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 - 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 - 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 - 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 - JOUR A1 - Antoniouk, Alexandra Viktorivna A1 - Kiselev, Oleg M. A1 - Tarkhanov, Nikolai Nikolaevich T1 - Asymptotic Solutions of the Dirichlet Problem for the Heat Equation at a Characteristic Point JF - Ukrainian mathematical journal N2 - The Dirichlet problem for the heat equation in a bounded domain aS, a"e (n+1) is characteristic because there are boundary points at which the boundary touches a characteristic hyperplane t = c, where c is a constant. For the first time, necessary and sufficient conditions on the boundary guaranteeing that the solution is continuous up to the characteristic point were established by Petrovskii (1934) under the assumption that the Dirichlet data are continuous. The appearance of Petrovskii's paper was stimulated by the existing interest to the investigation of general boundary-value problems for parabolic equations in bounded domains. We contribute to the study of this problem by finding a formal solution of the Dirichlet problem for the heat equation in a neighborhood of a cuspidal characteristic boundary point and analyzing its asymptotic behavior. Y1 - 2015 U6 - https://doi.org/10.1007/s11253-015-1038-8 SN - 0041-5995 SN - 1573-9376 VL - 66 IS - 10 SP - 1455 EP - 1474 PB - Springer CY - New York ER - TY - JOUR A1 - Kiy, Alexander A1 - Dehne, Julian A1 - Bussler, Dirk T1 - Aufbau einer Cloud-Speicherlösung und Integration in bestehende IuK-Infrastrukturen am Beispiel ownCloud an der Universität Potsdam JF - Cloudspeicher im Hochschuleinsatz 2015: Proceedings der Tagung "Cloudspeicher im Hochschuleinsatz" am 07. und 08. Mai 2015 am IT-Service-Center (tubIT) der Technischen Universität Berlin N2 - In 2015 the second conference „Cloud Storage Deployment in Academics“ took place. Interest regarding this issue was again high and topics established in 2014 like data security and scalability were complemented by new ones like federations or technical integration in existing infrastructures. This is caused by the advances in the establishment of cloud-based storage systems. This publication contains the contributions of the conference „Cloud Storage Deployment in Academics 2015“, which took place in may 2015 at TU Berlin. KW - Cloud Computing KW - Hochschule KW - Studium Y1 - 2015 SN - 978-3-7983-2780-1 SP - 61 EP - 72 PB - Universitätsverlag der TU Berlin CY - Berlin ER - TY - JOUR A1 - Hoegele, Michael A1 - Ruffino, Paulo T1 - Averaging along foliated Levy diffusions JF - Nonlinear analysis : theory, methods & applications ; an international multidisciplinary journal N2 - This article studies the dynamics of the strong solution of a SDE driven by a discontinuous Levy process taking values in a smooth foliated manifold with compact leaves. It is assumed that it is foliated in the sense that its trajectories stay on the leaf of their initial value for all times almost surely. Under a generic ergodicity assumption for each leaf, we determine the effective behaviour of the system subject to a small smooth perturbation of order epsilon > 0, which acts transversal to the leaves. The main result states that, on average, the transversal component of the perturbed SDE converges uniformly to the solution of a deterministic ODE as e tends to zero. This transversal ODE is generated by the average of the perturbing vector field with respect to the invariant measures of the unperturbed system and varies with the transversal height of the leaves. We give upper bounds for the rates of convergence and illustrate these results for the random rotations on the circle. This article complements the results by Gonzales and Ruffino for SDEs of Stratonovich type to general Levy driven SDEs of Marcus type. KW - Averaging principle KW - Levy diffusions on manifolds KW - Foliated spaces KW - Marcus canonical equation KW - Stochastic Hamiltonian KW - Stochastic geometry KW - Perturbation theory Y1 - 2015 U6 - https://doi.org/10.1016/j.na.2014.09.006 SN - 0362-546X SN - 1873-5215 VL - 112 SP - 1 EP - 14 PB - Elsevier CY - Oxford ER - TY - JOUR A1 - Pirhayati, Mohammad T1 - Boundary symbols in the cone algebra JF - Journal of pseudo-differential operators and applications N2 - Boundary value problems on a smooth manifold X with boundary have the structure of edge problems. Operators A are described in terms of a principal symbolic hierarchy, namely, according to the stratification of X, with the interior and the boundary We focus here on operators with and without the transmission property and establish a new relationship between boundary symbols and operators in the cone calculus transversal to the boundary. KW - Cone KW - Edge and corner pseudo-differential operators KW - Ellipticity of corner-degenerate operators KW - Iterated corner asymptotics of solutions Y1 - 2015 U6 - https://doi.org/10.1007/s11868-015-0123-y SN - 1662-9981 SN - 1662-999X VL - 6 IS - 3 SP - 307 EP - 339 PB - Springer CY - Basel ER - TY - JOUR A1 - Conforti, Giovanni A1 - Leonard, Christian A1 - Murr, Rüdiger A1 - Roelly, Sylvie T1 - Bridges of Markov counting processes. Reciprocal classes and duality formulas JF - Electronic communications in probability N2 - Processes sharing the same bridges are said to belong to the same reciprocal class. In this article we analyze reciprocal classes of Markov counting processes by identifying their reciprocal invariants and we characterize them as the set of counting processes satisfying some duality formula. KW - Counting process KW - bridge KW - reciprocal class KW - duality formula Y1 - 2015 U6 - https://doi.org/10.1214/ECP.v20-3697 SN - 1083-589X VL - 20 PB - Univ. of Washington, Mathematics Dep. CY - Seattle ER -