@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} } @misc{PornsawadSapsakulBoeckmann2019, author = {Pornsawad, Pornsarp and Sapsakul, Nantawan and B{\"o}ckmann, Christine}, title = {A modified asymptotical regularization of nonlinear ill-posed problems}, series = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, journal = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, number = {1335}, issn = {1866-8372}, doi = {10.25932/publishup-47343}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-473433}, 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{KellerMuench2019, author = {Keller, Matthias and M{\"u}nch, Florentin}, title = {A new discrete Hopf-Rinow theorem}, series = {Discrete Mathematics}, volume = {342}, journal = {Discrete Mathematics}, number = {9}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0012-365X}, doi = {10.1016/j.disc.2019.03.014}, pages = {2751 -- 2757}, year = {2019}, abstract = {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.}, language = {en} } @article{KucharskiErgintavAhmadetal.2019, author = {Kucharski, Maciej and Ergintav, Arzu and Ahmad, Wael Abdullah and Krstić, Miloš and Ng, Herman Jalli and Kissinger, Dietmar}, title = {A Scalable 79-GHz Radar Platform Based on Single-Channel Transceivers}, series = {IEEE Transactions on Microwave Theory and Techniques}, volume = {67}, journal = {IEEE Transactions on Microwave Theory and Techniques}, number = {9}, publisher = {Inst. of Electr. and Electronics Engineers}, address = {Piscataway}, issn = {0018-9480}, doi = {10.1109/TMTT.2019.2914104}, pages = {3882 -- 3896}, year = {2019}, abstract = {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).}, language = {en} } @article{EdlundGrisicSteenholdtetal.2019, author = {Edlund, Helena and Grisic, Ana-Marija and Steenholdt, Casper and Ainsworth, Mark Andrew and Brynskov, Torn and Huisinga, Wilhelm and Kloft, Charlotte}, title = {Absence of Relationship Between Crohn's Disease Activity Index or C-Reactive Protein and Infliximab Exposure Calls for Objective Crohn's Disease Activity Measures for the Evaluation of Treatment Effects at Treatment Failure}, series = {Therapeutic drug monitoring : official journal of the International Association of Therapeutic Drug Monitoring and Clinical Toxicology}, volume = {41}, journal = {Therapeutic drug monitoring : official journal of the International Association of Therapeutic Drug Monitoring and Clinical Toxicology}, number = {2}, publisher = {Lippincott Williams \& Wilkins}, address = {Philadelphia}, issn = {0163-4356}, doi = {10.1097/FTD.0000000000000590}, pages = {235 -- 242}, year = {2019}, abstract = {Background: Circulating infliximab (IFX) concentrations correlate with clinical outcomes, forming the basis of the IFX concentration monitoring in patients with Crohn's disease. This study aims to investigate and refine the exposure-response relationship by linking the disease activity markers "Crohn's disease activity index" (CDAI) and C-reactive protein (CRP) to IFX exposure. In addition, we aim to explore the correlations between different disease markers and exposure metrics. Methods: Data from 47 Crohn's disease patients of a randomized controlled trial were analyzed post hoc. All patients had secondary treatment failure at inclusion and had received intensified IFX of 5 mg/kg every 4 weeks for up to 20 weeks. Graphical analyses were performed to explore exposure-response relationships. Metrics of exposure included area under the concentration-time curve (AUC) and trough concentrations (Cmin). Disease activity was measured by CDAI and CRP values, their change from baseline/last visit, and response/remission outcomes at week 12. Results: Although trends toward lower Cmin and lower AUC in nonresponders were observed, neither CDAI nor CRP showed consistent trends of lower disease activity with higher IFX exposure across the 30 evaluated relationships. As can be expected, Cmin and AUC were strongly correlated with each other. Contrarily, the disease activity markers were only weakly correlated with each other. Conclusions: No significant relationship between disease activity, as evaluated by CDAI or CRP, and IFX exposure was identified. AUC did not add benefit compared with Cmin. These findings support the continued use of Cmin and call for stringent objective disease activity (bio-)markers (eg, endoscopy) to form the basis of personalized IFX therapy for Crohn's disease patients with IFX treatment failure.}, language = {en} } @article{ClavierGuoPaychaetal.2019, author = {Clavier, Pierre J. and Guo, Li and Paycha, Sylvie and Zhang, Bin}, title = {An algebraic formulation of the locality principle in renormalisation}, series = {European Journal of Mathematics}, volume = {5}, journal = {European Journal of Mathematics}, number = {2}, publisher = {Springer}, address = {Cham}, issn = {2199-675X}, doi = {10.1007/s40879-018-0255-8}, pages = {356 -- 394}, year = {2019}, abstract = {We study the mathematical structure underlying the concept of locality which lies at the heart of classical and quantum field theory, and develop a machinery used to preserve locality during the renormalisation procedure. Viewing renormalisation in the framework of Connes and Kreimer as the algebraic Birkhoff factorisation of characters on a Hopf algebra with values in a Rota-Baxter algebra, we build locality variants of these algebraic structures, leading to a locality variant of the algebraic Birkhoff factorisation. This provides an algebraic formulation of the conservation of locality while renormalising. As an application in the context of the Euler-Maclaurin formula on lattice cones, we renormalise the exponential generating function which sums over the lattice points in a lattice cone. As a consequence, for a suitable multivariate regularisation, renormalisation from the algebraic Birkhoff factorisation amounts to composition by a projection onto holomorphic multivariate germs.}, language = {en} } @article{BaerStrohmaier2019, author = {B{\"a}r, Christian and Strohmaier, Alexander}, title = {An index theorem for Lorentzian manifolds with compact spacelike Cauchy boundary}, series = {American Journal of Mathematics}, volume = {141}, journal = {American Journal of Mathematics}, number = {5}, publisher = {Johns Hopkins Univ. Press}, address = {Baltimore}, issn = {0002-9327}, doi = {10.1353/ajm.2019.0037}, pages = {1421 -- 1455}, year = {2019}, abstract = {We show that the Dirac operator on a compact globally hyperbolic Lorentzian spacetime with spacelike Cauchy boundary is a Fredholm operator if appropriate boundary conditions are imposed. We prove that the index of this operator is given by the same expression as in the index formula of Atiyah-Patodi-Singer for Riemannian manifolds with boundary. The index is also shown to equal that of a certain operator constructed from the evolution operator and a spectral projection on the boundary. In case the metric is of product type near the boundary a Feynman parametrix is constructed.}, language = {en} } @article{LeungLeutbecherReichetal.2019, author = {Leung, Tsz Yan and Leutbecher, Martin and Reich, Sebastian and Shepherd, Theodore G.}, title = {Atmospheric Predictability: Revisiting the Inherent Finite-Time Barrier}, series = {Journal of the atmospheric sciences}, volume = {76}, journal = {Journal of the atmospheric sciences}, number = {12}, publisher = {American Meteorological Soc.}, address = {Boston}, issn = {0022-4928}, doi = {10.1175/JAS-D-19-0057.1}, pages = {3883 -- 3892}, year = {2019}, abstract = {The accepted idea that there exists an inherent finite-time barrier in deterministically predicting atmospheric flows originates from Edward N. Lorenz's 1969 work based on two-dimensional (2D) turbulence. Yet, known analytic results on the 2D Navier-Stokes (N-S) equations suggest that one can skillfully predict the 2D N-S system indefinitely far ahead should the initial-condition error become sufficiently small, thereby presenting a potential conflict with Lorenz's theory. Aided by numerical simulations, the present work reexamines Lorenz's model and reviews both sides of the argument, paying particular attention to the roles played by the slope of the kinetic energy spectrum. It is found that when this slope is shallower than -3, the Lipschitz continuity of analytic solutions (with respect to initial conditions) breaks down as the model resolution increases, unless the viscous range of the real system is resolved—which remains practically impossible. This breakdown leads to the inherent finite-time limit. If, on the other hand, the spectral slope is steeper than -3, then the breakdown does not occur. In this way, the apparent contradiction between the analytic results and Lorenz's theory is reconciled.}, language = {en} } @article{KellerLenzSchmidtetal.2019, author = {Keller, Matthias and Lenz, Daniel and Schmidt, Marcel and Schwarz, Michael}, title = {Boundary representation of Dirichlet forms on discrete spaces}, series = {Journal de Math{\´e}matiques Pures et Appliqu{\´e}es}, volume = {126}, journal = {Journal de Math{\´e}matiques Pures et Appliqu{\´e}es}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0021-7824}, doi = {10.1016/j.matpur.2018.10.005}, pages = {109 -- 143}, year = {2019}, abstract = {We describe the set of all Dirichlet forms associated to a given infinite graph in terms of Dirichlet forms on its Royden boundary. Our approach is purely analytical and uses form methods. (C) 2018 Elsevier Masson SAS.}, language = {en} } @article{KhalilSchulze2019, author = {Khalil, Sara and Schulze, Bert-Wolfgang}, title = {Calculus on a Manifold with Edge and Boundary}, series = {Complex analysis and operator theory}, volume = {13}, journal = {Complex analysis and operator theory}, number = {6}, publisher = {Springer}, address = {Basel}, issn = {1661-8254}, doi = {10.1007/s11785-018-0800-y}, pages = {2627 -- 2670}, year = {2019}, abstract = {We study elements of the calculus of boundary value problems in a variant of Boutet de Monvel's algebra (Acta Math 126:11-51, 1971) on a manifold N with edge and boundary. If the boundary is empty then the approach corresponds to Schulze (Symposium on partial differential equations (Holzhau, 1988), BSB Teubner, Leipzig, 1989) and other papers from the subsequent development. For non-trivial boundary we study Mellin-edge quantizations and compositions within the structure in terms a new Mellin-edge quantization, compared with a more traditional technique. Similar structures in the closed case have been studied in Gil et al.}, language = {en} } @phdthesis{Fiedler2019, author = {Fiedler, Bernhard}, title = {Change-point detection for seismicity parameters}, school = {Universit{\"a}t Potsdam}, pages = {129}, year = {2019}, language = {en} } @article{BeckerBeniniSchenkeletal.2019, author = {Becker, Christian and Benini, Marco and Schenkel, Alexander and Szabo, Richard J.}, title = {Cheeger-Simons differential characters with compact support and Pontryagin duality}, series = {Communications in analysis and geometry}, volume = {27}, journal = {Communications in analysis and geometry}, number = {7}, publisher = {International Press of Boston}, address = {Somerville}, issn = {1019-8385}, doi = {10.4310/CAG.2019.v27.n7.a2}, pages = {1473 -- 1522}, year = {2019}, abstract = {By adapting the Cheeger-Simons approach to differential cohomology, we establish a notion of differential cohomology with compact support. We show that it is functorial with respect to open embeddings and that it fits into a natural diagram of exact sequences which compare it to compactly supported singular cohomology and differential forms with compact support, in full analogy to ordinary differential cohomology. We prove an excision theorem for differential cohomology using a suitable relative version. Furthermore, we use our model to give an independent proof of Pontryagin duality for differential cohomology recovering a result of [Harvey, Lawson, Zweck - Amer. J. Math. 125 (2003), 791]: On any oriented manifold, ordinary differential cohomology is isomorphic to the smooth Pontryagin dual of compactly supported differential cohomology. For manifolds of finite-type, a similar result is obtained interchanging ordinary with compactly supported differential cohomology.}, language = {en} } @misc{KrauseKloftHuisingaetal.2019, author = {Krause, Andreas and Kloft, Charlotte and Huisinga, Wilhelm and Karlsson, Mats and Pinheiro, Jos{\´e} and Bies, Robert and Rogers, James and Mentr{\´e}, France and Musser, Bret J.}, title = {Comment on Jaki et al., A proposal for a new PhD level curriculum on quantitative methods for drug development}, series = {Pharmaceutical statistics : the journal of applied statistics in the pharmaceutical industry}, volume = {18}, journal = {Pharmaceutical statistics : the journal of applied statistics in the pharmaceutical industry}, number = {3}, publisher = {Wiley}, address = {Hoboken}, organization = {ASA Special Interest Grp Stat Phar ASA Special Interest Grp Stat Phar}, issn = {1539-1604}, pages = {278 -- 281}, year = {2019}, language = {en} } @article{RingelSomogyvariJalalietal.2019, author = {Ringel, Lisa Maria and Somogyv{\´a}ri, M{\´a}rk and Jalali, Mohammadreza and Bayer, Peter}, title = {Comparison of hydraulic and tracer tomography for discrete fracture network inversion}, series = {Geosciences}, volume = {9}, journal = {Geosciences}, number = {6}, publisher = {MDPI}, address = {Basel}, issn = {2076-3263}, doi = {10.3390/geosciences9060274}, pages = {17}, year = {2019}, abstract = {Fractures serve as highly conductive preferential flow paths for fluids in rocks, which are difficult to exactly reconstruct in numerical models. Especially, in low-conductive rocks, fractures are often the only pathways for advection of solutes and heat. The presented study compares the results from hydraulic and tracer tomography applied to invert a theoretical discrete fracture network (DFN) that is based on data from synthetic cross-well testing. For hydraulic tomography, pressure pulses in various injection intervals are induced and the pressure responses in the monitoring intervals of a nearby observation well are recorded. For tracer tomography, a conservative tracer is injected in different well levels and the depth-dependent breakthrough of the tracer is monitored. A recently introduced transdimensional Bayesian inversion procedure is applied for both tomographical methods, which adjusts the fracture positions, orientations, and numbers based on given geometrical fracture statistics. The used Metropolis-Hastings-Green algorithm is refined by the simultaneous estimation of the measurement error's variance, that is, the measurement noise. Based on the presented application to invert the two-dimensional cross-section between source and the receiver well, the hydraulic tomography reveals itself to be more suitable for reconstructing the original DFN. This is based on a probabilistic representation of the inverted results by means of fracture probabilities.}, language = {en} } @article{BlanchardZadorozhnyi2019, author = {Blanchard, Gilles and Zadorozhnyi, Oleksandr}, title = {Concentration of weakly dependent Banach-valued sums and applications to statistical learning methods}, series = {Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability}, volume = {25}, journal = {Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability}, number = {4B}, publisher = {International Statistical Institute}, address = {Voorburg}, issn = {1350-7265}, doi = {10.3150/18-BEJ1095}, pages = {3421 -- 3458}, year = {2019}, abstract = {We obtain a Bernstein-type inequality for sums of Banach-valued random variables satisfying a weak dependence assumption of general type and under certain smoothness assumptions of the underlying Banach norm. We use this inequality in order to investigate in the asymptotical regime the error upper bounds for the broad family of spectral regularization methods for reproducing kernel decision rules, when trained on a sample coming from a tau-mixing process.}, language = {en} } @article{ConfortiKosenkovaRoelly2019, author = {Conforti, Giovanni and Kosenkova, Tetiana and Roelly, Sylvie}, title = {Conditioned Point Processes with Application to Levy Bridges}, series = {Journal of theoretical probability}, volume = {32}, journal = {Journal of theoretical probability}, number = {4}, publisher = {Springer}, address = {New York}, issn = {0894-9840}, doi = {10.1007/s10959-018-0863-8}, pages = {2111 -- 2134}, year = {2019}, abstract = {Our first result concerns a characterization by means of a functional equation of Poisson point processes conditioned by the value of their first moment. It leads to a generalized version of Mecke's formula. En passant, it also allows us to gain quantitative results about stochastic domination for Poisson point processes under linear constraints. Since bridges of a pure jump L{\´e}vy process in Rd with a height a can be interpreted as a Poisson point process on space-time conditioned by pinning its first moment to a, our approach allows us to characterize bridges of L{\´e}vy processes by means of a functional equation. The latter result has two direct applications: First, we obtain a constructive and simple way to sample L{\´e}vy bridge dynamics; second, it allows us to estimate the number of jumps for such bridges. We finally show that our method remains valid for linearly perturbed L{\´e}vy processes like periodic Ornstein-Uhlenbeck processes driven by L{\´e}vy noise.}, 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} } @phdthesis{Goebel2019, author = {G{\"o}bel, Franziska}, title = {Contributions to multiscale statistical analysis on random geometric graphs}, school = {Universit{\"a}t Potsdam}, pages = {127}, year = {2019}, language = {en} } @article{GerlachGlueck2019, author = {Gerlach, Moritz Reinhardt and Gl{\"u}ck, Jochen}, title = {Convergence of positive operator semigroups}, series = {Transactions of the American Mathematical Society}, volume = {372}, journal = {Transactions of the American Mathematical Society}, number = {9}, publisher = {American Mathematical Soc.}, address = {Providence}, issn = {0002-9947}, doi = {10.1090/tran/7836}, pages = {6603 -- 6627}, year = {2019}, abstract = {We present new conditions for semigroups of positive operators to converge strongly as time tends to infinity. Our proofs are based on a novel approach combining the well-known splitting theorem by Jacobs, de Leeuw, and Glicksberg with a purely algebraic result about positive group representations. Thus, we obtain convergence theorems not only for one-parameter semigroups but also for a much larger class of semigroup representations. Our results allow for a unified treatment of various theorems from the literature that, under technical assumptions, a bounded positive C-0-semigroup containing or dominating a kernel operator converges strongly as t ->infinity. We gain new insights into the structure theoretical background of those theorems and generalize them in several respects; especially we drop any kind of continuity or regularity assumption with respect to the time parameter.}, language = {en} } @misc{BeckusBellissardDeNittis2019, author = {Beckus, Siegfried and Bellissard, Jean and De Nittis, Giuseppe}, title = {Corrigendum to: Spectral continuity for aperiodic quantum systems I. General theory. - [Journal of functional analysis. - 275 (2018), 11, S. 2917 - 2977]}, series = {Journal of functional analysis}, volume = {277}, journal = {Journal of functional analysis}, number = {9}, publisher = {Elsevier}, address = {San Diego}, issn = {0022-1236}, doi = {10.1016/j.jfa.2019.06.001}, pages = {3351 -- 3353}, year = {2019}, abstract = {A correct statement of Theorem 4 in [1] is provided. The change does not affect the main results.}, 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{Reich2019, author = {Reich, Sebastian}, title = {Data assimilation}, series = {Acta numerica}, volume = {28}, journal = {Acta numerica}, publisher = {Cambridge Univ. Press}, address = {New York}, issn = {0962-4929}, doi = {10.1017/S0962492919000011}, pages = {635 -- 711}, year = {2019}, abstract = {Data assimilation addresses the general problem of how to combine model-based predictions with partial and noisy observations of the process in an optimal manner. This survey focuses on sequential data assimilation techniques using probabilistic particle-based algorithms. In addition to surveying recent developments for discrete- and continuous-time data assimilation, both in terms of mathematical foundations and algorithmic implementations, we also provide a unifying framework from the perspective of coupling of measures, and Schr{\"o}dinger's boundary value problem for stochastic processes in particular.}, 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} } @phdthesis{Muench2019, author = {M{\"u}nch, Florentin}, title = {Discrete Ricci curvature, diameter bounds and rigidity}, school = {Universit{\"a}t Potsdam}, pages = {68}, year = {2019}, language = {en} } @phdthesis{Jakobs2019, author = {Jakobs, Friedrich}, title = {Dubrovin-rings and their connection to Hughes-free skew fields of fractions}, doi = {10.25932/publishup-43556}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-435561}, school = {Universit{\"a}t Potsdam}, pages = {ix, 62}, year = {2019}, abstract = {One method of embedding groups into skew fields was introduced by A. I. Mal'tsev and B. H. Neumann (cf. [18, 19]). If G is an ordered group and F is a skew field, the set F((G)) of formal power series over F in G with well-ordered support forms a skew field into which the group ring F[G] can be embedded. Unfortunately it is not suficient that G is left-ordered since F((G)) is only an F-vector space in this case as there is no natural way to define a multiplication on F((G)). One way to extend the original idea onto left-ordered groups is to examine the endomorphism ring of F((G)) as explored by N. I. Dubrovin (cf. [5, 6]). It is possible to embed any crossed product ring F[G; η, σ] into the endomorphism ring of F((G)) such that each non-zero element of F[G; η, σ] defines an automorphism of F((G)) (cf. [5, 10]). Thus, the rational closure of F[G; η, σ] in the endomorphism ring of F((G)), which we will call the Dubrovin-ring of F[G; η, σ], is a potential candidate for a skew field of fractions of F[G; η, σ]. The methods of N. I. Dubrovin allowed to show that specific classes of groups can be embedded into a skew field. For example, N. I. Dubrovin contrived some special criteria, which are applicable on the universal covering group of SL(2, R). These methods have also been explored by J. Gr{\"a}ter and R. P. Sperner (cf. [10]) as well as N.H. Halimi and T. Ito (cf. [11]). Furthermore, it is of interest to know if skew fields of fractions are unique. For example, left and right Ore domains have unique skew fields of fractions (cf. [2]). This is not the general case as for example the free group with 2 generators can be embedded into non-isomorphic skew fields of fractions (cf. [12]). It seems likely that Ore domains are the most general case for which unique skew fields of fractions exist. One approach to gain uniqueness is to restrict the search to skew fields of fractions with additional properties. I. Hughes has defined skew fields of fractions of crossed product rings F[G; η, σ] with locally indicable G which fulfill a special condition. These are called Hughes-free skew fields of fractions and I. Hughes has proven that they are unique if they exist [13, 14]. This thesis will connect the ideas of N. I. Dubrovin and I. Hughes. The first chapter contains the basic terminology and concepts used in this thesis. We present methods provided by N. I. Dubrovin such as the complexity of elements in rational closures and special properties of endomorphisms of the vector space of formal power series F((G)). To combine the ideas of N.I. Dubrovin and I. Hughes we introduce Conradian left-ordered groups of maximal rank and examine their connection to locally indicable groups. Furthermore we provide notations for crossed product rings, skew fields of fractions as well as Dubrovin-rings and prove some technical statements which are used in later parts. The second chapter focuses on Hughes-free skew fields of fractions and their connection to Dubrovin-rings. For that purpose we introduce series representations to interpret elements of Hughes-free skew fields of fractions as skew formal Laurent series. This 1 Introduction allows us to prove that for Conradian left-ordered groups G of maximal rank the statement "F[G; η, σ] has a Hughes-free skew field of fractions" implies "The Dubrovin ring of F [G; η, σ] is a skew field". We will also prove the reverse and apply the results to give a new prove of Theorem 1 in [13]. Furthermore we will show how to extend injective ring homomorphisms of some crossed product rings onto their Hughes-free skew fields of fractions. At last we will be able to answer the open question whether Hughes--free skew fields are strongly Hughes-free (cf. [17, page 53]).}, language = {en} } @article{RosenblumFruehwirthMoseretal.2019, author = {Rosenblum, Michael and Fr{\"u}hwirth, Martha and Moser, Maximilian and Pikovskij, Arkadij}, title = {Dynamical disentanglement in an analysis of oscillatory systems: an application to respiratory sinus arrhythmia}, series = {Philosophical Transactions of the Royal Society of London, Series A : Mathematical, Physical and Engineering Sciences}, volume = {377}, journal = {Philosophical Transactions of the Royal Society of London, Series A : Mathematical, Physical and Engineering Sciences}, number = {2160}, publisher = {Royal Society}, address = {London}, issn = {1364-503X}, doi = {10.1098/rsta.2019.0045}, pages = {14}, year = {2019}, abstract = {We develop a technique for the multivariate data analysis of perturbed self-sustained oscillators. The approach is based on the reconstruction of the phase dynamics model from observations and on a subsequent exploration of this model. For the system, driven by several inputs, we suggest a dynamical disentanglement procedure, allowing us to reconstruct the variability of the system's output that is due to a particular observed input, or, alternatively, to reconstruct the variability which is caused by all the inputs except for the observed one. We focus on the application of the method to the vagal component of the heart rate variability caused by a respiratory influence. We develop an algorithm that extracts purely respiratory-related variability, using a respiratory trace and times of R-peaks in the electrocardiogram. The algorithm can be applied to other systems where the observed bivariate data can be represented as a point process and a slow continuous signal, e.g. for the analysis of neuronal spiking. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.}, 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{ShcherbakovZhuangZoelleretal.2019, author = {Shcherbakov, Robert and Zhuang, Jiancang and Z{\"o}ller, Gert and Ogata, Yosihiko}, title = {Forecasting the magnitude of the largest expected earthquake}, series = {Nature Communications}, volume = {10}, journal = {Nature Communications}, publisher = {Nature Publishing Group}, address = {London}, issn = {2041-1723}, doi = {10.1038/s41467-019-11958-4}, pages = {11}, year = {2019}, abstract = {The majority of earthquakes occur unexpectedly and can trigger subsequent sequences of events that can culminate in more powerful earthquakes. This self-exciting nature of seismicity generates complex clustering of earthquakes in space and time. Therefore, the problem of constraining the magnitude of the largest expected earthquake during a future time interval is of critical importance in mitigating earthquake hazard. We address this problem by developing a methodology to compute the probabilities for such extreme earthquakes to be above certain magnitudes. We combine the Bayesian methods with the extreme value theory and assume that the occurrence of earthquakes can be described by the Epidemic Type Aftershock Sequence process. We analyze in detail the application of this methodology to the 2016 Kumamoto, Japan, earthquake sequence. We are able to estimate retrospectively the probabilities of having large subsequent earthquakes during several stages of the evolution of this sequence.}, language = {en} } @article{KoltaiLiePlonka2019, author = {Koltai, Peter and Lie, Han Cheng and Plonka, Martin}, title = {Frechet differentiable drift dependence of Perron-Frobenius and Koopman operators for non-deterministic dynamics}, series = {Nonlinearity}, volume = {32}, journal = {Nonlinearity}, number = {11}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {0951-7715}, doi = {10.1088/1361-6544/ab1f2a}, pages = {4232 -- 4257}, year = {2019}, abstract = {We prove the Fr{\´e}chet differentiability with respect to the drift of Perron-Frobenius and Koopman operators associated to time-inhomogeneous ordinary stochastic differential equations. This result relies on a similar differentiability result for pathwise expectations of path functionals of the solution of the stochastic differential equation, which we establish using Girsanov's formula. We demonstrate the significance of our result in the context of dynamical systems and operator theory, by proving continuously differentiable drift dependence of the simple eigen- and singular values and the corresponding eigen- and singular functions of the stochastic Perron-Frobenius and Koopman operators.}, language = {en} } @phdthesis{Lewandowski2019, author = {Lewandowski, Max}, title = {Hadamard states for bosonic quantum field theory on globally hyperbolic spacetimes}, doi = {10.25932/publishup-43938}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-439381}, school = {Universit{\"a}t Potsdam}, pages = {v, 69}, year = {2019}, abstract = {Quantenfeldtheorie auf gekr{\"u}mmten Raumzeiten ist eine semiklassische N{\"a}herung einer Quantentheorie der Gravitation, im Rahmen derer ein Quantenfeld unter dem Einfluss eines klassisch modellierten Gravitationsfeldes, also einer gekr{\"u}mmten Raumzeit, beschrieben wird. Eine der bemerkenswertesten Vorhersagen dieses Ansatzes ist die Erzeugung von Teilchen durch die gekr{\"u}mmte Raumzeit selbst, wie zum Beispiel durch Hawkings Verdampfen schwarzer L{\"o}cher und den Unruh Effekt. Andererseits deuten diese Aspekte bereits an, dass fundamentale Grundpfeiler der Theorie auf dem Minkowskiraum, insbesondere ein ausgezeichneter Vakuumzustand und damit verbunden der Teilchenbegriff, f{\"u}r allgemeine gekr{\"u}mmte Raumzeiten keine sinnvolle Entsprechung besitzen. Gleichermaßen ben{\"o}tigen wir eine alternative Implementierung von Kovarianz in die Theorie, da gekr{\"u}mmte Raumzeiten im Allgemeinen keine nicht-triviale globale Symmetrie aufweisen. Letztere Problematik konnte im Rahmen lokal-kovarianter Quantenfeldtheorie gel{\"o}st werden, wohingegen die Abwesenheit entsprechender Konzepte f{\"u}r Vakuum und Teilchen in diesem allgemeinen Fall inzwischen sogar in Form von no-go-Aussagen manifestiert wurde. Beim algebraischen Ansatz f{\"u}r eine Quantenfeldtheorie werden zun{\"a}chst Observablen eingef{\"u}hrt und erst anschließend Zust{\"a}nde via Zuordnung von Erwartungswerten. Obwohl die Observablen unter physikalischen Gesichtspunkten konstruiert werden, existiert dennoch eine große Anzahl von m{\"o}glichen Zust{\"a}nden, von denen viele, aus physikalischen Blickwinkeln betrachtet, nicht sinnvoll sind. Dieses Konzept von Zust{\"a}nden ist daher noch zu allgemein und bedarf weiterer physikalisch motivierter Einschr{\"a}nkungen. Beispielsweise ist es nat{\"u}rlich, sich im Falle freier Quantenfeldtheorien mit linearen Feldgleichungen auf quasifreie Zust{\"a}nde zu konzentrieren. Dar{\"u}ber hinaus ist die Renormierung von Erwartungswerten f{\"u}r Produkte von Feldern von zentraler Bedeutung. Dies betrifft insbesondere den Energie-Impuls-Tensor, dessen Erwartungswert durch distributionelle Bil{\"o}sungen der Feldgleichungen gegeben ist. Tats{\"a}chlich liefert J. Hadamard Theorie hyperbolischer Differentialgleichungen Bil{\"o}sungen mit festem singul{\"a}ren Anteil, so dass ein geeignetes Renormierungsverfahren definiert werden kann. Die sogenannte Hadamard-Bedingung an Bidistributionen steht f{\"u}r die Forderung einer solchen Singularit{\"a}tenstruktur und sie hat sich etabliert als nat{\"u}rliche Verallgemeinerung der f{\"u}r flache Raumzeiten formulierten Spektralbedingung. Seit Radzikowskis wegweisenden Resultaten l{\"a}sst sie sich außerdem lokal ausdr{\"u}cken, n{\"a}mlich als eine Bedingung an die Wellenfrontenmenge der Bil{\"o}sung. Diese Formulierung schl{\"a}gt eine Br{\"u}cke zu der von Duistermaat und H{\"o}rmander entwickelten mikrolokalen Analysis, die seitdem bei der {\"U}berpr{\"u}fung der Hadamard-Bedingung sowie der Konstruktion von Hadamard Zust{\"a}nden vielfach Verwendung findet und rasante Fortschritte auf diesem Gebiet ausgel{\"o}st hat. Obwohl unverzichtbar f{\"u}r die Analyse der Charakteristiken von Operatoren und ihrer Parametrizen sind die Methoden und Aussagen der mikrolokalen Analysis ungeeignet f{\"u}r die Analyse von nicht-singul{\"a}ren Strukturen und zentrale Aussagen sind typischerweise bis auf glatte Anteile formuliert. Beispielsweise lassen sich aus Radzikowskis Resultaten nahezu direkt Existenzaussagen und sogar ein konkretes Konstruktionsschema f{\"u}r Hadamard Zust{\"a}nde ableiten, die {\"u}brigen Eigenschaften (Bil{\"o}sung, Kausalit{\"a}t, Positivit{\"a}t) k{\"o}nnen jedoch auf diesem Wege nur modulo glatte Funktionen gezeigt werden. Es ist das Ziel dieser Dissertation, diesen Ansatz f{\"u}r lineare Wellenoperatoren auf Schnitten in Vektorb{\"u}ndeln {\"u}ber global-hyperbolischen Lorentz-Mannigfaltigkeiten zu vollenden und, ausgehend von einer lokalen Hadamard Reihe, Hadamard Zust{\"a}nde zu konstruieren. Beruhend auf Wightmans L{\"o}sung f{\"u}r die d'Alembert-Gleichung auf dem Minkowski-Raum und der Herleitung der avancierten und retardierten Fundamentall{\"o}sung konstruieren wir lokal Parametrizen in Form von Hadamard-Reihen und f{\"u}gen sie zu globalen Bil{\"o}sungen zusammen. Diese besitzen dann die Hadamard-Eigenschaft und wir zeigen anschließend, dass glatte Bischnitte existieren, die addiert werden k{\"o}nnen, so dass die verbleibenden Bedingungen erf{\"u}llt sind.}, language = {en} } @article{BeckusBellissardCornean2019, author = {Beckus, Siegfried and Bellissard, Jean and Cornean, Horia}, title = {Holder Continuity of the Spectra for Aperiodic Hamiltonians}, series = {Annales de l'Institut Henri Poincar{\´e}}, volume = {20}, journal = {Annales de l'Institut Henri Poincar{\´e}}, number = {11}, publisher = {Springer}, address = {Cham}, issn = {1424-0637}, doi = {10.1007/s00023-019-00848-6}, pages = {3603 -- 3631}, year = {2019}, abstract = {We study the spectral location of a strongly pattern equivariant Hamiltonians arising through configurations on a colored lattice. Roughly speaking, two configurations are "close to each other" if, up to a translation, they "almost coincide" on a large fixed ball. The larger this ball, the more similar they are, and this induces a metric on the space of the corresponding dynamical systems. Our main result states that the map which sends a given configuration into the spectrum of its associated Hamiltonian, is Holder (even Lipschitz) continuous in the usual Hausdorff metric. Specifically, the spectral distance of two Hamiltonians is estimated by the distance of the corresponding dynamical systems.}, language = {en} } @book{OPUS4-43561, title = {Implementation research on problem solving in school settings}, series = {Ars inveniendi et dejudicandi ; 13}, journal = {Ars inveniendi et dejudicandi ; 13}, editor = {Kuzle, Ana and Rott, Benjamin and Gebel, Inga}, publisher = {WTM-Verlag}, address = {M{\"u}nster}, isbn = {978-3-95987-116-7}, pages = {IV, 220}, year = {2019}, language = {en} } @article{GrottKnollenbergHammetal.2019, author = {Grott, Matthias and Knollenberg, J. and Hamm, M. and Ogawa, K. and Jaumann, R. and Otto, Katharina Alexandra and Delbo, M. and Michel, Patrick and Biele, J. and Neumann, Wladimir and Knapmeyer, Martin and K{\"u}hrt, E. and Senshu, H. and Okada, T. and Helbert, Jorn and Maturilli, A. and M{\"u}ller, N. and Hagermann, A. and Sakatani, Naoya and Tanaka, S. and Arai, T. and Mottola, Stefano and Tachibana, Shogo and Pelivan, Ivanka and Drube, Line and Vincent, J-B and Yano, Hajime and Pilorget, C. and Matz, K. D. and Schmitz, N. and Koncz, A. and Schr{\"o}der, Stefan E. and Trauthan, F. and Schlotterer, Markus and Krause, C. and Ho, T-M and Moussi-Soffys, A.}, title = {Low thermal conductivity boulder with high porosity identified on C-type asteroid (162173) Ryugu}, series = {Nature astronomy}, volume = {3}, journal = {Nature astronomy}, number = {11}, publisher = {Nature Publishing Group}, address = {London}, issn = {2397-3366}, doi = {10.1038/s41550-019-0832-x}, pages = {971 -- 976}, year = {2019}, abstract = {C-type asteroids are among the most pristine objects in the Solar System, but little is known about their interior structure and surface properties. Telescopic thermal infrared observations have so far been interpreted in terms of a regolith-covered surface with low thermal conductivity and particle sizes in the centimetre range. This includes observations of C-type asteroid (162173) Ryugu1,2,3. However, on arrival of the Hayabusa2 spacecraft at Ryugu, a regolith cover of sand- to pebble-sized particles was found to be absent4,5 (R.J. et al., manuscript in preparation). Rather, the surface is largely covered by cobbles and boulders, seemingly incompatible with the remote-sensing infrared observations. Here we report on in situ thermal infrared observations of a boulder on the C-type asteroid Ryugu. We found that the boulder's thermal inertia was much lower than anticipated based on laboratory measurements of meteorites, and that a surface covered by such low-conductivity boulders would be consistent with remote-sensing observations. Our results furthermore indicate high boulder porosities as well as a low tensile strength in the few hundred kilopascal range. The predicted low tensile strength confirms the suspected observational bias6 in our meteorite collections, as such asteroidal material would be too frail to survive atmospheric entry7}, language = {en} } @article{GrottKnollenbergHammetal.2019, author = {Grott, Matthias and Knollenberg, J. and Hamm, M. and Ogawa, K. and Jaumann, R. and Otto, Katharina Alexandra and Delbo, M. and Michel, P. and Biele, J. and Neumann, W. and Knapmeyer, M. and Kuehrt, E. and Senshu, H. and Okada, T. and Helbert, J. and Maturilli, A. and M{\"u}ller, N. and Hagermann, A. and Sakatani, N. and Tanaka, S. and Arai, T. and Mottola, S. and Tachibana, S. and Pelivan, Ivanka and Drube, L. and Vincent, J-B and Yano, H. and Pilorget, C. and Matz, K. D. and Schmitz, N. and Koncz, A. and Schr{\"o}der, S. E. and Trauthan, F. and Schlotterer, M. and Krause, C. and Ho, T-M and Moussi-Soffys, A.}, title = {Low thermal conductivity boulder with high porosity identified on C-type asteroid (162173) Ryugu}, series = {Nature astronomy}, volume = {3}, journal = {Nature astronomy}, number = {11}, publisher = {Nature Publishing Group}, address = {London}, issn = {2397-3366}, doi = {10.1038/s41550-019-0832-x}, pages = {971 -- 976}, year = {2019}, abstract = {C-type asteroids are among the most pristine objects in the Solar System, but little is known about their interior structure and surface properties. Telescopic thermal infrared observations have so far been interpreted in terms of a regolith-covered surface with low thermal conductivity and particle sizes in the centimetre range. This includes observations of C-type asteroid (162173) Ryugu1,2,3. However, on arrival of the Hayabusa2 spacecraft at Ryugu, a regolith cover of sand- to pebble-sized particles was found to be absent4,5 (R.J. et al., manuscript in preparation). Rather, the surface is largely covered by cobbles and boulders, seemingly incompatible with the remote-sensing infrared observations. Here we report on in situ thermal infrared observations of a boulder on the C-type asteroid Ryugu. We found that the boulder's thermal inertia was much lower than anticipated based on laboratory measurements of meteorites, and that a surface covered by such low-conductivity boulders would be consistent with remote-sensing observations. Our results furthermore indicate high boulder porosities as well as a low tensile strength in the few hundred kilopascal range. The predicted low tensile strength confirms the suspected observational bias6 in our meteorite collections, as such asteroidal material would be too frail to survive atmospheric entry7.}, language = {en} } @article{TyFangGonzalezetal.2019, author = {Ty, Alexander J. A. and Fang, Zheng and Gonzalez, Rivver A. and Rozdeba, Paul J. and Abarbanel, Henry D.}, title = {Machine learning of time series using time-delay embedding and precision annealing}, series = {Neural Computation}, volume = {31}, journal = {Neural Computation}, number = {10}, publisher = {MIT Press}, address = {Cambridge}, issn = {0899-7667}, doi = {10.1162/neco_a_01224}, pages = {2004 -- 2024}, year = {2019}, abstract = {Tasking machine learning to predict segments of a time series requires estimating the parameters of a ML model with input/output pairs from the time series. We borrow two techniques used in statistical data assimilation in order to accomplish this task: time-delay embedding to prepare our input data and precision annealing as a training method. The precision annealing approach identifies the global minimum of the action (-log[P]). In this way, we are able to identify the number of training pairs required to produce good generalizations (predictions) for the time series. We proceed from a scalar time series s(tn);tn=t0+n Delta t and, using methods of nonlinear time series analysis, show how to produce a DE>1-dimensional time-delay embedding space in which the time series has no false neighbors as does the observed s(tn) time series. In that DE-dimensional space, we explore the use of feedforward multilayer perceptrons as network models operating on DE-dimensional input and producing DE-dimensional outputs.}, 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{EdekoGerlachKuehner2019, author = {Edeko, Nikolai and Gerlach, Moritz Reinhardt and K{\"u}hner, Viktoria}, title = {Measure-preserving semiflows and one-parameter Koopman semigroups}, series = {Semigroup forum}, volume = {98}, journal = {Semigroup forum}, number = {1}, publisher = {Springer}, address = {New York}, issn = {0037-1912}, doi = {10.1007/s00233-018-9960-3}, pages = {48 -- 63}, year = {2019}, abstract = {For a finite measure space X, we characterize strongly continuous Markov lattice semigroups on Lp(X) by showing that their generator A acts as a derivation on the dense subspace D(A)L(X). We then use this to characterize Koopman semigroups on Lp(X) if X is a standard probability space. In addition, we show that every measurable and measure-preserving flow on a standard probability space is isomorphic to a continuous flow on a compact Borel probability space.}, language = {en} } @phdthesis{Knoechel2019, author = {Kn{\"o}chel, Jane}, title = {Model reduction of mechanism-based pharmacodynamic models and its link to classical drug effect models}, doi = {10.25932/publishup-44059}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-440598}, school = {Universit{\"a}t Potsdam}, pages = {vii, 147}, year = {2019}, abstract = {Continuous insight into biological processes has led to the development of large-scale, mechanistic systems biology models of pharmacologically relevant networks. While these models are typically designed to study the impact of diverse stimuli or perturbations on multiple system variables, the focus in pharmacological research is often on a specific input, e.g., the dose of a drug, and a specific output related to the drug effect or response in terms of some surrogate marker. To study a chosen input-output pair, the complexity of the interactions as well as the size of the models hinders easy access and understanding of the details of the input-output relationship. The objective of this thesis is the development of a mathematical approach, in specific a model reduction technique, that allows (i) to quantify the importance of the different state variables for a given input-output relationship, and (ii) to reduce the dynamics to its essential features -- allowing for a physiological interpretation of state variables as well as parameter estimation in the statistical analysis of clinical data. We develop a model reduction technique using a control theoretic setting by first defining a novel type of time-limited controllability and observability gramians for nonlinear systems. We then show the superiority of the time-limited generalised gramians for nonlinear systems in the context of balanced truncation for a benchmark system from control theory. The concept of time-limited controllability and observability gramians is subsequently used to introduce a state and time-dependent quantity called the input-response (ir) index that quantifies the importance of state variables for a given input-response relationship at a particular time. We subsequently link our approach to sensitivity analysis, thus, enabling for the first time the use of sensitivity coefficients for state space reduction. The sensitivity based ir-indices are given as a product of two sensitivity coefficients. This allows not only for a computational more efficient calculation but also for a clear distinction of the extent to which the input impacts a state variable and the extent to which a state variable impacts the output. The ir-indices give insight into the coordinated action of specific state variables for a chosen input-response relationship. Our developed model reduction technique results in reduced models that still allow for a mechanistic interpretation in terms of the quantities/state variables of the original system, which is a key requirement in the field of systems pharmacology and systems biology and distinguished the reduced models from so-called empirical drug effect models. The ir-indices are explicitly defined with respect to a reference trajectory and thereby dependent on the initial state (this is an important feature of the measure). This is demonstrated for an example from the field of systems pharmacology, showing that the reduced models are very informative in their ability to detect (genetic) deficiencies in certain physiological entities. Comparing our novel model reduction technique to the already existing techniques shows its superiority. The novel input-response index as a measure of the importance of state variables provides a powerful tool for understanding the complex dynamics of large-scale systems in the context of a specific drug-response relationship. Furthermore, the indices provide a means for a very efficient model order reduction and, thus, an important step towards translating insight from biological processes incorporated in detailed systems pharmacology models into the population analysis of clinical data.}, 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{DombrowskyUndRoelly2019, author = {Dombrowsky, Charlotte and Und, Myriam Fradon and Roelly, Sylvie}, title = {Packungen aus Kreisscheiben}, series = {Elemente der Mathematik}, volume = {74}, journal = {Elemente der Mathematik}, number = {2}, publisher = {EMS Publ.}, address = {Z{\"u}rich}, issn = {0013-6018}, doi = {10.4171/EM/381}, pages = {45 -- 62}, year = {2019}, abstract = {Der englische Seefahrer Sir Walter Raleigh fragte sich einst, wie er in seinem Schiffsladeraum moeglichst viele Kanonenkugeln stapeln koennte. Johannes Kepler entwickelte daraufhin 1611 eine Vermutung ueber die optimale Anordnung der Kugeln. Diese Vermutung sollte sich als eine der haertesten mathematischen Nuesse der Geschichte erweisen. Selbst in der Ebene sind dichteste Packungen kongruenter Kreise eine Herausforderung. 1892 und 1910 veroeffentlichte Axel Thue (kritisierte) Beweise, dass die hexagonale Kreispackung optimal sei. Erst 1940 lieferte Laszlo Fejes Toth schliesslich einen wasserdichten Beweis fuer diese Tatsache. Eine Variante des Problems verlangt, Packungen mit endlich vielen kongruenten Kugeln zu finden, die eine gewisse quadratische Energie minimieren: Diese spannende geometrische Aufgabe wurde 1967 von Toth gestellt. Sie ist auch heute noch nicht vollstaendig gelaest. In diesem Beitrag schlagen die Autorinnen eine originelle wahrscheinlichkeitstheoretische Methode vor, um in der Ebene N{\"a}herungen der L{\"o}sung zu konstruieren.}, language = {de} } @misc{vanLeeuwenKunschNergeretal.2019, author = {van Leeuwen, Peter Jan and Kunsch, Hans R. and Nerger, Lars and Potthast, Roland and Reich, Sebastian}, title = {Particle filters for high-dimensional geoscience applications: A review}, series = {Quarterly journal of the Royal Meteorological Society}, volume = {145}, journal = {Quarterly journal of the Royal Meteorological Society}, number = {723}, publisher = {Wiley}, address = {Hoboken}, issn = {0035-9009}, doi = {10.1002/qj.3551}, pages = {2335 -- 2365}, year = {2019}, abstract = {Particle filters contain the promise of fully nonlinear data assimilation. They have been applied in numerous science areas, including the geosciences, but their application to high-dimensional geoscience systems has been limited due to their inefficiency in high-dimensional systems in standard settings. However, huge progress has been made, and this limitation is disappearing fast due to recent developments in proposal densities, the use of ideas from (optimal) transportation, the use of localization and intelligent adaptive resampling strategies. Furthermore, powerful hybrids between particle filters and ensemble Kalman filters and variational methods have been developed. We present a state-of-the-art discussion of present efforts of developing particle filters for high-dimensional nonlinear geoscience state-estimation problems, with an emphasis on atmospheric and oceanic applications, including many new ideas, derivations and unifications, highlighting hidden connections, including pseudo-code, and generating a valuable tool and guide for the community. Initial experiments show that particle filters can be competitive with present-day methods for numerical weather prediction, suggesting that they will become mainstream soon.}, language = {en} } @misc{ButuzovNefedovReckeetal.2019, author = {Butuzov, Valentin F. and Nefedov, N. N. and Recke, Lutz and Omel'chenko, Oleh}, title = {Partly dissipative system with multizonal initial and boundary layers}, series = {Journal of Physics: Conference Series}, volume = {1205}, journal = {Journal of Physics: Conference Series}, publisher = {IOP Publ.}, address = {Bristol}, issn = {1742-6588}, doi = {10.1088/1742-6596/1205/1/012009}, pages = {7}, year = {2019}, abstract = {For a singularly perturbed parabolic - ODE system we construct the asymptotic expansion in the small parameter in the case, when the degenerate equation has a double root. Such systems, which are called partly dissipative reaction-diffusion systems, are used to model various natural processes, including the signal transmission along axons, solid combustion and the kinetics of some chemical reactions. It turns out that the algorithm of the construction of the boundary layer functions and the behavior of the solution in the boundary layers essentially differ from that ones in case of a simple root. The multizonal initial and boundary layers behaviour was stated.}, language = {en} } @article{BiskabornSmithNoetzlietal.2019, author = {Biskaborn, Boris and Smith, Sharon L. and Noetzli, Jeannette and Matthes, Heidrun and Vieira, Goncalo and Streletskiy, Dmitry A. and Schoeneich, Philippe and Romanovsky, Vladimir E. and Lewkowicz, Antoni G. and Abramov, Andrey and Allard, Michel and Boike, Julia and Cable, William L. and Christiansen, Hanne H. and Delaloye, Reynald and Diekmann, Bernhard and Drozdov, Dmitry and Etzelmueller, Bernd and Grosse, Guido and Guglielmin, Mauro and Ingeman-Nielsen, Thomas and Isaksen, Ketil and Ishikawa, Mamoru and Johansson, Margareta and Johannsson, Halldor and Joo, Anseok and Kaverin, Dmitry and Kholodov, Alexander and Konstantinov, Pavel and Kroeger, Tim and Lambiel, Christophe and Lanckman, Jean-Pierre and Luo, Dongliang and Malkova, Galina and Meiklejohn, Ian and Moskalenko, Natalia and Oliva, Marc and Phillips, Marcia and Ramos, Miguel and Sannel, A. Britta K. and Sergeev, Dmitrii and Seybold, Cathy and Skryabin, Pavel and Vasiliev, Alexander and Wu, Qingbai and Yoshikawa, Kenji and Zheleznyak, Mikhail and Lantuit, Hugues}, title = {Permafrost is warming at a global scale}, series = {Nature Communications}, volume = {10}, journal = {Nature Communications}, publisher = {Nature Publ. Group}, address = {London}, issn = {2041-1723}, doi = {10.1038/s41467-018-08240-4}, pages = {11}, year = {2019}, abstract = {Permafrost warming has the potential to amplify global climate change, because when frozen sediments thaw it unlocks soil organic carbon. Yet to date, no globally consistent assessment of permafrost temperature change has been compiled. Here we use a global data set of permafrost temperature time series from the Global Terrestrial Network for Permafrost to evaluate temperature change across permafrost regions for the period since the International Polar Year (2007-2009). During the reference decade between 2007 and 2016, ground temperature near the depth of zero annual amplitude in the continuous permafrost zone increased by 0.39 +/- 0.15 degrees C. Over the same period, discontinuous permafrost warmed by 0.20 +/- 0.10 degrees C. Permafrost in mountains warmed by 0.19 +/- 0.05 degrees C and in Antarctica by 0.37 +/- 0.10 degrees C. Globally, permafrost temperature increased by 0.29 +/- 0.12 degrees C. The observed trend follows the Arctic amplification of air temperature increase in the Northern Hemisphere. In the discontinuous zone, however, ground warming occurred due to increased snow thickness while air temperature remained statistically unchanged.}, language = {en} } @article{SalamatZoellerAmini2019, author = {Salamat, Mona and Z{\"o}ller, Gert and Amini, Morteza}, title = {Prediction of the Maximum Expected Earthquake Magnitude in Iran:}, series = {Pure and applied geophysics}, volume = {176}, journal = {Pure and applied geophysics}, number = {8}, publisher = {Springer}, address = {Basel}, issn = {0033-4553}, doi = {10.1007/s00024-019-02141-3}, pages = {3425 -- 3438}, year = {2019}, abstract = {This paper concerns the problem of predicting the maximum expected earthquake magnitude μ in a future time interval Tf given a catalog covering a time period T in the past. Different studies show the divergence of the confidence interval of the maximum possible earthquake magnitude m_{ max } for high levels of confidence (Salamat et al. 2017). Therefore, m_{ max } should be better replaced by μ (Holschneider et al. 2011). In a previous study (Salamat et al. 2018), μ is estimated for an instrumental earthquake catalog of Iran from 1900 onwards with a constant level of completeness ( {m0 = 5.5} ). In the current study, the Bayesian methodology developed by Z{\"o}ller et al. (2014, 2015) is applied for the purpose of predicting μ based on the catalog consisting of both historical and instrumental parts. The catalog is first subdivided into six subcatalogs corresponding to six seismotectonic zones, and each of those zone catalogs is subsequently subdivided according to changes in completeness level and magnitude uncertainty. For this, broad and small error distributions are considered for historical and instrumental earthquakes, respectively. We assume that earthquakes follow a Poisson process in time and Gutenberg-Richter law in the magnitude domain with a priori unknown a and b values which are first estimated by Bayes' theorem and subsequently used to estimate μ. Imposing different values of m_{ max } for different seismotectonic zones namely Alborz, Azerbaijan, Central Iran, Zagros, Kopet Dagh and Makran, the results show considerable probabilities for the occurrence of earthquakes with Mw ≥ 7.5 in short Tf , whereas for long Tf, μ is almost equal to m_{ max }}, language = {en} } @article{KuckelkornStueblerTextorisTaubeetal.2019, author = {Kuckelkorn, Ulrike and St{\"u}bler, Sabine and Textoris-Taube, Kathrin and Kilian, Christiane and Niewienda, Agathe and Henklein, Petra and Janek, Katharina and Stumpf, Michael P. H. and Mishto, Michele and Liepe, Juliane}, title = {Proteolytic dynamics of human 20S thymoproteasome}, series = {The journal of biological chemistry}, volume = {294}, journal = {The journal of biological chemistry}, number = {19}, publisher = {American Society for Biochemistry and Molecular Biology}, address = {Bethesda}, issn = {1083-351X}, doi = {10.1074/jbc.RA118.007347}, pages = {7740 -- 7754}, year = {2019}, abstract = {An efficient immunosurveillance of CD8(+) T cells in the periphery depends on positive/negative selection of thymocytes and thus on the dynamics of antigen degradation and epitope production by thymoproteasome and immunoproteasome in the thymus. Although studies in mouse systems have shown how thymoproteasome activity differs from that of immunoproteasome and strongly impacts the T cell repertoire, the proteolytic dynamics and the regulation of human thymoproteasome are unknown. By combining biochemical and computational modeling approaches, we show here that human 20S thymoproteasome and immunoproteasome differ not only in the proteolytic activity of the catalytic sites but also in the peptide transport. These differences impinge upon the quantity of peptide products rather than where the substrates are cleaved. The comparison of the two human 20S proteasome isoforms depicts different processing of antigens that are associated to tumors and autoimmune diseases.}, language = {en} } @phdthesis{Tinpun2019, author = {Tinpun, Kittisak}, title = {Relative rank of infinite full transformation semigroups with restricted range}, school = {Universit{\"a}t Potsdam}, year = {2019}, language = {en} } @article{BandaraRosen2019, author = {Bandara, Menaka Lashitha and Rosen, Andreas}, title = {Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of local boundary conditions}, series = {Communications in partial differential equations}, volume = {44}, journal = {Communications in partial differential equations}, number = {12}, publisher = {Taylor \& Francis Group}, address = {Philadelphia}, issn = {0360-5302}, doi = {10.1080/03605302.2019.1611847}, pages = {1253 -- 1284}, year = {2019}, abstract = {On a smooth complete Riemannian spin manifold with smooth compact boundary, we demonstrate that Atiyah-Singer Dirac operator in depends Riesz continuously on perturbations of local boundary conditions The Lipschitz bound for the map depends on Lipschitz smoothness and ellipticity of and bounds on Ricci curvature and its first derivatives as well as a lower bound on injectivity radius away from a compact neighbourhood of the boundary. More generally, we prove perturbation estimates for functional calculi of elliptic operators on manifolds with local boundary conditions.}, language = {en} } @article{SanchezWichtBaerenzungetal.2019, author = {Sanchez, S. and Wicht, J. and Baerenzung, Julien and Holschneider, Matthias}, title = {Sequential assimilation of geomagnetic observations}, series = {Geophysical journal international}, volume = {217}, journal = {Geophysical journal international}, number = {2}, publisher = {Oxford Univ. Press}, address = {Oxford}, issn = {0956-540X}, doi = {10.1093/gji/ggz090}, pages = {1434 -- 1450}, year = {2019}, abstract = {High-precision observations of the present-day geomagnetic field by ground-based observatories and satellites provide unprecedented conditions for unveiling the dynamics of the Earth's core. Combining geomagnetic observations with dynamo simulations in a data assimilation (DA) framework allows the reconstruction of past and present states of the internal core dynamics. The essential information that couples the internal state to the observations is provided by the statistical correlations from a numerical dynamo model in the form of a model covariance matrix. Here we test a sequential DA framework, working through a succession of forecast and analysis steps, that extracts the correlations from an ensemble of dynamo models. The primary correlations couple variables of the same azimuthal wave number, reflecting the predominant axial symmetry of the magnetic field. Synthetic tests show that the scheme becomes unstable when confronted with high-precision geomagnetic observations. Our study has identified spurious secondary correlations as the origin of the problem. Keeping only the primary correlations by localizing the covariance matrix with respect to the azimuthal wave number suffices to stabilize the assimilation. While the first analysis step is fundamental in constraining the large-scale interior state, further assimilation steps refine the smaller and more dynamical scales. This refinement turns out to be critical for long-term geomagnetic predictions. Increasing the assimilation steps from one to 18 roughly doubles the prediction horizon for the dipole from about  tree to six centuries, and from 30 to about  60 yr for smaller observable scales. This improvement is also reflected on the predictability of surface intensity features such as the South Atlantic Anomaly. Intensity prediction errors are decreased roughly by a half when assimilating long observation sequences.}, language = {en} } @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} } @misc{PereraBoeckmann2019, author = {Perera, Upeksha and B{\"o}ckmann, Christine}, title = {Solutions of direct and inverse even-order Sturm-Liouville problems using Magnus expansion}, series = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, journal = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, number = {1336}, issn = {1866-8372}, doi = {10.25932/publishup-47341}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-473414}, 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{NueskenReichRozdeba2019, author = {N{\"u}sken, Nikolas and Reich, Sebastian and Rozdeba, Paul J.}, title = {State and parameter estimation from observed signal increments}, series = {Entropy : an international and interdisciplinary journal of entropy and information studies}, volume = {21}, journal = {Entropy : an international and interdisciplinary journal of entropy and information studies}, number = {5}, publisher = {MDPI}, address = {Basel}, issn = {1099-4300}, doi = {10.3390/e21050505}, pages = {23}, year = {2019}, abstract = {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.}, language = {en} } @article{LieStuartSullivan2019, author = {Lie, Han Cheng and Stuart, A. M. and Sullivan, Tim J.}, title = {Strong convergence rates of probabilistic integrators for ordinary differential equations}, series = {Statistics and Computing}, volume = {29}, journal = {Statistics and Computing}, number = {6}, publisher = {Springer}, address = {Dordrecht}, issn = {0960-3174}, doi = {10.1007/s11222-019-09898-6}, pages = {1265 -- 1283}, year = {2019}, abstract = {Probabilistic integration of a continuous dynamical system is a way of systematically introducing discretisation error, at scales no larger than errors introduced by standard numerical discretisation, in order to enable thorough exploration of possible responses of the system to inputs. It is thus a potentially useful approach in a number of applications such as forward uncertainty quantification, inverse problems, and data assimilation. We extend the convergence analysis of probabilistic integrators for deterministic ordinary differential equations, as proposed by Conrad et al. (Stat Comput 27(4):1065-1082, 2017. ), to establish mean-square convergence in the uniform norm on discrete- or continuous-time solutions under relaxed regularity assumptions on the driving vector fields and their induced flows. Specifically, we show that randomised high-order integrators for globally Lipschitz flows and randomised Euler integrators for dissipative vector fields with polynomially bounded local Lipschitz constants all have the same mean-square convergence rate as their deterministic counterparts, provided that the variance of the integration noise is not of higher order than the corresponding deterministic integrator. These and similar results are proven for probabilistic integrators where the random perturbations may be state-dependent, non-Gaussian, or non-centred random variables.}, language = {en} } @article{Baer2019, author = {B{\"a}r, Christian}, title = {The curl operator on odd-dimensional manifolds}, series = {Journal of mathematical physics}, volume = {60}, journal = {Journal of mathematical physics}, number = {3}, publisher = {American Institute of Physics}, address = {Melville}, issn = {0022-2488}, doi = {10.1063/1.5082528}, pages = {16}, year = {2019}, abstract = {We study the spectral properties of curl, a linear differential operator of first order acting on differential forms of appropriate degree on an odd-dimensional closed oriented Riemannian manifold. In three dimensions, its eigenvalues are the electromagnetic oscillation frequencies in vacuum without external sources. In general, the spectrum consists of the eigenvalue 0 with infinite multiplicity and further real discrete eigenvalues of finite multiplicity. We compute the Weyl asymptotics and study the zeta-function. We give a sharp lower eigenvalue bound for positively curved manifolds and analyze the equality case. Finally, we compute the spectrum for flat tori, round spheres, and 3-dimensional spherical space forms. Published under license by AIP Publishing.}, 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} } @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{Denecke2019, author = {Denecke, Klaus-Dieter}, title = {The partial clone of linear formulas}, series = {Siberian mathematical journal}, volume = {60}, journal = {Siberian mathematical journal}, number = {4}, publisher = {Pleiades Publ.}, address = {New York}, issn = {0037-4466}, doi = {10.1134/S0037446619040037}, pages = {572 -- 584}, year = {2019}, abstract = {A term t is linear if no variable occurs more than once in t. An identity s ≈ t is said to be linear if s and t are linear terms. Identities are particular formulas. As for terms superposition operations can be defined for formulas too. We define the arbitrary linear formulas and seek for a condition for the set of all linear formulas to be closed under superposition. This will be used to define the partial superposition operations on the set of linear formulas and a partial many-sorted algebra Formclonelin(τ, τ′). This algebra has similar properties with the partial many-sorted clone of all linear terms. We extend the concept of a hypersubstitution of type τ to the linear hypersubstitutions of type (τ, τ′) for algebraic systems. The extensions of linear hypersubstitutions of type (τ, τ′) send linear formulas to linear formulas, presenting weak endomorphisms of Formclonelin(τ, τ′).}, language = {en} } @article{LekkoksungDenecke2019, author = {Lekkoksung, Nareupanat and Denecke, Klaus-Dieter}, title = {The partial clone of linear tree languages}, series = {Siberian mathematical journal}, volume = {60}, journal = {Siberian mathematical journal}, number = {3}, publisher = {Pleiades Publ.}, address = {New York}, issn = {0037-4466}, doi = {10.1134/S0037446619030121}, pages = {497 -- 507}, year = {2019}, abstract = {A term, also called a tree, is said to be linear, if each variable occurs in the term only once. The linear terms and sets of linear terms, the so-called linear tree languages, play some role in automata theory and in the theory of formal languages in connection with recognizability. We define a partial superposition operation on sets of linear trees of a given type and study the properties of some many-sorted partial clones that have sets of linear trees as elements and partial superposition operations as fundamental operations. The endomorphisms of those algebras correspond to nondeterministic linear hypersubstitutions.}, language = {en} } @article{FernandesKoppitzMusunthia2019, author = {Fernandes, Vitor H. and Koppitz, J{\"o}rg and Musunthia, Tiwadee}, title = {The Rank of the Semigroup of All Order-Preserving Transformations on a Finite Fence}, series = {Bulletin of the Malaysian Mathematical Sciences Society volume}, volume = {42}, journal = {Bulletin of the Malaysian Mathematical Sciences Society volume}, number = {5}, publisher = {Malaysian mathematical sciences sciences soc}, address = {Pulau Punang}, issn = {0126-6705}, doi = {10.1007/s40840-017-0598-1}, pages = {2191 -- 2211}, year = {2019}, abstract = {A zig-zag (or fence) order is a special partial order on a (finite) set. In this paper, we consider the semigroup TFn of all order-preserving transformations on an n-element zig-zag-ordered set. We determine the rank of TFn and provide a minimal generating set for TFn. Moreover, a formula for the number of idempotents in TFn is given.}, language = {en} } @phdthesis{Angwenyi2019, author = {Angwenyi, David}, title = {Time-continuous state and parameter estimation with application to hyperbolic SPDEs}, doi = {10.25932/publishup-43654}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-436542}, school = {Universit{\"a}t Potsdam}, pages = {xi, 101}, year = {2019}, abstract = {Data assimilation has been an active area of research in recent years, owing to its wide utility. At the core of data assimilation are filtering, prediction, and smoothing procedures. Filtering entails incorporation of measurements' information into the model to gain more insight into a given state governed by a noisy state space model. Most natural laws are governed by time-continuous nonlinear models. For the most part, the knowledge available about a model is incomplete; and hence uncertainties are approximated by means of probabilities. Time-continuous filtering, therefore, holds promise for wider usefulness, for it offers a means of combining noisy measurements with imperfect model to provide more insight on a given state. The solution to time-continuous nonlinear Gaussian filtering problem is provided for by the Kushner-Stratonovich equation. Unfortunately, the Kushner-Stratonovich equation lacks a closed-form solution. Moreover, the numerical approximations based on Taylor expansion above third order are fraught with computational complications. For this reason, numerical methods based on Monte Carlo methods have been resorted to. Chief among these methods are sequential Monte-Carlo methods (or particle filters), for they allow for online assimilation of data. Particle filters are not without challenges: they suffer from particle degeneracy, sample impoverishment, and computational costs arising from resampling. The goal of this thesis is to:— i) Review the derivation of Kushner-Stratonovich equation from first principles and its extant numerical approximation methods, ii) Study the feedback particle filters as a way of avoiding resampling in particle filters, iii) Study joint state and parameter estimation in time-continuous settings, iv) Apply the notions studied to linear hyperbolic stochastic differential equations. The interconnection between It{\^o} integrals and stochastic partial differential equations and those of Stratonovich is introduced in anticipation of feedback particle filters. With these ideas and motivated by the variants of ensemble Kalman-Bucy filters founded on the structure of the innovation process, a feedback particle filter with randomly perturbed innovation is proposed. Moreover, feedback particle filters based on coupling of prediction and analysis measures are proposed. They register a better performance than the bootstrap particle filter at lower ensemble sizes. We study joint state and parameter estimation, both by means of extended state spaces and by use of dual filters. Feedback particle filters seem to perform well in both cases. Finally, we apply joint state and parameter estimation in the advection and wave equation, whose velocity is spatially varying. Two methods are employed: Metropolis Hastings with filter likelihood and a dual filter comprising of Kalman-Bucy filter and ensemble Kalman-Bucy filter. The former performs better than the latter.}, language = {en} } @article{AzzaliWahl2019, author = {Azzali, Sara and Wahl, Charlotte}, title = {Two-cocycle twists and Atiyah-Patodi-Singer index theory}, series = {Mathematical Proceedings of the Cambridge Philosophical Society}, volume = {167}, journal = {Mathematical Proceedings of the Cambridge Philosophical Society}, number = {3}, publisher = {Cambridge Univ. Press}, address = {New York}, issn = {0305-0041}, doi = {10.1017/S0305004118000427}, pages = {437 -- 487}, year = {2019}, abstract = {We construct eta- and rho-invariants for Dirac operators, on the universal covering of a closed manifold, that are invariant under the projective action associated to a 2-cocycle of the fundamental group. We prove an Atiyah-Patodi-Singer index theorem in this setting, as well as its higher generalisation. Applications concern the classification of positive scalar curvature metrics on closed spin manifolds. We also investigate the properties of these twisted invariants for the signature operator and the relation to the higher invariants.}, language = {en} }