TY - GEN
A1 - Keller, Matthias
A1 - Pinchover, Yehuda
A1 - Pogorzelski, Felix
T1 - From hardy to rellich inequalities on graphs
T2 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2 - We show how to deduce Rellich inequalities from Hardy inequalities on infinite graphs. Specifically, the obtained Rellich inequality gives an upper bound on a function by the Laplacian of the function in terms of weighted norms. These weights involve the Hardy weight and a function which satisfies an eikonal inequality. The results are proven first for Laplacians and are extended to Schrodinger operators afterwards.
T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1379
KW - 35R02
KW - 39A12 (primary)
KW - 26D15
KW - 31C20
KW - 35B09
KW - 58E35 (secondary)
Y1 - 2020
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-542140
SN - 1866-8372
IS - 3
ER -
TY - JOUR
A1 - Kürschner, Patrick
A1 - Freitag, Melina A.
T1 - Inexact methods for the low rank solution to large scale Lyapunov equations
JF - BIT : numerical mathematics ; the leading applied mathematics journal for all computational mathematicians
N2 - The rational Krylov subspace method (RKSM) and the low-rank alternating directions implicit (LR-ADI) iteration are established numerical tools for computing low-rank solution factors of large-scale Lyapunov equations. In order to generate the basis vectors for the RKSM, or extend the low-rank factors within the LR-ADI method, the repeated solution to a shifted linear system of equations is necessary. For very large systems this solve is usually implemented using iterative methods, leading to inexact solves within this inner iteration (and therefore to "inexact methods"). We will show that one can terminate this inner iteration before full precision has been reached and still obtain very good accuracy in the final solution to the Lyapunov equation. In particular, for both the RKSM and the LR-ADI method we derive theory for a relaxation strategy (e.g. increasing the solve tolerance of the inner iteration, as the outer iteration proceeds) within the iterative methods for solving the large linear systems. These theoretical choices involve unknown quantities, therefore practical criteria for relaxing the solution tolerance within the inner linear system are then provided. The theory is supported by several numerical examples, which show that the total amount of work for solving Lyapunov equations can be reduced significantly.
KW - Lyapunov equation
KW - alternating direction implicit
KW - rational Krylov
KW - subspaces
KW - low-rank approximations
Y1 - 2019
U6 - https://doi.org/10.1007/s10543-020-00813-4
SN - 0006-3835
SN - 1572-9125
VL - 60
IS - 4
SP - 1221
EP - 1259
PB - Springer
CY - Dordrecht
ER -
TY - JOUR
A1 - Flad, Heinz-Jürgen
A1 - Flad-Harutyunyan, Gohar
A1 - Schulze, Bert-Wolfgang
T1 - Explicit Green operators for quantum mechanical Hamiltonians
BT - II. edge-type singularities of the helium atom
JF - Asian-European journal of mathematics : AEJM
N2 - We extend our approach of asymptotic parametrix construction for Hamiltonian operators from conical to edge-type singularities which is applicable to coalescence points of two particles of the helium atom and related two electron systems including the hydrogen molecule. Up to second-order, we have calculated the symbols of an asymptotic parametrix of the nonrelativistic Hamiltonian of the helium atom within the Born-Oppenheimer approximation and provide explicit formulas for the corresponding Green operators which encode the asymptotic behavior of the eigenfunctions near an edge.
KW - Singular analysis
KW - Schrodinger equation
KW - many-electron systems
KW - asymptotic properties of eigenfunctions
Y1 - 2020
U6 - https://doi.org/10.1142/S1793557120501223
SN - 1793-5571
SN - 1793-7183
VL - 13
IS - 7
PB - World Scientific
CY - Singapore
ER -
TY - CHAP
A1 - Rungrottheera, Wannarut
A1 - Chang, Der-Chen
A1 - Schulze, Bert-Wolfgang
T1 - The edge calculus of singularity order >3
T2 - Journal of nonlinear and convex analysis : an international journal
N2 - We study Mellin pseudo-differential algebras on singular straight cones and manifolds with singularity of order >= 3. Those are necessary to express parametrices of elliptic differential operators with a corresponding cornerdegenerate behavior, and we obtain regularity in weighted spaces.
KW - Pseudo-differential algebras
KW - symbols
KW - singular manifolds
KW - Mellin
KW - operator calculus
Y1 - 2020
SN - 1345-4773
SN - 1880-5221
VL - 21
IS - 2
SP - 387
EP - 401
PB - Yokohama Publishers
CY - Yokohama
ER -
TY - JOUR
A1 - Zöller, Gert
A1 - Hainzl, Sebastian
A1 - Tilmann, Frederik
A1 - Woith, Heiko
A1 - Dahm, Torsten
T1 - Comment on: Wikelski, Martin; Müller, Uschi; Scocco, Paola; Catorci, Andrea; Desinov, Lev V.; Belyaev, Mikhail Y.; Keim, Daniel A.; Pohlmeier, Winfried; Fechteler, Gerhard; Mai, Martin P. : Potential short-term earthquake forecasting by farm animal monitoring. - Ethology. - 126 (2020), 9. - S. 931 - 941. -ISSN 0179-1613. - eISSN 1439-0310. - doi 10.1111/eth.13078
JF - Ethology
N2 - Based on an analysis of continuous monitoring of farm animal behavior in the region of the 2016 M6.6 Norcia earthquake in Italy, Wikelski et al., 2020; (Seismol Res Lett, 89, 2020, 1238) conclude that animal activity can be anticipated with subsequent seismic activity and that this finding might help to design a "short-term earthquake forecasting method." We show that this result is based on an incomplete analysis and misleading interpretations. Applying state-of-the-art methods of statistics, we demonstrate that the proposed anticipatory patterns cannot be distinguished from random patterns, and consequently, the observed anomalies in animal activity do not have any forecasting power.
KW - animal behavior
KW - earthquake precursor
KW - error diagram
KW - prediction
KW - randomness
KW - statistics
Y1 - 2020
U6 - https://doi.org/10.1111/eth.13105
SN - 0179-1613
SN - 1439-0310
VL - 127
IS - 3
SP - 302
EP - 306
PB - Wiley
CY - Hoboken
ER -
TY - JOUR
A1 - Mueller-Schoell, Anna
A1 - Groenland, Stefanie L.
A1 - Scherf-Clavel, Oliver
A1 - van Dyk, Madele
A1 - Huisinga, Wilhelm
A1 - Michelet, Robin
A1 - Jaehde, Ulrich
A1 - Steeghs, Neeltje
A1 - Huitema, Alwin D. R.
A1 - Kloft, Charlotte
T1 - Therapeutic drug monitoring of oral targeted antineoplastic drugs
JF - European journal of clinical pharmacology
N2 - Purpose This review provides an overview of the current challenges in oral targeted antineoplastic drug (OAD) dosing and outlines the unexploited value of therapeutic drug monitoring (TDM). Factors influencing the pharmacokinetic exposure in OAD therapy are depicted together with an overview of different TDM approaches. Finally, current evidence for TDM for all approved OADs is reviewed. Methods A comprehensive literature search (covering literature published until April 2020), including primary and secondary scientific literature on pharmacokinetics and dose individualisation strategies for OADs, together with US FDA Clinical Pharmacology and Biopharmaceutics Reviews and the Committee for Medicinal Products for Human Use European Public Assessment Reports was conducted. Results OADs are highly potent drugs, which have substantially changed treatment options for cancer patients. Nevertheless, high pharmacokinetic variability and low treatment adherence are risk factors for treatment failure. TDM is a powerful tool to individualise drug dosing, ensure drug concentrations within the therapeutic window and increase treatment success rates. After reviewing the literature for 71 approved OADs, we show that exposure-response and/or exposure-toxicity relationships have been established for the majority. Moreover, TDM has been proven to be feasible for individualised dosing of abiraterone, everolimus, imatinib, pazopanib, sunitinib and tamoxifen in prospective studies. There is a lack of experience in how to best implement TDM as part of clinical routine in OAD cancer therapy. Conclusion Sub-therapeutic concentrations and severe adverse events are current challenges in OAD treatment, which can both be addressed by the application of TDM-guided dosing, ensuring concentrations within the therapeutic window.
KW - targeted antineoplastic drugs
KW - tyrosine kinase inhibitors
KW - therapeutic
KW - drug monitoring
KW - oral anticancer drugs
KW - personalised medicine
Y1 - 2020
U6 - https://doi.org/10.1007/s00228-020-03014-8
SN - 0031-6970
SN - 1432-1041
VL - 77
IS - 4
SP - 441
EP - 464
PB - Springer
CY - Heidelberg
ER -
TY - JOUR
A1 - Grisic, Ana-Marija
A1 - Eser, Alexander
A1 - Huisinga, Wilhelm
A1 - Reinisch, Walter
A1 - Kloft, Charlotte
T1 - Quantitative relationship between infliximab exposure and inhibition of C-reactive protein synthesis to support inflammatory bowel disease management
JF - British journal of clinical pharmacology
N2 - Aim Quantitative and kinetic insights into the drug exposure-disease response relationship might enhance our knowledge on loss of response and support more effective monitoring of inflammatory activity by biomarkers in patients with inflammatory bowel disease (IBD) treated with infliximab (IFX). This study aimed to derive recommendations for dose adjustment and treatment optimisation based on mechanistic characterisation of the relationship between IFX serum concentration and C-reactive protein (CRP) concentration.
Methods Data from an investigator-initiated trial included 121 patients with IBD during IFX maintenance treatment. Serum concentrations of IFX, antidrug antibodies (ADA), CRP, and disease-related covariates were determined at the mid-term and end of a dosing interval. Data were analysed using a pharmacometric nonlinear mixed-effects modelling approach. An IFX exposure-CRP model was generated and applied to evaluate dosing regimens to achieve CRP remission.
Results The generated quantitative model showed that IFX has the potential to inhibit up to 72% (9% relative standard error [RSE]) of CRP synthesis in a patient. IFX concentration leading to 90% of the maximum CRP synthesis inhibition was 18.4 mu g/mL (43% RSE). Presence of ADA was the most influential factor on IFX exposure. With standard dosing strategy, >= 55% of ADA+ patients experienced CRP nonremission. Shortening the dosing interval and co-therapy with immunomodulators were found to be the most beneficial strategies to maintain CRP remission.
Conclusions With the generated model we could for the first time establish a robust relationship between IFX exposure and CRP synthesis inhibition, which could be utilised for treatment optimisation in IBD patients.
KW - C‐ reactive protein remission
KW - inflammatory bowel disease
KW - infliximab dosing
Y1 - 2020
U6 - https://doi.org/10.1111/bcp.14648
SN - 0306-5251
SN - 1365-2125
VL - 87
IS - 5
SP - 2374
EP - 2384
PB - Wiley
CY - Hoboken
ER -
TY - JOUR
A1 - Kluwe, Franziska
A1 - Michelet, Robin
A1 - Müller-Schöll, Anna
A1 - Maier, Corinna
A1 - Klopp-Schulze, Lena
A1 - van Dyk, Madele
A1 - Mikus, Gerd
A1 - Huisinga, Wilhelm
A1 - Kloft, Charlotte
T1 - Perspectives on model-informed precision dosing in the digital health era
BT - challenges, opportunities, and recommendations
JF - Clinical pharmacology & therapeutics
Y1 - 2020
U6 - https://doi.org/10.1002/cpt.2049
SN - 0009-9236
SN - 1532-6535
VL - 109
IS - 1
SP - 29
EP - 36
PB - Wiley
CY - Hoboken
ER -
TY - JOUR
A1 - Sharma, Shubham
A1 - Hainzl, Sebastian
A1 - Zöller, Gert
A1 - Holschneider, Matthias
T1 - Is Coulomb stress the best choice for aftershock forecasting?
JF - Journal of geophysical research : Solid earth
N2 - The Coulomb failure stress (CFS) criterion is the most commonly used method for predicting spatial distributions of aftershocks following large earthquakes. However, large uncertainties are always associated with the calculation of Coulomb stress change. The uncertainties mainly arise due to nonunique slip inversions and unknown receiver faults; especially for the latter, results are highly dependent on the choice of the assumed receiver mechanism. Based on binary tests (aftershocks yes/no), recent studies suggest that alternative stress quantities, a distance-slip probabilistic model as well as deep neural network (DNN) approaches, all are superior to CFS with predefined receiver mechanism. To challenge this conclusion, which might have large implications, we use 289 slip inversions from SRCMOD database to calculate more realistic CFS values for a layered half-space and variable receiver mechanisms. We also analyze the effect of the magnitude cutoff, grid size variation, and aftershock duration to verify the use of receiver operating characteristic (ROC) analysis for the ranking of stress metrics. The observations suggest that introducing a layered half-space does not improve the stress maps and ROC curves. However, results significantly improve for larger aftershocks and shorter time periods but without changing the ranking. We also go beyond binary testing and apply alternative statistics to test the ability to estimate aftershock numbers, which confirm that simple stress metrics perform better than the classic Coulomb failure stress calculations and are also better than the distance-slip probabilistic model.
Y1 - 2020
U6 - https://doi.org/10.1029/2020JB019553
SN - 2169-9313
SN - 2169-9356
VL - 125
IS - 9
PB - American Geophysical Union
CY - Washington
ER -
TY - JOUR
A1 - Dimitrova, Ilinka
A1 - Koppitz, Jörg
T1 - On relative ranks of the semigroup of orientation-preserving transformations on infinite chains
JF - Asian-European journal of mathematics
N2 - In this paper, we determine the relative rank of the semigroup OP(X) of all orientation-preserving transformations on infinite chains modulo the semigroup O(X) of all order-preserving transformations.
KW - Transformation semigroups on infinite chains
KW - order-preserving
KW - transformations
KW - orientation-preserving transformations
KW - relative rank
Y1 - 2020
U6 - https://doi.org/10.1142/S1793557121501461
SN - 1793-5571
SN - 1793-7183
VL - 14
IS - 08
PB - World Scientific
CY - Singapore
ER -