TY - JOUR A1 - Fedchenko, Dmitry A1 - Tarkhanov, Nikolai Nikolaevich T1 - A Class of Toeplitz Operators in Several Variables JF - Advances in applied Clifford algebras N2 - 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. KW - Cauchy data spaces KW - Laplace-Beltrami operator KW - Toeplitz operators KW - Fredholm property Y1 - 2015 U6 - https://doi.org/10.1007/s00006-015-0546-9 SN - 0188-7009 SN - 1661-4909 VL - 25 IS - 4 SP - 811 EP - 828 PB - Springer CY - Basel ER - TY - JOUR A1 - Mühlenbruch, Kristin A1 - Kuxhaus, Olga A1 - Pencina, Michael J. A1 - Boeing, Heiner A1 - Liero, Hannelore A1 - Schulze, Matthias Bernd T1 - A confidence ellipse for the Net Reclassification Improvement JF - European journal of epidemiology N2 - 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. KW - Risk assessment KW - Risk model KW - Model comparison KW - Reclassification KW - Confidence intervals Y1 - 2015 U6 - https://doi.org/10.1007/s10654-015-0001-1 SN - 0393-2990 SN - 1573-7284 VL - 30 IS - 4 SP - 299 EP - 304 PB - Springer CY - Dordrecht ER - TY - INPR A1 - Makhmudov, K. O. A1 - Makhmudov, O. I. A1 - Tarkhanov, Nikolai Nikolaevich T1 - A nonstandard Cauchy problem for the heat equation N2 - We consider a Cauchy problem for the heat equation in a cylinder X x (0,T) over a domain X in the n-dimensional space 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. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 4 (2015)11 KW - heat equation KW - Cauchy problem KW - Carleman formulas Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-83830 SN - 2193-6943 VL - 4 IS - 11 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Keller, Peter A1 - Roelly, Sylvie A1 - Valleriani, Angelo T1 - A Quasi Random Walk to Model a Biological Transport Process JF - Methodology and computing in applied probability N2 - 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. KW - Molecular motor KW - Kinesin V KW - Birth-and-death process KW - Markov Chain KW - Quasi Random Walk Y1 - 2015 U6 - https://doi.org/10.1007/s11009-013-9372-5 SN - 1387-5841 SN - 1573-7713 VL - 17 IS - 1 SP - 125 EP - 137 PB - Springer CY - Dordrecht ER - TY - INPR A1 - Ly, Ibrahim A1 - Tarkhanov, Nikolai Nikolaevich T1 - A Radó theorem for p-harmonic functions N2 - Let A be a nonlinear differential operator on an open set X in 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 the complement of S 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. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 4 (2015) 3 KW - Quasilinear equations KW - removable sets KW - p-Laplace Operator Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-71492 SN - 2193-6943 VL - 4 IS - 3 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Ludewig, Matthias T1 - A semiclassical heat kernel proof of the Poincare-Hopf theorem JF - Manuscripta mathematica N2 - 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. Y1 - 2015 U6 - https://doi.org/10.1007/s00229-015-0741-y SN - 0025-2611 SN - 1432-1785 VL - 148 IS - 1-2 SP - 29 EP - 58 PB - Springer CY - Heidelberg ER - TY - INPR A1 - Tarkhanov, Nikolai Nikolaevich T1 - A spectral theorem for deformation quantisation N2 - We present a construction of the eigenstate at a noncritical level of the Hamiltonian function. Moreover, we evaluate the contributions of Morse critical points to the spectral decomposition. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 4 (2015) 4 KW - star product KW - WKB method KW - spectral theorem Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-72425 SN - 2193-6943 VL - 4 IS - 4 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - INPR A1 - Dereudre, David A1 - Mazzonetto, Sara A1 - Roelly, Sylvie T1 - An explicit representation of the transition densities of the skew Brownian motion with drift and two semipermeable barriers N2 - In this paper we obtain an explicit representation of the transition density of the one-dimensional skew Brownian motion with (a constant drift and) two semipermeable barriers. Moreover we propose a rejection method to simulate this density in an exact way. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 4 (2015) 9 KW - skew Brownian motion KW - semipermeable barriers KW - distorted Brownian motion KW - local time KW - rejection sampling KW - exact simulation Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-80613 SN - 2193-6943 VL - 4 IS - 9 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Fedchenko, Dmitri A1 - Tarkhanov, Nikolai Nikolaevich T1 - An index formula for Toeplitz operators JF - Complex variables and elliptic equations N2 - We prove a Fedosov index formula for the index of Toeplitz operators connected with the Hardy space of solutions to an elliptic system of first-order partial differential equations in a bounded domain in R-n with smooth boundary. KW - Toeplitz operators KW - Fredholm property KW - index KW - Primary: 47B35 KW - Secondary: 47L80 Y1 - 2015 U6 - https://doi.org/10.1080/17476933.2015.1050007 SN - 1747-6933 SN - 1747-6941 VL - 60 IS - 12 SP - 1764 EP - 1787 PB - Routledge, Taylor & Francis Group CY - Abingdon ER - TY - INPR A1 - Elin, Mark A1 - Shoikhet, David A1 - Tarkhanov, Nikolai Nikolaevich T1 - Analytic semigroups of holomorphic mappings and composition operators N2 - In this paper we study the problem of analytic extension in parameter for a semigroup of holomorphic self-mappings of the unit ball in a complex Banach space and its relation to the linear continuous semigroup of composition operators. We also provide a brief review around this topic. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 4 (2015) 6 KW - nonlinear semigroup KW - composition operator Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-77914 SN - 2193-6943 VL - 4 IS - 6 PB - Universitätsverlag Potsdam CY - Potsdam ER -