Mathematik und Statistikhttp://kops.uni-konstanz.de:80/handle/123456789/82019-01-24T14:04:58Z2019-01-24T14:04:58ZMatrix methods for the tensorial Bernstein formTiti, Jihadpop258933Garloff, Jürgenpop45676123456789/43397.22019-01-09T13:03:47Z2019Matrix methods for the tensorial Bernstein form
Titi, Jihad; Garloff, Jürgen
In this paper, multivariate polynomials in the Bernstein basis over a box (tensorial Bernstein representation) are considered. A new matrix method for the computation of the polynomial coefficients with respect to the Bernstein basis, the so-called Bernstein coefficients, are presented and compared with existing methods. Also matrix methods for the calculation of the Bernstein coefficients over subboxes generated by subdivision of the original box are proposed. All the methods solely use matrix operations such as multiplication, transposition, and reshaping; some of them rely also on the bidiagonal factorization of the lower triangular Pascal matrix or the factorization of this matrix by a Toeplitz matrix. In the case that the coefficients of the polynomial are due to uncertainties and can be represented in the form of intervals it is shown that the developed methods can be extended to compute the set of the Bernstein coefficients of all members of the polynomial family.
2019Titi, JihadGarloff, Jürgen510In this paper, multivariate polynomials in the Bernstein basis over a box (tensorial Bernstein representation) are considered. A new matrix method for the computation of the polynomial coefficients with respect to the Bernstein basis, the so-called Bernstein coefficients, are presented and compared with existing methods. Also matrix methods for the calculation of the Bernstein coefficients over subboxes generated by subdivision of the original box are proposed. All the methods solely use matrix operations such as multiplication, transposition, and reshaping; some of them rely also on the bidiagonal factorization of the lower triangular Pascal matrix or the factorization of this matrix by a Toeplitz matrix. In the case that the coefficients of the polynomial are due to uncertainties and can be represented in the form of intervals it is shown that the developed methods can be extended to compute the set of the Bernstein coefficients of all members of the polynomial family.JOURNAL_ARTICLEeng10.1016/j.amc.2018.08.0490096-30031873-5649254271346Applied Mathematics and Computation2019-01-09T14:03:23+01:00123456789/39Applied Mathematics and Computation ; 346 (2019). - S. 254-271. - ISSN 0096-3003. - eISSN 1873-5649unknown2019-01-09T13:03:23ZMeasures and Integrals in Conditional Set TheoryJamneshan, Asgarpop254373Kupper, Michaelpop243845Streckfuß, Martin123456789/444462019-01-09T02:14:13Z2018-12Measures and Integrals in Conditional Set Theory
Jamneshan, Asgar; Kupper, Michael; Streckfuß, Martin
The aim of this article is to establish basic results in a conditional measure theory. The results are applied to prove that arbitrary kernels and conditional distributions are represented by measures in a conditional set theory. In particular, this extends the usual representation results for separable spaces.
2018-12Jamneshan, AsgarKupper, MichaelStreckfuß, Martin51003C90The aim of this article is to establish basic results in a conditional measure theory. The results are applied to prove that arbitrary kernels and conditional distributions are represented by measures in a conditional set theory. In particular, this extends the usual representation results for separable spaces.JOURNAL_ARTICLEeng10.1007/s11228-018-0478-31877-05331877-0541947973264Set-Valued and Variational Analysis2019-01-08T14:08:06+01:00123456789/39Set-Valued and Variational Analysis ; 26 (2018), 4. - S. 947-973. - ISSN 1877-0533. - eISSN 1877-0541unknown2019-01-08T13:08:06ZRobust expected utility maximization with medial limitsBartl, Danielpop224057Cheridito, PatrickKupper, Michaelpop243845123456789/444412019-01-09T02:14:39Z2019-03Robust expected utility maximization with medial limits
Bartl, Daniel; Cheridito, Patrick; Kupper, Michael
In this paper we study a robust expected utility maximization problem with random endowment in discrete time. We give conditions under which an optimal strategy exists and derive a dual representation for the optimal utility. Our approach is based on a general representation result for monotone convex functionals, a functional version of Choquet's capacitability theorem and medial limits. The novelty is that it works under nondominated model uncertainty without any assumptions of time-consistency. As applications, we discuss robust utility maximization problems with moment constraints, Wasserstein constraints and Wasserstein penalties.
2019-03Bartl, DanielCheridito, PatrickKupper, Michael510In this paper we study a robust expected utility maximization problem with random endowment in discrete time. We give conditions under which an optimal strategy exists and derive a dual representation for the optimal utility. Our approach is based on a general representation result for monotone convex functionals, a functional version of Choquet's capacitability theorem and medial limits. The novelty is that it works under nondominated model uncertainty without any assumptions of time-consistency. As applications, we discuss robust utility maximization problems with moment constraints, Wasserstein constraints and Wasserstein penalties.JOURNAL_ARTICLEeng10.1016/j.jmaa.2018.11.0120022-247X1096-08137527754711-2Journal of Mathematical Analysis and Applications2019-01-08T11:48:03+01:00123456789/39Journal of Mathematical Analysis and Applications ; 471 (2019), 1-2. - S. 752-775. - ISSN 0022-247X. - eISSN 1096-0813true2019-01-08T10:48:03ZtrueTarget-Mediated Drug Disposition Model for Bispecific Antibodies : Properties, Approximation and Optimal Dosing StrategySchropp, Johannespop03713Khot, AntariShah, Dhaval K.Koch, Gilbertpop164441123456789/443922018-12-20T02:14:55Z2018-11-27Target-Mediated Drug Disposition Model for Bispecific Antibodies : Properties, Approximation and Optimal Dosing Strategy
Schropp, Johannes; Khot, Antari; Shah, Dhaval K.; Koch, Gilbert
Bispecific antibodies (BsAb) bind to two different targets, and create two binary and one ternary complex (TC). These molecules have shown promise as immuno-oncology drugs, and the TC is considered the pharmacologically active species that drives their pharmacodynamic effect. Here we have presented a general target-mediated drug disposition model for these BsAbs, which bind to two different targets on different cell membranes. The model includes four different binding events for BsAb, turnover of the targets, and internalization of the complexes. In addition, a quasi-equilibrium approximation with decreased number of binding parameters and, if necessary, reduced internalization parameters is presented. The model is further used to investigate the kinetics of BsAb and TC concentrations. Our analysis shows that larger doses of BsAbs may delay the build-up of the TC. Consequently, a method to compute the optimal dosing strategy of BsAb, which will immediately create and maintain maximal possible TC concentration, is presented.
2018-11-27Schropp, JohannesKhot, AntariShah, Dhaval K.Koch, Gilbert510Bispecific antibodies (BsAb) bind to two different targets, and create two binary and one ternary complex (TC). These molecules have shown promise as immuno-oncology drugs, and the TC is considered the pharmacologically active species that drives their pharmacodynamic effect. Here we have presented a general target-mediated drug disposition model for these BsAbs, which bind to two different targets on different cell membranes. The model includes four different binding events for BsAb, turnover of the targets, and internalization of the complexes. In addition, a quasi-equilibrium approximation with decreased number of binding parameters and, if necessary, reduced internalization parameters is presented. The model is further used to investigate the kinetics of BsAb and TC concentrations. Our analysis shows that larger doses of BsAbs may delay the build-up of the TC. Consequently, a method to compute the optimal dosing strategy of BsAb, which will immediately create and maintain maximal possible TC concentration, is presented.JOURNAL_ARTICLEeng10.1002/psp4.123692163-8306CPT : pharmacometrics & systems pharmacology2018-12-19T15:32:22+01:00123456789/39CPT : pharmacometrics & systems pharmacology ; 2018. - eISSN 2163-8306true2018-12-19T14:32:22Ztrue