. We illustrate this continued learning approach with neutrophil-guided dosing of paclitaxel. The present study constitutes an important step toward building confidence in MIPD and eventually establishing MIPD increasingly in everyday therapeutic use.}, language = {en} }