TY - GEN A1 - Nüsken, Nikolas A1 - Reich, Sebastian A1 - Rozdeba, Paul J. T1 - State and parameter estimation from observed signal increments T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - The success of the ensemble Kalman filter has triggered a strong interest in expanding its scope beyond classical state estimation problems. In this paper, we focus on continuous-time data assimilation where the model and measurement errors are correlated and both states and parameters need to be identified. Such scenarios arise from noisy and partial observations of Lagrangian particles which move under a stochastic velocity field involving unknown parameters. We take an appropriate class of McKean–Vlasov equations as the starting point to derive ensemble Kalman–Bucy filter algorithms for combined state and parameter estimation. We demonstrate their performance through a series of increasingly complex multi-scale model systems. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 916 KW - parameter estimation KW - continuous-time data assimilation KW - ensemble Kalman filter KW - correlated noise KW - multi-scale diffusion processes Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-442609 SN - 1866-8372 IS - 916 ER - TY - GEN A1 - Molahajloo, Shahla A1 - Pirhayati, Mohammad T1 - Traces of pseudo-differential operators on compact and Hausdorff groups T2 - Postprints der Universität Potsdam : Mathematisch Naturwissenschaftliche Reihe N2 - We give a characterization of and a trace formula for trace class pseudo-differential operators on compact Hausdorff groups. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 893 KW - pseudo-differential operators KW - compact groups Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-436371 SN - 1866-8372 IS - 893 SP - 361 EP - 369 ER - TY - GEN A1 - Mickelsson, Jouko A1 - Paycha, Sylvie T1 - The logarithmic residue density of a generalized Laplacian T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - We show that the residue density of the logarithm of a generalized Laplacian on a closed manifold defines an invariant polynomial-valued differential form. We express it in terms of a finite sum of residues of classical pseudodifferential symbols. In the case of the square of a Dirac operator, these formulas provide a pedestrian proof of the Atiyah–Singer formula for a pure Dirac operator in four dimensions and for a twisted Dirac operator on a flat space of any dimension. These correspond to special cases of a more general formula by Scott and Zagier. In our approach, which is of perturbative nature, we use either a Campbell–Hausdorff formula derived by Okikiolu or a noncommutative Taylor-type formula. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 649 KW - residue KW - index KW - Dirac operators Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-413680 SN - 1866-8372 IS - 649 ER - TY - GEN A1 - Mazzonetto, Sara A1 - Salimova, Diyora T1 - Existence, uniqueness, and numerical approximations for stochastic burgers equations T2 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - In this article, we propose an all-in-one statement which includes existence, uniqueness, regularity, and numerical approximations of mild solutions for a class of stochastic partial differential equations (SPDEs) with non-globally monotone nonlinearities. The proof of this result exploits the properties of an existing fully explicit space-time discrete approximation scheme, in particular the fact that it satisfies suitable a priori estimates. We also obtain almost sure and strong convergence of the approximation scheme to the mild solutions of the considered SPDEs. We conclude by applying the main result of the article to the stochastic Burgers equations with additive space-time white noise. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1393 KW - stochastic Burgers equations KW - SPDEs KW - mild solution KW - existence KW - numerical approximation Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-515796 SN - 1866-8372 IS - 4 ER - TY - GEN A1 - Louis, Pierre-Yves T1 - Ergodicity of PCA BT - equivalence between spatial and temporal mixing conditions N2 - For a general attractive Probabilistic Cellular Automata on S-Zd, we prove that the (time-) convergence towards equilibrium of this Markovian parallel dynamics, exponentially fast in the uniform norm, is equivalent to a condition (A). This condition means the exponential decay of the influence from the boundary for the invariant measures of the system restricted to finite boxes. For a class of reversible PCA dynamics on {1,+1}(Zd), wit a naturally associated Gibbsian potential rho, we prove that a (spatial-) weak mixing condition (WM) for rho implies the validity of the assumption (A); thus exponential (time-) ergodicity of these dynamics towards the unique Gibbs measure associated to rho hods. On some particular examples we state that exponential ergodicity holds as soon as there is no phase transition. KW - Wahrscheinlichkeitstheorie KW - Wechselwirkende Teilchensysteme KW - Stochastische Zellulare Automaten KW - Interacting particle systems KW - Probabilistic Cellular Automata KW - ERgodicity of Markov Chains KW - Gibbs measures Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-6589 ER - TY - GEN A1 - Louis, Pierre-Yves T1 - Increasing coupling for probabilistic cellular automata N2 - We give a necessary and sufficient condition for the existence of an increasing coupling of N (N >= 2) synchronous dynamics on S-Zd (PCA). Increasing means the coupling preserves stochastic ordering. We first present our main construction theorem in the case where S is totally ordered; applications to attractive PCAs are given. When S is only partially ordered, we show on two examples that a coupling of more than two synchronous dynamics may not exist. We also prove an extension of our main result for a particular class of partially ordered spaces. KW - Wahrscheinlichkeitstheorie KW - stochastische Anordnung KW - stochastische Zellulare Automaten KW - Kopplung KW - stochastic ordering KW - Probabilistic Cellular Automata KW - monotone coupling Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-6593 ER - TY - GEN A1 - Leimkuhler, Benedict A1 - Reich, Sebastian T1 - Symplectic integration of constrained Hamiltonian systems N2 - A Hamiltonian system in potential form (formula in the original abstract) subject to smooth constraints on q can be viewed as a Hamiltonian system on a manifold, but numerical computations must be performed in Rn. In this paper methods which reduce "Hamiltonian differential algebraic equations" to ODEs in Euclidean space are examined. The authors study the construction of canonical parameterizations or local charts as well as methods based on the construction of ODE systems in the space in which the constraint manifold is embedded which preserve the constraint manifold as an invariant manifold. In each case, a Hamiltonian system of ordinary differential equations is produced. The stability of the constraint invariants and the behavior of the original Hamiltonian along solutions are investigated both numerically and analytically. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 032 KW - differential-algebraic equations KW - constrained Hamiltonian systems KW - canonical discretization schemes KW - symplectic methods Y1 - 1994 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-15653 ER - TY - GEN A1 - Kolbe, Benedikt Maximilian A1 - Evans, Myfanwy E. T1 - Isotopic tiling theory for hyperbolic surfaces T2 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - In this paper, we develop the mathematical tools needed to explore isotopy classes of tilings on hyperbolic surfaces of finite genus, possibly nonorientable, with boundary, and punctured. More specifically, we generalize results on Delaney-Dress combinatorial tiling theory using an extension of mapping class groups to orbifolds, in turn using this to study tilings of covering spaces of orbifolds. Moreover, we study finite subgroups of these mapping class groups. Our results can be used to extend the Delaney-Dress combinatorial encoding of a tiling to yield a finite symbol encoding the complexity of an isotopy class of tilings. The results of this paper provide the basis for a complete and unambiguous enumeration of isotopically distinct tilings of hyperbolic surfaces. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1347 KW - isotopic tiling theory KW - Delaney–Dress tiling theory KW - mapping class groups KW - Orbifolds KW - maps on surfaces KW - hyperbolic tilings Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-544285 SN - 1866-8372 IS - 1 ER - TY - GEN A1 - Keller, Matthias A1 - Pinchover, Yehuda A1 - Pogorzelski, Felix T1 - From hardy to rellich inequalities on graphs T2 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - We show how to deduce Rellich inequalities from Hardy inequalities on infinite graphs. Specifically, the obtained Rellich inequality gives an upper bound on a function by the Laplacian of the function in terms of weighted norms. These weights involve the Hardy weight and a function which satisfies an eikonal inequality. The results are proven first for Laplacians and are extended to Schrodinger operators afterwards. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1379 KW - 35R02 KW - 39A12 (primary) KW - 26D15 KW - 31C20 KW - 35B09 KW - 58E35 (secondary) Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-542140 SN - 1866-8372 IS - 3 ER - TY - GEN A1 - Karpuz, Eylem Guzel A1 - Çevik, Ahmet Sinan A1 - Koppitz, Jörg A1 - Cangul, Ismail Naci T1 - Some fixed-point results on (generalized) Bruck-Reilly ∗-extensions of monoids T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - In this paper, we determine necessary and sufficient conditions for Bruck-Reilly and generalized Bruck-Reilly ∗-extensions of arbitrary monoids to be regular, coregular and strongly π-inverse. These semigroup classes have applications in various field of mathematics, such as matrix theory, discrete mathematics and p-adic analysis (especially in operator theory). In addition, while regularity and coregularity have so many applications in the meaning of boundaries (again in operator theory), inverse monoids and Bruck-Reilly extensions contain a mixture fixed-point results of algebra, topology and geometry within the purposes of this journal. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 942 KW - Bruck-Reilly extension KW - generalized Bruck-Reilly ∗-extension KW - π -inverse monoid KW - regular monoid Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-432701 SN - 1866-8372 IS - 942 ER -