@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}
}
@book{DahlkeMaass1994,
author = {Dahlke, Stephan and Maaß, Peter},
title = {A continuous wavelet transform on tangent bundles of spheres},
series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
volume = {1994, 16},
journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
publisher = {Univ.},
address = {Potsdam},
pages = {18 Bl.},
year = {1994},
language = {en}
}
@article{CvetkovićConradLie2021,
author = {Cvetković, Nada and Conrad, Tim and Lie, Han Cheng},
title = {A convergent discretization method for transition path theory for diffusion processes},
series = {Multiscale modeling \& simulation : a SIAM interdisciplinary journal},
volume = {19},
journal = {Multiscale modeling \& simulation : a SIAM interdisciplinary journal},
number = {1},
publisher = {Society for Industrial and Applied Mathematics},
address = {Philadelphia},
issn = {1540-3459},
doi = {10.1137/20M1329354},
pages = {242 -- 266},
year = {2021},
abstract = {Transition path theory (TPT) for diffusion processes is a framework for analyzing the transitions of multiscale ergodic diffusion processes between disjoint metastable subsets of state space. Most methods for applying TPT involve the construction of a Markov state model on a discretization of state space that approximates the underlying diffusion process. However, the assumption of Markovianity is difficult to verify in practice, and there are to date no known error bounds or convergence results for these methods. We propose a Monte Carlo method for approximating the forward committor, probability current, and streamlines from TPT for diffusion processes. Our method uses only sample trajectory data and partitions of state space based on Voronoi tessellations. It does not require the construction of a Markovian approximating process. We rigorously prove error bounds for the approximate TPT objects and use these bounds to show convergence to their exact counterparts in the limit of arbitrarily fine discretization. We illustrate some features of our method by application to a process that solves the Smoluchowski equation on a triple-well potential.},
language = {en}
}
@book{GauthierTarkhanov2004,
author = {Gauthier, P. M. and Tarkhanov, Nikolai Nikolaevich},
title = {A covering proberty of the Riemann zeta-funktion},
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 = {11 S.},
year = {2004},
language = {en}
}
@book{Korey2001,
author = {Korey, Michael Brian},
title = {A Decomposition of functions with vanishing mean oscillation},
series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgrupe Partielle Differentialgleichun},
journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgrupe Partielle Differentialgleichun},
publisher = {Univ.},
address = {Potsdam},
issn = {1437-339X},
pages = {16 S.},
year = {2001},
language = {en}
}
@book{KorramiMansouriMohazzab1996,
author = {Korrami, M. and Mansouri, R. and Mohazzab, Masoud},
title = {A decrumpling model of the universe},
series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
volume = {1996, 09},
journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
publisher = {Univ.},
address = {Potsdam},
pages = {6 Bl.},
year = {1996},
language = {en}
}
@article{AlSaedyTarchanov2020,
author = {Al-Saedy, Ammar Jaffar Muhesin and Tarchanov, Nikolaj Nikolaevič},
title = {A degree theory for Lagrangian boundary value problems},
series = {Žurnal Sibirskogo Federalʹnogo Universiteta = Journal of Siberian Federal University; mathematics \& physics},
volume = {13},
journal = {Žurnal Sibirskogo Federalʹnogo Universiteta = Journal of Siberian Federal University; mathematics \& physics},
number = {1},
publisher = {Sibirskij Federalʹnyj Universitet},
address = {Krasnojarsk},
issn = {1997-1397},
doi = {10.17516/1997-1397-2020-13-1-5-25},
pages = {5 -- 25},
year = {2020},
abstract = {We study those nonlinear partial differential equations which appear as Euler-Lagrange equations of variational problems. On defining weak boundary values of solutions to such equations we initiate the theory of Lagrangian boundary value problems in spaces of appropriate smoothness. We also analyse if the concept of mapping degree of current importance applies to Lagrangian problems.},
language = {en}
}
@phdthesis{Hanke2001,
author = {Hanke, Timo},
title = {A direct approach to noncrossed product division algebras},
pages = {64 S.},
year = {2001},
language = {en}
}
@phdthesis{Kaersten1998,
author = {K{\"a}rsten, Fatma},
title = {A duality for a compact group and a second cohomology of its dual},
pages = {76 S.},
year = {1998},
language = {en}
}
@article{Reich2011,
author = {Reich, Sebastian},
title = {A dynamical systems framework for intermittent data assimilation},
series = {BIT : numerical mathematics ; the leading applied mathematics journal for all computational mathematicians},
volume = {51},
journal = {BIT : numerical mathematics ; the leading applied mathematics journal for all computational mathematicians},
number = {1},
publisher = {Springer},
address = {Dordrecht},
issn = {0006-3835},
doi = {10.1007/s10543-010-0302-4},
pages = {235 -- 249},
year = {2011},
abstract = {We consider the problem of discrete time filtering (intermittent data assimilation) for differential equation models and discuss methods for its numerical approximation. The focus is on methods based on ensemble/particle techniques and on the ensemble Kalman filter technique in particular. We summarize as well as extend recent work on continuous ensemble Kalman filter formulations, which provide a concise dynamical systems formulation of the combined dynamics-assimilation problem. Possible extensions to fully nonlinear ensemble/particle based filters are also outlined using the framework of optimal transportation theory.},
language = {en}
}
@article{Lledo1997,
author = {Lled{\´o}, Fernando},
title = {A family of examples with quantum constraints},
year = {1997},
language = {en}
}
@book{Lledo1996,
author = {Lled{\´o}, Fernando},
title = {A family of examples with quantum constraints},
series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
volume = {1996, 01},
journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
publisher = {Univ.},
address = {Potsdam},
pages = {10 S.},
year = {1996},
language = {en}
}
@article{ZieheLaskovNolteetal.2004,
author = {Ziehe, Andreas and Laskov, Pavel and Nolte, G and M{\"u}ller, Klaus-Robert},
title = {A fast algorithm for joint diagonalization with non-orthogonal transformations and its application to blind source separation},
year = {2004},
abstract = {A new efficient algorithm is presented for joint diagonalization of several matrices. The algorithm is based on the Frobenius-norm formulation of the joint diagonalization problem, and addresses diagonalization with a general, non- orthogonal transformation. The iterative scheme of the algorithm is based on a multiplicative update which ensures the invertibility of the diagonalizer. The algorithm's efficiency stems from the special approximation of the cost function resulting in a sparse, block-diagonal Hessian to be used in the computation of the quasi-Newton update step. Extensive numerical simulations illustrate the performance of the algorithm and provide a comparison to other leading diagonalization methods. The results of such comparison demonstrate that the proposed algorithm is a viable alternative to existing state-of-the-art joint diagonalization algorithms. The practical use of our algorithm is shown for blind source separation problems},
language = {en}
}
@book{Tarkhanov2003,
author = {Tarkhanov, Nikolai Nikolaevich},
title = {A fixed point formula in one complex variable},
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 = {14 S.},
year = {2003},
language = {en}
}
@article{Reich2012,
author = {Reich, Sebastian},
title = {A Gaussian-mixture ensemble transform filter},
series = {Quarterly journal of the Royal Meteorological Society},
volume = {138},
journal = {Quarterly journal of the Royal Meteorological Society},
number = {662},
publisher = {Wiley-Blackwell},
address = {Malden},
issn = {0035-9009},
doi = {10.1002/qj.898},
pages = {222 -- 233},
year = {2012},
abstract = {We generalize the popular ensemble Kalman filter to an ensemble transform filter, in which the prior distribution can take the form of a Gaussian mixture or a Gaussian kernel density estimator. The design of the filter is based on a continuous formulation of the Bayesian filter analysis step. We call the new filter algorithm the ensemble Gaussian-mixture filter (EGMF). The EGMF is implemented for three simple test problems (Brownian dynamics in one dimension, Langevin dynamics in two dimensions and the three-dimensional Lorenz-63 model). It is demonstrated that the EGMF is capable of tracking systems with non-Gaussian uni- and multimodal ensemble distributions.},
language = {en}
}
@article{FedosovSchulzeTarkhanov2001,
author = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
title = {A general index formula on toric manifolds with conical point},
year = {2001},
language = {en}
}
@article{ShojaeiFard2013,
author = {Shojaei-Fard, Ali},
title = {A GEOMETRIC PERSPECTIVE ON COUNTERTERMS RELATED TO DYSON-SCHWINGER EQUATIONS},
series = {INTERNATIONAL JOURNAL OF MODERN PHYSICS A},
volume = {28},
journal = {INTERNATIONAL JOURNAL OF MODERN PHYSICS A},
number = {32},
publisher = {WORLD SCIENTIFIC PUBL CO PTE LTD},
address = {SINGAPORE},
issn = {0217-751X},
doi = {10.1142/S0217751X13501704},
pages = {15},
year = {2013},
abstract = {We study Dyson-Schwinger equations (DSEs) in terms of some groups of diffeographisms to provide a new geometric formulation for their corresponding counterterms on the basis of systems of ordinary differential equations.},
language = {en}
}
@article{Zass2020,
author = {Zass, Alexander},
title = {A Gibbs point process of diffusions: Existence and uniqueness},
series = {Lectures in pure and applied mathematics},
journal = {Lectures in pure and applied mathematics},
number = {6},
publisher = {Universit{\"a}tsverlag Potsdam},
address = {Potsdam},
isbn = {978-3-86956-485-2},
issn = {2199-4951},
doi = {10.25932/publishup-47195},
url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-471951},
pages = {13 -- 22},
year = {2020},
language = {en}
}
@article{KlingSchneidenbachSchnor2005,
author = {Kling, Christoph and Schneidenbach, Lars and Schnor, Bettina},
title = {A high performance gigabit ethernet messaging method for PVFS},
isbn = {0-88986-525-6},
year = {2005},
abstract = {Parallel File Systems like PVFS2 are a necessary compo nent for high-performance computing. The design of ef ;cient communication layers for these systems is still of great research interest. This paper presents a low- latency messaging method for PVFS2 dedicated for Gigabit Ether net networks and discusses relevant design issues. In con trast to other approaches, we argue that zero-copying can be achieved also for big messages without use of a rendez vous protocol. Further, ef;ciency within the communica tion layer like a small call stack plays an important role.},
language = {en}
}
@unpublished{AlsaedyTarkhanov2016,
author = {Alsaedy, Ammar and Tarkhanov, Nikolai Nikolaevich},
title = {A Hilbert boundary value problem for generalised Cauchy-Riemann equations},
volume = {5},
number = {1},
publisher = {Universit{\"a}tsverlag Potsdam},
address = {Potsdam},
issn = {2193-6943},
url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-86109},
pages = {21},
year = {2016},
abstract = {We elaborate a boundary Fourier method for studying an analogue of the Hilbert problem for analytic functions within the framework of generalised Cauchy-Riemann equations. The boundary value problem need not satisfy the Shapiro-Lopatinskij condition and so it fails to be Fredholm in Sobolev spaces. We show a solvability condition of the Hilbert problem, which looks like those for ill-posed problems, and construct an explicit formula for approximate solutions.},
language = {en}
}
@article{KemptonMuenchYau2021,
author = {Kempton, Mark and M{\"u}nch, Florentin and Yau, Shing-Tung},
title = {A homology vanishing theorem for graphs with positive curvature},
series = {Communications in analysis and geometry},
volume = {29},
journal = {Communications in analysis and geometry},
number = {6},
publisher = {International Press of Boston},
address = {Somerville},
issn = {1019-8385},
doi = {10.4310/CAG.2021.v29.n6.a5},
pages = {1449 -- 1473},
year = {2021},
abstract = {We prove a homology vanishing theorem for graphs with positive Bakry-' Emery curvature, analogous to a classic result of Bochner on manifolds [3]. Specifically, we prove that if a graph has positive curvature at every vertex, then its first homology group is trivial, where the notion of homology that we use for graphs is the path homology developed by Grigor'yan, Lin, Muranov, and Yau [11]. We moreover prove that the fundamental group is finite for graphs with positive Bakry-' Emery curvature, analogous to a classic result of Myers on manifolds [22]. The proofs draw on several separate areas of graph theory, including graph coverings, gain graphs, and cycle spaces, in addition to the Bakry-Emery curvature, path homology, and graph homotopy. The main results follow as a consequence of several different relationships developed among these different areas. Specifically, we show that a graph with positive curvature cannot have a non-trivial infinite cover preserving 3-cycles and 4-cycles, and give a combinatorial interpretation of the first path homology in terms of the cycle space of a graph. Furthermore, we relate gain graphs to graph homotopy and the fundamental group developed by Grigor'yan, Lin, Muranov, and Yau [12], and obtain an alternative proof of their result that the abelianization of the fundamental group of a graph is isomorphic to the first path homology over the integers.},
language = {en}
}
@unpublished{MeleardRoelly2011,
author = {M{\´e}l{\´e}ard, Sylvie and Roelly, Sylvie},
title = {A host-parasite multilevel interacting process and continuous approximations},
url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51694},
year = {2011},
abstract = {We are interested in modeling some two-level population dynamics, resulting from the interplay of ecological interactions and phenotypic variation of individuals (or hosts) and the evolution of cells (or parasites) of two types living in these individuals. The ecological parameters of the individual dynamics depend on the number of cells of each type contained by the individual and the cell dynamics depends on the trait of the invaded individual. Our models are rooted in the microscopic description of a random (discrete) population of individuals characterized by one or several adaptive traits and cells characterized by their type. The population is modeled as a stochastic point process whose generator captures the probabilistic dynamics over continuous time of birth, mutation and death for individuals and birth and death for cells. The interaction between individuals (resp. between cells) is described by a competition between individual traits (resp. between cell types). We look for tractable large population approximations. By combining various scalings on population size, birth and death rates and mutation step, the single microscopic model is shown to lead to contrasting nonlinear macroscopic limits of different nature: deterministic approximations, in the form of ordinary, integro- or partial differential equations, or probabilistic ones, like stochastic partial differential equations or superprocesses. The study of the long time behavior of these processes seems very hard and we only develop some simple cases enlightening the difficulties involved.},
language = {en}
}
@article{Wallenta2014,
author = {Wallenta, Daniel},
title = {A Lefschetz fixed point formula for elliptic quasicomplexes},
series = {Integral equations and operator theor},
volume = {78},
journal = {Integral equations and operator theor},
number = {4},
publisher = {Springer},
address = {Basel},
issn = {0378-620X},
doi = {10.1007/s00020-014-2122-4},
pages = {577 -- 587},
year = {2014},
abstract = {In a recent paper, the Lefschetz number for endomorphisms (modulo trace class operators) of sequences of trace class curvature was introduced. We show that this is a well defined, canonical extension of the classical Lefschetz number and establish the homotopy invariance of this number. Moreover, we apply the results to show that the Lefschetz fixed point formula holds for geometric quasiendomorphisms of elliptic quasicomplexes.},
language = {en}
}
@unpublished{Wallenta2013,
author = {Wallenta, Daniel},
title = {A Lefschetz fixed point formula for elliptic quasicomplexes},
url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-67016},
year = {2013},
abstract = {In a recent paper with N. Tarkhanov, the Lefschetz number for endomorphisms (modulo trace class operators) of sequences of trace class curvature was introduced. We show that this is a well defined, canonical extension of the classical Lefschetz number and establish the homotopy invariance of this number. Moreover, we apply the results to show that the Lefschetz fixed point formula holds for geometric quasiendomorphisms of elliptic quasicomplexes.},
language = {en}
}
@article{BoesenbergAlpersBoeckmannetal.1998,
author = {B{\"o}senberg, Jens and Alpers, Matthias and B{\"o}ckmann, Christine and J{\"a}ger, Horst and Matthias, Volker and Trickl, Thomas and Wandinger, Ulla and Wiegner, Matthias},
title = {A Lidar Network for the Establishment of an Aerosol Climatology},
year = {1998},
language = {en}
}
@article{BergemannReich2010,
author = {Bergemann, Kay and Reich, Sebastian},
title = {A localization technique for ensemble Kalman filters},
issn = {0035-9009},
doi = {10.1002/Qj.591},
year = {2010},
abstract = {Ensemble Kalman filter techniques are widely used to assimilate observations into dynamical models. The phase- space dimension is typically much larger than the number of ensemble members, which leads to inaccurate results in the computed covariance matrices. These inaccuracies can lead, among other things, to spurious long-range correlations, which can be eliminated by Schur-product-based localization techniques. In this article, we propose a new technique for implementing such localization techniques within the class of ensemble transform/square-root Kalman filters. Our approach relies on a continuous embedding of the Kalman filter update for the ensemble members, i.e. we state an ordinary differential equation (ODE) with solutions that, over a unit time interval, are equivalent to the Kalman filter update. The ODE formulation forms a gradient system with the observations as a cost functional. Besides localization, the new ODE ensemble formulation should also find useful application in the context of nonlinear observation operators and observations that arrive continuously in time.},
language = {en}
}
@article{MalemShinitskiOpperReichetal.2020,
author = {Malem-Shinitski, Noa and Opper, Manfred and Reich, Sebastian and Schwetlick, Lisa and Seelig, Stefan A. and Engbert, Ralf},
title = {A mathematical model of local and global attention in natural scene viewing},
series = {PLoS Computational Biology : a new community journal},
volume = {16},
journal = {PLoS Computational Biology : a new community journal},
number = {12},
publisher = {PLoS},
address = {San Fransisco},
issn = {1553-734X},
doi = {10.1371/journal.pcbi.1007880},
pages = {21},
year = {2020},
abstract = {Author summary
Switching between local and global attention is a general strategy in human information processing. We investigate whether this strategy is a viable approach to model sequences of fixations generated by a human observer in a free viewing task with natural scenes. Variants of the basic model are used to predict the experimental data based on Bayesian inference. Results indicate a high predictive power for both aggregated data and individual differences across observers. The combination of a novel model with state-of-the-art Bayesian methods lends support to our two-state model using local and global internal attention states for controlling eye movements.
Understanding the decision process underlying gaze control is an important question in cognitive neuroscience with applications in diverse fields ranging from psychology to computer vision. The decision for choosing an upcoming saccade target can be framed as a selection process between two states: Should the observer further inspect the information near the current gaze position (local attention) or continue with exploration of other patches of the given scene (global attention)? Here we propose and investigate a mathematical model motivated by switching between these two attentional states during scene viewing. The model is derived from a minimal set of assumptions that generates realistic eye movement behavior. We implemented a Bayesian approach for model parameter inference based on the model's likelihood function. In order to simplify the inference, we applied data augmentation methods that allowed the use of conjugate priors and the construction of an efficient Gibbs sampler. This approach turned out to be numerically efficient and permitted fitting interindividual differences in saccade statistics. Thus, the main contribution of our modeling approach is two-fold; first, we propose a new model for saccade generation in scene viewing. Second, we demonstrate the use of novel methods from Bayesian inference in the field of scan path modeling.},
language = {en}
}
@article{HartungBorghardt2020,
author = {Hartung, Niklas and Borghardt, Jens Markus},
title = {A mechanistic framework for a priori pharmacokinetic predictions of orally inhaled drugs},
series = {PLoS Computational Biology : a new community journal},
volume = {16},
journal = {PLoS Computational Biology : a new community journal},
number = {12},
publisher = {PLoS},
address = {San Fransisco},
issn = {1553-734X},
doi = {10.1371/journal.pcbi.1008466},
pages = {24},
year = {2020},
abstract = {Author summary
The use of orally inhaled drugs for treating lung diseases is appealing since they have the potential for lung selectivity, i.e. high exposure at the site of action -the lung- without excessive side effects. However, the degree of lung selectivity depends on a large number of factors, including physiochemical properties of drug molecules, patient disease state, and inhalation devices. To predict the impact of these factors on drug exposure and thereby to understand the characteristics of an optimal drug for inhalation, we develop a predictive mathematical framework (a "pharmacokinetic model"). In contrast to previous approaches, our model allows combining knowledge from different sources appropriately and its predictions were able to adequately predict different sets of clinical data. Finally, we compare the impact of different factors and find that the most important factors are the size of the inhaled particles, the affinity of the drug to the lung tissue, as well as the rate of drug dissolution in the lung. In contrast to the common belief, the solubility of a drug in the lining fluids is not found to be relevant. These findings are important to understand how inhaled drugs should be designed to achieve best treatment results in patients.
The fate of orally inhaled drugs is determined by pulmonary pharmacokinetic processes such as particle deposition, pulmonary drug dissolution, and mucociliary clearance. Even though each single process has been systematically investigated, a quantitative understanding on the interaction of processes remains limited and therefore identifying optimal drug and formulation characteristics for orally inhaled drugs is still challenging. To investigate this complex interplay, the pulmonary processes can be integrated into mathematical models. However, existing modeling attempts considerably simplify these processes or are not systematically evaluated against (clinical) data. In this work, we developed a mathematical framework based on physiologically-structured population equations to integrate all relevant pulmonary processes mechanistically. A tailored numerical resolution strategy was chosen and the mechanistic model was evaluated systematically against data from different clinical studies. Without adapting the mechanistic model or estimating kinetic parameters based on individual study data, the developed model was able to predict simultaneously (i) lung retention profiles of inhaled insoluble particles, (ii) particle size-dependent pharmacokinetics of inhaled monodisperse particles, (iii) pharmacokinetic differences between inhaled fluticasone propionate and budesonide, as well as (iv) pharmacokinetic differences between healthy volunteers and asthmatic patients. Finally, to identify the most impactful optimization criteria for orally inhaled drugs, the developed mechanistic model was applied to investigate the impact of input parameters on both the pulmonary and systemic exposure. Interestingly, the solubility of the inhaled drug did not have any relevant impact on the local and systemic pharmacokinetics. Instead, the pulmonary dissolution rate, the particle size, the tissue affinity, and the systemic clearance were the most impactful potential optimization parameters. In the future, the developed prediction framework should be considered a powerful tool for identifying optimal drug and formulation characteristics.},
language = {en}
}
@article{LeimkuhlerReich2009,
author = {Leimkuhler, Benedict and Reich, Sebastian},
title = {A metropolis adjusted Nos{\´e}-Hoover thermostat},
issn = {0764-583X},
doi = {10.1051/M2an/2009023},
year = {2009},
abstract = {We present a Monte Carlo technique for sampling from the canonical distribution in molecular dynamics. The method is built upon the Nose-Hoover constant temperature formulation and the generalized hybrid Monte Carlo method. In contrast to standard hybrid Monte Carlo methods only the thermostat degree of freedom is stochastically resampled during a Monte Carlo step.},
language = {en}
}
@article{Boeckmann1995,
author = {B{\"o}ckmann, Christine},
title = {A modification of the trust-region Gauss-Newton method to solve separable nonlinear least squares problems},
year = {1995},
language = {en}
}
@book{Boeckmann1992,
author = {B{\"o}ckmann, Christine},
title = {A modification of the Trust-Region Gauss-Newton method to solve separable nonlinear least squares problems},
series = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik},
volume = {1992, 17},
journal = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik},
publisher = {Univ.},
address = {Potsdam},
pages = {14 Bl.},
year = {1992},
language = {en}
}