@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}
}
@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{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}
}
@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}
}
@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}
}
@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 <br /> 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. <br /> 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 <br /> 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. <br /> 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}
}
@book{Baumgaertel1994,
  author    = {Baumg{\"a}rtel, Hellmut},
  title     = {A modified approach to the Doplicher-Roberts theorem on the construction of field algebra and the symmetry group in superselection theory},
  series = {Preprint / SFB 288, Differentialgeometrie und Quantenphysik},
  volume    = {134},
  journal   = {Preprint / SFB 288, Differentialgeometrie und Quantenphysik},
  address   = {Berlin},
  pages     = {33 S.},
  year      = {1994},
  language  = {en}
}
@article{Baumgaertel1997,
  author    = {Baumg{\"a}rtel, Hellmut},
  title     = {A modified approach to the Doplicher-Roberts theorem on the construction of the field algebra and the symmetry group in superselection theory},
  year      = {1997},
  language  = {en}
}
@article{PornsawadSapsakulBoeckmann2019,
  author    = {Pornsawad, Pornsarp and Sapsakul, Nantawan and B{\"o}ckmann, Christine},
  title     = {A modified asymptotical regularization of nonlinear ill-posed problems},
  series = {Mathematics},
  volume    = {7},
  journal   = {Mathematics},
  edition   = {5},
  publisher = {MDPI},
  address   = {Basel, Schweiz},
  issn      = {2227-7390},
  doi       = {10.3390/math7050419},
  pages     = {19},
  year      = {2019},
  abstract  = {In this paper, we investigate the continuous version of modified iterative Runge-Kutta-type methods for nonlinear inverse ill-posed problems proposed in a previous work. The convergence analysis is proved under the tangential cone condition, a modified discrepancy principle, i.e., the stopping time T is a solution of ∥𝐹(𝑥𝛿(𝑇))-𝑦𝛿∥=𝜏𝛿+ for some 𝛿+>𝛿, and an appropriate source condition. We yield the optimal rate of convergence.},
  language  = {en}
}
@book{Ramlau1997,
  author    = {Ramlau, Ronny},
  title     = {A modified Landweber-method for inverse problems},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  volume    = {1997, 03},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {24 Bl.},
  year      = {1997},
  language  = {en}
}
@article{BergemannReich2010,
  author    = {Bergemann, Kay and Reich, Sebastian},
  title     = {A mollified ensemble Kalman filter},
  issn      = {0035-9009},
  doi       = {10.1002/Qj.672},
  year      = {2010},
  abstract  = {It is well recognized that discontinuous analysis increments of sequential data assimilation systems, such as ensemble Kalman filters, might lead to spurious high-frequency adjustment processes in the model dynamics. Various methods have been devised to spread out the analysis increments continuously over a fixed time interval centred about the analysis time. Among these techniques are nudging and incremental analysis updates (IAU). Here we propose another alternative, which may be viewed as a hybrid of nudging and IAU and which arises naturally from a recently proposed continuous formulation of the ensemble Kalman analysis step. A new slow-fast extension of the popular Lorenz-96 model is introduced to demonstrate the properties of the proposed mollified ensemble Kalman filter.},
  language  = {en}
}
@book{BoeckmannNiebsch1996,
  author    = {B{\"o}ckmann, Christine and Niebsch, Jenny},
  title     = {A mollifier method for aerosol size},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  volume    = {1996, 07},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {[5] Bl.},
  year      = {1996},
  language  = {en}
}
@article{ShinZoellerHolschneideretal.2011,
  author    = {Shin, Seoleun and Z{\"o}ller, Gert and Holschneider, Matthias and Reich, Sebastian},
  title     = {A multigrid solver for modeling complex interseismic stress fields},
  series = {Computers \& geosciences : an international journal devoted to the publication of papers on all aspects of geocomputation and to the distribution of computer programs and test data sets ; an official journal of the International Association for Mathematical Geology},
  volume    = {37},
  journal   = {Computers \& geosciences : an international journal devoted to the publication of papers on all aspects of geocomputation and to the distribution of computer programs and test data sets ; an official journal of the International Association for Mathematical Geology},
  number    = {8},
  publisher = {Elsevier},
  address   = {Oxford},
  issn      = {0098-3004},
  doi       = {10.1016/j.cageo.2010.11.011},
  pages     = {1075 -- 1082},
  year      = {2011},
  abstract  = {We develop a multigrid, multiple time stepping scheme to reduce computational efforts for calculating complex stress interactions in a strike-slip 2D planar fault for the simulation of seismicity. The key elements of the multilevel solver are separation of length scale, grid-coarsening, and hierarchy. In this study the complex stress interactions are split into two parts: the first with a small contribution is computed on a coarse level, and the rest for strong interactions is on a fine level. This partition leads to a significant reduction of the number of computations. The reduction of complexity is even enhanced by combining the multigrid with multiple time stepping. Computational efficiency is enhanced by a factor of 10 while retaining a reasonable accuracy, compared to the original full matrix-vortex multiplication. The accuracy of solution and computational efficiency depend on a given cut-off radius that splits multiplications into the two parts. The multigrid scheme is constructed in such a way that it conserves stress in the entire half-space.},
  language  = {en}
}
@article{HedayatMahmoudiSchulze2018,
  author    = {Hedayat Mahmoudi, Mahdi and Schulze, Bert-Wolfgang},
  title     = {A new approach to the second order edge calculus},
  series = {Journal of pseudo-differential operators and applications},
  volume    = {9},
  journal   = {Journal of pseudo-differential operators and applications},
  number    = {2},
  publisher = {Springer},
  address   = {Basel},
  issn      = {1662-9981},
  doi       = {10.1007/s11868-017-0191-2},
  pages     = {265 -- 300},
  year      = {2018},
  abstract  = {We establish essential steps of an iterative approach to operator algebras, ellipticity and Fredholm property on stratified spaces with singularities of second order. We cover, in particular, corner-degenerate differential operators. Our constructions are focused on the case where no additional conditions of trace and potential type are posed, but this case works well and will be considered in a forthcoming paper as a conclusion of the present calculus.},
  language  = {en}
}
@book{KamaniMansouri1995,
  author    = {Kamani, D. and Mansouri, R.},
  title     = {A new class of inhomogeneous cosmological solutions},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  volume    = {1995, 07},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {12 S.},
  year      = {1995},
  language  = {en}
}
@article{RaschSchindler2005,
  author    = {Rasch, T. and Schindler, R.},
  title     = {A new condensation principle},
  issn      = {1432-0665},
  year      = {2005},
  abstract  = {We generalize del(A), which was introduced in [Schinfinity], to larger cardinals. For a regular cardinal kappa>N-0 we denote by del(kappa)(A) the statement that Asubset of or equal tokappa and for all regular theta>kappa(o), {X is an element of[L-theta[A]](<) : X \&AND; \&ISIN; \&AND; otp (X \&AND; Ord) \&ISIN; Card (L[A\&AND;X\&AND;])} is stationary in [L-[A]](<). It was shown in [Sch\&INFIN;] that \&DEL;(N1) (A) can hold in a set-generic extension of L. We here prove that \&DEL;(N2) (A) can hold in a set-generic extension of L as well. In both cases we in fact get equiconsistency theorems. This strengthens results of [Ra00] and [Ran01]. \&DEL;(N3) () is equivalent with the existence of 0\#},
  language  = {en}
}
@article{KellerMuench2019,
  author    = {Keller, Matthias and M{\"u}nch, Florentin},
  title     = {A new discrete Hopf-Rinow theorem},
  series = {Discrete Mathematics},
  volume    = {342},
  journal   = {Discrete Mathematics},
  number    = {9},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0012-365X},
  doi       = {10.1016/j.disc.2019.03.014},
  pages     = {2751 -- 2757},
  year      = {2019},
  abstract  = {We prove a version of the Hopf-Rinow theorem with respect to path metrics on discrete spaces. The novel aspect is that we do not a priori assume local finiteness but isolate a local finiteness type condition, called essentially locally finite, that is indeed necessary. As a side product we identify the maximal weight, called the geodesic weight, generating the path metric in the situation when the space is complete with respect to any of the equivalent notions of completeness proven in the Hopf-Rinow theorem. As an application we characterize the graphs for which the resistance metric is a path metric induced by the graph structure.},
  language  = {en}
}
@article{Schmidt1997,
  author    = {Schmidt, Hans-J{\"u}rgen},
  title     = {A new duality transformation for fouth-order gravity},
  year      = {1997},
  language  = {en}
}
@article{ArwornDenecke1997,
  author    = {Arworn, Srichan and Denecke, Klaus-Dieter},
  title     = {A new methods to study subvariety lattices of semigroup varieties},
  year      = {1997},
  language  = {en}
}
@article{Schmidt1997,
  author    = {Schmidt, Hans-J{\"u}rgen},
  title     = {A new proof of Birkhoff{\"i}s theorem},
  year      = {1997},
  language  = {en}
}
@article{Reich2013,
  author    = {Reich, Sebastian},
  title     = {A nonparametric ensemble transform method for bayesian inference},
  series = {SIAM journal on scientific computing},
  volume    = {35},
  journal   = {SIAM journal on scientific computing},
  number    = {4},
  publisher = {Society for Industrial and Applied Mathematics},
  address   = {Philadelphia},
  issn      = {1064-8275},
  doi       = {10.1137/130907367},
  pages     = {A2013 -- A2024},
  year      = {2013},
  abstract  = {Many applications, such as intermittent data assimilation, lead to a recursive application of Bayesian inference within a Monte Carlo context. Popular data assimilation algorithms include sequential Monte Carlo methods and ensemble Kalman filters (EnKFs). These methods differ in the way Bayesian inference is implemented. Sequential Monte Carlo methods rely on importance sampling combined with a resampling step, while EnKFs utilize a linear transformation of Monte Carlo samples based on the classic Kalman filter. While EnKFs have proven to be quite robust even for small ensemble sizes, they are not consistent since their derivation relies on a linear regression ansatz. In this paper, we propose another transform method, which does not rely on any a priori assumptions on the underlying prior and posterior distributions. The new method is based on solving an optimal transportation problem for discrete random variables.},
  language  = {en}
}
@article{MakhmudovMakhmudovTarkhanov2017,
  author    = {Makhmudov, K. O. and Makhmudov, O. I. and Tarkhanov, Nikolai Nikolaevich},
  title     = {A nonstandard Cauchy problem for the heat equation},
  series = {Mathematical Notes},
  volume    = {102},
  journal   = {Mathematical Notes},
  publisher = {Pleiades Publ.},
  address   = {New York},
  issn      = {0001-4346},
  doi       = {10.1134/S0001434617070264},
  pages     = {250 -- 260},
  year      = {2017},
  abstract  = {We consider the Cauchy problem for the heat equation in a cylinder C (T) = X x (0, T) over a domain X in R (n) , with data on a strip lying on the lateral surface. The strip is of the form S x (0, T), where S is an open subset of the boundary of X. The problem is ill-posed. Under natural restrictions on the configuration of S, we derive an explicit formula for solutions of this problem.},
  language  = {en}
}
@book{Braunss1998,
  author    = {Braunß, Hans-Andreas},
  title     = {A note about ranks of m-homogeneous polynomials on Banach spaces},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  volume    = {1998, 18a},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {4 Bl.},
  year      = {1998},
  language  = {en}
}
@article{KellerLiuPeyerimhoff2021,
  author    = {Keller, Matthias and Liu, Shiping and Peyerimhoff, Norbert},
  title     = {A note on eigenvalue bounds for non-compact manifolds},
  series = {Mathematische Nachrichten},
  volume    = {294},
  journal   = {Mathematische Nachrichten},
  number    = {6},
  publisher = {Wiley-VCH},
  address   = {Weinheim},
  issn      = {0025-584X},
  doi       = {10.1002/mana.201900209},
  pages     = {1134 -- 1139},
  year      = {2021},
  abstract  = {In this article we prove upper bounds for the Laplace eigenvalues lambda(k) below the essential spectrum for strictly negatively curved Cartan-Hadamard manifolds. Our bound is given in terms of k(2) and specific geometric data of the manifold. This applies also to the particular case of non-compact manifolds whose sectional curvature tends to -infinity, where no essential spectrum is present due to a theorem of Donnelly/Li. The result stands in clear contrast to Laplacians on graphs where such a bound fails to be true in general.},
  language  = {en}
}
@article{DimitrovaFernandesKoppitz2017,
  author    = {Dimitrova, Ilinka and Fernandes, Vitor H. and Koppitz, J{\"o}rg},
  title     = {A note on generators of the endomorphism semigroup of an infinite countable chain},
  series = {Journal of Algebra and its Applications},
  volume    = {16},
  journal   = {Journal of Algebra and its Applications},
  number    = {2},
  publisher = {World Scientific},
  address   = {Singapore},
  issn      = {0219-4988},
  doi       = {10.1142/S0219498817500311},
  pages     = {9},
  year      = {2017},
  abstract  = {In this note, we consider the semigroup O(X) of all order endomorphisms of an infinite chain X and the subset J of O(X) of all transformations alpha such that vertical bar Im(alpha)vertical bar = vertical bar X vertical bar. For an infinite countable chain X, we give a necessary and sufficient condition on X for O(X) = < J > to hold. We also present a sufficient condition on X for O(X) = < J > to hold, for an arbitrary infinite chain X.},
  language  = {en}
}
@article{HinzSchwarz2022,
  author    = {Hinz, Michael and Schwarz, Michael},
  title     = {A note on Neumann problems on graphs},
  series = {Positivity},
  volume    = {26},
  journal   = {Positivity},
  number    = {4},
  publisher = {Springer},
  address   = {Dordrecht},
  issn      = {1385-1292},
  doi       = {10.1007/s11117-022-00930-0},
  pages     = {23},
  year      = {2022},
  abstract  = {We discuss Neumann problems for self-adjoint Laplacians on (possibly infinite) graphs. Under the assumption that the heat semigroup is ultracontractive we discuss the unique solvability for non-empty subgraphs with respect to the vertex boundary and provide analytic and probabilistic representations for Neumann solutions. A second result deals with Neumann problems on canonically compactifiable graphs with respect to the Royden boundary and provides conditions for unique solvability and analytic and probabilistic representations.},
  language  = {en}
}
@book{Pincus1997,
  author    = {Pincus, Richard},
  title     = {A note on symmetric unimodal distributions ordered by peakedness},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  volume    = {1997, 27},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {8 Bl.},
  year      = {1997},
  language  = {en}
}
@article{Zoeller2022,
  author    = {Z{\"o}ller, Gert},
  title     = {A note on the estimation of the maximum possible earthquake magnitude based on extreme value theory for the Groningen Gas Field},
  series = {The bulletin of the Seismological Society of America : BSSA},
  volume    = {112},
  journal   = {The bulletin of the Seismological Society of America : BSSA},
  number    = {4},
  publisher = {Seismological Society of America},
  address   = {El Cerito, Calif.},
  issn      = {0037-1106},
  doi       = {10.1785/0120210307},
  pages     = {1825 -- 1831},
  year      = {2022},
  abstract  = {Extreme value statistics is a popular and frequently used tool to model the occurrence of large earthquakes. The problem of poor statistics arising from rare events is addressed by taking advantage of the validity of general statistical properties in asymptotic regimes. In this note, I argue that the use of extreme value statistics for the purpose of practically modeling the tail of the frequency-magnitude distribution of earthquakes can produce biased and thus misleading results because it is unknown to what degree the tail of the true distribution is sampled by data. Using synthetic data allows to quantify this bias in detail. The implicit assumption that the true M-max is close to the maximum observed magnitude M-max,M-observed restricts the class of the potential models a priori to those with M-max = M-max,M-observed + Delta M with an increment Delta M approximate to 0.5... 1.2. This corresponds to the simple heuristic method suggested by Wheeler (2009) and labeled :M-max equals M-obs plus an increment." The incomplete consideration of the entire model family for the frequency-magnitude distribution neglects, however, the scenario of a large so far unobserved earthquake.},
  language  = {en}
}
@book{Camales2003,
  author    = {Camal{\`e}s, Renaud},
  title     = {A Note on the Ramified Cauchy Problem},
  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      = {2003},
  language  = {en}
}
@article{MalassTarkhanov2020,
  author    = {Malass, Ihsane and Tarkhanov, Nikolaj Nikolaevič},
  title     = {A perturbation of the de Rham complex},
  series = {Journal of Siberian Federal University : Mathematics \& Physics},
  volume    = {13},
  journal   = {Journal of Siberian Federal University : Mathematics \& Physics},
  number    = {5},
  publisher = {Siberian Federal University},
  address   = {Krasnojarsk},
  issn      = {1997-1397},
  doi       = {10.17516/1997-1397-2020-13-5-519-532},
  pages     = {519 -- 532},
  year      = {2020},
  abstract  = {We consider a perturbation of the de Rham complex on a compact manifold with boundary. This perturbation goes beyond the framework of complexes, and so cohomology does not apply to it. On the other hand, its curvature is "small", hence there is a natural way to introduce an Euler characteristic and develop a Lefschetz theory for the perturbation. This work is intended as an attempt to develop a cohomology theory for arbitrary sequences of linear mappings.},
  language  = {en}
}
@article{KellerRoellyValleriani2015,
  author    = {Keller, Peter and Roelly, Sylvie and Valleriani, Angelo},
  title     = {A Quasi Random Walk to Model a Biological Transport Process},
  series = {Methodology and computing in applied probability},
  volume    = {17},
  journal   = {Methodology and computing in applied probability},
  number    = {1},
  publisher = {Springer},
  address   = {Dordrecht},
  issn      = {1387-5841},
  doi       = {10.1007/s11009-013-9372-5},
  pages     = {125 -- 137},
  year      = {2015},
  abstract  = {Transport molecules play a crucial role for cell viability. Amongst others, linear motors transport cargos along rope-like structures from one location of the cell to another in a stochastic fashion. Thereby each step of the motor, either forwards or backwards, bridges a fixed distance and requires several biochemical transformations, which are modeled as internal states of the motor. While moving along the rope, the motor can also detach and the walk is interrupted. We give here a mathematical formalization of such dynamics as a random process which is an extension of Random Walks, to which we add an absorbing state to model the detachment of the motor from the rope. We derive particular properties of such processes that have not been available before. Our results include description of the maximal distance reached from the starting point and the position from which detachment takes place. Finally, we apply our theoretical results to a concrete established model of the transport molecule Kinesin V.},
  language  = {en}
}
@article{LyTarkhanov2016,
  author    = {Ly, Ibrahim and Tarkhanov, Nikolai Nikolaevich},
  title     = {A Rado theorem for p-harmonic functions},
  series = {Boletin de la Sociedad Matem{\~A}!'tica Mexicana},
  volume    = {22},
  journal   = {Boletin de la Sociedad Matem{\~A}!'tica Mexicana},
  publisher = {Springer},
  address   = {Basel},
  issn      = {1405-213X},
  doi       = {10.1007/s40590-016-0109-7},
  pages     = {461 -- 472},
  year      = {2016},
  abstract  = {Let A be a nonlinear differential operator on an open set X subset of R-n and S a closed subset of X. Given a class F of functions in X, the set S is said to be removable for F relative to A if any weak solution of A(u) = 0 in XS of class F satisfies this equation weakly in all of X. For the most extensively studied classes F, we show conditions on S which guarantee that S is removable for F relative to A.},
  language  = {en}
}
@article{FedchenkoTarkhanov2017,
  author    = {Fedchenko, Dmitry and Tarkhanov, Nikolai Nikolaevich},
  title     = {A Rado theorem for the porous medium equation},
  series = {Boletin de la Sociedad Matem{\´a}tica Mexicana},
  volume    = {24},
  journal   = {Boletin de la Sociedad Matem{\´a}tica Mexicana},
  number    = {2},
  publisher = {Springer},
  address   = {Cham},
  issn      = {1405-213X},
  doi       = {10.1007/s40590-017-0169-3},
  pages     = {427 -- 437},
  year      = {2017},
  abstract  = {We prove that if u is a locally Lipschitz continuous function on an open set chi subset of Rn + 1 satisfying the nonlinear heat equation partial derivative(t)u = Delta(vertical bar u vertical bar(p-1) u), p > 1, weakly away from the zero set u(-1) (0) in chi, then u is a weak solution to this equation in all of chi.},
  language  = {en}
}
@book{BaumgaertelJurkeLledo1994,
  author    = {Baumg{\"a}rtel, Hellmut and Jurke, Matthias and Lled{\´o}, Fernando},
  title     = {A remark on covariant and causal nets of CAR-resp.CCR-type local algebras assigned to the irreducible unitary representation of the poincare group labeled by (m>0, s, +)},
  series = {Preprint / SFB 288, Differentialgeometrie und Quantenphysik},
  volume    = {120},
  journal   = {Preprint / SFB 288, Differentialgeometrie und Quantenphysik},
  address   = {Berlin},
  year      = {1994},
  language  = {en}
}
@book{FedosovSchulzeTarchanov1998,
  author    = {Fedosov, Boris V. and Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.},
  title     = {A remark on the index of symmetric operators},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  volume    = {1998, 04},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {12 S.},
  year      = {1998},
  language  = {en}
}
@article{ChelkhLyTarkhanov2020,
  author    = {Chelkh, W. and Ly, Ibrahim and Tarkhanov, Nikolai},
  title     = {A remark on the Laplace transform},
  series = {Siberian Mathematical Journal},
  volume    = {61},
  journal   = {Siberian Mathematical Journal},
  number    = {4},
  publisher = {Consultants Bureau, Springer},
  address   = {New York},
  issn      = {0037-4466},
  doi       = {10.1134/S0037446620040151},
  pages     = {755 -- 762},
  year      = {2020},
  abstract  = {The study of the Cauchy problem for solutions of the heat equation in a cylindrical domain with data on the lateral surface by the Fourier method raises the problem of calculating the inverse Laplace transform of the entire function cos root z. This problem has no solution in the standard theory of the Laplace transform. We give an explicit formula for the inverse Laplace transform of cos root z using the theory of analytic functionals. This solution suits well to efficiently develop the regularization of solutions to Cauchy problems for parabolic equations with data on noncharacteristic surfaces.},
  language  = {en}
}
@article{NehringZessin2012,
  author    = {Nehring, Benjamin and Zessin, Hans},
  title     = {A representation of the moment measures of the general ideal Boe gas},
  series = {Mathematische Nachrichten},
  volume    = {285},
  journal   = {Mathematische Nachrichten},
  number    = {7},
  publisher = {Wiley-VCH},
  address   = {Weinheim},
  issn      = {0025-584X},
  doi       = {10.1002/mana.201000111},
  pages     = {878 -- 888},
  year      = {2012},
  abstract  = {We reconsider the fundamental work of Fichtner 2 and exhibit the permanental structure of the ideal Bose gas again, using a new approach which combines a characterization of infinitely divisible random measures (due to Kerstan, Kummer and Matthes 4, 6 and Mecke 9, 10) with a decomposition of the moment measures into its factorial measures due to Krickeberg 5. To be more precise, we exhibit the moment measures of all orders of the general ideal Bose gas in terms of certain loop integrals. This representation can be considered as a point process analogue of the old idea of Symanzik 15 that local times and self-crossings of the Brownian motion can be used as a tool in quantum field theory. Behind the notion of a general ideal Bose gas there is a class of infinitely divisible point processes of all orders with a Levy-measure belonging to some large class of measures containing that of the classical ideal Bose gas considered by Fichtner. It is well-known that the calculation of moments of higher order of point processes is notoriously complicated. See for instance Krickebergs calculations for the Poisson or the Cox process in 5. Relations to the work of Shirai, Takahashi 12 and Soshnikov 14 on permanental and determinantal processes are outlined.},
  language  = {en}
}
@article{HanischLudewig2022,
  author    = {Hanisch, Florian and Ludewig, Matthias},
  title     = {A rigorous construction of the supersymmetric path integral associated to a compact spin manifold},
  series = {Communications in mathematical physics},
  volume    = {391},
  journal   = {Communications in mathematical physics},
  number    = {3},
  publisher = {Springer},
  address   = {Berlin ; Heidelberg},
  issn      = {0010-3616},
  doi       = {10.1007/s00220-022-04336-7},
  pages     = {1209 -- 1239},
  year      = {2022},
  abstract  = {We give a rigorous construction of the path integral in N = 1/2 supersymmetry as an integral map for differential forms on the loop space of a compact spin manifold. It is defined on the space of differential forms which can be represented by extended iterated integrals in the sense of Chen and Getzler-Jones-Petrack. Via the iterated integral map, we compare our path integral to the non-commutative loop space Chern character of Guneysu and the second author. Our theory provides a rigorous background to various formal proofs of the Atiyah-Singer index theorem for twisted Dirac operators using supersymmetric path integrals, as investigated by Alvarez-Gaume, Atiyah, Bismut and Witten.},
  language  = {en}
}
@article{BaerStrohmaier2016,
  author    = {B{\"a}r, Christian and Strohmaier, Alexander},
  title     = {A Rigorous Geometric Derivation of the Chiral Anomaly in Curved Backgrounds},
  series = {Communications in mathematical physics},
  volume    = {347},
  journal   = {Communications in mathematical physics},
  publisher = {Springer},
  address   = {New York},
  issn      = {0010-3616},
  doi       = {10.1007/s00220-016-2664-1},
  pages     = {703 -- 721},
  year      = {2016},
  abstract  = {We discuss the chiral anomaly for a Weyl field in a curved background and show that a novel index theorem for the Lorentzian Dirac operator can be applied to describe the gravitational chiral anomaly. A formula for the total charge generated by the gravitational and gauge field background is derived directly in Lorentzian signature and in a mathematically rigorous manner. It contains a term identical to the integrand in the Atiyah-Singer index theorem and another term involving the.-invariant of the Cauchy hypersurfaces.},
  language  = {en}
}
@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{Ludewig2015,
  author    = {Ludewig, Matthias},
  title     = {A semiclassical heat kernel proof of the Poincare-Hopf theorem},
  series = {Manuscripta mathematica},
  volume    = {148},
  journal   = {Manuscripta mathematica},
  number    = {1-2},
  publisher = {Springer},
  address   = {Heidelberg},
  issn      = {0025-2611},
  doi       = {10.1007/s00229-015-0741-y},
  pages     = {29 -- 58},
  year      = {2015},
  abstract  = {We consider the semiclassical asymptotic expansion of the heat kernel coming from Witten's perturbation of the de Rham complex by a given function. For the index, one obtains a time-dependent integral formula which is evaluated by the method of stationary phase to derive the Poincare-Hopf theorem. We show how this method is related to approaches using the Thom form of Mathai and Quillen. Afterwards, we use a more general version of the stationary phase approximation in the case that the perturbing function has critical submanifolds to derive a degenerate version of the Poincare-Hopf theorem.},
  language  = {en}
}
@book{NazajkinskijSchulzeSternin1998,
  author    = {Nazajkinskij, Vladimir E. and Schulze, Bert-Wolfgang and Sternin, Boris Ju.},
  title     = {A semiclassical quantization on manifolds with singularities and the Lefschetz formula for elliptic operators},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  volume    = {1998, 19},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {25 S.},
  year      = {1998},
  language  = {en}
}
@article{Schrohe2001,
  author    = {Schrohe, Elmar},
  title     = {A short introduction to Boutet de Monvel's calculus},
  year      = {2001},
  language  = {en}
}
@book{Schrohe2000,
  author    = {Schrohe, Elmar},
  title     = {A short introduction to Boutet de Monvel`s calculus},
  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     = {23 S. : graph. Darst.},
  year      = {2000},
  language  = {en}
}
@article{Zoeller2018,
  author    = {Z{\"o}ller, Gert},
  title     = {A statistical model for earthquake recurrence based on the assimilation of paleoseismicity, historic seismicity, and instrumental seismicity},
  series = {Journal of geophysical research : Solid earth},
  volume    = {123},
  journal   = {Journal of geophysical research : Solid earth},
  number    = {6},
  publisher = {American Geophysical Union},
  address   = {Washington},
  issn      = {2169-9313},
  doi       = {10.1029/2017JB015099},
  pages     = {4906 -- 4921},
  year      = {2018},
  abstract  = {Paleoearthquakes and historic earthquakes are the most important source of information for the estimation of long-term earthquake recurrence intervals in fault zones, because corresponding sequences cover more than one seismic cycle. However, these events are often rare, dating uncertainties are enormous, and missing or misinterpreted events lead to additional problems. In the present study, I assume that the time to the next major earthquake depends on the rate of small and intermediate events between the large ones in terms of a clock change model. Mathematically, this leads to a Brownian passage time distribution for recurrence intervals. I take advantage of an earlier finding that under certain assumptions the aperiodicity of this distribution can be related to the Gutenberg-Richter b value, which can be estimated easily from instrumental seismicity in the region under consideration. In this way, both parameters of the Brownian passage time distribution can be attributed with accessible seismological quantities. This allows to reduce the uncertainties in the estimation of the mean recurrence interval, especially for short paleoearthquake sequences and high dating errors. Using a Bayesian framework for parameter estimation results in a statistical model for earthquake recurrence intervals that assimilates in a simple way paleoearthquake sequences and instrumental data. I present illustrative case studies from Southern California and compare the method with the commonly used approach of exponentially distributed recurrence times based on a stationary Poisson process.},
  language  = {en}
}
@article{SchroheSchulze1997,
  author    = {Schrohe, Elmar and Schulze, Bert-Wolfgang},
  title     = {A symbol algebra for pseudodifferential boundary value problems on manifolds with edges},
  year      = {1997},
  language  = {en}
}
@article{RodriguezZuluagaStolleYamazakietal.2021,
  author    = {Rodr{\´i}guez Zuluaga, Juan and Stolle, Claudia and Yamazaki, Yosuke and Xiong, Chao and England, Scott L.},
  title     = {A synoptic-scale wavelike structure in the nighttime equatorial ionization anomaly},
  series = {Earth and Space Science : ESS},
  volume    = {8},
  journal   = {Earth and Space Science : ESS},
  number    = {2},
  publisher = {American Geophysical Union},
  address   = {Malden, Mass.},
  issn      = {2333-5084},
  doi       = {10.1029/2020EA001529},
  pages     = {10},
  year      = {2021},
  abstract  = {Both ground- and satellite-based airglow imaging have significantly contributed to understanding the low-latitude ionosphere, especially the morphology and dynamics of the equatorial ionization anomaly (EIA). The NASA Global-scale Observations of the Limb and Disk (GOLD) mission focuses on far-ultraviolet airglow images from a geostationary orbit at 47.5 degrees W. This region is of particular interest at low magnetic latitudes because of the high magnetic declination (i.e., about -20 degrees) and proximity of the South Atlantic magnetic anomaly. In this study, we characterize an exciting feature of the nighttime EIA using GOLD observations from October 5, 2018 to June 30, 2020. It consists of a wavelike structure of a few thousand kilometers seen as poleward and equatorward displacements of the EIA-crests. Initial analyses show that the synoptic-scale structure is symmetric about the dip equator and appears nearly stationary with time over the night. In quasi-dipole coordinates, maxima poleward displacements of the EIA-crests are seen at about +/- 12 degrees latitude and around 20 and 60 degrees longitude (i.e., in geographic longitude at the dip equator, about 53 degrees W and 14 degrees W). The wavelike structure presents typical zonal wavelengths of about 6.7 x 10(3) km and 3.3 x 10(3) km. The structure's occurrence and wavelength are highly variable on a day-to-day basis with no apparent dependence on geomagnetic activity. In addition, a cluster or quasi-periodic wave train of equatorial plasma depletions (EPDs) is often detected within the synoptic-scale structure. We further outline the difference in observing these EPDs from FUV images and in situ measurements during a GOLD and Swarm mission conjunction.},
  language  = {en}
}
@article{StaniforthWoodReich2006,
  author    = {Staniforth, Andrew and Wood, Nigel and Reich, Sebastian},
  title     = {A time-staggered semi-Lagrangian discretization of the rotating shallow-water equations},
  series = {Quarterly journal of the Royal Meteorological Society},
  volume    = {132},
  journal   = {Quarterly journal of the Royal Meteorological Society},
  number    = {621C},
  publisher = {Wiley},
  address   = {Weinheim},
  issn      = {0035-9009},
  doi       = {10.1256/qj.06.30},
  pages     = {3107 -- 3116},
  year      = {2006},
  abstract  = {A time-staggered semi-Lagrangian discretization of the rotating shallow-water equations is proposed and analysed. Application of regularization to the geopotential field used in the momentum equations leads to an unconditionally stable scheme. The analysis, together with a fully nonlinear example application, suggests that this approach is a promising, efficient, and accurate alternative to traditional schemes.},
  language  = {en}
}
@article{Schmidt1998,
  author    = {Schmidt, Hans-J{\"u}rgen},
  title     = {A two-dimensional representation of four-dimensional graviational waves},
  year      = {1998},
  language  = {en}
}
@article{Klotzek1999,
  author    = {Klotzek, Benno},
  title     = {About newer results to the discontinuous motion groups of different degrees with respect to different geometries},
  year      = {1999},
  language  = {en}
}
@article{Klotzek1999,
  author    = {Klotzek, Benno},
  title     = {About newer results to the discontinuous motion groups of different degrees with respect to different geometries},
  year      = {1999},
  language  = {en}
}
@article{Klotzek1999,
  author    = {Klotzek, Benno},
  title     = {About the geometry of normed space},
  year      = {1999},
  language  = {en}
}
@article{HermannHumbert2016,
  author    = {Hermann, Andreas and Humbert, Emmanuel},
  title     = {About the mass of certain second order elliptic operators},
  series = {Advances in mathematics},
  volume    = {294},
  journal   = {Advances in mathematics},
  publisher = {Elsevier},
  address   = {San Diego},
  issn      = {0001-8708},
  doi       = {10.1016/j.aim.2016.03.008},
  pages     = {596 -- 633},
  year      = {2016},
  abstract  = {Let (M, g) be a closed Riemannian manifold of dimension n >= 3 and let f is an element of C-infinity (M), such that the operator P-f := Delta g + f is positive. If g is flat near some point p and f vanishes around p, we can define the mass of P1 as the constant term in the expansion of the Green function of P-f at p. In this paper, we establish many results on the mass of such operators. In particular, if f := n-2/n(n-1)s(g), i.e. if P-f is the Yamabe operator, we show the following result: assume that there exists a closed simply connected non-spin manifold M such that the mass is non-negative for every metric g as above on M, then the mass is non-negative for every such metric on every closed manifold of the same dimension as M. (C) 2016 Elsevier Inc. All rights reserved.},
  language  = {en}
}
@article{EdlundGrisicSteenholdtetal.2019,
  author    = {Edlund, Helena and Grisic, Ana-Marija and Steenholdt, Casper and Ainsworth, Mark Andrew and Brynskov, Torn and Huisinga, Wilhelm and Kloft, Charlotte},
  title     = {Absence of Relationship Between Crohn's Disease Activity Index or C-Reactive Protein and Infliximab Exposure Calls for Objective Crohn's Disease Activity Measures for the Evaluation of Treatment Effects at Treatment Failure},
  series = {Therapeutic drug monitoring : official journal of the International Association of Therapeutic Drug Monitoring and Clinical Toxicology},
  volume    = {41},
  journal   = {Therapeutic drug monitoring : official journal of the International Association of Therapeutic Drug Monitoring and Clinical Toxicology},
  number    = {2},
  publisher = {Lippincott Williams \& Wilkins},
  address   = {Philadelphia},
  issn      = {0163-4356},
  doi       = {10.1097/FTD.0000000000000590},
  pages     = {235 -- 242},
  year      = {2019},
  abstract  = {Background: Circulating infliximab (IFX) concentrations correlate with clinical outcomes, forming the basis of the IFX concentration monitoring in patients with Crohn's disease. This study aims to investigate and refine the exposure-response relationship by linking the disease activity markers "Crohn's disease activity index" (CDAI) and C-reactive protein (CRP) to IFX exposure. In addition, we aim to explore the correlations between different disease markers and exposure metrics. Methods: Data from 47 Crohn's disease patients of a randomized controlled trial were analyzed post hoc. All patients had secondary treatment failure at inclusion and had received intensified IFX of 5 mg/kg every 4 weeks for up to 20 weeks. Graphical analyses were performed to explore exposure-response relationships. Metrics of exposure included area under the concentration-time curve (AUC) and trough concentrations (Cmin). Disease activity was measured by CDAI and CRP values, their change from baseline/last visit, and response/remission outcomes at week 12. Results: Although trends toward lower Cmin and lower AUC in nonresponders were observed, neither CDAI nor CRP showed consistent trends of lower disease activity with higher IFX exposure across the 30 evaluated relationships. As can be expected, Cmin and AUC were strongly correlated with each other. Contrarily, the disease activity markers were only weakly correlated with each other. Conclusions: No significant relationship between disease activity, as evaluated by CDAI or CRP, and IFX exposure was identified. AUC did not add benefit compared with Cmin. These findings support the continued use of Cmin and call for stringent objective disease activity (bio-)markers (eg, endoscopy) to form the basis of personalized IFX therapy for Crohn's disease patients with IFX treatment failure.},
  language  = {en}
}
@book{Baumgaertel1999,
  author    = {Baumg{\"a}rtel, Hellmut},
  title     = {Actions of finite abelian groups on abelian C*-algebras Z: Second cohomology and description by C*-extensions F ) Z},
  series = {Preprint / SFB 288, Differentialgeometrie und Quantenphysik},
  volume    = {383},
  journal   = {Preprint / SFB 288, Differentialgeometrie und Quantenphysik},
  address   = {Berlin},
  year      = {1999},
  language  = {en}
}
@article{CarpentierKloppLoeffleretal.2018,
  author    = {Carpentier, Alexandra and Klopp, Olga and L{\"o}ffler, Matthias and Nickl, Richard},
  title     = {Adaptive confidence sets for matrix completion},
  series = {Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability},
  volume    = {24},
  journal   = {Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability},
  number    = {4A},
  publisher = {International Statistical Institute},
  address   = {Voorburg},
  issn      = {1350-7265},
  doi       = {10.3150/17-BEJ933},
  pages     = {2429 -- 2460},
  year      = {2018},
  abstract  = {In the present paper, we study the problem of existence of honest and adaptive confidence sets for matrix completion. We consider two statistical models: the trace regression model and the Bernoulli model. In the trace regression model, we show that honest confidence sets that adapt to the unknown rank of the matrix exist even when the error variance is unknown. Contrary to this, we prove that in the Bernoulli model, honest and adaptive confidence sets exist only when the error variance is known a priori. In the course of our proofs, we obtain bounds for the minimax rates of certain composite hypothesis testing problems arising in low rank inference.},
  language  = {en}
}
@book{JunkerSchrohe2001,
  author    = {Junker, W. and Schrohe, Elmar},
  title     = {Adiabatic vacuum states on general spacetime manifolds : definition, construction and physical properties},
  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     = {67 S.},
  year      = {2001},
  language  = {en}
}
@phdthesis{Waltz1994,
  author    = {Waltz, Christine},
  title     = {Adjungierte Polynomideale und duale Typen auf Banachr{\"a}umen und ihre Anwendung},
  pages     = {109 Bl.},
  year      = {1994},
  language  = {de}
}
@article{GuntherZhukBezerraetal.2005,
  author    = {Gunther, U. and Zhuk, Alexandre and Bezerra, Valdir B. and Romero, C.},
  title     = {AdS and stabilized extra dimensions in multi-dimensional gravitational models with nonlinear scalar curvature terms R-1 and R-4},
  issn      = {0264-9381},
  year      = {2005},
  abstract  = {We study multi-dimensional gravitational models with scalar curvature nonlinearities of types R-1 and R-4. It is assumed that the corresponding higher dimensional spacetime manifolds undergo a spontaneous compactification to manifolds with a warped product structure. Special attention has been paid to the stability of the extra-dimensional factor spaces. It is shown that for certain parameter regions the systems allow for a freezing stabilization of these spaces. In particular, we find for the R-1 model that configurations with stabilized extra dimensions do not provide a late-time Acceleration (they are AdS), whereas the solution branch which allows. for accelerated expansion (the dS branch) is incompatible with stabilized factor spaces. In the case of the R-4 model, we obtain that the stability region in parameter space depends on the total dimension D = dim(M) of the higher dimensional spacetime M. Tor D > 8 the stability region consists of a single (absolutely stable) sector which is shielded from a conformal singularity (and an antigravity sector beyond it) by a potential barrier of infinite height and width. This sector is smoothly connected with the stability region of a curvature-linear model. For D < 8 an additional (metastable) sector exists Which is separated from the conformal singularity by a potential barrier of finite height and width so that systems in this sector are prone to collapse into the conformal singularity. This second sector is not smoothly connected with the first (absolutely stable) one. Several limiting cases and the possibility of inflation are discussed for the R-4 model},
  language  = {en}
}
@book{SchulzeDemuthAlbeverioetal.2001,
  author    = {Schulze, Bert-Wolfgang and Demuth, Michael and Albeverio, Sergio and Schrohe, Elmar},
  title     = {Advances in Partial differential equations},
  publisher = {Birkh{\"a}user},
  address   = {Basel},
  year      = {2001},
  language  = {en}
}
@article{BoeckmannWandingerAnsmannetal.2004,
  author    = {B{\"o}ckmann, Christine and Wandinger, Ulla and Ansmann, Albert and B{\"o}senberg, Jens and Amiridis, Vassilis and Boselli, Antonella and Delaval, Arnaud and De Tomasi, Ferdinando de and Frioud, Max and Grigorov, Ivan Videnov and Hagard, Arne and Horvat, Matej and Iarlori, Marco and Komguem, Leonce and Kreipl, Stephan and Larchevque, Gilles and Matthias, Volker and Papayannis, Alexandros and Pappalardo, GGelsomina and Rocadenbosch, Francesc and Rodrigues, Jose Ant{\´o}nio and Schneider, Johannes and Shcherbakov, Valery and Wiegner, Matthias},
  title     = {Aerosol lidar intercomparison in the framework of the EARLINET project : 2. Aerosol backscatter algorithms},
  issn      = {0003-6935},
  year      = {2004},
  abstract  = {An intercomparison of aerosol backscatter lidar algorithms was performed in 2001 within the framework of the European Aerosol Research Lidar Network to Establish an Aerosol Climatology (EARLINET). The objective of this research was to test the correctness of the algorithms and the influence of the lidar ratio used by the various lidar teams involved in the EARLINET for calculation of backscatter-coefficient profiles from the lidar signals. The exercise consisted of processing synthetic lidar signals of various degrees of difficulty. One of these profiles contained height- dependent lidar ratios to test the vertical influence of those profiles on the various retrieval algorithms. Furthermore, a realistic incomplete overlap of laser beam and receiver field of view was introduced to remind the teams to take great care in the nearest range to the lidar. The intercomparison was performed in three stages with increasing knowledge on the input parameters. First, only the lidar signals were distributed; this is the most realistic stage. Afterward the lidar ratio profiles and the reference values at calibration height were provided. The unknown height- dependent lidar ratio had the largest influence on the retrieval, whereas the unknown reference value was of minor importance. These results show the necessity of making additional independent measurements, which can provide us with a suitable approximation of the lidar ratio. The final stage proves in general, that the data evaluation schemes of the different groups of lidar systems work well. (C) 2004 Optical Society of America},
  language  = {en}
}