TY - JOUR A1 - Carpentier, Alexandra A1 - Nickl, Richard T1 - On signal detection and confidence sets for low rank inference problems JF - Electronic journal of statistics N2 - We consider the signal detection problem in the Gaussian design trace regression model with low rank alternative hypotheses. We derive the precise (Ingster-type) detection boundary for the Frobenius and the nuclear norm. We then apply these results to show that honest confidence sets for the unknown matrix parameter that adapt to all low rank sub-models in nuclear norm do not exist. This shows that recently obtained positive results in [5] for confidence sets in low rank recovery problems are essentially optimal. KW - Low rank matrices KW - confidence sets KW - signal detection KW - nuclear norm Y1 - 2015 U6 - https://doi.org/10.1214/15-EJS1087 SN - 1935-7524 VL - 9 IS - 2 SP - 2675 EP - 2688 PB - Institute of Mathematical Statistics CY - Cleveland ER - TY - JOUR A1 - Keller, Peter A1 - Roelly, Sylvie A1 - Valleriani, Angelo T1 - On time duality for Markov Chains JF - Stochastic models N2 - For an irreducible continuous time Markov chain, we derive the distribution of the first passage time from a given state i to another given state j and the reversed passage time from j to i, each under the condition of no return to the starting point. When these two distributions are identical, we say that i and j are in time duality. We introduce a new condition called permuted balance that generalizes the concept of reversibility and provides sufficient criteria, based on the structure of the transition graph of the Markov chain. Illustrative examples are provided. KW - Time duality KW - Detailed balance KW - First passage time KW - Reversibility KW - Permuted balance KW - Markov chain Y1 - 2015 U6 - https://doi.org/10.1080/15326349.2014.969736 SN - 1532-6349 SN - 1532-4214 VL - 31 IS - 1 SP - 98 EP - 118 PB - Taylor & Francis Group CY - Philadelphia 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 - 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 - Kröncke, Klaus T1 - On infinitesimal Einstein deformations JF - Differential geometry and its applications N2 - We study infinitesimal Einstein deformations on compact flat manifolds and on product manifolds. Moreover, we prove refinements of results by Koiso and Bourguignon which yield obstructions on the existence of infinitesimal Einstein deformations under certain curvature conditions. (C) 2014 Elsevier B.V. All rights reserved. Y1 - 2015 U6 - https://doi.org/10.1016/j.difgeo.2014.11.007 SN - 0926-2245 SN - 1872-6984 VL - 38 SP - 41 EP - 57 PB - Elsevier CY - Amsterdam 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 - Escribano, Bruno A1 - Akhmatskaya, Elena A1 - Reich, Sebastian A1 - Azpiroz, Jon M. T1 - Multiple-time-stepping generalized hybrid Monte Carlo methods JF - Journal of computational physics N2 - Performance of the generalized shadow hybrid Monte Carlo (GSHMC) method [1], which proved to be superior in sampling efficiency over its predecessors [2-4], molecular dynamics and hybrid Monte Carlo, can be further improved by combining it with multi-time-stepping (MTS) and mollification of slow forces. We demonstrate that the comparatively simple modifications of the method not only lead to better performance of GSHMC itself but also allow for beating the best performed methods, which use the similar force splitting schemes. In addition we show that the same ideas can be successfully applied to the conventional generalized hybrid Monte Carlo method (GHMC). The resulting methods, MTS-GHMC and MTS-GSHMC, provide accurate reproduction of thermodynamic and dynamical properties, exact temperature control during simulation and computational robustness and efficiency. MTS-GHMC uses a generalized momentum update to achieve weak stochastic stabilization to the molecular dynamics (MD) integrator. MTS-GSHMC adds the use of a shadow (modified) Hamiltonian to filter the MD trajectories in the HMC scheme. We introduce a new shadow Hamiltonian formulation adapted to force-splitting methods. The use of such Hamiltonians improves the acceptance rate of trajectories and has a strong impact on the sampling efficiency of the method. Both methods were implemented in the open-source MD package ProtoMol and were tested on a water and a protein systems. Results were compared to those obtained using a Langevin Molly (LM) method [5] on the same systems. The test results demonstrate the superiority of the new methods over LM in terms of stability, accuracy and sampling efficiency. This suggests that putting the MTS approach in the framework of hybrid Monte Carlo and using the natural stochasticity offered by the generalized hybrid Monte Carlo lead to improving stability of MTS and allow for achieving larger step sizes in the simulation of complex systems. KW - Force splitting KW - Mollification KW - Generalized hybrid Monte Carlo KW - Molecular dynamics KW - Modified Hamiltonians Y1 - 2015 U6 - https://doi.org/10.1016/j.jcp.2014.08.052 SN - 0021-9991 SN - 1090-2716 VL - 280 SP - 1 EP - 20 PB - Elsevier CY - San Diego ER - TY - JOUR A1 - Kroencke, Klaus T1 - On the stability of Einstein manifolds JF - Annals of global analysis and geometry N2 - Certain curvature conditions for the stability of Einstein manifolds with respect to the Einstein-Hilbert action are given. These conditions are given in terms of quantities involving the Weyl tensor and the Bochner tensor. In dimension six, a stability criterion involving the Euler characteristic is given. KW - Einstein-Hilbert action KW - variational stability KW - Eigenvalue problem KW - Weyl tensor Y1 - 2015 U6 - https://doi.org/10.1007/s10455-014-9436-y SN - 0232-704X SN - 1572-9060 VL - 47 IS - 1 SP - 81 EP - 98 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Graeter, Joachim A1 - Sperner, Robert P. T1 - On embedding left-ordered groups into division rings JF - Forum mathematicum KW - Left-ordered groups KW - division rings KW - embeddings KW - formal power series Y1 - 2015 U6 - https://doi.org/10.1515/forum-2012-0070 SN - 0933-7741 SN - 1435-5337 VL - 27 IS - 1 SP - 485 EP - 518 PB - De Gruyter CY - Berlin ER - TY - JOUR A1 - Gräter, Joachim A1 - Wirths, Karl-Joachim T1 - On Elementary Bounds for Sigma(infinity)(k=n)k(-s) JF - The American mathematical monthly : an official publication of the Mathematical Association of America N2 - By means of elementary arguments, we derive lower and upper bounds for the infinite series Sigma(infinity)(k=n)k(-s), s is an element of R and s > 1. Y1 - 2015 U6 - https://doi.org/10.4169/amer.math.monthly.122.02.155 SN - 0002-9890 SN - 1930-0972 VL - 122 IS - 2 SP - 155 EP - 158 PB - Mathematical Assoc. of America CY - Washington ER - TY - JOUR A1 - Bär, Christian A1 - Wafo, Roger Tagne T1 - Initial value problems for wave equations on manifolds JF - Mathematical physics, analysis and geometry : an international journal devoted to the theory and applications of analysis and geometry to physics N2 - We study the global theory of linear wave equations for sections of vector bundles over globally hyperbolic Lorentz manifolds. We introduce spaces of finite energy sections and show well-posedness of the Cauchy problem in those spaces. These spaces depend in general on the choice of a time function but it turns out that certain spaces of finite energy solutions are independent of this choice and hence invariantly defined. We also show existence and uniqueness of solutions for the Goursat problem where one prescribes initial data on a characteristic partial Cauchy hypersurface. This extends classical results due to Hormander. KW - Wave equation KW - Globally hyperbolic Lorentz manifold KW - Cauchy problem KW - Goursat problem KW - Finite energy sections Y1 - 2015 U6 - https://doi.org/10.1007/s11040-015-9176-7 SN - 1385-0172 SN - 1572-9656 VL - 18 IS - 1 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Bagderina, Yulia Yu. A1 - Tarkhanov, Nikolai Nikolaevich T1 - Solution of the equivalence problem for the third Painleve equation JF - Journal of mathematical physics N2 - We find necessary conditions for a second order ordinary differential equation to be equivalent to the Painleve III equation under a general point transformation. Their sufficiency is established by reduction to known results for the equations of the form y ' = f (x, y). We consider separately the generic case and the case of reducibility to an autonomous equation. The results are illustrated by the primary resonance equation. Y1 - 2015 U6 - https://doi.org/10.1063/1.4905383 SN - 0022-2488 SN - 1089-7658 VL - 56 IS - 1 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Aizinger, Vadym A1 - Korn, Peter A1 - Giorgetta, Marco A1 - Reich, Sebastian T1 - Large-scale turbulence modelling via alpha-regularisation for atmospheric simulations JF - Journal of turbulence N2 - We study the possibility of obtaining a computational turbulence model by means of non-dissipative regularisation of the compressible atmospheric equations for climate-type applications. We use an -regularisation (Lagrangian averaging) of the atmospheric equations. For the hydrostatic and compressible atmospheric equations discretised using a finite volume method on unstructured grids, deterministic and non-deterministic numerical experiments are conducted to compare the individual solutions and the statistics of the regularised equations to those of the original model. The impact of the regularisation parameter is investigated. Our results confirm the principal compatibility of -regularisation with atmospheric dynamics and encourage further investigations within atmospheric model including complex physical parametrisations. KW - hydrostatic atmosphere KW - non-dissipative regularisations KW - Lagrangian-averaged equations Y1 - 2015 U6 - https://doi.org/10.1080/14685248.2014.991443 SN - 1468-5248 VL - 16 IS - 4 SP - 367 EP - 391 PB - Routledge, Taylor & Francis Group CY - Abingdon 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 - 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 - THES A1 - Wallenta, Daniel T1 - Sequences of compact curvature T1 - Sequenzen mit kompakter Krümmung N2 - By perturbing the differential of a (cochain-)complex by "small" operators, one obtains what is referred to as quasicomplexes, i.e. a sequence whose curvature is not equal to zero in general. In this situation the cohomology is no longer defined. Note that it depends on the structure of the underlying spaces whether or not an operator is "small." This leads to a magical mix of perturbation and regularisation theory. In the general setting of Hilbert spaces compact operators are "small." In order to develop this theory, many elements of diverse mathematical disciplines, such as functional analysis, differential geometry, partial differential equation, homological algebra and topology have to be combined. All essential basics are summarised in the first chapter of this thesis. This contains classical elements of index theory, such as Fredholm operators, elliptic pseudodifferential operators and characteristic classes. Moreover we study the de Rham complex and introduce Sobolev spaces of arbitrary order as well as the concept of operator ideals. In the second chapter, the abstract theory of (Fredholm) quasicomplexes of Hilbert spaces will be developed. From the very beginning we will consider quasicomplexes with curvature in an ideal class. We introduce the Euler characteristic, the cone of a quasiendomorphism and the Lefschetz number. In particular, we generalise Euler's identity, which will allow us to develop the Lefschetz theory on nonseparable Hilbert spaces. Finally, in the third chapter the abstract theory will be applied to elliptic quasicomplexes with pseudodifferential operators of arbitrary order. We will show that the Atiyah-Singer index formula holds true for those objects and, as an example, we will compute the Euler characteristic of the connection quasicomplex. In addition to this we introduce geometric quasiendomorphisms and prove a generalisation of the Lefschetz fixed point theorem of Atiyah and Bott. N2 - Die Theorie der Sequenzen mit kompakter Krümmung, sogenannter Quasikomplexe, ist eine Verallgemeinerung der Theorie der Fredholm Komplexe. Um ein Verständnis für (Quasi-)Komplexe zu gewinnen, müssen Inhalte aus verschiedenen Teilgebieten der Mathematik kombiniert werden. Alle hierfür wesentlichen Grundlagen sind im ersten Kapitel dieser Dissertation zusammengefasst. Dies betrifft unter anderem gewisse Elemente der Funktionalanalysis und der Differentialgeometrie, sowie die Theorie der klassischen Pseudodifferentialoperatoren. Im zweiten Kapitel wird anschließend die abstrakte Theorie der Quasikomplexe und zugehöriger Quasimorphismen im Kontext der Funktionalanalysis entwickelt. Dabei werden verschiedene Typen von Quasikomplexen und Quasimorphismen klassifiziert, deren Eigenschaften analysiert und Beispiele betrachtet. Ein zentraler Punkt hierbei ist die Lösung des Problems, für welche dieser Objekte sich eine besondere charakteristische Zahl, die sogenannte Lefschetz-Zahl, definieren lässt. Die dargestellten Resultate zeigen, dass die in dieser Arbeit gegebene Definition eine natürliche Erweiterung der klassischen Lefschetz-Zahl darstellt. Abschließend wird die entwickelte Theorie im dritten Kapitel auf elliptische Quasikomplexe von Pseudodifferentialoperatoren angewendet. Dabei werden insbesondere Verallgemeinerungen der berühmten Atiyah-Singer-Index-Formel und des Lefschetz-Fixpunkt-Theorems von Atiyah and Bott bewiesen. KW - Index Theorie KW - Fredholm Komplexe KW - Elliptische Komplexe KW - Index theory KW - Elliptic complexes KW - Fredholm complexes Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-87489 ER - TY - BOOK A1 - Kulik, Alexei Michajlovič ED - Roelly, Sylvie T1 - Introduction to Ergodic rates for Markov chains and processes BT - with applications to limit theorems N2 - The present lecture notes aim for an introduction to the ergodic behaviour of Markov Processes and addresses graduate students, post-graduate students and interested readers. Different tools and methods for the study of upper bounds on uniform and weak ergodic rates of Markov Processes are introduced. These techniques are then applied to study limit theorems for functionals of Markov processes. This lecture course originates in two mini courses held at University of Potsdam, Technical University of Berlin and Humboldt University in spring 2013 and Ritsumameikan University in summer 2013. Alexei Kulik, Doctor of Sciences, is a Leading researcher at the Institute of Mathematics of Ukrainian National Academy of Sciences. T3 - Lectures in pure and applied mathematics - 2 KW - Markov processes KW - Markovprozesse KW - long-time behaviour KW - Langzeitverhalten KW - ergodic rates KW - Konvergenzrate Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-79360 SN - 978-3-86956-338-1 SN - 2199-4951 SN - 2199-496X PB - Universitätsverlag Potsdam CY - Potsdam 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 - GEN A1 - Flad, Heinz-Jürgen A1 - Harutyunyan, Gohar A1 - Schulze, Bert-Wolfgang T1 - Singular analysis and coupled cluster theory N2 - The primary motivation for systematic bases in first principles electronic structure simulations is to derive physical and chemical properties of molecules and solids with predetermined accuracy. This requires a detailed understanding of the asymptotic behaviour of many-particle Coulomb systems near coalescence points of particles. Singular analysis provides a convenient framework to study the asymptotic behaviour of wavefunctions near these singularities. In the present work, we want to introduce the mathematical framework of singular analysis and discuss a novel asymptotic parametrix construction for Hamiltonians of many-particle Coulomb systems. This corresponds to the construction of an approximate inverse of a Hamiltonian operator with remainder given by a so-called Green operator. The Green operator encodes essential asymptotic information and we present as our main result an explicit asymptotic formula for this operator. First applications to many-particle models in quantum chemistry are presented in order to demonstrate the feasibility of our approach. The focus is on the asymptotic behaviour of ladder diagrams, which provide the dominant contribution to shortrange correlation in coupled cluster theory. Furthermore, we discuss possible consequences of our asymptotic analysis with respect to adaptive wavelet approximation. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 302 Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-102306 SP - 31530 EP - 31541 ER - TY - JOUR A1 - Mahmoudi, Mahdi Hedayat A1 - Schulze, Bert-Wolfgang A1 - Tepoyan, Liparit T1 - Continuous and variable branching asymptotics JF - Journal of pseudo-differential operators and applications N2 - The regularity of solutions to elliptic equations on a manifold with singularities, say, an edge, can be formulated in terms of asymptotics in the distance variable r > 0 to the singularity. In simplest form such asymptotics turn to a meromorphic behaviour under applying the Mellin transform on the half-axis. Poles, multiplicity, and Laurent coefficients form a system of asymptotic data which depend on the specific operator. Moreover, these data may depend on the variable y along the edge. We then have y-dependent families of meromorphic functions with variable poles, jumping multiplicities and a discontinuous dependence of Laurent coefficients on y. We study here basic phenomena connected with such variable branching asymptotics, formulated in terms of variable continuous asymptotics with a y-wise discrete behaviour. KW - Asymptotics of solutions KW - Weighted edge spaces KW - Edge symbols Y1 - 2015 U6 - https://doi.org/10.1007/s11868-015-0110-3 SN - 1662-9981 SN - 1662-999X VL - 6 IS - 1 SP - 69 EP - 112 PB - Springer CY - Basel ER -