TY - JOUR
A1 - Böckmann, Christine
A1 - Brückner, Axel
T1 - 100 years of the Runge-Kutta method : a brief editing for schools
BT - Hundred years of the Runge-Kutta method : a brief editing for schools
N2 - This paper reports on the historical development of the Runge-Kutta methods beginning with the simple Euler method up to an embedded 13-stage method. Moreover, the design and the use of those methods under error order, stability and computation time conditions is edited for students of numerical analysis at undergraduate level. The second part presents applications in natural sciences, compares different methods and illustrates some of the difficulties of numerical solutions.
Y1 - 2001
SN - 0268-3679
ER -
TY - JOUR
A1 - Dzhunushaliev, Vladimir
A1 - Schmidt, Hans-Jürgen
T1 - 2+2-decomposable solutions of weyl gravity
BT - Zwei plus zwei-decomposable solutions of wey gravity
Y1 - 1999
ER -
TY - JOUR
A1 - Gonzáles-Diaz, P. F.
A1 - Kasper, Uwe
A1 - Rainer, Martin
T1 - 2-Dimensional dilatonic gravity from multidimensional Einstein gravity
Y1 - 1998
ER -
TY - BOOK
A1 - Gonzáles-Diaz, P. F.
A1 - Kasper, Uwe
A1 - Rainer, Martin
T1 - 2-Dimensional dilatonic gravity from multidimensional Einstein gravity
T3 - Preprint / Universität Potsdam, Institut für Mathematik
Y1 - 1997
VL - 1997, 22
PB - Univ.
CY - Potsdam
ER -
TY - JOUR
A1 - Schmidt, Hans-Jürgen
T1 - 2-dimensional representations of 4-dimensional gravitational waves
Y1 - 1998
ER -
TY - JOUR
A1 - Hoehnke, Hans-Jürgen
A1 - Johnson, K. W.
T1 - 3-characters are sufficient for the group determinant
BT - Three-characters are sufficient for the group determinant
Y1 - 1995
ER -
TY - JOUR
A1 - Dzhunushaliev, Vladimir
A1 - Schmidt, Hans-Jürgen
T1 - 4D wormhole with signature change in the presence of extra dimensions
BT - VierD wormhole with signature change in the presence of extra dimensions
JF - General relativity and quantum cosmology : preprints gr-qc
Y1 - 1999
UR - http://xxx.soton.ac.uk/form/gr-qc?
VL - 9908076
ER -
TY - JOUR
A1 - Mariucci, Ester
A1 - Ray, Kolyan
A1 - Szabo, Botond
T1 - A Bayesian nonparametric approach to log-concave density estimation
JF - Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability
N2 - The estimation of a log-concave density on R is a canonical problem in the area of shape-constrained nonparametric inference. We present a Bayesian nonparametric approach to this problem based on an exponentiated Dirichlet process mixture prior and show that the posterior distribution converges to the log-concave truth at the (near-) minimax rate in Hellinger distance. Our proof proceeds by establishing a general contraction result based on the log-concave maximum likelihood estimator that prevents the need for further metric entropy calculations. We further present computationally more feasible approximations and both an empirical and hierarchical Bayes approach. All priors are illustrated numerically via simulations.
KW - convergence rate
KW - density estimation
KW - Dirichlet mixture
KW - log-concavity
KW - nonparametric hypothesis testing
KW - posterior distribution
Y1 - 2020
U6 - https://doi.org/10.3150/19-BEJ1139
SN - 1350-7265
SN - 1573-9759
VL - 26
IS - 2
SP - 1070
EP - 1097
PB - International Statistical Institute
CY - The Hague
ER -
TY - JOUR
A1 - Hoehnke, Hans-Jürgen
T1 - A Birkhoff theorem for partial algebras via completion
Y1 - 1996
ER -
TY - BOOK
A1 - Aizenberg, Lev A.
A1 - Tarchanov, Nikolaj N.
T1 - A Bohr phenomenon for elliptic equations
T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1 - 1999
SN - 1437-739X
PB - Univ.
CY - Potsdam
ER -
TY - BOOK
A1 - Witt, Ingo
T1 - A calculus for a class of finitely degenerate pseudodifferential operators
T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1 - 2002
SN - 1437-739X
PB - Univ.
CY - Potsdam
ER -
TY - BOOK
A1 - Rabinovich, Vladimir
A1 - Schulze, Bert-Wolfgang
A1 - Tarchanov, Nikolaj N.
T1 - A calculus of boundary value problems in domains with Non-Lipschitz singular points
T3 - Preprint / Universität Potsdam, Institut für Mathematik
Y1 - 1997
VL - 1997, 09
PB - Univ.
CY - Potsdam
ER -
TY - JOUR
A1 - Ly, Ibrahim
T1 - A Cauchy problem for the Cauchy-Riemann operator
JF - Afrika Matematika
N2 - We study the Cauchy problem for a nonlinear elliptic equation with data on a piece S of the boundary surface partial derivative X. By the Cauchy problem is meant any boundary value problem for an unknown function u in a domain X with the property that the data on S, if combined with the differential equations in X, allows one to determine all derivatives of u on S by means of functional equations. In the case of real analytic data of the Cauchy problem, the existence of a local solution near S is guaranteed by the Cauchy-Kovalevskaya theorem. We discuss a variational setting of the Cauchy problem which always possesses a generalized solution.
KW - nonlinear PDI
KW - Cauchy problem
KW - Zaremba problem
Y1 - 2020
U6 - https://doi.org/10.1007/s13370-020-00810-4
SN - 1012-9405
SN - 2190-7668
VL - 32
IS - 1-2
SP - 69
EP - 76
PB - Springer
CY - Heidelberg
ER -
TY - JOUR
A1 - Denecke, Klaus-Dieter
A1 - Wismath, Shelly
T1 - A characterization of k-normal varieties
N2 - Let v be a valuation of terms of type tau, assigning to each term t of type tau a value v(t) greater than or equal to 0. Let k greater than or equal to 1 be a natural number. An identity s approximate to t of type tau is called k- normal if either s = t or both s and t have value greater than or equal to k, and otherwise is called non-k-normal. A variety V of type tau is said to be k-normal if all its identities are k-normal, and non-k-normal otherwise. In the latter case, there is a unique smallest k-normal variety N-k(A) (V) to contain V , called the k-normalization of V. Inthe case k = 1, for the usual depth valuation of terms, these notions coincide with the well-known concepts of normal identity, normal variety, and normalization of a variety. I. Chajda has characterized the normalization of a variety by means of choice algebras. In this paper we generalize his results to a characterization of the k-normalization of a variety, using k-choice algebras. We also introduce the concept of a k-inflation algebra, and for the case that v is the usual depth valuation of terms, we prove that a variety V is k-normal iff it is closed under the formation of k- inflations, and that the k-normalization of V consists precisely of all homomorphic images of k-inflations of algebras in V
Y1 - 2004
SN - 0002-5240
ER -
TY - JOUR
A1 - Denecke, Klaus-Dieter
A1 - Koppitz, Jörg
T1 - A characterization of M-solid varieties of semigroups
Y1 - 1999
ER -
TY - INPR
A1 - Fedchenko, Dmitry
A1 - Tarkhanov, Nikolai Nikolaevich
T1 - A Class of Toeplitz Operators in Several Variables
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.
T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 2(2013)17
KW - Cauchy data spaces
KW - Laplace-Beltrami operator
KW - Toeplitz operators
KW - Fredholm property
Y1 - 2013
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-68932
SN - 2193-6943
ER -
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 - Akhmatskaya, Elena
A1 - Bou-Rabee, Nawaf
A1 - Reich, Sebastian
T1 - A comparison of generalized hybrid Monte Carlo methods with and without momentum flip
N2 - The generalized hybrid Monte Carlo (GHMC) method combines Metropolis corrected constant energy simulations with a partial random refreshment step in the particle momenta. The standard detailed balance condition requires that momenta are negated upon rejection of a molecular dynamics proposal step. The implication is a trajectory reversal upon rejection, which is undesirable when interpreting GHMC as thermostated molecular dynamics. We show that a modified detailed balance condition can be used to implement GHMC without momentum flips. The same modification can be applied to the generalized shadow hybrid Monte Carlo (GSHMC) method. Numerical results indicate that GHMC/GSHMC implementations with momentum flip display a favorable behavior in terms of sampling efficiency, i.e., the traditional GHMC/GSHMC implementations with momentum flip got the advantage of a higher acceptance rate and faster decorrelation of Monte Carlo samples. The difference is more pronounced for GHMC. We also numerically investigate the behavior of the GHMC method as a Langevin-type thermostat. We find that the GHMC method without momentum flip interferes less with the underlying stochastic molecular dynamics in terms of autocorrelation functions and it to be preferred over the GHMC method with momentum flip. The same finding applies to GSHMC.
Y1 - 2009
UR - http://www.sciencedirect.com/science/journal/00219991
U6 - https://doi.org/10.1016/j.jcp.2008.12.014
SN - 0021-9991
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 - Maier, Corinna Sabrina
A1 - Wiljes, Jana de
A1 - Hartung, Niklas
A1 - Kloft, Charlotte
A1 - Huisinga, Wilhelm
T1 - A continued learning approach for model-informed precision dosing
BT - Updating models in clinical practice
JF - CPT: pharmacometrics & systems pharmacology
N2 - Model-informed precision dosing (MIPD) is a quantitative dosing framework that combines prior knowledge on the drug-disease-patient system with patient data from therapeutic drug/ biomarker monitoring (TDM) to support individualized dosing in ongoing treatment. Structural models and prior parameter distributions used in MIPD approaches typically build on prior clinical trials that involve only a limited number of patients selected according to some exclusion/inclusion criteria. Compared to the prior clinical trial population, the patient population in clinical practice can be expected to also include altered behavior and/or increased interindividual variability, the extent of which, however, is typically unknown. Here, we address the question of how to adapt and refine models on the level of the model parameters to better reflect this real-world diversity. We propose an approach for continued learning across patients during MIPD using a sequential hierarchical Bayesian framework. The approach builds on two stages to separate the update of the individual patient parameters from updating the population parameters. Consequently, it enables continued learning across hospitals or study centers, because only summary patient data (on the level of model parameters) need to be shared, but no individual TDM data. We illustrate this continued learning approach with neutrophil-guided dosing of paclitaxel. The present study constitutes an important step toward building confidence in MIPD and eventually establishing MIPD increasingly in everyday therapeutic use.
Y1 - 2021
U6 - https://doi.org/10.1002/psp4.12745
SN - 2163-8306
VL - 11
IS - 2
SP - 185
EP - 198
PB - London
CY - Nature Publ. Group
ER -
TY - BOOK
A1 - Dahlke, Stephan
A1 - Maaß, Peter
T1 - A continuous wavelet transform on tangent bundles of spheres
T3 - Preprint / Universität Potsdam, Institut für Mathematik
Y1 - 1994
VL - 1994, 16
PB - Univ.
CY - Potsdam
ER -
TY - JOUR
A1 - Cvetković, Nada
A1 - Conrad, Tim
A1 - Lie, Han Cheng
T1 - A convergent discretization method for transition path theory for diffusion processes
JF - Multiscale modeling & simulation : a SIAM interdisciplinary journal
N2 - Transition path theory (TPT) for diffusion processes is a framework for analyzing the transitions of multiscale ergodic diffusion processes between disjoint metastable subsets of state space. Most methods for applying TPT involve the construction of a Markov state model on a discretization of state space that approximates the underlying diffusion process. However, the assumption of Markovianity is difficult to verify in practice, and there are to date no known error bounds or convergence results for these methods. We propose a Monte Carlo method for approximating the forward committor, probability current, and streamlines from TPT for diffusion processes. Our method uses only sample trajectory data and partitions of state space based on Voronoi tessellations. It does not require the construction of a Markovian approximating process. We rigorously prove error bounds for the approximate TPT objects and use these bounds to show convergence to their exact counterparts in the limit of arbitrarily fine discretization. We illustrate some features of our method by application to a process that solves the Smoluchowski equation on a triple-well potential.
KW - ergodic diffusion processes
KW - transition paths
KW - rare events
KW - Monte Carlo
KW - methods
Y1 - 2021
U6 - https://doi.org/10.1137/20M1329354
SN - 1540-3459
SN - 1540-3467
VL - 19
IS - 1
SP - 242
EP - 266
PB - Society for Industrial and Applied Mathematics
CY - Philadelphia
ER -
TY - BOOK
A1 - Gauthier, P. M.
A1 - Tarkhanov, Nikolai Nikolaevich
T1 - A covering proberty of the Riemann zeta-funktion
T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1 - 2004
SN - 1437-739X
PB - Univ.
CY - Potsdam
ER -
TY - BOOK
A1 - Korey, Michael Brian
T1 - A Decomposition of functions with vanishing mean oscillation
T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgrupe Partielle Differentialgleichun
Y1 - 2001
SN - 1437-339X
PB - Univ.
CY - Potsdam
ER -
TY - BOOK
A1 - Korrami, M.
A1 - Mansouri, R.
A1 - Mohazzab, Masoud
T1 - A decrumpling model of the universe
T3 - Preprint / Universität Potsdam, Institut für Mathematik
Y1 - 1996
VL - 1996, 09
PB - Univ.
CY - Potsdam
ER -
TY - JOUR
A1 - Al-Saedy, Ammar Jaffar Muhesin
A1 - Tarchanov, Nikolaj Nikolaevič
T1 - A degree theory for Lagrangian boundary value problems
JF - Žurnal Sibirskogo Federalʹnogo Universiteta = Journal of Siberian Federal University; mathematics & physics
N2 - We study those nonlinear partial differential equations which appear as Euler-Lagrange equations of variational problems. On defining weak boundary values of solutions to such equations we initiate the theory of Lagrangian boundary value problems in spaces of appropriate smoothness. We also analyse if the concept of mapping degree of current importance applies to Lagrangian problems.
N2 - Мы изучаем те нелинейные уравнения с частными производными, которые возникают как уравнения Эйлера-Лагранжа вариационных задач. Определяя слабые граничные значения решений таких уравнений, мы инициируем теорию лагранжевых краевых задач в функциональных пространствах подходящей гладкости. Мы также анализируем, применяется ли современная концепция степени отображения к лагранжевым проблемам.
KW - nonlinear equations
KW - Lagrangian system
KW - weak boundary values
KW - quasilinear Fredholm operators
KW - mapping degree
Y1 - 2020
U6 - https://doi.org/10.17516/1997-1397-2020-13-1-5-25
SN - 1997-1397
SN - 2313-6022
VL - 13
IS - 1
SP - 5
EP - 25
PB - Sibirskij Federalʹnyj Universitet
CY - Krasnojarsk
ER -
TY - THES
A1 - Hanke, Timo
T1 - A direct approach to noncrossed product division algebras
Y1 - 2001
ER -
TY - THES
A1 - Kärsten, Fatma
T1 - A duality for a compact group and a second cohomology of its dual
Y1 - 1998
ER -
TY - JOUR
A1 - Reich, Sebastian
T1 - A dynamical systems framework for intermittent data assimilation
JF - BIT : numerical mathematics ; the leading applied mathematics journal for all computational mathematicians
N2 - We consider the problem of discrete time filtering (intermittent data assimilation) for differential equation models and discuss methods for its numerical approximation. The focus is on methods based on ensemble/particle techniques and on the ensemble Kalman filter technique in particular. We summarize as well as extend recent work on continuous ensemble Kalman filter formulations, which provide a concise dynamical systems formulation of the combined dynamics-assimilation problem. Possible extensions to fully nonlinear ensemble/particle based filters are also outlined using the framework of optimal transportation theory.
KW - Data assimilation
KW - Ensemble Kalman filter
KW - Dynamical systems
KW - Nonlinear filters
KW - Optimal transportation
Y1 - 2011
U6 - https://doi.org/10.1007/s10543-010-0302-4
SN - 0006-3835
VL - 51
IS - 1
SP - 235
EP - 249
PB - Springer
CY - Dordrecht
ER -
TY - JOUR
A1 - Lledó, Fernando
T1 - A family of examples with quantum constraints
Y1 - 1997
ER -
TY - BOOK
A1 - Lledó, Fernando
T1 - A family of examples with quantum constraints
T3 - Preprint / Universität Potsdam, Institut für Mathematik
Y1 - 1996
VL - 1996, 01
PB - Univ.
CY - Potsdam
ER -
TY - JOUR
A1 - Ziehe, Andreas
A1 - Laskov, Pavel
A1 - Nolte, G
A1 - Müller, Klaus-Robert
T1 - A fast algorithm for joint diagonalization with non-orthogonal transformations and its application to blind source separation
N2 - A new efficient algorithm is presented for joint diagonalization of several matrices. The algorithm is based on the Frobenius-norm formulation of the joint diagonalization problem, and addresses diagonalization with a general, non- orthogonal transformation. The iterative scheme of the algorithm is based on a multiplicative update which ensures the invertibility of the diagonalizer. The algorithm's efficiency stems from the special approximation of the cost function resulting in a sparse, block-diagonal Hessian to be used in the computation of the quasi-Newton update step. Extensive numerical simulations illustrate the performance of the algorithm and provide a comparison to other leading diagonalization methods. The results of such comparison demonstrate that the proposed algorithm is a viable alternative to existing state-of-the-art joint diagonalization algorithms. The practical use of our algorithm is shown for blind source separation problems
Y1 - 2004
ER -
TY - BOOK
A1 - Tarkhanov, Nikolai Nikolaevich
T1 - A fixed point formula in one complex variable
T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1 - 2003
SN - 1437-739X
PB - Univ.
CY - Potsdam
ER -
TY - JOUR
A1 - Reich, Sebastian
T1 - A Gaussian-mixture ensemble transform filter
JF - Quarterly journal of the Royal Meteorological Society
N2 - We generalize the popular ensemble Kalman filter to an ensemble transform filter, in which the prior distribution can take the form of a Gaussian mixture or a Gaussian kernel density estimator. The design of the filter is based on a continuous formulation of the Bayesian filter analysis step. We call the new filter algorithm the ensemble Gaussian-mixture filter (EGMF). The EGMF is implemented for three simple test problems (Brownian dynamics in one dimension, Langevin dynamics in two dimensions and the three-dimensional Lorenz-63 model). It is demonstrated that the EGMF is capable of tracking systems with non-Gaussian uni- and multimodal ensemble distributions.
KW - data assimilation
KW - ensemble Kalman filter
KW - nonlinear filtering
KW - Gaussian mixtures
KW - Gaussian kernel estimators
Y1 - 2012
U6 - https://doi.org/10.1002/qj.898
SN - 0035-9009
VL - 138
IS - 662
SP - 222
EP - 233
PB - Wiley-Blackwell
CY - Malden
ER -
TY - JOUR
A1 - Fedosov, Boris
A1 - Schulze, Bert-Wolfgang
A1 - Tarkhanov, Nikolai Nikolaevich
T1 - A general index formula on toric manifolds with conical point
Y1 - 2001
ER -
TY - JOUR
A1 - Shojaei-Fard, Ali
T1 - A GEOMETRIC PERSPECTIVE ON COUNTERTERMS RELATED TO DYSON-SCHWINGER
EQUATIONS
JF - INTERNATIONAL JOURNAL OF MODERN PHYSICS A
N2 - We study Dyson-Schwinger equations (DSEs) in terms of some groups of diffeographisms to provide a new geometric formulation for their corresponding counterterms on the basis of systems of ordinary differential equations.
KW - Dyson-Schwinger equations
KW - Hopf algebra of Feynman diagrams
KW - counterterms
KW - Picard-Fuchs equations
KW - equi-singular connections
Y1 - 2013
U6 - https://doi.org/10.1142/S0217751X13501704
SN - 0217-751X
SN - 1793-656X
VL - 28
IS - 32
PB - WORLD SCIENTIFIC PUBL CO PTE LTD
CY - SINGAPORE
ER -
TY - JOUR
A1 - Zass, Alexander
T1 - A Gibbs point process of diffusions: Existence and uniqueness
JF - Lectures in pure and applied mathematics
KW - random point processes
KW - statistical mechanics
KW - stochastic analysis
Y1 - 2020
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-471951
SN - 978-3-86956-485-2
SN - 2199-4951
SN - 2199-496X
IS - 6
SP - 13
EP - 22
PB - Universitätsverlag Potsdam
CY - Potsdam
ER -
TY - JOUR
A1 - Kling, Christoph
A1 - Schneidenbach, Lars
A1 - Schnor, Bettina
T1 - A high performance gigabit ethernet messaging method for PVFS
N2 - Parallel File Systems like PVFS2 are a necessary compo nent for high-performance computing. The design of ef ;cient communication layers for these systems is still of great research interest. This paper presents a low- latency messaging method for PVFS2 dedicated for Gigabit Ether net networks and discusses relevant design issues. In con trast to other approaches, we argue that zero-copying can be achieved also for big messages without use of a rendez vous protocol. Further, ef;ciency within the communica tion layer like a small call stack plays an important role.
Y1 - 2005
SN - 0-88986-525-6
ER -
TY - INPR
A1 - Alsaedy, Ammar
A1 - Tarkhanov, Nikolai Nikolaevich
T1 - A Hilbert boundary value problem for generalised Cauchy-Riemann equations
N2 - We elaborate a boundary Fourier method for studying an analogue of the Hilbert problem for analytic functions within the framework of generalised Cauchy-Riemann equations. The boundary value problem need not satisfy the Shapiro-Lopatinskij condition and so it fails to be Fredholm in Sobolev spaces. We show a solvability condition of the Hilbert problem, which looks like those for ill-posed
problems, and construct an explicit formula for approximate solutions.
T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 5 (2016) 1
KW - Dirac operator
KW - Clifford algebra
KW - Riemann-Hilbert problem
KW - Fredholm operator
Y1 - 2016
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-86109
SN - 2193-6943
VL - 5
IS - 1
PB - Universitätsverlag Potsdam
CY - Potsdam
ER -
TY - JOUR
A1 - Kempton, Mark
A1 - Münch, Florentin
A1 - Yau, Shing-Tung
T1 - A homology vanishing theorem for graphs with positive curvature
JF - Communications in analysis and geometry
N2 - We prove a homology vanishing theorem for graphs with positive Bakry-' Emery curvature, analogous to a classic result of Bochner on manifolds [3]. Specifically, we prove that if a graph has positive curvature at every vertex, then its first homology group is trivial, where the notion of homology that we use for graphs is the path homology developed by Grigor'yan, Lin, Muranov, and Yau [11]. We moreover prove that the fundamental group is finite for graphs with positive Bakry-' Emery curvature, analogous to a classic result of Myers on manifolds [22]. The proofs draw on several separate areas of graph theory, including graph coverings, gain graphs, and cycle spaces, in addition to the Bakry-Emery curvature, path homology, and graph homotopy. The main results follow as a consequence of several different relationships developed among these different areas. Specifically, we show that a graph with positive curvature cannot have a non-trivial infinite cover preserving 3-cycles and 4-cycles, and give a combinatorial interpretation of the first path homology in terms of the cycle space of a graph. Furthermore, we relate gain graphs to graph homotopy and the fundamental group developed by Grigor'yan, Lin, Muranov, and Yau [12], and obtain an alternative proof of their result that the abelianization of the fundamental group of a graph is isomorphic to the first path homology over the integers.
Y1 - 2021
UR - https://www.intlpress.com/site/pub/files/_fulltext/journals/cag/2021/0029/0006/CAG-2021-0029-0006-a005.pdf
U6 - https://doi.org/10.4310/CAG.2021.v29.n6.a5
SN - 1019-8385
SN - 1944-9992
VL - 29
IS - 6
SP - 1449
EP - 1473
PB - International Press of Boston
CY - Somerville
ER -
TY - INPR
A1 - Méléard, Sylvie
A1 - Roelly, Sylvie
T1 - A host-parasite multilevel interacting process and continuous approximations
N2 - We are interested in modeling some two-level population dynamics, resulting from the interplay of ecological interactions and phenotypic variation of individuals (or hosts) and the evolution of cells (or parasites) of two types living in these individuals. The ecological parameters of the individual dynamics depend on the number of cells of each type contained by the individual and the cell dynamics depends on the trait of the invaded individual. Our models are rooted in the microscopic description of a random (discrete) population of individuals characterized by one or several adaptive traits and cells characterized by their type. The population is modeled as a stochastic point process whose generator captures the probabilistic dynamics over continuous time of birth, mutation and death for individuals and birth and death for cells. The interaction between individuals (resp. between cells) is described by a competition between individual traits (resp. between cell types). We look for tractable large population approximations. By combining various scalings on population size, birth and death rates and mutation step, the single microscopic model is shown to lead to contrasting nonlinear macroscopic limits of different nature: deterministic approximations, in the form of ordinary, integro- or partial differential equations, or probabilistic ones, like stochastic partial differential equations or superprocesses. The study of the long time behavior of these processes seems very hard and we only develop some simple cases enlightening the difficulties involved.
T3 - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2011, 01
KW - two-level interacting processes
KW - birth-death-mutation-competition point process
KW - host-parasite stochastic particle system
Y1 - 2011
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-51694
ER -
TY - JOUR
A1 - Wallenta, Daniel
T1 - A Lefschetz fixed point formula for elliptic quasicomplexes
JF - Integral equations and operator theor
N2 - In a recent paper, the Lefschetz number for endomorphisms (modulo trace class operators) of sequences of trace class curvature was introduced. We show that this is a well defined, canonical extension of the classical Lefschetz number and establish the homotopy invariance of this number. Moreover, we apply the results to show that the Lefschetz fixed point formula holds for geometric quasiendomorphisms of elliptic quasicomplexes.
KW - Elliptic complexes
KW - Fredholm complexes
KW - Lefschetz number
Y1 - 2014
U6 - https://doi.org/10.1007/s00020-014-2122-4
SN - 0378-620X
SN - 1420-8989
VL - 78
IS - 4
SP - 577
EP - 587
PB - Springer
CY - Basel
ER -
TY - INPR
A1 - Wallenta, Daniel
T1 - A Lefschetz fixed point formula for elliptic quasicomplexes
N2 - In a recent paper with N. Tarkhanov, the Lefschetz number for endomorphisms (modulo trace class operators) of sequences of trace class curvature was introduced. We show that this is a well defined, canonical extension of the classical Lefschetz number and establish the homotopy invariance of this number. Moreover, we apply the results to show that the Lefschetz fixed point formula holds for geometric quasiendomorphisms of elliptic quasicomplexes.
T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 2(2013)12
KW - Perturbed complexes
KW - curvature
KW - Lefschetz number
KW - fixed point formula
Y1 - 2013
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-67016
ER -
TY - JOUR
A1 - Bösenberg, Jens
A1 - Alpers, Matthias
A1 - Böckmann, Christine
A1 - Jäger, Horst
A1 - Matthias, Volker
A1 - Trickl, Thomas
A1 - Wandinger, Ulla
A1 - Wiegner, Matthias
T1 - A Lidar Network for the Establishment of an Aerosol Climatology
Y1 - 1998
ER -
TY - JOUR
A1 - Bergemann, Kay
A1 - Reich, Sebastian
T1 - A localization technique for ensemble Kalman filters
N2 - Ensemble Kalman filter techniques are widely used to assimilate observations into dynamical models. The phase- space dimension is typically much larger than the number of ensemble members, which leads to inaccurate results in the computed covariance matrices. These inaccuracies can lead, among other things, to spurious long-range correlations, which can be eliminated by Schur-product-based localization techniques. In this article, we propose a new technique for implementing such localization techniques within the class of ensemble transform/square-root Kalman filters. Our approach relies on a continuous embedding of the Kalman filter update for the ensemble members, i.e. we state an ordinary differential equation (ODE) with solutions that, over a unit time interval, are equivalent to the Kalman filter update. The ODE formulation forms a gradient system with the observations as a cost functional. Besides localization, the new ODE ensemble formulation should also find useful application in the context of nonlinear observation operators and observations that arrive continuously in time.
Y1 - 2010
UR - http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1477-870X
U6 - https://doi.org/10.1002/Qj.591
SN - 0035-9009
ER -
TY - JOUR
A1 - Malem-Shinitski, Noa
A1 - Opper, Manfred
A1 - Reich, Sebastian
A1 - Schwetlick, Lisa
A1 - Seelig, Stefan A.
A1 - Engbert, Ralf
T1 - A mathematical model of local and global attention in natural scene viewing
JF - PLoS Computational Biology : a new community journal
N2 - Author summary
Switching between local and global attention is a general strategy in human information processing. We investigate whether this strategy is a viable approach to model sequences of fixations generated by a human observer in a free viewing task with natural scenes. Variants of the basic model are used to predict the experimental data based on Bayesian inference. Results indicate a high predictive power for both aggregated data and individual differences across observers. The combination of a novel model with state-of-the-art Bayesian methods lends support to our two-state model using local and global internal attention states for controlling eye movements.
Understanding the decision process underlying gaze control is an important question in cognitive neuroscience with applications in diverse fields ranging from psychology to computer vision. The decision for choosing an upcoming saccade target can be framed as a selection process between two states: Should the observer further inspect the information near the current gaze position (local attention) or continue with exploration of other patches of the given scene (global attention)? Here we propose and investigate a mathematical model motivated by switching between these two attentional states during scene viewing. The model is derived from a minimal set of assumptions that generates realistic eye movement behavior. We implemented a Bayesian approach for model parameter inference based on the model's likelihood function. In order to simplify the inference, we applied data augmentation methods that allowed the use of conjugate priors and the construction of an efficient Gibbs sampler. This approach turned out to be numerically efficient and permitted fitting interindividual differences in saccade statistics. Thus, the main contribution of our modeling approach is two-fold; first, we propose a new model for saccade generation in scene viewing. Second, we demonstrate the use of novel methods from Bayesian inference in the field of scan path modeling.
Y1 - 2020
U6 - https://doi.org/10.1371/journal.pcbi.1007880
SN - 1553-734X
SN - 1553-7358
VL - 16
IS - 12
PB - PLoS
CY - San Fransisco
ER -
TY - JOUR
A1 - Hartung, Niklas
A1 - Borghardt, Jens Markus
T1 - A mechanistic framework for a priori pharmacokinetic predictions of orally inhaled drugs
JF - PLoS Computational Biology : a new community journal
N2 - Author summary
The use of orally inhaled drugs for treating lung diseases is appealing since they have the potential for lung selectivity, i.e. high exposure at the site of action -the lung- without excessive side effects. However, the degree of lung selectivity depends on a large number of factors, including physiochemical properties of drug molecules, patient disease state, and inhalation devices. To predict the impact of these factors on drug exposure and thereby to understand the characteristics of an optimal drug for inhalation, we develop a predictive mathematical framework (a "pharmacokinetic model"). In contrast to previous approaches, our model allows combining knowledge from different sources appropriately and its predictions were able to adequately predict different sets of clinical data. Finally, we compare the impact of different factors and find that the most important factors are the size of the inhaled particles, the affinity of the drug to the lung tissue, as well as the rate of drug dissolution in the lung. In contrast to the common belief, the solubility of a drug in the lining fluids is not found to be relevant. These findings are important to understand how inhaled drugs should be designed to achieve best treatment results in patients.
The fate of orally inhaled drugs is determined by pulmonary pharmacokinetic processes such as particle deposition, pulmonary drug dissolution, and mucociliary clearance. Even though each single process has been systematically investigated, a quantitative understanding on the interaction of processes remains limited and therefore identifying optimal drug and formulation characteristics for orally inhaled drugs is still challenging. To investigate this complex interplay, the pulmonary processes can be integrated into mathematical models. However, existing modeling attempts considerably simplify these processes or are not systematically evaluated against (clinical) data. In this work, we developed a mathematical framework based on physiologically-structured population equations to integrate all relevant pulmonary processes mechanistically. A tailored numerical resolution strategy was chosen and the mechanistic model was evaluated systematically against data from different clinical studies. Without adapting the mechanistic model or estimating kinetic parameters based on individual study data, the developed model was able to predict simultaneously (i) lung retention profiles of inhaled insoluble particles, (ii) particle size-dependent pharmacokinetics of inhaled monodisperse particles, (iii) pharmacokinetic differences between inhaled fluticasone propionate and budesonide, as well as (iv) pharmacokinetic differences between healthy volunteers and asthmatic patients. Finally, to identify the most impactful optimization criteria for orally inhaled drugs, the developed mechanistic model was applied to investigate the impact of input parameters on both the pulmonary and systemic exposure. Interestingly, the solubility of the inhaled drug did not have any relevant impact on the local and systemic pharmacokinetics. Instead, the pulmonary dissolution rate, the particle size, the tissue affinity, and the systemic clearance were the most impactful potential optimization parameters. In the future, the developed prediction framework should be considered a powerful tool for identifying optimal drug and formulation characteristics.
Y1 - 2020
U6 - https://doi.org/10.1371/journal.pcbi.1008466
SN - 1553-734X
SN - 1553-7358
VL - 16
IS - 12
PB - PLoS
CY - San Fransisco
ER -
TY - JOUR
A1 - Leimkuhler, Benedict
A1 - Reich, Sebastian
T1 - A metropolis adjusted Nosé-Hoover thermostat
N2 - We present a Monte Carlo technique for sampling from the canonical distribution in molecular dynamics. The method is built upon the Nose-Hoover constant temperature formulation and the generalized hybrid Monte Carlo method. In contrast to standard hybrid Monte Carlo methods only the thermostat degree of freedom is stochastically resampled during a Monte Carlo step.
Y1 - 2009
UR - http://www.edpsciences.org/journal/index.cfm?edpsname=m2an
U6 - https://doi.org/10.1051/M2an/2009023
SN - 0764-583X
ER -
TY - JOUR
A1 - Böckmann, Christine
T1 - A modification of the trust-region Gauss-Newton method to solve separable nonlinear least squares problems
Y1 - 1995
ER -
TY - BOOK
A1 - Böckmann, Christine
T1 - A modification of the Trust-Region Gauss-Newton method to solve separable nonlinear least squares problems
T3 - Preprint / Universität Potsdam, Fachbereich Mathematik
Y1 - 1992
VL - 1992, 17
PB - Univ.
CY - Potsdam
ER -
TY - BOOK
A1 - Baumgärtel, Hellmut
T1 - A modified approach to the Doplicher-Roberts theorem on the construction of field algebra and the symmetry group in superselection theory
T3 - Preprint / SFB 288, Differentialgeometrie und Quantenphysik
Y1 - 1994
VL - 134
CY - Berlin
ER -
TY - JOUR
A1 - Baumgärtel, Hellmut
T1 - A modified approach to the Doplicher-Roberts theorem on the construction of the field algebra and the symmetry group in superselection theory
Y1 - 1997
ER -
TY - JOUR
A1 - Pornsawad, Pornsarp
A1 - Sapsakul, Nantawan
A1 - Böckmann, Christine
T1 - A modified asymptotical regularization of nonlinear ill-posed problems
JF - Mathematics
N2 - In this paper, we investigate the continuous version of modified iterative Runge–Kutta-type methods for nonlinear inverse ill-posed problems proposed in a previous work. The convergence analysis is proved under the tangential cone condition, a modified discrepancy principle, i.e., the stopping time T is a solution of ∥𝐹(𝑥𝛿(𝑇))−𝑦𝛿∥=𝜏𝛿+ for some 𝛿+>𝛿, and an appropriate source condition. We yield the optimal rate of convergence.
KW - nonlinear operator
KW - regularization
KW - discrepancy principle
KW - asymptotic method
KW - optimal rate
Y1 - 2019
U6 - https://doi.org/10.3390/math7050419
SN - 2227-7390
VL - 7
PB - MDPI
CY - Basel, Schweiz
ET - 5
ER -
TY - GEN
A1 - Pornsawad, Pornsarp
A1 - Sapsakul, Nantawan
A1 - Böckmann, Christine
T1 - A modified asymptotical regularization of nonlinear ill-posed problems
T2 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2 - In this paper, we investigate the continuous version of modified iterative Runge–Kutta-type methods for nonlinear inverse ill-posed problems proposed in a previous work. The convergence analysis is proved under the tangential cone condition, a modified discrepancy principle, i.e., the stopping time T is a solution of ∥𝐹(𝑥𝛿(𝑇))−𝑦𝛿∥=𝜏𝛿+ for some 𝛿+>𝛿, and an appropriate source condition. We yield the optimal rate of convergence.
T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1335
KW - nonlinear operator
KW - regularization
KW - discrepancy principle
KW - asymptotic method
KW - optimal rate
Y1 - 2019
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-473433
SN - 1866-8372
IS - 1335
ER -
TY - BOOK
A1 - Ramlau, Ronny
T1 - A modified Landweber-method for inverse problems
T3 - Preprint / Universität Potsdam, Institut für Mathematik
Y1 - 1997
VL - 1997, 03
PB - Univ.
CY - Potsdam
ER -
TY - JOUR
A1 - Bergemann, Kay
A1 - Reich, Sebastian
T1 - A mollified ensemble Kalman filter
N2 - It is well recognized that discontinuous analysis increments of sequential data assimilation systems, such as ensemble Kalman filters, might lead to spurious high-frequency adjustment processes in the model dynamics. Various methods have been devised to spread out the analysis increments continuously over a fixed time interval centred about the analysis time. Among these techniques are nudging and incremental analysis updates (IAU). Here we propose another alternative, which may be viewed as a hybrid of nudging and IAU and which arises naturally from a recently proposed continuous formulation of the ensemble Kalman analysis step. A new slow-fast extension of the popular Lorenz-96 model is introduced to demonstrate the properties of the proposed mollified ensemble Kalman filter.
Y1 - 2010
UR - http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1477-870X
U6 - https://doi.org/10.1002/Qj.672
SN - 0035-9009
ER -
TY - BOOK
A1 - Böckmann, Christine
A1 - Niebsch, Jenny
T1 - A mollifier method for aerosol size
T3 - Preprint / Universität Potsdam, Institut für Mathematik
Y1 - 1996
VL - 1996, 07
PB - Univ.
CY - Potsdam
ER -
TY - THES
A1 - Zass, Alexander
T1 - A multifaceted study of marked Gibbs point processes
T1 - Facetten von markierten Gibbsschen Punktprozessen
N2 - This thesis focuses on the study of marked Gibbs point processes, in particular presenting some results on their existence and uniqueness, with ideas and techniques drawn from different areas of statistical mechanics: the entropy method from large deviations theory, cluster expansion and the Kirkwood--Salsburg equations, the Dobrushin contraction principle and disagreement percolation.
We first present an existence result for infinite-volume marked Gibbs point processes. More precisely, we use the so-called entropy method (and large-deviation tools) to construct marked Gibbs point processes in R^d under quite general assumptions. In particular, the random marks belong to a general normed space S and are not bounded. Moreover, we allow for interaction functionals that may be unbounded and whose range is finite but random. The entropy method relies on showing that a family of finite-volume Gibbs point processes belongs to sequentially compact entropy level sets, and is therefore tight.
We then present infinite-dimensional Langevin diffusions, that we put in interaction via a Gibbsian description. In this setting, we are able to adapt the general result above to show the existence of the associated infinite-volume measure. We also study its correlation functions via cluster expansion techniques, and obtain the uniqueness of the Gibbs process for all inverse temperatures β and activities z below a certain threshold. This method relies in first showing that the correlation functions of the process satisfy a so-called Ruelle bound, and then using it to solve a fixed point problem in an appropriate Banach space. The uniqueness domain we obtain consists then of the model parameters z and β for which such a problem has exactly one solution.
Finally, we explore further the question of uniqueness of infinite-volume Gibbs point processes on R^d, in the unmarked setting. We present, in the context of repulsive interactions with a hard-core component, a novel approach to uniqueness by applying the discrete Dobrushin criterion to the continuum framework. We first fix a discretisation parameter a>0 and then study the behaviour of the uniqueness domain as a goes to 0. With this technique we are able to obtain explicit thresholds for the parameters z and β, which we then compare to existing results coming from the different methods of cluster expansion and disagreement percolation.
Throughout this thesis, we illustrate our theoretical results with various examples both from classical statistical mechanics and stochastic geometry.
N2 - Diese Arbeit konzentriert sich auf die Untersuchung von markierten Gibbs-Punkt-Prozessen und stellt insbesondere einige Ergebnisse zu deren Existenz und Eindeutigkeit vor. Dabei werden Ideen und Techniken aus verschiedenen Bereichen der statistischen Mechanik verwendet: die Entropie-Methode aus der Theorie der großen Abweichungen, die Cluster-Expansion und die Kirkwood-Salsburg-Gleichungen, das Dobrushin-Kontraktionsprinzip und die Disagreement-Perkolation.
Wir präsentieren zunächst ein Existenzergebnis für unendlich-volumige markierte Gibbs-Punkt-Prozesse. Genauer gesagt verwenden wir die sogenannte Entropie-Methode (und Werkzeuge der großen Abweichung), um markierte Gibbs-Punkt-Prozesse in R^d unter möglichst allgemeinen Annahmen zu konstruieren. Insbesondere gehören die zufälligen Markierungen zu einem allgemeinen normierten Raum und sind nicht beschränkt. Außerdem lassen wir Interaktionsfunktionale zu, die unbeschränkt sein können und deren Reichweite endlich, aber zufällig ist. Die Entropie-Methode beruht darauf, zu zeigen, dass eine Familie von endlich-volumigen Gibbs-Punkt-Prozessen zu sequentiell kompakten Entropie-Niveau-Mengen gehört, und daher dicht ist.
Wir stellen dann unendlich-dimensionale Langevin-Diffusionen vor, die wir über eine Gibbssche Beschreibung in Wechselwirkung setzen. In dieser Umgebung sind wir in der Lage, das vorangehend vorgestellte allgemeine Ergebnis anzupassen, um die Existenz des zugehörigen unendlich-dimensionalen Maßes zu zeigen. Wir untersuchen auch seine Korrelationsfunktionen über Cluster-Expansions Techniken und erhalten die Eindeutigkeit des Gibbs-Prozesses für alle inversen Temperaturen β und Aktivitäten z unterhalb einer bestimmten Schwelle. Diese Methode beruht darauf, zunächst zu zeigen, dass die Korrelationsfunktionen des Prozesses eine so genannte Ruelle-Schranke erfüllen, um diese dann zur Lösung eines Fixpunktproblems in einem geeigneten Banach-Raum zu verwenden. Der Eindeutigkeitsbereich, den wir erhalten, wird dann aus den Modellparametern z und β definiert, für die ein solches Problem genau eine Lösung hat.
Schließlich untersuchen wir die Frage nach der Eindeutigkeit von unendlich-volumigen Gibbs-Punkt-Prozessen auf R^d im unmarkierten Fall weiter. Im Zusammenhang mit repulsiven Wechselwirkungen basierend auf einer Hartkernkomponente stellen wir einen neuen Ansatz zur Eindeutigkeit vor, indem wir das diskrete Dobrushin-Kriterium im kontinuierlichen Rahmen anwenden. Wir legen zunächst einen Diskretisierungsparameter a>0 fest und untersuchen dann das Verhalten des Bereichs der Eindeutigkeit, wenn a gegen 0 geht. Mit dieser Technik sind wir in der Lage, explizite Schwellenwerte für die Parameter z und β zu erhalten, die wir dann mit bestehenden Ergebnissen aus den verschiedenen Methoden der Cluster-Expansion und der Disagreement-Perkolation vergleichen.
In dieser Arbeit illustrieren wir unsere theoretischen Ergebnisse mit verschiedenen Beispielen sowohl aus der klassischen statistischen Mechanik als auch aus der stochastischen Geometrie.
KW - marked Gibbs point processes
KW - Langevin diffusions
KW - Dobrushin criterion
KW - Entropy method
KW - Cluster expansion
KW - Kirkwood--Salsburg equations
KW - DLR equations
KW - Markierte Gibbs-Punkt-Prozesse
KW - Entropiemethode
KW - Cluster-Expansion
KW - DLR-Gleichungen
KW - Dobrushin-Kriterium
KW - Kirkwood-Salsburg-Gleichungen
KW - Langevin-Diffusions
Y1 - 2021
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-512775
ER -
TY - JOUR
A1 - Shin, Seoleun
A1 - Zöller, Gert
A1 - Holschneider, Matthias
A1 - Reich, Sebastian
T1 - A multigrid solver for modeling complex interseismic stress fields
JF - Computers & geosciences : an international journal devoted to the publication of papers on all aspects of geocomputation and to the distribution of computer programs and test data sets ; an official journal of the International Association for Mathematical Geology
N2 - We develop a multigrid, multiple time stepping scheme to reduce computational efforts for calculating complex stress interactions in a strike-slip 2D planar fault for the simulation of seismicity. The key elements of the multilevel solver are separation of length scale, grid-coarsening, and hierarchy. In this study the complex stress interactions are split into two parts: the first with a small contribution is computed on a coarse level, and the rest for strong interactions is on a fine level. This partition leads to a significant reduction of the number of computations. The reduction of complexity is even enhanced by combining the multigrid with multiple time stepping. Computational efficiency is enhanced by a factor of 10 while retaining a reasonable accuracy, compared to the original full matrix-vortex multiplication. The accuracy of solution and computational efficiency depend on a given cut-off radius that splits multiplications into the two parts. The multigrid scheme is constructed in such a way that it conserves stress in the entire half-space.
KW - Multigrid
KW - Multiple time stepping
KW - Strike-slip fault model
Y1 - 2011
U6 - https://doi.org/10.1016/j.cageo.2010.11.011
SN - 0098-3004
VL - 37
IS - 8
SP - 1075
EP - 1082
PB - Elsevier
CY - Oxford
ER -
TY - JOUR
A1 - Hedayat Mahmoudi, Mahdi
A1 - Schulze, Bert-Wolfgang
T1 - A new approach to the second order edge calculus
JF - Journal of pseudo-differential operators and applications
N2 - We establish essential steps of an iterative approach to operator algebras, ellipticity and Fredholm property on stratified spaces with singularities of second order. We cover, in particular, corner-degenerate differential operators. Our constructions are focused on the case where no additional conditions of trace and potential type are posed, but this case works well and will be considered in a forthcoming paper as a conclusion of the present calculus.
KW - Operators on singular manifolds
KW - Mellin transform
KW - Stratified spaces
KW - Ellipticity and parametrices
Y1 - 2018
U6 - https://doi.org/10.1007/s11868-017-0191-2
SN - 1662-9981
SN - 1662-999X
VL - 9
IS - 2
SP - 265
EP - 300
PB - Springer
CY - Basel
ER -
TY - BOOK
A1 - Kamani, D.
A1 - Mansouri, R.
T1 - A new class of inhomogeneous cosmological solutions
T3 - Preprint / Universität Potsdam, Institut für Mathematik
Y1 - 1995
VL - 1995, 07
PB - Univ.
CY - Potsdam
ER -
TY - JOUR
A1 - Rasch, T.
A1 - Schindler, R.
T1 - A new condensation principle
N2 - We generalize del(A), which was introduced in [Schinfinity], to larger cardinals. For a regular cardinal kappa>N-0 we denote by del(kappa)(A) the statement that Asubset of or equal tokappa and for all regular theta>kappa(o), {X is an element of[L-theta[A]](<) : X &AND; &ISIN; &AND; otp (X &AND; Ord) &ISIN; Card (L[A&AND;X&AND;])} is stationary in [L-[A]](<). It was shown in [Sch&INFIN;] that &DEL;(N1) (A) can hold in a set-generic extension of L. We here prove that &DEL;(N2) (A) can hold in a set-generic extension of L as well. In both cases we in fact get equiconsistency theorems. This strengthens results of [Ra00] and [Ran01]. &DEL;(N3) () is equivalent with the existence of 0#
Y1 - 2005
SN - 1432-0665
ER -
TY - JOUR
A1 - Keller, Matthias
A1 - Münch, Florentin
T1 - A new discrete Hopf-Rinow theorem
JF - Discrete Mathematics
N2 - We prove a version of the Hopf-Rinow theorem with respect to path metrics on discrete spaces. The novel aspect is that we do not a priori assume local finiteness but isolate a local finiteness type condition, called essentially locally finite, that is indeed necessary. As a side product we identify the maximal weight, called the geodesic weight, generating the path metric in the situation when the space is complete with respect to any of the equivalent notions of completeness proven in the Hopf-Rinow theorem. As an application we characterize the graphs for which the resistance metric is a path metric induced by the graph structure.
Y1 - 2019
U6 - https://doi.org/10.1016/j.disc.2019.03.014
SN - 0012-365X
SN - 1872-681X
VL - 342
IS - 9
SP - 2751
EP - 2757
PB - Elsevier
CY - Amsterdam
ER -
TY - JOUR
A1 - Schmidt, Hans-Jürgen
T1 - A new duality transformation for fouth-order gravity
Y1 - 1997
ER -
TY - JOUR
A1 - Arworn, Srichan
A1 - Denecke, Klaus-Dieter
T1 - A new methods to study subvariety lattices of semigroup varieties
Y1 - 1997
ER -
TY - JOUR
A1 - Schmidt, Hans-Jürgen
T1 - A new proof of Birkhoffïs theorem
Y1 - 1997
ER -
TY - JOUR
A1 - Reich, Sebastian
T1 - A nonparametric ensemble transform method for bayesian inference
JF - SIAM journal on scientific computing
N2 - Many applications, such as intermittent data assimilation, lead to a recursive application of Bayesian inference within a Monte Carlo context. Popular data assimilation algorithms include sequential Monte Carlo methods and ensemble Kalman filters (EnKFs). These methods differ in the way Bayesian inference is implemented. Sequential Monte Carlo methods rely on importance sampling combined with a resampling step, while EnKFs utilize a linear transformation of Monte Carlo samples based on the classic Kalman filter. While EnKFs have proven to be quite robust even for small ensemble sizes, they are not consistent since their derivation relies on a linear regression ansatz. In this paper, we propose another transform method, which does not rely on any a priori assumptions on the underlying prior and posterior distributions. The new method is based on solving an optimal transportation problem for discrete random variables.
KW - Bayesian inference
KW - Monte Carlo method
KW - sequential data assimilation
KW - linear programming
KW - resampling
Y1 - 2013
U6 - https://doi.org/10.1137/130907367
SN - 1064-8275
VL - 35
IS - 4
SP - A2013
EP - A2024
PB - Society for Industrial and Applied Mathematics
CY - Philadelphia
ER -
TY - JOUR
A1 - Makhmudov, K. O.
A1 - Makhmudov, O. I.
A1 - Tarkhanov, Nikolai Nikolaevich
T1 - A nonstandard Cauchy problem for the heat equation
JF - Mathematical Notes
N2 - We consider the Cauchy problem for the heat equation in a cylinder C (T) = X x (0, T) over a domain X in R (n) , 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.
Y1 - 2017
U6 - https://doi.org/10.1134/S0001434617070264
SN - 0001-4346
SN - 1573-8876
VL - 102
SP - 250
EP - 260
PB - Pleiades Publ.
CY - New York
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 - BOOK
A1 - Braunß, Hans-Andreas
T1 - A note about ranks of m-homogeneous polynomials on Banach spaces
T3 - Preprint / Universität Potsdam, Institut für Mathematik
Y1 - 1998
VL - 1998, 18a
PB - Univ.
CY - Potsdam
ER -
TY - JOUR
A1 - Keller, Matthias
A1 - Liu, Shiping
A1 - Peyerimhoff, Norbert
T1 - A note on eigenvalue bounds for non-compact manifolds
JF - Mathematische Nachrichten
N2 - In this article we prove upper bounds for the Laplace eigenvalues lambda(k) below the essential spectrum for strictly negatively curved Cartan-Hadamard manifolds. Our bound is given in terms of k(2) and specific geometric data of the manifold. This applies also to the particular case of non-compact manifolds whose sectional curvature tends to -infinity, where no essential spectrum is present due to a theorem of Donnelly/Li. The result stands in clear contrast to Laplacians on graphs where such a bound fails to be true in general.
KW - Cheeger inequality
KW - eigenvalues
KW - Laplacian
KW - negative curvature
KW - Riemannian manifold
Y1 - 2021
U6 - https://doi.org/10.1002/mana.201900209
SN - 0025-584X
SN - 1522-2616
VL - 294
IS - 6
SP - 1134
EP - 1139
PB - Wiley-VCH
CY - Weinheim
ER -
TY - JOUR
A1 - Dimitrova, Ilinka
A1 - Fernandes, Vitor H.
A1 - Koppitz, Jörg
T1 - A note on generators of the endomorphism semigroup of an infinite countable chain
JF - Journal of Algebra and its Applications
N2 - In this note, we consider the semigroup O(X) of all order endomorphisms of an infinite chain X and the subset J of O(X) of all transformations alpha such that vertical bar Im(alpha)vertical bar = vertical bar X vertical bar. For an infinite countable chain X, we give a necessary and sufficient condition on X for O(X) = < J > to hold. We also present a sufficient condition on X for O(X) = < J > to hold, for an arbitrary infinite chain X.
KW - Infinite chain
KW - endomorphism semigroup
KW - generators
KW - relative rank
Y1 - 2016
U6 - https://doi.org/10.1142/S0219498817500311
SN - 0219-4988
SN - 1793-6829
VL - 16
IS - 2
PB - World Scientific
CY - Singapore
ER -
TY - JOUR
A1 - Hinz, Michael
A1 - Schwarz, Michael
T1 - A note on Neumann problems on graphs
JF - Positivity
N2 - We discuss Neumann problems for self-adjoint Laplacians on (possibly infinite) graphs. Under the assumption that the heat semigroup is ultracontractive we discuss the unique solvability for non-empty subgraphs with respect to the vertex boundary and provide analytic and probabilistic representations for Neumann solutions. A second result deals with Neumann problems on canonically compactifiable graphs with respect to the Royden boundary and provides conditions for unique solvability and analytic and probabilistic representations.
KW - Graphs
KW - Discrete Dirichlet forms
KW - Neumann problem
KW - Royden boundary
Y1 - 2022
U6 - https://doi.org/10.1007/s11117-022-00930-0
SN - 1385-1292
SN - 1572-9281
VL - 26
IS - 4
PB - Springer
CY - Dordrecht
ER -
TY - BOOK
A1 - Pincus, Richard
T1 - A note on symmetric unimodal distributions ordered by peakedness
T3 - Preprint / Universität Potsdam, Institut für Mathematik
Y1 - 1997
VL - 1997, 27
PB - Univ.
CY - Potsdam
ER -
TY - JOUR
A1 - Zöller, Gert
T1 - A note on the estimation of the maximum possible earthquake magnitude based on extreme value theory for the Groningen Gas Field
JF - The bulletin of the Seismological Society of America : BSSA
N2 - Extreme value statistics is a popular and frequently used tool to model the occurrence of large earthquakes. The problem of poor statistics arising from rare events is addressed by taking advantage of the validity of general statistical properties in asymptotic regimes. In this note, I argue that the use of extreme value statistics for the purpose of practically modeling the tail of the frequency-magnitude distribution of earthquakes can produce biased and thus misleading results because it is unknown to what degree the tail of the true distribution is sampled by data. Using synthetic data allows to quantify this bias in detail. The implicit assumption that the true M-max is close to the maximum observed magnitude M-max,M-observed restricts the class of the potential models a priori to those with M-max = M-max,M-observed + Delta M with an increment Delta M approximate to 0.5... 1.2. This corresponds to the simple heuristic method suggested by Wheeler (2009) and labeled :M-max equals M-obs plus an increment." The incomplete consideration of the entire model family for the frequency-magnitude distribution neglects, however, the scenario of a large so far unobserved earthquake.
Y1 - 2022
U6 - https://doi.org/10.1785/0120210307
SN - 0037-1106
SN - 1943-3573
VL - 112
IS - 4
SP - 1825
EP - 1831
PB - Seismological Society of America
CY - El Cerito, Calif.
ER -
TY - BOOK
A1 - Camalès, Renaud
T1 - A Note on the Ramified Cauchy Problem
T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1 - 2003
SN - 1437-739X
PB - Univ.
CY - Potsdam
ER -
TY - JOUR
A1 - Malass, Ihsane
A1 - Tarkhanov, Nikolaj Nikolaevič
T1 - A perturbation of the de Rham complex
T1 - Возмущение комплекса де Рама
JF - Journal of Siberian Federal University : Mathematics & Physics
JF - Žurnal Sibirskogo Federalʹnogo Universiteta : Matematika i fizika
N2 - We consider a perturbation of the de Rham complex on a compact manifold with boundary. This perturbation goes beyond the framework of complexes, and so cohomology does not apply to it. On the other hand, its curvature is "small", hence there is a natural way to introduce an Euler characteristic and develop a Lefschetz theory for the perturbation. This work is intended as an attempt to develop a cohomology theory for arbitrary sequences of linear mappings.
N2 - Рассмотрим возмущение комплекса де Рама на компактном многообразии с краем. Это возмущение выходит за рамки комплексов, и поэтому когомологии к нему не относятся. С другой стороны, его кривизна "мала", поэтому существует естественный способ ввести характеристику Эйлера и разработать теорию Лефшеца для возмущения. Данная работа предназначена для попытки разработать теорию когомологий для произвольных последовательностей линейных отображений.
KW - de Rham complex
KW - cohomology
KW - Hodge theory
KW - Neumann problem
KW - комплекс де Рама
KW - когомологии
KW - теория Ходжа
KW - проблема Неймана
Y1 - 2020
U6 - https://doi.org/10.17516/1997-1397-2020-13-5-519-532
SN - 1997-1397
SN - 2313-6022
VL - 13
IS - 5
SP - 519
EP - 532
PB - Siberian Federal University
CY - Krasnojarsk
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 - Keller, Peter
A1 - Roelly, Sylvie
A1 - Valleriani, Angelo
T1 - A quasi-random-walk to model a biological transport process
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. While moving along the rope the motor can also detach and is lost. 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.
T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 2 (2013) 3
KW - Markov chain
KW - random walk
KW - molecular motor
KW - step process
Y1 - 2013
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-63582
ER -
TY - JOUR
A1 - Ly, Ibrahim
A1 - Tarkhanov, Nikolai Nikolaevich
T1 - A Rado theorem for p-harmonic functions
JF - Boletin de la Sociedad Matemática Mexicana
N2 - Let A be a nonlinear differential operator on an open set X subset of 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 XS 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.
KW - Quasilinear equations
KW - Removable sets
KW - p-Laplace equation
Y1 - 2016
U6 - https://doi.org/10.1007/s40590-016-0109-7
SN - 1405-213X
SN - 2296-4495
VL - 22
SP - 461
EP - 472
PB - Springer
CY - Basel
ER -
TY - JOUR
A1 - Fedchenko, Dmitry
A1 - Tarkhanov, Nikolai Nikolaevich
T1 - A Rado theorem for the porous medium equation
JF - Boletin de la Sociedad Matemática Mexicana
N2 - We prove that if u is a locally Lipschitz continuous function on an open set chi subset of Rn + 1 satisfying the nonlinear heat equation partial derivative(t)u = Delta(vertical bar u vertical bar(p-1) u), p > 1, weakly away from the zero set u(-1) (0) in chi, then u is a weak solution to this equation in all of chi.
KW - Quasilinear equations
KW - Removable sets
KW - Porous medium equation
Y1 - 2017
U6 - https://doi.org/10.1007/s40590-017-0169-3
SN - 1405-213X
SN - 2296-4495
VL - 24
IS - 2
SP - 427
EP - 437
PB - Springer
CY - Cham
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 - INPR
A1 - Fedchenko, Dmitry
A1 - Tarkhanov, Nikolai Nikolaevich
T1 - A Radó Theorem for the Porous Medium Equation
T2 - Preprints des Instituts für Mathematik der Universität Potsdam
N2 - We prove that each locally Lipschitz continuous function satisfying the porous medium equation away from the set of its zeroes is actually a weak solution of this equation in the whole domain.
T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 6 (2017) 1
KW - quasilinear equation
KW - removable set
KW - porous medium equation
Y1 - 2017
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-102735
VL - 6
IS - 1
PB - Universitätsverlag Potsdam
CY - Potsdam
ER -
TY - BOOK
A1 - Baumgärtel, Hellmut
A1 - Jurke, Matthias
A1 - Lledó, Fernando
T1 - A remark on covariant and causal nets of CAR-resp.CCR-type local algebras assigned to the irreducible unitary representation of the poincare group labeled by (m>0, s, +)
T3 - Preprint / SFB 288, Differentialgeometrie und Quantenphysik
Y1 - 1994
VL - 120
CY - Berlin
ER -
TY - BOOK
A1 - Fedosov, Boris V.
A1 - Schulze, Bert-Wolfgang
A1 - Tarchanov, Nikolaj N.
T1 - A remark on the index of symmetric operators
T3 - Preprint / Universität Potsdam, Institut für Mathematik
Y1 - 1998
VL - 1998, 04
PB - Univ.
CY - Potsdam
ER -
TY - JOUR
A1 - Chelkh, W.
A1 - Ly, Ibrahim
A1 - Tarkhanov, Nikolai
T1 - A remark on the Laplace transform
JF - Siberian Mathematical Journal
N2 - The study of the Cauchy problem for solutions of the heat equation in a cylindrical domain with data on the lateral surface by the Fourier method raises the problem of calculating the inverse Laplace transform of the entire function cos root z. This problem has no solution in the standard theory of the Laplace transform. We give an explicit formula for the inverse Laplace transform of cos root z using the theory of analytic functionals. This solution suits well to efficiently develop the regularization of solutions to Cauchy problems for parabolic equations with data on noncharacteristic surfaces.
KW - Fourier-Laplace transform
KW - distributions with one-sided support
KW - holomorphic function
KW - analytic functional
Y1 - 2020
U6 - https://doi.org/10.1134/S0037446620040151
SN - 0037-4466
SN - 1573-9260
VL - 61
IS - 4
SP - 755
EP - 762
PB - Consultants Bureau, Springer
CY - New York
ER -
TY - JOUR
A1 - Nehring, Benjamin
A1 - Zessin, Hans
T1 - A representation of the moment measures of the general ideal Boe gas
JF - Mathematische Nachrichten
N2 - We reconsider the fundamental work of Fichtner 2 and exhibit the permanental structure of the ideal Bose gas again, using a new approach which combines a characterization of infinitely divisible random measures (due to Kerstan, Kummer and Matthes 4, 6 and Mecke 9, 10) with a decomposition of the moment measures into its factorial measures due to Krickeberg 5. To be more precise, we exhibit the moment measures of all orders of the general ideal Bose gas in terms of certain loop integrals. This representation can be considered as a point process analogue of the old idea of Symanzik 15 that local times and self-crossings of the Brownian motion can be used as a tool in quantum field theory. Behind the notion of a general ideal Bose gas there is a class of infinitely divisible point processes of all orders with a Levy-measure belonging to some large class of measures containing that of the classical ideal Bose gas considered by Fichtner. It is well-known that the calculation of moments of higher order of point processes is notoriously complicated. See for instance Krickebergs calculations for the Poisson or the Cox process in 5. Relations to the work of Shirai, Takahashi 12 and Soshnikov 14 on permanental and determinantal processes are outlined.
KW - Infinitely divisible point processes
KW - integration by parts formula
KW - random KMM-measure
KW - permanental and determinantal point processes (MSC 2010) 35K55
KW - 35K65
Y1 - 2012
U6 - https://doi.org/10.1002/mana.201000111
SN - 0025-584X
VL - 285
IS - 7
SP - 878
EP - 888
PB - Wiley-VCH
CY - Weinheim
ER -
TY - INPR
A1 - Polkovnikov, Alexander
A1 - Tarkhanov, Nikolai Nikolaevich
T1 - A Riemann-Hilbert problem for the Moisil-Teodorescu system
N2 - In a bounded domain with smooth boundary in R^3 we consider the stationary Maxwell equations
for a function u with values in R^3 subject to a nonhomogeneous condition
(u,v)_x = u_0 on
the boundary, where v is a given vector field and u_0 a function on the boundary. We specify this problem within the framework of the Riemann-Hilbert boundary value problems for the Moisil-Teodorescu system. This latter is proved to satisfy the Shapiro-Lopaniskij condition if an only if the vector v is at no point tangent to the boundary. The Riemann-Hilbert problem for the Moisil-Teodorescu system fails to possess an adjoint boundary value problem with respect to the Green formula, which satisfies the Shapiro-Lopatinskij condition. We develop the construction of Green formula to get a proper concept of adjoint boundary value problem.
T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 6 (2017) 3
KW - Dirac operator
KW - Riemann-Hilbert problem
KW - Fredholm operators
Y1 - 2017
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-397036
VL - 6
IS - 3
ER -
TY - JOUR
A1 - Hanisch, Florian
A1 - Ludewig, Matthias
T1 - A rigorous construction of the supersymmetric path integral associated to a compact spin manifold
JF - Communications in mathematical physics
N2 - We give a rigorous construction of the path integral in N = 1/2 supersymmetry as an integral map for differential forms on the loop space of a compact spin manifold. It is defined on the space of differential forms which can be represented by extended iterated integrals in the sense of Chen and Getzler-Jones-Petrack. Via the iterated integral map, we compare our path integral to the non-commutative loop space Chern character of Guneysu and the second author. Our theory provides a rigorous background to various formal proofs of the Atiyah-Singer index theorem for twisted Dirac operators using supersymmetric path integrals, as investigated by Alvarez-Gaume, Atiyah, Bismut and Witten.
Y1 - 2022
U6 - https://doi.org/10.1007/s00220-022-04336-7
SN - 0010-3616
SN - 1432-0916
VL - 391
IS - 3
SP - 1209
EP - 1239
PB - Springer
CY - Berlin ; Heidelberg
ER -
TY - JOUR
A1 - Bär, Christian
A1 - Strohmaier, Alexander
T1 - A Rigorous Geometric Derivation of the Chiral Anomaly in Curved Backgrounds
JF - Communications in mathematical physics
N2 - We discuss the chiral anomaly for a Weyl field in a curved background and show that a novel index theorem for the Lorentzian Dirac operator can be applied to describe the gravitational chiral anomaly. A formula for the total charge generated by the gravitational and gauge field background is derived directly in Lorentzian signature and in a mathematically rigorous manner. It contains a term identical to the integrand in the Atiyah-Singer index theorem and another term involving the.-invariant of the Cauchy hypersurfaces.
Y1 - 2016
U6 - https://doi.org/10.1007/s00220-016-2664-1
SN - 0010-3616
SN - 1432-0916
VL - 347
SP - 703
EP - 721
PB - Springer
CY - New York
ER -
TY - JOUR
A1 - Kucharski, Maciej
A1 - Ergintav, Arzu
A1 - Ahmad, Wael Abdullah
A1 - Krstić, Miloš
A1 - Ng, Herman Jalli
A1 - Kissinger, Dietmar
T1 - A Scalable 79-GHz Radar Platform Based on Single-Channel Transceivers
JF - IEEE Transactions on Microwave Theory and Techniques
N2 - This paper presents a scalable E-band radar platform based on single-channel fully integrated transceivers (TRX) manufactured using 130-nm silicon-germanium (SiGe) BiCMOS technology. The TRX is suitable for flexible radar systems exploiting massive multiple-input-multipleoutput (MIMO) techniques for multidimensional sensing. A fully integrated fractional-N phase-locked loop (PLL) comprising a 39.5-GHz voltage-controlled oscillator is used to generate wideband frequency-modulated continuous-wave (FMCW) chirp for E-band radar front ends. The TRX is equipped with a vector modulator (VM) for high-speed carrier modulation and beam-forming techniques. A single TRX achieves 19.2-dBm maximum output power and 27.5-dB total conversion gain with input-referred 1-dB compression point of -10 dBm. It consumes 220 mA from 3.3-V supply and occupies 3.96 mm(2) silicon area. A two-channel radar platform based on full-custom TRXs and PLL was fabricated to demonstrate high-precision and high-resolution FMCW sensing. The radar enables up to 10-GHz frequency ramp generation in 74-84-GHz range, which results in 1.5-cm spatial resolution. Due to high output power, thus high signal-to-noise ratio (SNR), a ranging precision of 7.5 mu m for a target at 2 m was achieved. The proposed architecture supports scalable multichannel applications for automotive FMCW using a single local oscillator (LO).
KW - Automotive
KW - E-band
KW - frequency-modulated continuous-wave (FMCW)
KW - patch antenna
KW - phase-locked loop (PLL)
KW - power amplifier (PA)
KW - radar
KW - scalable
KW - transceiver (TRX)
Y1 - 2019
U6 - https://doi.org/10.1109/TMTT.2019.2914104
SN - 0018-9480
SN - 1557-9670
VL - 67
IS - 9
SP - 3882
EP - 3896
PB - Inst. of Electr. and Electronics Engineers
CY - Piscataway
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 - BOOK
A1 - Nazajkinskij, Vladimir E.
A1 - Schulze, Bert-Wolfgang
A1 - Sternin, Boris Ju.
T1 - A semiclassical quantization on manifolds with singularities and the Lefschetz formula for elliptic operators
T3 - Preprint / Universität Potsdam, Institut für Mathematik
Y1 - 1998
VL - 1998, 19
PB - Univ.
CY - Potsdam
ER -
TY - JOUR
A1 - Schrohe, Elmar
T1 - A short introduction to Boutet de Monvel's calculus
Y1 - 2001
ER -
TY - BOOK
A1 - Schrohe, Elmar
T1 - A short introduction to Boutet de Monvel`s calculus
T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1 - 2000
SN - 1437-739X
PB - Univ.
CY - Potsdam
ER -
TY - INPR
A1 - Tarkhanov, Nikolai Nikolaevich
T1 - A simple numerical approach to the Riemann hypothesis
N2 - The Riemann hypothesis is equivalent to the fact the the reciprocal function 1/zeta (s) extends from the interval (1/2,1) to an analytic function in the quarter-strip 1/2 < Re s < 1 and Im s > 0. Function theory allows one to rewrite the condition of analytic continuability in an elegant form amenable to numerical experiments.
T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1 (2012) 9
Y1 - 2012
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-57645
SN - 2193-6943
ER -
TY - INPR
A1 - Flandoli, Franco
A1 - Högele, Michael
T1 - A solution selection problem with small stable perturbations
N2 - The zero-noise limit of differential equations with singular coefficients is investigated for the first time in the case when the noise is a general alpha-stable process. It is proved that extremal solutions are selected and the probability of selection is computed. Detailed analysis of the characteristic function of an exit time form on the half-line is performed, with a suitable decomposition in small and large jumps adapted to the singular drift.
T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 3 (2014) 8
KW - stochastic differential equations
KW - singular drifts
KW - zero-noise limit
KW - Peano phenomena
KW - non-uniqueness
Y1 - 2014
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-71205
SN - 2193-6943
VL - 3
IS - 8
PB - Universitätsverlag Potsdam
CY - Potsdam
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 - JOUR
A1 - Zöller, Gert
T1 - A statistical model for earthquake recurrence based on the assimilation of paleoseismicity, historic seismicity, and instrumental seismicity
JF - Journal of geophysical research : Solid earth
N2 - Paleoearthquakes and historic earthquakes are the most important source of information for the estimation of long-term earthquake recurrence intervals in fault zones, because corresponding sequences cover more than one seismic cycle. However, these events are often rare, dating uncertainties are enormous, and missing or misinterpreted events lead to additional problems. In the present study, I assume that the time to the next major earthquake depends on the rate of small and intermediate events between the large ones in terms of a clock change model. Mathematically, this leads to a Brownian passage time distribution for recurrence intervals. I take advantage of an earlier finding that under certain assumptions the aperiodicity of this distribution can be related to the Gutenberg-Richter b value, which can be estimated easily from instrumental seismicity in the region under consideration. In this way, both parameters of the Brownian passage time distribution can be attributed with accessible seismological quantities. This allows to reduce the uncertainties in the estimation of the mean recurrence interval, especially for short paleoearthquake sequences and high dating errors. Using a Bayesian framework for parameter estimation results in a statistical model for earthquake recurrence intervals that assimilates in a simple way paleoearthquake sequences and instrumental data. I present illustrative case studies from Southern California and compare the method with the commonly used approach of exponentially distributed recurrence times based on a stationary Poisson process.
KW - statistical seismology
KW - paleoearthquakes
KW - stochastic models
KW - seismic hazard
Y1 - 2018
U6 - https://doi.org/10.1029/2017JB015099
SN - 2169-9313
SN - 2169-9356
VL - 123
IS - 6
SP - 4906
EP - 4921
PB - American Geophysical Union
CY - Washington
ER -
TY - JOUR
A1 - Schrohe, Elmar
A1 - Schulze, Bert-Wolfgang
T1 - A symbol algebra for pseudodifferential boundary value problems on manifolds with edges
Y1 - 1997
ER -