@article{PereraBoeckmann2019,
  author    = {Perera, Upeksha and B{\"o}ckmann, Christine},
  title     = {Solutions of Direct and Inverse Even-Order Sturm-Liouville Problems Using Magnus Expansion},
  series = {Mathematics},
  volume    = {7},
  journal   = {Mathematics},
  number    = {6},
  publisher = {MDPI},
  address   = {Basel, Schweiz},
  issn      = {2227-7390},
  doi       = {10.3390/math7060544},
  pages     = {24},
  year      = {2019},
  abstract  = {In this paper Lie group method in combination with Magnus expansion is utilized to develop a universal method applicable to solving a Sturm-Liouville problem (SLP) of any order with arbitrary boundary conditions. It is shown that the method has ability to solve direct regular (and some singular) SLPs of even orders (tested for up to eight), with a mix of (including non-separable and finite singular endpoints) boundary conditions, accurately and efficiently. The present technique is successfully applied to overcome the difficulties in finding suitable sets of eigenvalues so that the inverse SLP problem can be effectively solved. The inverse SLP algorithm proposed by Barcilon (1974) is utilized in combination with the Magnus method so that a direct SLP of any (even) order and an inverse SLP of order two can be solved effectively.},
  language  = {en}
}
@article{PornsawadSapsakulBoeckmann2019,
  author    = {Pornsawad, Pornsarp and Sapsakul, Nantawan and B{\"o}ckmann, Christine},
  title     = {A modified asymptotical regularization of nonlinear ill-posed problems},
  series = {Mathematics},
  volume    = {7},
  journal   = {Mathematics},
  edition   = {5},
  publisher = {MDPI},
  address   = {Basel, Schweiz},
  issn      = {2227-7390},
  doi       = {10.3390/math7050419},
  pages     = {19},
  year      = {2019},
  abstract  = {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.},
  language  = {en}
}
@article{KellerPinchoverPogorzelski2019,
  author    = {Keller, Matthias and Pinchover, Yehuda and Pogorzelski, Felix},
  title     = {Criticality theory for Schr{\"o}dinger operators on graphs},
  series = {Journal of spectral theory},
  volume    = {10},
  journal   = {Journal of spectral theory},
  number    = {1},
  publisher = {European Mathematical Society},
  address   = {Z{\"u}rich},
  issn      = {1664-039X},
  doi       = {10.4171/JST/286},
  pages     = {73 -- 114},
  year      = {2019},
  abstract  = {We study Schrodinger operators given by positive quadratic forms on infinite graphs. From there, we develop a criticality theory for Schrodinger operators on general weighted graphs.},
  language  = {en}
}
@article{Roos2019,
  author    = {Roos, Saskia},
  title     = {The Dirac operator under collapse to a smooth limit space},
  series = {Annals of global analysis and geometry},
  volume    = {57},
  journal   = {Annals of global analysis and geometry},
  number    = {1},
  publisher = {Springer},
  address   = {Dordrecht},
  issn      = {0232-704X},
  doi       = {10.1007/s10455-019-09691-8},
  pages     = {121 -- 151},
  year      = {2019},
  abstract  = {Let (M-i, g(i))(i is an element of N) be a sequence of spin manifolds with uniform bounded curvature and diameter that converges to a lower-dimensional Riemannian manifold (B, h) in the Gromov-Hausdorff topology. Then, it happens that the spectrum of the Dirac operator converges to the spectrum of a certain first-order elliptic differential operator D-B on B. We give an explicit description of D-B and characterize the special case where D-B equals the Dirac operator on B.},
  language  = {en}
}
@article{SchulzeSeiler2019,
  author    = {Schulze, Bert-Wolfgang and Seiler, J{\"o}rg},
  title     = {Elliptic complexes on manifolds with boundary},
  series = {The journal of geometric analysis},
  volume    = {29},
  journal   = {The journal of geometric analysis},
  number    = {1},
  publisher = {Springer},
  address   = {New York},
  issn      = {1050-6926},
  doi       = {10.1007/s12220-018-0014-6},
  pages     = {656 -- 706},
  year      = {2019},
  abstract  = {We show that elliptic complexes of (pseudo) differential operators on smooth compact manifolds with boundary can always be complemented to a Fredholm problem by boundary conditions involving global pseudodifferential projections on the boundary (similarly as the spectral boundary conditions of Atiyah, Patodi, and Singer for a single operator). We prove that boundary conditions without projections can be chosen if, and only if, the topological Atiyah-Bott obstruction vanishes. These results make use of a Fredholm theory for complexes of operators in algebras of generalized pseudodifferential operators of Toeplitz type which we also develop in the present paper.},
  language  = {en}
}
@article{MeraShlapunovTarkhanov2019,
  author    = {Mera, Azal and Shlapunov, Alexander A. and Tarkhanov, Nikolai Nikolaevich},
  title     = {Navier-Stokes Equations for Elliptic Complexes},
  series = {Journal of Siberian Federal University. Mathematics \& Physics},
  volume    = {12},
  journal   = {Journal of Siberian Federal University. Mathematics \& Physics},
  number    = {1},
  publisher = {Sibirskij Federalʹnyj Universitet},
  address   = {Krasnojarsk},
  issn      = {1997-1397},
  doi       = {10.17516/1997-1397-2019-12-1-3-27},
  pages     = {3 -- 27},
  year      = {2019},
  abstract  = {We continue our study of invariant forms of the classical equations of mathematical physics, such as the Maxwell equations or the Lam´e system, on manifold with boundary. To this end we interpret them in terms of the de Rham complex at a certain step. On using the structure of the complex we get an insight to predict a degeneracy deeply encoded in the equations. In the present paper we develop an invariant approach to the classical Navier-Stokes equations.},
  language  = {en}
}
@article{KatzSamuelsBlanchardScott2019,
  author    = {Katz-Samuels, Julian and Blanchard, Gilles and Scott, Clayton},
  title     = {Decontamination of Mutual Contamination Models},
  series = {Journal of machine learning research},
  volume    = {20},
  journal   = {Journal of machine learning research},
  publisher = {Microtome Publishing},
  address   = {Cambridge, Mass.},
  issn      = {1532-4435},
  pages     = {57},
  year      = {2019},
  abstract  = {Many machine learning problems can be characterized by mutual contamination models. In these problems, one observes several random samples from different convex combinations of a set of unknown base distributions and the goal is to infer these base distributions. This paper considers the general setting where the base distributions are defined on arbitrary probability spaces. We examine three popular machine learning problems that arise in this general setting: multiclass classification with label noise, demixing of mixed membership models, and classification with partial labels. In each case, we give sufficient conditions for identifiability and present algorithms for the infinite and finite sample settings, with associated performance guarantees.},
  language  = {en}
}
@article{NueskenPavhotis2019,
  author    = {N{\"u}sken, Nikolas and Pavhotis, Grigorios A.},
  title     = {Constructing Sampling Schemes via Coupling},
  series = {SIAM ASA journal on uncertainty quantification / Society for Industrial and Applied Mathematics ; American Statistical Association},
  volume    = {7},
  journal   = {SIAM ASA journal on uncertainty quantification / Society for Industrial and Applied Mathematics ; American Statistical Association},
  number    = {1},
  publisher = {Society for Industrial and Applied Mathematics},
  address   = {Philadelphia},
  issn      = {2166-2525},
  doi       = {10.1137/18M119896X},
  pages     = {324 -- 382},
  year      = {2019},
  abstract  = {In this paper we develop a general framework for constructing and analyzing coupled Markov chain Monte Carlo samplers, allowing for both (possibly degenerate) diffusion and piecewise deterministic Markov processes. For many performance criteria of interest, including the asymptotic variance, the task of finding efficient couplings can be phrased in terms of problems related to optimal transport theory. We investigate general structural properties, proving a singularity theorem that has both geometric and probabilistic interpretations. Moreover, we show that those problems can often be solved approximately and support our findings with numerical experiments. For the particular objective of estimating the variance of a Bayesian posterior, our analysis suggests using novel techniques in the spirit of antithetic variates. Addressing the convergence to equilibrium of coupled processes we furthermore derive a modified Poincare inequality.},
  language  = {en}
}
@article{GerlachGlueck2019,
  author    = {Gerlach, Moritz Reinhardt and Gl{\"u}ck, Jochen},
  title     = {Mean ergodicity vs weak almost periodicity},
  series = {Studia mathematica},
  volume    = {248},
  journal   = {Studia mathematica},
  number    = {1},
  publisher = {Polska Akademia Nauk, Instytut Matematyczny},
  address   = {Warszawa},
  issn      = {0039-3223},
  doi       = {10.4064/sm170918-20-3},
  pages     = {45 -- 56},
  year      = {2019},
  abstract  = {We provide explicit examples of positive and power-bounded operators on c(0) and l(infinity) which are mean ergodic but not weakly almost periodic. As a consequence we prove that a countably order complete Banach lattice on which every positive and power-bounded mean ergodic operator is weakly almost periodic is necessarily a KB-space. This answers several open questions from the literature. Finally, we prove that if T is a positive mean ergodic operator with zero fixed space on an arbitrary Banach lattice, then so is every power of T .},
  language  = {en}
}
@article{MalassTarkhanov2019,
  author    = {Malass, Ihsane and Tarkhanov, Nikolai Nikolaevich},
  title     = {The de Rham Cohomology through Hilbert Space Methods},
  series = {Journal of Siberian Federal University. Mathematics \& physics},
  volume    = {12},
  journal   = {Journal of Siberian Federal University. Mathematics \& physics},
  number    = {4},
  publisher = {Sibirskij Federalʹnyj Universitet},
  address   = {Krasnoyarsk},
  issn      = {1997-1397},
  doi       = {10.17516/1997-1397-2019-12-4-455-465},
  pages     = {455 -- 465},
  year      = {2019},
  abstract  = {We discuss canonical representations of the de Rham cohomology on a compact manifold with boundary. They are obtained by minimising the energy integral in a Hilbert space of differential forms that belong along with the exterior derivative to the domain of the adjoint operator. The corresponding Euler-Lagrange equations reduce to an elliptic boundary value problem on the manifold, which is usually referred to as the Neumann problem after Spencer.},
  language  = {en}
}