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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - INPR A1 - Nazaikinskii, Vladimir A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris A1 - Shatalov, Victor T1 - A Lefschetz fixed point theorem for manifolds with conical singularities N2 - We establish an Atiyah-Bott-Lefschetz formula for elliptic operators on manifolds with conical singular points. T3 - Preprint - (1997) 20 KW - elliptic operator KW - Fredholm property KW - conical singularities KW - pseudo-diferential operators KW - Lefschetz fixed point formula KW - regularizer Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25073 ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Tarkhanov, Nikolai Nikolaevich T1 - A Lefschetz fixed point formula in the relative elliptic theory N2 - A version of the classical Lefschetz fixed point formula is proved for the cohomology of the cone of a cochain mapping of elliptic complexes. As a particular case we show a Lefschetz formula for the relative de Rham cohomology. T3 - Preprint - (1998) 01 KW - elliptic complexes KW - relative cohomology KW - Lefschetz number Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25159 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 - 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 - 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 - 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 - 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 - 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 - 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 - INPR A1 - Fedosov, Boris A1 - Schulze, Bert-Wolfgang A1 - Tarkhanov, Nikolai Nikolaevich T1 - A general index formula on tropic manifolds with conical points N2 - We solve the index problem for general elliptic pseudodifferential operators on toric manifolds with conical points. T3 - Preprint - (1999) 15 Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25501 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 - 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 - 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 - INPR A1 - Tarkhanov, Nikolai Nikolaevich T1 - A fixed point formula in one complex variable N2 - We show a Lefschetz fixed point formula for holomorphic functions in a bounded domain D with smooth boundary in the complex plane. To introduce the Lefschetz number for a holomorphic map of D, we make use of the Bergman kernal of this domain. The Lefschetz number is proved to be the sum of usual contributions of fixed points of the map in D and contributions of boundary fixed points, these latter being different for attracting and repulsing fixed points. T3 - Preprint - (2003) 01 Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26495 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 - 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 - 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 - THES A1 - Kärsten, Fatma T1 - A duality for a compact group and a second cohomology of its dual Y1 - 1998 ER - TY - THES A1 - Hanke, Timo T1 - A direct approach to noncrossed product division algebras Y1 - 2001 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 - 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 - 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 - INPR A1 - Korey, Michael Brian T1 - A decomposition of functions with vanishing mean oscillation N2 - A function has vanishing mean oscillation (VMO) on R up(n) if its mean oscillation - the local average of its pointwise deviation from its mean value - both is uniformly bounded over all cubes within R up(n) and converges to zero with the volume of the cube. The more restrictive class of functions with vanishing lower oscillation (VLO) arises when the mean value is replaced by the minimum value in this definition. It is shown here that each VMO function is the difference of two functions in VLO. T3 - Preprint - (2001) 02 Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25929 ER - TY - INPR A1 - Gauthier, Paul M. A1 - Tarkhanov, Nikolai Nikolaevich T1 - A covering property of the Riemann zeta-function N2 - For each compact subset K of the complex plane C which does not surround zero, the Riemann surface Sζ of the Riemann zeta function restricted to the critical half-strip 0 < Rs < 1/2 contains infinitely many schlicht copies of K lying ‘over’ K. If Sζ also contains at least one such copy, for some K which surrounds zero, then the Riemann hypothesis fails. T3 - Preprint - (2004) 03 Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26683 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 - 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 - 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 - 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 - INPR A1 - Cattiaux, Patrick A1 - Dai Pra, Paolo A1 - Poelly, Sylvie T1 - A constructive approach to a class of ergodic HJB equations with nonsmooth cost N2 - We consider a class of ergodic Hamilton-Jacobi-Bellman (HJB) equations, related to large time asymptotics of non-smooth multiplicative functional of difusion processes. Under suitable ergodicity assumptions on the underlying difusion, we show existence of these asymptotics, and that they solve the related HJB equation in the viscosity sense. T3 - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2007, 02 Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49430 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 - 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 - 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 - Denecke, Klaus-Dieter A1 - Koppitz, Jörg T1 - A characterization of M-solid varieties of semigroups Y1 - 1999 ER -