@article{Weishaeupl2023, author = {Weish{\"a}upl, Sebastian}, title = {The weak Gram law for Hecke \(L\)-functions}, series = {The Ramanujan Journal}, volume = {60}, journal = {The Ramanujan Journal}, number = {4}, issn = {1382-4090}, doi = {10.1007/s11139-022-00638-5}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-324404}, pages = {981-997}, year = {2023}, abstract = {We generalize a theorem by Titchmarsh about the mean value of Hardy's \(Z\)-function at the Gram points to the Hecke \(L\)-functions, which in turn implies the weak Gram law for them. Instead of proceeding analogously to Titchmarsh with an approximate functional equation we employ a different method using contour integration.}, language = {en} } @article{LuMoenius2023, author = {Lu, Lu and M{\"o}nius, Katja}, title = {Algebraic degree of Cayley graphs over abelian groups and dihedral groups}, series = {Journal of Algebraic Combinatorics}, volume = {57}, journal = {Journal of Algebraic Combinatorics}, number = {3}, issn = {0925-9899}, doi = {10.1007/s10801-022-01190-7}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-324380}, pages = {753-761}, year = {2023}, abstract = {For a graph \(\Gamma\) , let K be the smallest field containing all eigenvalues of the adjacency matrix of \(\Gamma\) . The algebraic degree \(\deg (\Gamma )\) is the extension degree \([K:\mathbb {Q}]\). In this paper, we completely determine the algebraic degrees of Cayley graphs over abelian groups and dihedral groups.}, language = {en} } @article{GreefrathOldenburgSilleretal.2023, author = {Greefrath, Gilbert and Oldenburg, Reinhard and Siller, Hans-Stefan and Ulm, Volker and Weigand, Hans-Georg}, title = {Mathematics students' characteristics of basic mental models of the derivative}, series = {Journal f{\"u}r Mathematik-Didaktik}, volume = {44}, journal = {Journal f{\"u}r Mathematik-Didaktik}, number = {1}, issn = {0173-5322}, doi = {10.1007/s13138-022-00207-9}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-324317}, pages = {143-169}, year = {2023}, abstract = {The concept of derivative is characterised with reference to four basic mental models. These are described as theoretical constructs based on theoretical considerations. The four basic mental models—local rate of change, tangent slope, local linearity and amplification factor—are not only quantified empirically but are also validated. To this end, a test instrument for measuring students' characteristics of basic mental models is presented and analysed regarding quality criteria. Mathematics students (n = 266) were tested with this instrument. The test results show that the four basic mental models of the derivative can be reconstructed among the students with different characteristics. The tangent slope has the highest agreement values across all tasks. The agreement on explanations based on the basic mental model of rate of change is not as strongly established among students as one would expect due to framework settings in the school system by means of curricula and educational standards. The basic mental model of local linearity plays a rather subordinate role. The amplification factor achieves the lowest agreement values. In addition, cluster analysis was conducted to identify different subgroups of the student population. Moreover, the test results can be attributed to characteristics of the task types as well as to the students' previous experiences from mathematics classes by means of qualitative interpretation. These and other results of students' basic mental models of the derivative are presented and discussed in detail.}, language = {en} } @article{SillerElschenbroichGreefrathetal.2023, author = {Siller, Hans-Stefan and Elschenbroich, Hans-J{\"u}rgen and Greefrath, Gilbert and Vorh{\"o}lter, Katrin}, title = {Mathematical modelling of exponential growth as a rich learning environment for mathematics classrooms}, series = {ZDM Mathematics Education}, volume = {55}, journal = {ZDM Mathematics Education}, number = {1}, issn = {1863-9690}, doi = {10.1007/s11858-022-01433-8}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-324393}, pages = {17-33}, year = {2023}, abstract = {Mathematical concepts are regularly used in media reports concerning the Covid-19 pandemic. These include growth models, which attempt to explain or predict the effectiveness of interventions and developments, as well as the reproductive factor. Our contribution has the aim of showing that basic mental models about exponential growth are important for understanding media reports of Covid-19. Furthermore, we highlight how the coronavirus pandemic can be used as a context in mathematics classrooms to help students understand that they can and should question media reports on their own, using their mathematical knowledge. Therefore, we first present the role of mathematical modelling in achieving these goals in general. The same relevance applies to the necessary basic mental models of exponential growth. Following this description, based on three topics, namely, investigating the type of growth, questioning given course models, and determining exponential factors at different times, we show how the presented theoretical aspects manifest themselves in teaching examples when students are given the task of reflecting critically on existing media reports. Finally, the value of the three topics regarding the intended goals is discussed and conclusions concerning the possibilities and limits of their use in schools are drawn.}, language = {en} } @article{SteudingTongsomporn2023, author = {Steuding, J{\"o}rn and Tongsomporn, Janyarak}, title = {On the order of growth of Lerch zeta functions}, series = {Mathematics}, volume = {11}, journal = {Mathematics}, number = {3}, issn = {2227-7390}, doi = {10.3390/math11030723}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-303981}, year = {2023}, abstract = {We extend Bourgain's bound for the order of growth of the Riemann zeta function on the critical line to Lerch zeta functions. More precisely, we prove L(λ, α, 1/2 + it) ≪ t\(^{13/84+ϵ}\) as t → ∞. For both, the Riemann zeta function as well as for the more general Lerch zeta function, it is conjectured that the right-hand side can be replaced by t\(^ϵ\) (which is the so-called Lindel{\"o}f hypothesis). The growth of an analytic function is closely related to the distribution of its zeros.}, language = {en} } @article{HeinsRothWaldmann2023, author = {Heins, Michael and Roth, Oliver and Waldmann, Stefan}, title = {Convergent star products on cotangent bundles of Lie groups}, series = {Mathematische Annalen}, volume = {386}, journal = {Mathematische Annalen}, number = {1-2}, issn = {0025-5831}, doi = {10.1007/s00208-022-02384-x}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-324324}, pages = {151-206}, year = {2023}, abstract = {For a connected real Lie group G we consider the canonical standard-ordered star product arising from the canonical global symbol calculus based on the half-commutator connection of G. This star product trivially converges on polynomial functions on T\(^*\)G thanks to its homogeneity. We define a nuclear Fr{\´e}chet algebra of certain analytic functions on T\(^*\)G, for which the standard-ordered star product is shown to be a well-defined continuous multiplication, depending holomorphically on the deformation parameter \(\hbar\). This nuclear Fr{\´e}chet algebra is realized as the completed (projective) tensor product of a nuclear Fr{\´e}chet algebra of entire functions on G with an appropriate nuclear Fr{\´e}chet algebra of functions on \({\mathfrak {g}}^*\). The passage to the Weyl-ordered star product, i.e. the Gutt star product on T\(^*\)G, is shown to preserve this function space, yielding the continuity of the Gutt star product with holomorphic dependence on \(\hbar\).}, language = {en} } @article{JotzMehtaPapantonis2023, author = {Jotz, M. and Mehta, R. A. and Papantonis, T.}, title = {Modules and representations up to homotopy of Lie n-algebroids}, series = {Journal of Homotopy and Related Structures}, volume = {18}, journal = {Journal of Homotopy and Related Structures}, number = {1}, issn = {2193-8407}, doi = {10.1007/s40062-022-00322-x}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-324333}, pages = {23-70}, year = {2023}, abstract = {This paper studies differential graded modules and representations up to homotopy of Lie n-algebroids, for general \(n\in {\mathbb {N}}\). The adjoint and coadjoint modules are described, and the corresponding split versions of the adjoint and coadjoint representations up to homotopy are explained. In particular, the case of Lie 2-algebroids is analysed in detail. The compatibility of a Poisson bracket with the homological vector field of a Lie n-algebroid is shown to be equivalent to a morphism from the coadjoint module to the adjoint module, leading to an alternative characterisation of non-degeneracy of higher Poisson structures. Moreover, the Weil algebra of a Lie n-algebroid is computed explicitly in terms of splittings, and representations up to homotopy of Lie n-algebroids are used to encode decomposed VB-Lie n-algebroid structures on double vector bundles.}, language = {en} } @article{GerberQuarderGreefrathetal.2023, author = {Gerber, Sebastian and Quarder, Jascha and Greefrath, Gilbert and Siller, Hans-Stefan}, title = {Promoting adaptive intervention competence for teaching simulations and mathematical modelling with digital tools}, series = {Frontiers in Education}, volume = {8}, journal = {Frontiers in Education}, issn = {2504-284X}, doi = {10.3389/feduc.2023.1141063}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-323701}, year = {2023}, abstract = {Providing adaptive, independence-preserving and theory-guided support to students in dealing with real-world problems in mathematics lessons is a major challenge for teachers in their professional practice. This paper examines this challenge in the context of simulations and mathematical modelling with digital tools: in addition to mathematical difficulties when autonomously working out individual solutions, students may also experience challenges when using digital tools. These challenges need to be closely examined and diagnosed, and might - if necessary - have to be overcome by intervention in such a way that the students can subsequently continue working independently. Thus, if a difficulty arises in the working process, two knowledge dimensions are necessary in order to provide adapted support to students. For teaching simulations and mathematical modelling with digital tools, more specifically, these knowledge dimensions are: pedagogical content knowledge about simulation and modelling processes supported by digital tools (this includes knowledge about phases and difficulties in the working process) and pedagogical content knowledge about interventions during the mentioned processes (focussing on characteristics of suitable interventions as well as their implementation and effects on the students' working process). The two knowledge dimensions represent cognitive dispositions as the basis for the conceptualisation and operationalisation of a so-called adaptive intervention competence for teaching simulations and mathematical modelling with digital tools. In our article, we present a domain-specific process model and distinguish different types of teacher interventions. Then we describe the design and content of a university course at two German universities aiming to promote this domain-specific professional adaptive intervention competence, among others. In a study using a quasi-experimental pre-post design (N = 146), we confirm that the structure of cognitive dispositions of adaptive intervention competence for teaching simulations and mathematical modelling with digital tools can be described empirically by a two-dimensional model. In addition, the effectiveness of the course is examined and confirmed quantitatively. Finally, the results are discussed, especially against the background of the sample and the research design, and conclusions are derived for possibilities of promoting professional adaptive intervention competence in university courses.}, language = {en} } @article{KakaroumpasSoleriGibert2022, author = {Kakaroumpas, Spyridon and Soler i Gibert, Od{\´i}}, title = {Dyadic product BMO in the Bloom setting}, series = {Journal of the London Mathematical Society}, volume = {106}, journal = {Journal of the London Mathematical Society}, number = {2}, issn = {0024-6107}, doi = {10.1112/jlms.12588}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-318602}, pages = {899 -- 935}, year = {2022}, abstract = {{\´O}. Blasco and S. Pott showed that the supremum of operator norms over L\(^{2}\) of all bicommutators (with the same symbol) of one-parameter Haar multipliers dominates the biparameter dyadic product BMO norm of the symbol itself. In the present work we extend this result to the Bloom setting, and to any exponent 1 < p < ∞. The main tool is a new characterization in terms of paraproducts and two-weight John-Nirenberg inequalities for dyadic product BMO in the Bloom setting. We also extend our results to the whole scale of indexed spaces between little bmo and product BMO in the general multiparameter setting, with the appropriate iterated commutator in each case.}, language = {en} } @article{DashkovskiySlynko2022, author = {Dashkovskiy, Sergey and Slynko, Vitalii}, title = {Stability conditions for impulsive dynamical systems}, series = {Mathematics of Control, Signals, and Systems}, volume = {34}, journal = {Mathematics of Control, Signals, and Systems}, number = {1}, issn = {1435-568X}, doi = {10.1007/s00498-021-00305-y}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-268390}, pages = {95-128}, year = {2022}, abstract = {In this work, we consider impulsive dynamical systems evolving on an infinite-dimensional space and subjected to external perturbations. We look for stability conditions that guarantee the input-to-state stability for such systems. Our new dwell-time conditions allow the situation, where both continuous and discrete dynamics can be unstable simultaneously. Lyapunov like methods are developed for this purpose. Illustrative finite and infinite dimensional examples are provided to demonstrate the application of the main results. These examples cannot be treated by any other published approach and demonstrate the effectiveness of our results.}, language = {en} } @article{HelinKretschmann2022, author = {Helin, Tapio and Kretschmann, Remo}, title = {Non-asymptotic error estimates for the Laplace approximation in Bayesian inverse problems}, series = {Numerische Mathematik}, volume = {150}, journal = {Numerische Mathematik}, number = {2}, doi = {10.1007/s00211-021-01266-9}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-265399}, pages = {521-549}, year = {2022}, abstract = {In this paper we study properties of the Laplace approximation of the posterior distribution arising in nonlinear Bayesian inverse problems. Our work is motivated by Schillings et al. (Numer Math 145:915-971, 2020. https://doi.org/10.1007/s00211-020-01131-1), where it is shown that in such a setting the Laplace approximation error in Hellinger distance converges to zero in the order of the noise level. Here, we prove novel error estimates for a given noise level that also quantify the effect due to the nonlinearity of the forward mapping and the dimension of the problem. In particular, we are interested in settings in which a linear forward mapping is perturbed by a small nonlinear mapping. Our results indicate that in this case, the Laplace approximation error is of the size of the perturbation. The paper provides insight into Bayesian inference in nonlinear inverse problems, where linearization of the forward mapping has suitable approximation properties.}, language = {en} } @article{HellmuthKlingenberg2022, author = {Hellmuth, Kathrin and Klingenberg, Christian}, title = {Computing Black Scholes with uncertain volatility — a machine learning approach}, series = {Mathematics}, volume = {10}, journal = {Mathematics}, number = {3}, issn = {2227-7390}, doi = {10.3390/math10030489}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-262280}, year = {2022}, abstract = {In financial mathematics, it is a typical approach to approximate financial markets operating in discrete time by continuous-time models such as the Black Scholes model. Fitting this model gives rise to difficulties due to the discrete nature of market data. We thus model the pricing process of financial derivatives by the Black Scholes equation, where the volatility is a function of a finite number of random variables. This reflects an influence of uncertain factors when determining volatility. The aim is to quantify the effect of this uncertainty when computing the price of derivatives. Our underlying method is the generalized Polynomial Chaos (gPC) method in order to numerically compute the uncertainty of the solution by the stochastic Galerkin approach and a finite difference method. We present an efficient numerical variation of this method, which is based on a machine learning technique, the so-called Bi-Fidelity approach. This is illustrated with numerical examples.}, language = {en} } @article{FallMinlendRatzkin2022, author = {Fall, Mouhammed Moustapha and Minlend, Ignace Aristide and Ratzkin, Jesse}, title = {Foliation of an Asymptotically Flat End by Critical Capacitors}, series = {The Journal of Geometric Analysis}, volume = {32}, journal = {The Journal of Geometric Analysis}, number = {2}, issn = {1559-002X}, doi = {10.1007/s12220-021-00746-6}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-269997}, year = {2022}, abstract = {We construct a foliation of an asymptotically flat end of a Riemannian manifold by hypersurfaces which are critical points of a natural functional arising in potential theory. These hypersurfaces are perturbations of large coordinate spheres, and they admit solutions of a certain over-determined boundary value problem involving the Laplace-Beltrami operator. In a key step we must invert the Dirichlet-to-Neumann operator, highlighting the nonlocal nature of our problem.}, language = {en} } @article{EastonvanDalenGoebetal.2022, author = {Easton, Andrew and van Dalen, Okki and Goeb, Rainer and Di Bucchianico, Alessandro}, title = {Bivariate copula monitoring}, series = {Quality and Reliability Engineering International}, volume = {38}, journal = {Quality and Reliability Engineering International}, number = {3}, doi = {10.1002/qre.3034}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-276501}, pages = {1272 -- 1288}, year = {2022}, abstract = {The assumption of multivariate normality underlying the Hotelling T\(^{2}\) chart is often violated for process data. The multivariate dependency structure can be separated from marginals with the help of copula theory, which permits to model association structures beyond the covariance matrix. Copula-based estimation and testing routines have reached maturity regarding a variety of practical applications. We have constructed a rich design matrix for the comparison of the Hotelling T\(^{2}\) chart with the copula test by Verdier and the copula test by Vuong, which allows for weighting the observations adaptively. Based on the design matrix, we have conducted a large and computationally intensive simulation study. The results show that the copula test by Verdier performs better than Hotelling T\(^{2}\) in a large variety of out-of-control cases, whereas the weighted Vuong scheme often fails to provide an improvement.}, language = {en} } @article{CampanaBorzi2022, author = {Campana, Francesca Cal{\`a} and Borz{\`i}, Alfio}, title = {On the SQH Method for Solving Differential Nash Games}, series = {Journal of Dynamical and Control Systems}, volume = {28}, journal = {Journal of Dynamical and Control Systems}, issn = {1573-8698}, doi = {10.1007/s10883-021-09546-1}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-269111}, pages = {739-755}, year = {2022}, abstract = {A sequentialquadratic Hamiltonian schemefor solving open-loop differential Nash games is proposed and investigated. This method is formulated in the framework of the Pontryagin maximum principle and represents an efficient and robust extension of the successive approximations strategy for solving optimal control problems. Theoretical results are presented that prove the well-posedness of the proposed scheme, and results of numerical experiments are reported that successfully validate its computational performance.}, language = {en} } @article{KrausMouchaRoth2022, author = {Kraus, Daniela and Moucha, Annika and Roth, Oliver}, title = {A sharp Bernstein-type inequality and application to the Carleson embedding theorem with matrix weights}, series = {Analysis and Mathematical Physics}, volume = {12}, journal = {Analysis and Mathematical Physics}, number = {1}, issn = {1664-235X}, doi = {10.1007/s13324-021-00639-5}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-270485}, year = {2022}, abstract = {We prove a sharp Bernstein-type inequality for complex polynomials which are positive and satisfy a polynomial growth condition on the positive real axis. This leads to an improved upper estimate in the recent work of Culiuc and Treil (Int. Math. Res. Not. 2019: 3301-3312, 2019) on the weighted martingale Carleson embedding theorem with matrix weights. In the scalar case this new upper bound is optimal.}, language = {en} } @article{JustSiller2022, author = {Just, Janina and Siller, Hans-Stefan}, title = {The role of mathematics in STEM secondary classrooms: a systematic literature review}, series = {Education Sciences}, volume = {12}, journal = {Education Sciences}, number = {9}, issn = {2227-7102}, doi = {10.3390/educsci12090629}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-288075}, year = {2022}, abstract = {Nowadays, science, technology, engineering, and mathematics (STEM) play a critical role in a nation's global competitiveness and prosperity. Thus, there is a need to educate students in these subjects to meet the current and future demands of personal life and society. While applications, especially in science, engineering, and technology, are directly obvious, mathematics underpins the other STEM disciplines. It is recognized that mathematics is the foundation for all other STEM disciplines; the role of mathematics in classrooms is not clear yet. Therefore, the question arises: What is the current role of mathematics in secondary STEM classrooms? To answer this question, we conducted a systematic literature review based on three publication databases (Web of Science, ERIC, and EBSCO Teacher Referral Center). This literature review paper is intended to contribute to the current state of the role of mathematics in STEM education in secondary classrooms. Through the search, starting with 1910 documents, only 14 eligible documents were found. In these, mathematics is often seen as a minor matter and a means to an end in the eyes of science educators. From this, we conclude that the role of mathematics in the STEM classroom should be further strengthened. Overall, the paper highlights a major research gap, and proposes possible initial solutions to close it.}, language = {en} } @article{AppellBritoReinwand2022, author = {Appell, J{\"u}rgen and Brito, Bel{\´e}n L{\´o}pez and Reinwand, Simon}, title = {Counterexamples on compositions}, series = {Mathematische Semesterberichte}, volume = {70}, journal = {Mathematische Semesterberichte}, number = {1}, issn = {0720-728X}, doi = {10.1007/s00591-022-00318-x}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-324306}, pages = {43-56}, year = {2022}, abstract = {We give a collection of 16 examples which show that compositions \(g\) \(\circ\) \(f\) of well-behaved functions \(f\) and \(g\) can be badly behaved. Remarkably, in 10 of the 16 examples it suffices to take as outer function \(g\) simply a power-type or characteristic function. Such a collection of examples may serve as a source of exercises for a calculus course.}, language = {en} } @article{KanzowMehlitz2022, author = {Kanzow, Christian and Mehlitz, Patrick}, title = {Convergence properties of monotone and nonmonotone proximal gradient methods revisited}, series = {Journal of Optimization Theory and Applications}, volume = {195}, journal = {Journal of Optimization Theory and Applications}, number = {2}, issn = {0022-3239}, doi = {10.1007/s10957-022-02101-3}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-324351}, pages = {624-646}, year = {2022}, abstract = {Composite optimization problems, where the sum of a smooth and a merely lower semicontinuous function has to be minimized, are often tackled numerically by means of proximal gradient methods as soon as the lower semicontinuous part of the objective function is of simple enough structure. The available convergence theory associated with these methods (mostly) requires the derivative of the smooth part of the objective function to be (globally) Lipschitz continuous, and this might be a restrictive assumption in some practically relevant scenarios. In this paper, we readdress this classical topic and provide convergence results for the classical (monotone) proximal gradient method and one of its nonmonotone extensions which are applicable in the absence of (strong) Lipschitz assumptions. This is possible since, for the price of forgoing convergence rates, we omit the use of descent-type lemmas in our analysis.}, language = {en} } @article{KourouZarvalis2022, author = {Kourou, Maria and Zarvalis, Konstantinos}, title = {Compact sets in petals and their backward orbits under semigroups of holomorphic functions}, series = {Potential Analysis}, volume = {59}, journal = {Potential Analysis}, number = {4}, issn = {0926-2601}, doi = {10.1007/s11118-022-10036-7}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-324368}, pages = {1913-1939}, year = {2022}, abstract = {Let (ϕ\(_t\))\(_{t≥0}\) be a semigroup of holomorphic functions in the unit disk \(\mathbb {D}\) and K a compact subset of \(\mathbb {D}\). We investigate the conditions under which the backward orbit of K under the semigroup exists. Subsequently, the geometric characteristics, as well as, potential theoretic quantities for the backward orbit of K are examined. More specifically, results are obtained concerning the asymptotic behavior of its hyperbolic area and diameter, the harmonic measure and the capacity of the condenser that K forms with the unit disk.}, language = {en} } @article{DippellEspositoWaldmann2022, author = {Dippell, Marvin and Esposito, Chiara and Waldmann, Stefan}, title = {Deformation and Hochschild cohomology of coisotropic algebras}, series = {Annali di Matematica Pura ed Applicata}, volume = {201}, journal = {Annali di Matematica Pura ed Applicata}, number = {3}, doi = {10.1007/s10231-021-01158-7}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-329069}, pages = {1295-1323}, year = {2022}, abstract = {Coisotropic algebras consist of triples of algebras for which a reduction can be defined and unify in a very algebraic fashion coisotropic reduction in several settings. In this paper, we study the theory of (formal) deformation of coisotropic algebras showing that deformations are governed by suitable coisotropic DGLAs. We define a deformation functor and prove that it commutes with reduction. Finally, we study the obstructions to existence and uniqueness of coisotropic algebras and present some geometric examples.}, language = {en} } @article{GreefrathSillerKlocketal.2022, author = {Greefrath, Gilbert and Siller, Hans-Stefan and Klock, Heiner and Wess, Raphael}, title = {Pre-service secondary teachers' pedagogical content knowledge for the teaching of mathematical modelling}, series = {Educational Studies in Mathematics}, volume = {109}, journal = {Educational Studies in Mathematics}, number = {2}, issn = {0013-1954}, doi = {10.1007/s10649-021-10038-z}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-308259}, pages = {383-407}, year = {2022}, abstract = {The article deals with the pedagogical content knowledge of mathematical modelling as part of the professional competence of pre-service teachers. With the help of a test developed for this purpose from a conceptual model, we examine whether this pedagogical content knowledge can be promoted in its different facets—especially knowledge about modelling tasks and about interventions—by suitable university seminars. For this purpose, the test was administered to three groups in a seminar for the teaching of mathematical modelling: (1) to those respondents who created their own modelling tasks for use with students, (2) to those trained to intervene in mathematical modelling processes, and (3) participating students who are not required to address mathematical modelling. The findings of the study—based on variance analysis—indicate that certain facets (knowledge of modelling tasks, modelling processes, and interventions) have increased significantly in both experimental groups but to varying degrees. By contrast, pre-service teachers in the control group demonstrated no significant change to their level of pedagogical content knowledge.}, language = {en} } @article{KanzowRaharjaSchwartz2021, author = {Kanzow, Christian and Raharja, Andreas B. and Schwartz, Alexandra}, title = {An Augmented Lagrangian Method for Cardinality-Constrained Optimization Problems}, series = {Journal of Optimization Theory and Applications}, volume = {189}, journal = {Journal of Optimization Theory and Applications}, number = {3}, issn = {1573-2878}, doi = {10.1007/s10957-021-01854-7}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-269166}, pages = {793-813}, year = {2021}, abstract = {A reformulation of cardinality-constrained optimization problems into continuous nonlinear optimization problems with an orthogonality-type constraint has gained some popularity during the last few years. Due to the special structure of the constraints, the reformulation violates many standard assumptions and therefore is often solved using specialized algorithms. In contrast to this, we investigate the viability of using a standard safeguarded multiplier penalty method without any problem-tailored modifications to solve the reformulated problem. We prove global convergence towards an (essentially strongly) stationary point under a suitable problem-tailored quasinormality constraint qualification. Numerical experiments illustrating the performance of the method in comparison to regularization-based approaches are provided.}, language = {en} } @article{HellmuthKlingenbergLietal.2021, author = {Hellmuth, Kathrin and Klingenberg, Christian and Li, Qin and Tang, Min}, title = {Multiscale convergence of the inverse problem for chemotaxis in the Bayesian setting}, series = {Computation}, volume = {9}, journal = {Computation}, number = {11}, issn = {2079-3197}, doi = {10.3390/computation9110119}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-250216}, year = {2021}, abstract = {Chemotaxis describes the movement of an organism, such as single or multi-cellular organisms and bacteria, in response to a chemical stimulus. Two widely used models to describe the phenomenon are the celebrated Keller-Segel equation and a chemotaxis kinetic equation. These two equations describe the organism's movement at the macro- and mesoscopic level, respectively, and are asymptotically equivalent in the parabolic regime. The way in which the organism responds to a chemical stimulus is embedded in the diffusion/advection coefficients of the Keller-Segel equation or the turning kernel of the chemotaxis kinetic equation. Experiments are conducted to measure the time dynamics of the organisms' population level movement when reacting to certain stimulation. From this, one infers the chemotaxis response, which constitutes an inverse problem. In this paper, we discuss the relation between both the macro- and mesoscopic inverse problems, each of which is associated with two different forward models. The discussion is presented in the Bayesian framework, where the posterior distribution of the turning kernel of the organism population is sought. We prove the asymptotic equivalence of the two posterior distributions.}, language = {en} } @article{TongsompornWananiyakulSteuding2021, author = {Tongsomporn, Janyarak and Wananiyakul, Saeree and Steuding, J{\"o}rn}, title = {The values of the periodic zeta-function at the nontrivial zeros of Riemann's zeta-function}, series = {Symmetry}, volume = {13}, journal = {Symmetry}, number = {12}, issn = {2073-8994}, doi = {10.3390/sym13122410}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-252261}, year = {2021}, abstract = {In this paper, we prove an asymptotic formula for the sum of the values of the periodic zeta-function at the nontrivial zeros of the Riemann zeta-function (up to some height) which are symmetrical on the real line and the critical line. This is an extension of the previous results due to Garunkštis, Kalpokas, and, more recently, Sowa. Whereas Sowa's approach was assuming the yet unproved Riemann hypothesis, our result holds unconditionally.}, language = {en} } @article{GreefrathOldenburgSilleretal.2021, author = {Greefrath, Gilbert and Oldenburg, Reinhard and Siller, Hans-Stefan and Ulm, Volker and Weigand, Hans-Georg}, title = {Basic Mental Models of Integrals - Theoretical Conception, Development of a Test Instrument, and first Results}, series = {ZDM - Mathematics Education}, volume = {53}, journal = {ZDM - Mathematics Education}, issn = {1863-9690}, doi = {10.1007/s11858-020-01207-0}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-232830}, pages = {649-661}, year = {2021}, abstract = {A basic mental model (BMM—in German 'Grundvorstellung') of a mathematical concept is a content-related interpretation that gives meaning to this concept. This paper defines normative and individual BMMs and concretizes them using the integral as an example. Four BMMs are developed about the concept of definite integral, sometimes used in specific teaching approaches: the BMMs of area, reconstruction, average, and accumulation. Based on theoretical work, in this paper we ask how these BMMs could be identified empirically. A test instrument was developed, piloted, validated and applied with 428 students in first-year mathematics courses. The test results show that the four normative BMMs of the integral can be detected and separated empirically. Moreover, the results allow a comparison of the existing individual BMMs and the requested normative BMMs. Consequences for future developments are discussed.}, language = {en} } @article{HaackHauckKlingenbergetal.2021, author = {Haack, J. and Hauck, C. and Klingenberg, C. and Pirner, M. and Warnecke, S.}, title = {A Consistent BGK Model with Velocity-Dependent Collision Frequency for Gas Mixtures}, series = {Journal of Statistical Physics}, volume = {184}, journal = {Journal of Statistical Physics}, number = {3}, issn = {1572-9613}, doi = {10.1007/s10955-021-02821-2}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-269146}, pages = {31}, year = {2021}, abstract = {We derive a multi-species BGK model with velocity-dependent collision frequency for a non-reactive, multi-component gas mixture. The model is derived by minimizing a weighted entropy under the constraint that the number of particles of each species, total momentum, and total energy are conserved. We prove that this minimization problem admits a unique solution for very general collision frequencies. Moreover, we prove that the model satisfies an H-Theorem and characterize the form of equilibrium.}, language = {en} } @article{KanzowRaharjaSchwartz2021, author = {Kanzow, Christian and Raharja, Andreas B. and Schwartz, Alexandra}, title = {Sequential optimality conditions for cardinality-constrained optimization problems with applications}, series = {Computational Optimization and Applications}, volume = {80}, journal = {Computational Optimization and Applications}, number = {1}, issn = {1573-2894}, doi = {10.1007/s10589-021-00298-z}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-269052}, pages = {185-211}, year = {2021}, abstract = {Recently, a new approach to tackle cardinality-constrained optimization problems based on a continuous reformulation of the problem was proposed. Following this approach, we derive a problem-tailored sequential optimality condition, which is satisfied at every local minimizer without requiring any constraint qualification. We relate this condition to an existing M-type stationary concept by introducing a weak sequential constraint qualification based on a cone-continuity property. Finally, we present two algorithmic applications: We improve existing results for a known regularization method by proving that it generates limit points satisfying the aforementioned optimality conditions even if the subproblems are only solved inexactly. And we show that, under a suitable Kurdyka-Łojasiewicz-type assumption, any limit point of a standard (safeguarded) multiplier penalty method applied directly to the reformulated problem also satisfies the optimality condition. These results are stronger than corresponding ones known for the related class of mathematical programs with complementarity constraints.}, language = {en} } @article{BartschBorziFanellietal.2021, author = {Bartsch, Jan and Borz{\`i}, Alfio and Fanelli, Francesco and Roy, Souvik}, title = {A numerical investigation of Brockett's ensemble optimal control problems}, series = {Numerische Mathematik}, volume = {149}, journal = {Numerische Mathematik}, number = {1}, doi = {10.1007/s00211-021-01223-6}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-265352}, pages = {1-42}, year = {2021}, abstract = {This paper is devoted to the numerical analysis of non-smooth ensemble optimal control problems governed by the Liouville (continuity) equation that have been originally proposed by R.W. Brockett with the purpose of determining an efficient and robust control strategy for dynamical systems. A numerical methodology for solving these problems is presented that is based on a non-smooth Lagrange optimization framework where the optimal controls are characterized as solutions to the related optimality systems. For this purpose, approximation and solution schemes are developed and analysed. Specifically, for the approximation of the Liouville model and its optimization adjoint, a combination of a Kurganov-Tadmor method, a Runge-Kutta scheme, and a Strang splitting method are discussed. The resulting optimality system is solved by a projected semi-smooth Krylov-Newton method. Results of numerical experiments are presented that successfully validate the proposed framework.}, language = {en} } @article{HomburgWeissFrahmetal.2021, author = {Homburg, Annika and Weiß, Christian H. and Frahm, Gabriel and Alwan, Layth C. and G{\"o}b, Rainer}, title = {Analysis and forecasting of risk in count processes}, series = {Journal of Risk and Financial Management}, volume = {14}, journal = {Journal of Risk and Financial Management}, number = {4}, issn = {1911-8074}, doi = {10.3390/jrfm14040182}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-236692}, year = {2021}, abstract = {Risk measures are commonly used to prepare for a prospective occurrence of an adverse event. If we are concerned with discrete risk phenomena such as counts of natural disasters, counts of infections by a serious disease, or counts of certain economic events, then the required risk forecasts are to be computed for an underlying count process. In practice, however, the discrete nature of count data is sometimes ignored and risk forecasts are calculated based on Gaussian time series models. But even if methods from count time series analysis are used in an adequate manner, the performance of risk forecasting is affected by estimation uncertainty as well as certain discreteness phenomena. To get a thorough overview of the aforementioned issues in risk forecasting of count processes, a comprehensive simulation study was done considering a broad variety of risk measures and count time series models. It becomes clear that Gaussian approximate risk forecasts substantially distort risk assessment and, thus, should be avoided. In order to account for the apparent estimation uncertainty in risk forecasting, we use bootstrap approaches for count time series. The relevance and the application of the proposed approaches are illustrated by real data examples about counts of storm surges and counts of financial transactions.}, language = {en} } @article{Pirner2021, author = {Pirner, Marlies}, title = {A review on BGK models for gas mixtures of mono and polyatomic molecules}, series = {Fluids}, volume = {6}, journal = {Fluids}, number = {11}, issn = {2311-5521}, doi = {10.3390/fluids6110393}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-250161}, year = {2021}, abstract = {We consider the Bathnagar-Gross-Krook (BGK) model, an approximation of the Boltzmann equation, describing the time evolution of a single momoatomic rarefied gas and satisfying the same two main properties (conservation properties and entropy inequality). However, in practical applications, one often has to deal with two additional physical issues. First, a gas often does not consist of only one species, but it consists of a mixture of different species. Second, the particles can store energy not only in translational degrees of freedom but also in internal degrees of freedom such as rotations or vibrations (polyatomic molecules). Therefore, here, we will present recent BGK models for gas mixtures for mono- and polyatomic particles and the existing mathematical theory for these models.}, language = {en} } @article{AlmeidaHristovaDashkovskiy2021, author = {Almeida, R. and Hristova, S. and Dashkovskiy, S.}, title = {Uniform bounded input bounded output stability of fractional-order delay nonlinear systems with input}, series = {International Journal of Robust and Nonlinear Control}, volume = {31}, journal = {International Journal of Robust and Nonlinear Control}, number = {1}, doi = {10.1002/rnc.5273}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-218554}, pages = {225 -- 249}, year = {2021}, abstract = {The bounded input bounded output (BIBO) stability for a nonlinear Caputo fractional system with time-varying bounded delay and nonlinear output is studied. Utilizing the Razumikhin method, Lyapunov functions and appropriate fractional derivatives of Lyapunov functions some new bounded input bounded output stability criteria are derived. Also, explicit and independent on the initial time bounds of the output are provided. Uniform BIBO stability and uniform BIBO stability with input threshold are studied. A numerical simulation is carried out to show the system's dynamic response, and demonstrate the effectiveness of our theoretical results.}, language = {en} } @article{HomburgWeissAlwanetal.2021, author = {Homburg, Annika and Weiß, Christian H. and Alwan, Layth C. and Frahm, Gabriel and G{\"o}b, Rainer}, title = {A performance analysis of prediction intervals for count time series}, series = {Journal of Forecasting}, volume = {40}, journal = {Journal of Forecasting}, number = {4}, doi = {10.1002/for.2729}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-217906}, pages = {603 -- 609}, year = {2021}, abstract = {One of the major motivations for the analysis and modeling of time series data is the forecasting of future outcomes. The use of interval forecasts instead of point forecasts allows us to incorporate the apparent forecast uncertainty. When forecasting count time series, one also has to account for the discreteness of the range, which is done by using coherent prediction intervals (PIs) relying on a count model. We provide a comprehensive performance analysis of coherent PIs for diverse types of count processes. We also compare them to approximate PIs that are computed based on a Gaussian approximation. Our analyses rely on an extensive simulation study. It turns out that the Gaussian approximations do considerably worse than the coherent PIs. Furthermore, special characteristics such as overdispersion, zero inflation, or trend clearly affect the PIs' performance. We conclude by presenting two empirical applications of PIs for count time series: the demand for blood bags in a hospital and the number of company liquidations in Germany.}, language = {en} } @article{NatemeyerWachsmuth2021, author = {Natemeyer, Carolin and Wachsmuth, Daniel}, title = {A proximal gradient method for control problems with non-smooth and non-convex control cost}, series = {Computational Optimization and Applications}, volume = {80}, journal = {Computational Optimization and Applications}, number = {2}, issn = {1573-2894}, doi = {10.1007/s10589-021-00308-0}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-269069}, pages = {639-677}, year = {2021}, abstract = {We investigate the convergence of the proximal gradient method applied to control problems with non-smooth and non-convex control cost. Here, we focus on control cost functionals that promote sparsity, which includes functionals of L\(^{p}\)-type for p\in [0,1). We prove stationarity properties of weak limit points of the method. These properties are weaker than those provided by Pontryagin's maximum principle and weaker than L-stationarity.}, language = {en} } @article{FalkFuller2021, author = {Falk, Michael and Fuller, Timo}, title = {New characterizations of multivariate Max-domain of attraction and D-Norms}, series = {Extremes}, volume = {24}, journal = {Extremes}, number = {4}, issn = {1572-915X}, doi = {10.1007/s10687-021-00416-4}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-269071}, pages = {849-879}, year = {2021}, abstract = {In this paper we derive new results on multivariate extremes and D-norms. In particular we establish new characterizations of the multivariate max-domain of attraction property. The limit distribution of certain multivariate exceedances above high thresholds is derived, and the distribution of that generator of a D-norm on R\(^{d}\), whose components sum up to d, is obtained. Finally we introduce exchangeable D-norms and show that the set of exchangeable D-norms is a simplex.}, language = {en} } @article{Moenius2021, author = {M{\"o}nius, Katja}, title = {Eigenvalues of zero-divisor graphs of finite commutative rings}, series = {Journal of Algebraic Combinatorics}, volume = {54}, journal = {Journal of Algebraic Combinatorics}, issn = {0925-9899}, doi = {10.1007/s10801-020-00989-6}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-232792}, pages = {787-802}, year = {2021}, abstract = {We investigate eigenvalues of the zero-divisor graph Γ(R) of finite commutative rings R and study the interplay between these eigenvalues, the ring-theoretic properties of R and the graph-theoretic properties of Γ(R). The graph Γ(R) is defined as the graph with vertex set consisting of all nonzero zero-divisors of R and adjacent vertices x, y whenever xy=0. We provide formulas for the nullity of Γ(R), i.e., the multiplicity of the eigenvalue 0 of Γ(R). Moreover, we precisely determine the spectra of \(\Gamma ({\mathbb {Z}}_p \times {\mathbb {Z}}_p \times {\mathbb {Z}}_p)\) and \(\Gamma ({\mathbb {Z}}_p \times {\mathbb {Z}}_p \times {\mathbb {Z}}_p \times {\mathbb {Z}}_p)\) for a prime number p. We introduce a graph product ×Γ with the property that Γ(R)≅Γ(R\(_1\))×Γ⋯×ΓΓ(R\(_r\)) whenever R≅R\(_1\)×⋯×R\(_r\). With this product, we find relations between the number of vertices of the zero-divisor graph Γ(R), the compressed zero-divisor graph, the structure of the ring R and the eigenvalues of Γ(R).}, language = {en} } @article{KalousekMitraSchloemerkemper2021, author = {Kalousek, Martin and Mitra, Sourav and Schl{\"o}merkemper, Anja}, title = {Existence of weak solutions of diffuse interface models for magnetic fluids}, series = {Proceedings in Applied Mathematics and Mechanics}, volume = {21}, journal = {Proceedings in Applied Mathematics and Mechanics}, number = {1}, doi = {10.1002/pamm.202100205}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-257642}, year = {2021}, abstract = {In this article we collect some recent results on the global existence of weak solutions for diffuse interface models involving incompressible magnetic fluids. We consider both the cases of matched and unmatched specific densities. For the model involving fluids with identical densities we consider the free energy density to be a double well potential whereas for the unmatched density case it is crucial to work with a singular free energy density.}, language = {en} } @article{BreitenbachHelfrichFoersterDandekar2021, author = {Breitenbach, Tim and Helfrich-F{\"o}rster, Charlotte and Dandekar, Thomas}, title = {An effective model of endogenous clocks and external stimuli determining circadian rhythms}, series = {Scientific Reports}, volume = {11}, journal = {Scientific Reports}, number = {1}, doi = {10.1038/s41598-021-95391-y}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-261655}, pages = {16165}, year = {2021}, abstract = {Circadian endogenous clocks of eukaryotic organisms are an established and rapidly developing research field. To investigate and simulate in an effective model the effect of external stimuli on such clocks and their components we developed a software framework for download and simulation. The application is useful to understand the different involved effects in a mathematical simple and effective model. This concerns the effects of Zeitgebers, feedback loops and further modifying components. We start from a known mathematical oscillator model, which is based on experimental molecular findings. This is extended with an effective framework that includes the impact of external stimuli on the circadian oscillations including high dose pharmacological treatment. In particular, the external stimuli framework defines a systematic procedure by input-output-interfaces to couple different oscillators. The framework is validated by providing phase response curves and ranges of entrainment. Furthermore, Aschoffs rule is computationally investigated. It is shown how the external stimuli framework can be used to study biological effects like points of singularity or oscillators integrating different signals at once. The mathematical framework and formalism is generic and allows to study in general the effect of external stimuli on oscillators and other biological processes. For an easy replication of each numerical experiment presented in this work and an easy implementation of the framework the corresponding Mathematica files are fully made available. They can be downloaded at the following link: https://www.biozentrum.uni-wuerzburg.de/bioinfo/computing/circadian/.}, language = {en} } @article{KanzowLechner2021, author = {Kanzow, Christian and Lechner, Theresa}, title = {Globalized inexact proximal Newton-type methods for nonconvex composite functions}, series = {Computational Optimization and Applications}, volume = {78}, journal = {Computational Optimization and Applications}, number = {2}, doi = {10.1007/s10589-020-00243-6}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-283715}, pages = {377-410}, year = {2021}, abstract = {Optimization problems with composite functions consist of an objective function which is the sum of a smooth and a (convex) nonsmooth term. This particular structure is exploited by the class of proximal gradient methods and some of their generalizations like proximal Newton and quasi-Newton methods. The current literature on these classes of methods almost exclusively considers the case where also the smooth term is convex. Here we present a globalized proximal Newton-type method which allows the smooth term to be nonconvex. The method is shown to have nice global and local convergence properties, and some numerical results indicate that this method is very promising also from a practical point of view.}, language = {en} } @article{CampanaCiaramellaBorzi2021, author = {Campana, Francesca Cal{\`a} and Ciaramella, Gabriele and Borz{\`i}, Alfio}, title = {Nash Equilibria and Bargaining Solutions of Differential Bilinear Games}, series = {Dynamic Games and Applications}, volume = {11}, journal = {Dynamic Games and Applications}, number = {1}, doi = {10.1007/s13235-020-00351-2}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-283897}, pages = {1-28}, year = {2021}, abstract = {This paper is devoted to a theoretical and numerical investigation of Nash equilibria and Nash bargaining problems governed by bilinear (input-affine) differential models. These systems with a bilinear state-control structure arise in many applications in, e.g., biology, economics, physics, where competition between different species, agents, and forces needs to be modelled. For this purpose, the concept of Nash equilibria (NE) appears appropriate, and the building blocks of the resulting differential Nash games are different control functions associated with different players that pursue different non-cooperative objectives. In this framework, existence of Nash equilibria is proved and computed with a semi-smooth Newton scheme combined with a relaxation method. Further, a related Nash bargaining (NB) problem is discussed. This aims at determining an improvement of all players' objectives with respect to the Nash equilibria. Results of numerical experiments successfully demonstrate the effectiveness of the proposed NE and NB computational framework.}, language = {en} } @article{GuensterWeigand2020, author = {G{\"u}nster, Stephan Michael and Weigand, Hans-Georg}, title = {Designing digital technology tasks for the development of functional thinking}, series = {ZDM - Mathematics Education}, volume = {52}, journal = {ZDM - Mathematics Education}, doi = {10.1007/s11858-020-01179-1}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-231913}, pages = {1259-1274}, year = {2020}, abstract = {In this paper we introduce a theoretical framework concerned with fostering functional thinking in Grade 8 students by utilizing digital technologies. This framework is meant to be used to guide the systematic variation of tasks for implementation in the classroom while using digital technologies. Examples of problems and tasks illustrate this process. Additionally, results of an empirical investigation with Grade 8 students, which focusses on the students' skills with digital technologies, how they utilize these tools when engaging with the developed tasks, and how they influence their functional thinking, are presented. The research aim is to investigate in which way tasks designed according to the theoretical framework could promote functional thinking while using digital technologies in the sense of the operative principle. The results show that the developed framework — Function-Operation-Matrix — is a sound basis for initiating students' actions in the sense of the operative principle, to foster the development of functional thinking in its three aspects, namely, assignment, co-variation and object, and that digital technologies can support this process in a meaningful way.}, language = {en} } @article{KarlNeitzelWachsmuth2020, author = {Karl, Veronika and Neitzel, Ira and Wachsmuth, Daniel}, title = {A Lagrange multiplier method for semilinear elliptic state constrained optimal control problems}, series = {Computational Optimization and Applications}, volume = {77}, journal = {Computational Optimization and Applications}, issn = {0926-6003}, doi = {10.1007/s10589-020-00223-w}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-232811}, pages = {7831-869}, year = {2020}, abstract = {In this paper we apply an augmented Lagrange method to a class of semilinear ellip-tic optimal control problems with pointwise state constraints. We show strong con-vergence of subsequences of the primal variables to a local solution of the original problem as well as weak convergence of the adjoint states and weak-* convergence of the multipliers associated to the state constraint. Moreover, we show existence of stationary points in arbitrary small neighborhoods of local solutions of the original problem. Additionally, various numerical results are presented.}, language = {en} } @article{delAlamoLiMunketal.2020, author = {del Alamo, Miguel and Li, Housen and Munk, Axel and Werner, Frank}, title = {Variational Multiscale Nonparametric Regression: Algorithms and Implementation}, series = {Algorithms}, volume = {13}, journal = {Algorithms}, number = {11}, issn = {1999-4893}, doi = {10.3390/a13110296}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-219332}, year = {2020}, abstract = {Many modern statistically efficient methods come with tremendous computational challenges, often leading to large-scale optimisation problems. In this work, we examine such computational issues for recently developed estimation methods in nonparametric regression with a specific view on image denoising. We consider in particular certain variational multiscale estimators which are statistically optimal in minimax sense, yet computationally intensive. Such an estimator is computed as the minimiser of a smoothness functional (e.g., TV norm) over the class of all estimators such that none of its coefficients with respect to a given multiscale dictionary is statistically significant. The so obtained multiscale Nemirowski-Dantzig estimator (MIND) can incorporate any convex smoothness functional and combine it with a proper dictionary including wavelets, curvelets and shearlets. The computation of MIND in general requires to solve a high-dimensional constrained convex optimisation problem with a specific structure of the constraints induced by the statistical multiscale testing criterion. To solve this explicitly, we discuss three different algorithmic approaches: the Chambolle-Pock, ADMM and semismooth Newton algorithms. Algorithmic details and an explicit implementation is presented and the solutions are then compared numerically in a simulation study and on various test images. We thereby recommend the Chambolle-Pock algorithm in most cases for its fast convergence. We stress that our analysis can also be transferred to signal recovery and other denoising problems to recover more general objects whenever it is possible to borrow statistical strength from data patches of similar object structure.}, language = {en} } @article{BreitenbachBorzi2020, author = {Breitenbach, Tim and Borz{\`i}, Alfio}, title = {The Pontryagin maximum principle for solving Fokker-Planck optimal control problems}, series = {Computational Optimization and Applications}, volume = {76}, journal = {Computational Optimization and Applications}, issn = {0926-6003}, doi = {10.1007/s10589-020-00187-x}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-232665}, pages = {499-533}, year = {2020}, abstract = {The characterization and numerical solution of two non-smooth optimal control problems governed by a Fokker-Planck (FP) equation are investigated in the framework of the Pontryagin maximum principle (PMP). The two FP control problems are related to the problem of determining open- and closed-loop controls for a stochastic process whose probability density function is modelled by the FP equation. In both cases, existence and PMP characterisation of optimal controls are proved, and PMP-based numerical optimization schemes are implemented that solve the PMP optimality conditions to determine the controls sought. Results of experiments are presented that successfully validate the proposed computational framework and allow to compare the two control strategies.}, language = {en} } @article{SteudingSuriajaya2020, author = {Steuding, J{\"o}rn and Suriajaya, Ade Irma}, title = {Value-Distribution of the Riemann Zeta-Function Along Its Julia Lines}, series = {Computational Methods and Function Theory}, volume = {20}, journal = {Computational Methods and Function Theory}, issn = {1617-9447}, doi = {10.1007/s40315-020-00316-x}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-232621}, pages = {389-401}, year = {2020}, abstract = {For an arbitrary complex number a≠0 we consider the distribution of values of the Riemann zeta-function ζ at the a-points of the function Δ which appears in the functional equation ζ(s)=Δ(s)ζ(1-s). These a-points δa are clustered around the critical line 1/2+i\(\mathbb {R}\) which happens to be a Julia line for the essential singularity of ζ at infinity. We observe a remarkable average behaviour for the sequence of values ζ(δ\(_a\)).}, language = {en} } @article{FeireislKlingenbergMarkfelder2020, author = {Feireisl, Eduard and Klingenberg, Christian and Markfelder, Simon}, title = {On the density of "wild" initial data for the compressible Euler system}, series = {Calculus of Variations and Partial Differential Equations}, volume = {59}, journal = {Calculus of Variations and Partial Differential Equations}, issn = {0944-2669}, doi = {10.1007/s00526-020-01806-5}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-232607}, year = {2020}, abstract = {We consider a class of "wild" initial data to the compressible Euler system that give rise to infinitely many admissible weak solutions via the method of convex integration. We identify the closure of this class in the natural L1-topology and show that its complement is rather large, specifically it is an open dense set.}, language = {en} } @article{Mitra2020, author = {Mitra, Sourav}, title = {Local Existence of Strong Solutions of a Fluid-Structure Interaction Model}, series = {Journal of Mathematical Fluid Mechanics}, volume = {22}, journal = {Journal of Mathematical Fluid Mechanics}, issn = {1422-6928}, doi = {10.1007/s00021-020-00520-8}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-235097}, year = {2020}, abstract = {We are interested in studying a system coupling the compressible Navier-Stokes equations with an elastic structure located at the boundary of the fluid domain. Initially the fluid domain is rectangular and the beam is located on the upper side of the rectangle. The elastic structure is modeled by an Euler-Bernoulli damped beam equation. We prove the local in time existence of strong solutions for that coupled system.}, language = {en} } @article{Schoenlein2020, author = {Sch{\"o}nlein, Michael}, title = {Ensemble reachability of homogenous parameter-depedent systems}, series = {Proceedings in Applied Mathematics and Mechanics}, volume = {20}, journal = {Proceedings in Applied Mathematics and Mechanics}, number = {1}, doi = {10.1002/pamm.202000342}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-257637}, year = {2020}, abstract = {In this paper we consider the class (θA, B) of parameter-dependent linear systems given by matrices A ∈ ℂ\(^{nxn}\) and B ∈ ℂ\(^{nxm}\). This class is of interest for several applications and the frequently met task for such systems is to steer the origin toward a given target family f(θ) by using an input that is independent from the parameter. This paper provides a collection of necessary and sufficient conditions for ensemble reachability for these systems.}, language = {en} } @article{DashkovskiyKapustyanSchmid2020, author = {Dashkovskiy, Sergey and Kapustyan, Oleksiy and Schmid, Jochen}, title = {A local input-to-state stability result w.r.t. attractors of nonlinear reaction-diffusion equations}, series = {Mathematics of Control, Signals, and Systems}, volume = {32}, journal = {Mathematics of Control, Signals, and Systems}, number = {3}, doi = {10.1007/s00498-020-00256-w}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-281099}, pages = {309-326}, year = {2020}, abstract = {We establish the local input-to-state stability of a large class of disturbed nonlinear reaction-diffusion equations w.r.t. the global attractor of the respective undisturbed system.}, language = {en} } @article{HomburgWeissAlwanetal.2019, author = {Homburg, Annika and Weiß, Christian H. and Alwan, Layth C. and Frahm, Gabriel and G{\"o}b, Rainer}, title = {Evaluating approximate point forecasting of count processes}, series = {Econometrics}, volume = {7}, journal = {Econometrics}, number = {3}, issn = {2225-1146}, doi = {10.3390/econometrics7030030}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-196929}, year = {2019}, abstract = {In forecasting count processes, practitioners often ignore the discreteness of counts and compute forecasts based on Gaussian approximations instead. For both central and non-central point forecasts, and for various types of count processes, the performance of such approximate point forecasts is analyzed. The considered data-generating processes include different autoregressive schemes with varying model orders, count models with overdispersion or zero inflation, counts with a bounded range, and counts exhibiting trend or seasonality. We conclude that Gaussian forecast approximations should be avoided.}, language = {en} } @article{LauerbachNeukammSchaeffneretal.2019, author = {Lauerbach, Laura and Neukamm, Stefan and Sch{\"a}ffner, Mathias and Schl{\"o}merkemper, Anja}, title = {Continuum Limit and Homogenization of Stochastic and Periodic Discrete Systems - Fracture in Composite Materials}, series = {Proceedings in Applied Mathematics \& Mechanics}, volume = {19}, journal = {Proceedings in Applied Mathematics \& Mechanics}, number = {1}, doi = {10.1002/pamm.201900070}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-211835}, pages = {e201900070}, year = {2019}, abstract = {The limiting behaviour of a one-dimensional discrete system is studied by means of Γ-convergence. We consider a toy model of a chain of atoms. The interaction potentials are of Lennard-Jones type and periodically or stochastically distributed. The energy of the system is considered in the discrete to continuum limit, i.e. as the number of atoms tends to infinity. During that limit, a homogenization process takes place. The limiting functional is discussed, especially with regard to fracture. Secondly, we consider a rescaled version of the problem, which yields a limiting energy of Griffith's type consisting of a quadratic integral term and a jump contribution. The periodic case can be found in [8], the stochastic case in [6,7].}, language = {en} } @article{SchaeffnerSchloemerkemper2018, author = {Sch{\"a}ffner, M. and Schl{\"o}merkemper, A.}, title = {On Lennard-Jones systems with finite range interactions and their asymptotic analysis}, series = {Networks and Heterogeneous Media}, volume = {13}, journal = {Networks and Heterogeneous Media}, number = {1}, doi = {10.3934/nhm.2018005}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-228428}, pages = {95-118}, year = {2018}, abstract = {The aim of this work is to provide further insight into the qualitative behavior of mechanical systems that are well described by Lennard-Jones type interactions on an atomistic scale. By means of Gamma-convergence techniques, we study the continuum limit of one-dimensional chains of atoms with finite range interactions of Lennard-Jones type, including the classical Lennard-Jones potentials. So far, explicit formula for the continuum limit were only available for the case of nearest and next-to-nearest neighbour interactions. In this work, we provide an explicit expression for the continuum limit in the case of finite range interactions. The obtained homogenization formula is given by the convexification of a Cauchy-Born energy density. Furthermore, we study rescaled energies in which bulk and surface contributions scale in the same way. The related discrete-to-continuum limit yields a rigorous derivation of a one-dimensional version of Griffith' fracture energy and thus generalizes earlier derivations for nearest and next-to-nearest neighbors to the case of finite range interactions. A crucial ingredient to our proofs is a novel decomposition of the energy that allows for re fined estimates.}, language = {en} } @article{KienleGarridoBreitenbachChudejetal.2018, author = {Kienle-Garrido, Melina-Lor{\´e}n and Breitenbach, Tim and Chudej, Kurt and Borz{\`i}, Alfio}, title = {Modeling and numerical solution of a cancer therapy optimal control problem}, series = {Applied Mathematics}, volume = {9}, journal = {Applied Mathematics}, number = {8}, doi = {10.4236/am.2018.98067}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-177152}, pages = {985-1004}, year = {2018}, abstract = {A mathematical optimal-control tumor therapy framework consisting of radio- and anti-angiogenesis control strategies that are included in a tumor growth model is investigated. The governing system, resulting from the combination of two well established models, represents the differential constraint of a non-smooth optimal control problem that aims at reducing the volume of the tumor while keeping the radio- and anti-angiogenesis chemical dosage to a minimum. Existence of optimal solutions is proved and necessary conditions are formulated in terms of the Pontryagin maximum principle. Based on this principle, a so-called sequential quadratic Hamiltonian (SQH) method is discussed and benchmarked with an "interior point optimizer―a mathematical programming language" (IPOPT-AMPL) algorithm. Results of numerical experiments are presented that successfully validate the SQH solution scheme. Further, it is shown how to choose the optimisation weights in order to obtain treatment functions that successfully reduce the tumor volume to zero.}, language = {en} } @article{RoyBorziHabbal2017, author = {Roy, S. and Borz{\`i}, A. and Habbal, A.}, title = {Pedestrian motion modelled by Fokker-Planck Nash games}, series = {Royal Society Open Science}, volume = {4}, journal = {Royal Society Open Science}, number = {9}, doi = {10.1098/rsos.170648}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-170395}, pages = {170648}, year = {2017}, abstract = {A new approach to modelling pedestrians' avoidance dynamics based on a Fokker-Planck (FP) Nash game framework is presented. In this framework, two interacting pedestrians are considered, whose motion variability is modelled through the corresponding probability density functions (PDFs) governed by FP equations. Based on these equations, a Nash differential game is formulated where the game strategies represent controls aiming at avoidance by minimizing appropriate collision cost functionals. The existence of Nash equilibria solutions is proved and characterized as a solution to an optimal control problem that is solved numerically. Results of numerical experiments are presented that successfully compare the computed Nash equilibria to the output of real experiments (conducted with humans) for four test cases.}, language = {en} } @article{GathunguBorzi2017, author = {Gathungu, Duncan Kioi and Borz{\`i}, Alfio}, title = {Multigrid Solution of an Elliptic Fredholm Partial Integro-Differential Equation with a Hilbert-Schmidt Integral Operator}, series = {Applied Mathematics}, volume = {8}, journal = {Applied Mathematics}, number = {7}, doi = {10.4236/am.2017.87076}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-158525}, pages = {967-986}, year = {2017}, abstract = {An efficient multigrid finite-differences scheme for solving elliptic Fredholm partial integro-differential equations (PIDE) is discussed. This scheme combines a second-order accurate finite difference discretization of the PIDE problem with a multigrid scheme that includes a fast multilevel integration of the Fredholm operator allowing the fast solution of the PIDE problem. Theoretical estimates of second-order accuracy and results of local Fourier analysis of convergence of the proposed multigrid scheme are presented. Results of numerical experiments validate these estimates and demonstrate optimal computational complexity of the proposed framework.}, language = {en} } @article{KasangKalluvyaMajingeetal.2016, author = {Kasang, Christa and Kalluvya, Samuel and Majinge, Charles and Kongola, Gilbert and Mlewa, Mathias and Massawe, Irene and Kabyemera, Rogatus and Magambo, Kinanga and Ulmer, Albrecht and Klinker, Hartwig and Gschmack, Eva and Horn, Anne and Koutsilieri, Eleni and Preiser, Wolfgang and Hofmann, Daniela and Hain, Johannes and M{\"u}ller, Andreas and D{\"o}lken, Lars and Weissbrich, Benedikt and Rethwilm, Axel and Stich, August and Scheller, Carsten}, title = {Effects of Prednisolone on Disease Progression in Antiretroviral-Untreated HIV Infection: A 2-Year Randomized, Double-Blind Placebo-Controlled Clinical Trial}, series = {PLoS One}, volume = {11}, journal = {PLoS One}, number = {1}, doi = {10.1371/journal.pone.0146678}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-146479}, pages = {e0146678}, year = {2016}, abstract = {Background HIV-disease progression correlates with immune activation. Here we investigated whether corticosteroid treatment can attenuate HIV disease progression in antiretroviral-untreated patients. Methods Double-blind, placebo-controlled randomized clinical trial including 326 HIV-patients in a resource-limited setting in Tanzania (clinicaltrials.gov NCT01299948). Inclusion criteria were a CD4 count above 300 cells/μl, the absence of AIDS-defining symptoms and an ART-na{\"i}ve therapy status. Study participants received 5 mg prednisolone per day or placebo for 2 years. Primary endpoint was time to progression to an AIDS-defining condition or to a CD4-count below 200 cells/μl. Results No significant change in progression towards the primary endpoint was observed in the intent-to-treat (ITT) analysis (19 cases with prednisolone versus 28 cases with placebo, p = 0.1407). In a per-protocol (PP)-analysis, 13 versus 24 study participants progressed to the primary study endpoint (p = 0.0741). Secondary endpoints: Prednisolone-treatment decreased immune activation (sCD14, suPAR, CD38/HLA-DR/CD8+) and increased CD4-counts (+77.42 ± 5.70 cells/μl compared to -37.42 ± 10.77 cells/μl under placebo, p < 0.0001). Treatment with prednisolone was associated with a 3.2-fold increase in HIV viral load (p < 0.0001). In a post-hoc analysis stratifying for sex, females treated with prednisolone progressed significantly slower to the primary study endpoint than females treated with placebo (ITT-analysis: 11 versus 21 cases, p = 0.0567; PP-analysis: 5 versus 18 cases, p = 0.0051): No changes in disease progression were observed in men. Conclusions This study could not detect any significant effects of prednisolone on disease progression in antiretroviral-untreated HIV infection within the intent-to-treat population. However, significant effects were observed on CD4 counts, immune activation and HIV viral load. This study contributes to a better understanding of the role of immune activation in the pathogenesis of HIV infection.}, language = {en} } @article{SchindeleBorzi2016, author = {Schindele, Andreas and Borz{\`i}, Alfio}, title = {Proximal Methods for Elliptic Optimal Control Problems with Sparsity Cost Functional}, series = {Applied Mathematics}, volume = {7}, journal = {Applied Mathematics}, number = {9}, doi = {10.4236/am.2016.79086}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-145850}, pages = {967-992}, year = {2016}, abstract = {First-order proximal methods that solve linear and bilinear elliptic optimal control problems with a sparsity cost functional are discussed. In particular, fast convergence of these methods is proved. For benchmarking purposes, inexact proximal schemes are compared to an inexact semismooth Newton method. Results of numerical experiments are presented to demonstrate the computational effectiveness of proximal schemes applied to infinite-dimensional elliptic optimal control problems and to validate the theoretical estimates.}, language = {en} } @article{GaviraghiSchindeleAnnunziatoetal.2016, author = {Gaviraghi, Beatrice and Schindele, Andreas and Annunziato, Mario and Borz{\`i}, Alfio}, title = {On Optimal Sparse-Control Problems Governed by Jump-Diffusion Processes}, series = {Applied Mathematics}, volume = {7}, journal = {Applied Mathematics}, number = {16}, doi = {10.4236/am.2016.716162}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-147819}, pages = {1978 -- 2004}, year = {2016}, abstract = {A framework for the optimal sparse-control of the probability density function of a jump-diffusion process is presented. This framework is based on the partial integro-differential Fokker-Planck (FP) equation that governs the time evolution of the probability density function of this process. In the stochastic process and, correspondingly, in the FP model the control function enters as a time-dependent coefficient. The objectives of the control are to minimize a discrete-in-time, resp. continuous-in-time, tracking functionals and its L2- and L1-costs, where the latter is considered to promote control sparsity. An efficient proximal scheme for solving these optimal control problems is considered. Results of numerical experiments are presented to validate the theoretical results and the computational effectiveness of the proposed control framework.}, language = {en} } @article{MatlachDhillonHainetal.2015, author = {Matlach, Juliane and Dhillon, Christine and Hain, Johannes and Schlunck, G{\"u}nther and Grehn, Franz and Klink, Thomas}, title = {Trabeculectomy versus canaloplasty (TVC study) in the treatment of patients with open-angle glaucoma: a prospective randomized clinical trial}, series = {Acta Ophthalmologica}, volume = {93}, journal = {Acta Ophthalmologica}, doi = {10.1111/aos.12722}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-149263}, pages = {753-761}, year = {2015}, abstract = {Purpose: To compare the outcomes of canaloplasty and trabeculectomy in open-angle glaucoma. Methods: This prospective, randomized clinical trial included 62 patients who randomly received trabeculectomy (n = 32) or canaloplasty (n = 30) and were followed up prospectively for 2 years. Primary endpoint was complete (without medication) and qualified success (with or without medication) defined as an intraocular pressure (IOP) of ≤18 mmHg (definition 1) or IOP ≤21 mmHg and ≥20\% IOP reduction (definition 2), IOP ≥5 mmHg, no vision loss and no further glaucoma surgery. Secondary endpoints were the absolute IOP reduction, visual acuity, medication, complications and second surgeries. Results: Surgical treatment significantly reduced IOP in both groups (p < 0.001). Complete success was achieved in 74.2\% and 39.1\% (definition 1, p = 0.01), and 67.7\% and 39.1\% (definition 2, p = 0.04) after 2 years in the trabeculectomy and canaloplasty group, respectively. Mean absolute IOP reduction was 10.8 ± 6.9 mmHg in the trabeculectomy and 9.3 ± 5.7 mmHg in the canaloplasty group after 2 years (p = 0.47). Mean IOP was 11.5 ± 3.4 mmHg in the trabeculectomy and 14.4 ± 4.2 mmHg in the canaloplasty group after 2 years. Following trabeculectomy, complications were more frequent including hypotony (37.5\%), choroidal detachment (12.5\%) and elevated IOP (25.0\%). Conclusions: Trabeculectomy is associated with a stronger IOP reduction and less need for medication at the cost of a higher rate of complications. If target pressure is attainable by moderate IOP reduction, canaloplasty may be considered for its relative ease of postoperative care and lack of complications.}, language = {en} } @article{HeldMittnachtKolbetal.2014, author = {Held, Matthias and Mittnacht, Maria and Kolb, Martin and Karl, Sabine and Jany, Berthold}, title = {Pulmonary and Cardiac Function in Asymptomatic Obese Subjects and Changes following a Structured Weight Reduction Program: A Prospective Observational Study}, series = {PLOS ONE}, volume = {9}, journal = {PLOS ONE}, number = {9}, doi = {10.1371/journal.pone.0107480}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-119239}, pages = {e107480}, year = {2014}, abstract = {Background The prevalence of obesity is rising. Obesity can lead to cardiovascular and ventilatory complications through multiple mechanisms. Cardiac and pulmonary function in asymptomatic subjects and the effect of structured dietary programs on cardiac and pulmonary function is unclear. Objective To determine lung and cardiac function in asymptomatic obese adults and to evaluate whether weight loss positively affects functional parameters. Methods We prospectively evaluated bodyplethysmographic and echocardiographic data in asymptomatic subjects undergoing a structured one-year weight reduction program. Results 74 subjects (32 male, 42 female; mean age 42±12 years) with an average BMI 42.5±7.9, body weight 123.7±24.9 kg were enrolled. Body weight correlated negatively with vital capacity (R = -0.42, p<0.001), FEV1 (R = -0.497, p<0.001) and positively with P 0.1 (R = 0.32, p = 0.02) and myocardial mass (R = 0.419, p = 0.002). After 4 months the study subjects had significantly reduced their body weight (-26.0±11.8 kg) and BMI (-8.9±3.8) associated with a significant improvement of lung function (absolute changes: vital capacity +5.5±7.5\% pred., p<0.001; FEV1+9.8±8.3\% pred., p<0.001, ITGV+16.4±16.0\% pred., p<0.001, SR tot -17.4±41.5\% pred., p<0.01). Moreover, P0.1/Pimax decreased to 47.7\% (p<0.01) indicating a decreased respiratory load. The change of FEV1 correlated significantly with the change of body weight (R = -0.31, p = 0.03). Echocardiography demonstrated reduced myocardial wall thickness (-0.08±0.2 cm, p = 0.02) and improved left ventricular myocardial performance index (-0.16±0.35, p = 0.02). Mitral annular plane systolic excursion (+0.14, p = 0.03) and pulmonary outflow acceleration time (AT +26.65±41.3 ms, p = 0.001) increased. Conclusion Even in asymptomatic individuals obesity is associated with abnormalities in pulmonary and cardiac function and increased myocardial mass. All the abnormalities can be reversed by a weight reduction program.}, language = {en} } @article{LuKlingenbergRendonetal.2014, author = {Lu, Yun-guang and Klingenberg, Christian and Rendon, Leonardo and Zheng, De-Yin}, title = {Global Solutions for a Simplified Shallow Elastic Fluids Model}, series = {Abstract and Applied Analytics}, journal = {Abstract and Applied Analytics}, number = {920248}, issn = {1687-0409}, doi = {10.1155/2014/920248}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-117978}, year = {2014}, abstract = {The Cauchy problem for a simplified shallow elastic fluids model, one 3 x 3 system of Temple's type, is studied and a global weak solution is obtained by using the compensated compactness theorem coupled with the total variation estimates on the first and third Riemann invariants, where the second Riemann invariant is singular near the zero layer depth (rho - 0). This work extends in some sense the previous works, (Serre, 1987) and (Leveque and Temple, 1985), which provided the global existence of weak solutions for 2 x 2 strictly hyperbolic system and (Heibig, 1994) for n x n strictly hyperbolic system with smooth Riemann invariants.}, language = {en} } @article{TrautmannSeitzBrockowetal.2014, author = {Trautmann, Axel and Seitz, Cornelia S. and Brockow, Knut and Hain, Johannes}, title = {Non-steroidal anti-inflammatory drug hypersensitivity: association with elevated basal serum tryptase?}, doi = {10.1186/1710-1492-10-19}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-110399}, year = {2014}, abstract = {Background It is hypothesized that because of higher mast cell numbers and mediator release, mastocytosis predisposes patients for systemic immediate-type hypersensitivity reactions to certain drugs including non-steroidal anti-inflammatory drugs (NSAID). Objective To clarify whether patients with NSAID hypersensitivity show increased basal serum tryptase levels as sign for underlying mast cell disease. Methods As part of our allergy work-up, basal serum tryptase levels were determined in all patients with a diagnosis of NSAID hypersensitivity and the severity of the reaction was graded. Patients with confirmed IgE-mediated hymenoptera venom allergy served as a comparison group. Results Out of 284 patients with NSAID hypersensitivity, 26 were identified with basal serum tryptase > 10.0 ng/mL (9.2\%). In contrast, significantly (P = .004) more hymenoptera venom allergic patients had elevated tryptase > 10.0 ng/mL (83 out of 484; 17.1\%). Basal tryptase > 20.0 ng/mL was indicative for severe anaphylaxis only in venom allergic subjects (29 patients; 4x grade 2 and 25x grade 3 anaphylaxis), but not in NSAID hypersensitive patients (6 patients; 4x grade 1, 2x grade 2). Conclusions In contrast to hymenoptera venom allergy, NSAID hypersensitivity do not seem to be associated with elevated basal serum tryptase levels and levels > 20 ng/mL were not related to increased severity of the clinical reaction. This suggests that mastocytosis patients may be treated with NSAID without special precautions.}, language = {en} } @article{HornSchellerduPlessisetal.2013, author = {Horn, Anne and Scheller, Carsten and du Plessis, Stefan and Arendt, Gabriele and Nolting, Thorsten and Joska, John and Sopper, Sieghart and Maschke, Matthias and Obermann, Mark and Husstedt, Ingo W. and Hain, Johannes and Maponga, Tongai and Riederer, Peter and Koutsilieri, Eleni}, title = {Increases in CSF dopamine in HIV patients are due to the dopamine transporter 10/10-repeat allele which is more frequent in HIV-infected individuals}, series = {Journal of Neural Transmission}, volume = {120}, journal = {Journal of Neural Transmission}, doi = {10.1007/s00702-013-1086-x}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-132385}, pages = {1411-1419}, year = {2013}, abstract = {Dysfunction of dopaminergic neurotransmission has been implicated in HIV infection. We showed previously increased dopamine (DA) levels in CSF of therapy-na{\"i}ve HIV patients and an inverse correlation between CSF DA and CD4 counts in the periphery, suggesting adverse effects of high levels of DA on HIV infection. In the current study including a total of 167 HIV-positive and negative donors from Germany and South Africa (SA), we investigated the mechanistic background for the increase of CSF DA in HIV individuals. Interestingly, we found that the DAT 10/10-repeat allele is present more frequently within HIV individuals than in uninfected subjects. Logistic regression analysis adjusted for gender and ethnicity showed an odds ratio for HIV infection in DAT 10/10 allele carriers of 3.93 (95 \% CI 1.72-8.96; p = 0.001, Fishers exact test). 42.6 \% HIV-infected patients harbored the DAT 10/10 allele compared to only 10.5 \% uninfected DAT 10/10 carriers in SA (odds ratio 6.31), whereas 68.1 versus 40.9 \%, respectively, in Germany (odds ratio 3.08). Subjects homozygous for the 10-repeat allele had higher amounts of CSF DA and reduced DAT mRNA expression but similar disease severity compared with those carrying other DAT genotypes. These intriguing and novel findings show the mutual interaction between DA and HIV, suggesting caution in the interpretation of CNS DA alterations in HIV infection solely as a secondary phenomenon to the virus and open the door for larger studies investigating consequences of the DAT functional polymorphism on HIV epidemiology and progression of disease.}, language = {en} } @article{RudelPrustySiegletal.2013, author = {Rudel, Thomas and Prusty, Bhupesh K. and Siegl, Christine and Hauck, Petra and Hain, Johannes and Korhonen, Suvi J. and Hiltunen-Back, Eija and Poulakkainen, Mirja}, title = {Chlamydia trachomatis Infection Induces Replication of Latent HHV-6}, series = {PLoS ONE}, journal = {PLoS ONE}, doi = {10.1371/journal.pone.0061400}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-96731}, year = {2013}, abstract = {Human herpesvirus-6 (HHV-6) exists in latent form either as a nuclear episome or integrated into human chromosomes in more than 90\% of healthy individuals without causing clinical symptoms. Immunosuppression and stress conditions can reactivate HHV-6 replication, associated with clinical complications and even death. We have previously shown that co-infection of Chlamydia trachomatis and HHV-6 promotes chlamydial persistence and increases viral uptake in an in vitro cell culture model. Here we investigated C. trachomatis-induced HHV-6 activation in cell lines and fresh blood samples from patients having Chromosomally integrated HHV-6 (CiHHV-6). We observed activation of latent HHV-6 DNA replication in CiHHV-6 cell lines and fresh blood cells without formation of viral particles. Interestingly, we detected HHV-6 DNA in blood as well as cervical swabs from C. trachomatis-infected women. Low virus titers correlated with high C. trachomatis load and vice versa, demonstrating a potentially significant interaction of these pathogens in blood cells and in the cervix of infected patients. Our data suggest a thus far underestimated interference of HHV-6 and C. trachomatis with a likely impact on the disease outcome as consequence of co-infection.}, language = {en} } @article{StoevesandtHofmannHainetal.2013, author = {Stoevesandt, Johanna and Hofmann, Bernd and Hain, Johannes and Kerstan, Andreas and Trautmann, Axel}, title = {Single venom-based immunotherapy effectively protects patients with double positive tests to honey bee and Vespula venom}, series = {Allergy, Asthma \& Clinical Immunology}, journal = {Allergy, Asthma \& Clinical Immunology}, doi = {10.1186/1710-1492-9-33}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-96808}, year = {2013}, abstract = {Background Referring to individuals with reactivity to honey bee and Vespula venom in diagnostic tests, the umbrella terms "double sensitization" or "double positivity" cover patients with true clinical double allergy and those allergic to a single venom with asymptomatic sensitization to the other. There is no international consensus on whether immunotherapy regimens should generally include both venoms in double sensitized patients. Objective We investigated the long-term outcome of single venom-based immunotherapy with regard to potential risk factors for treatment failure and specifically compared the risk of relapse in mono sensitized and double sensitized patients. Methods Re-sting data were obtained from 635 patients who had completed at least 3 years of immunotherapy between 1988 and 2008. The adequate venom for immunotherapy was selected using an algorithm based on clinical details and the results of diagnostic tests. Results Of 635 patients, 351 (55.3\%) were double sensitized to both venoms. The overall re-exposure rate to Hymenoptera stings during and after immunotherapy was 62.4\%; the relapse rate was 7.1\% (6.0\% in mono sensitized, 7.8\% in double sensitized patients). Recurring anaphylaxis was statistically less severe than the index sting reaction (P = 0.004). Double sensitization was not significantly related to relapsing anaphylaxis (P = 0.56), but there was a tendency towards an increased risk of relapse in a subgroup of patients with equal reactivity to both venoms in diagnostic tests (P = 0.15). Conclusions Single venom-based immunotherapy over 3 to 5 years effectively and long-lastingly protects the vast majority of both mono sensitized and double sensitized Hymenoptera venom allergic patients. Double venom immunotherapy is indicated in clinically double allergic patients reporting systemic reactions to stings of both Hymenoptera and in those with equal reactivity to both venoms in diagnostic tests who have not reliably identified the culprit stinging insect.}, language = {en} } @article{FreibergMatlachGrehnetal.2013, author = {Freiberg, Florentina Joyce and Matlach, Juliane and Grehn, Franz and Karl, Sabine and Klink, Thomas}, title = {Postoperative subconjunctival bevacizumab injection as an adjunct to 5-fluorouracil in the management of scarring after trabeculectomy}, series = {Clinical Ophthalmology}, journal = {Clinical Ophthalmology}, doi = {10.2147/OPTH.S41750}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-96546}, year = {2013}, abstract = {Purpose: Scarring after glaucoma filtering surgery remains the most frequent cause for bleb failure. The aim of this study was to assess if the postoperative injection of bevacizumab reduces the number of postoperative subconjunctival 5-fluorouracil (5-FU) injections. Further, the effect of bevacizumab as an adjunct to 5-FU on the intraocular pressure (IOP) outcome, bleb morphology, postoperative medications, and complications was evaluated. Methods: Glaucoma patients (N = 61) who underwent trabeculectomy with mitomycin C were analyzed retrospectively (follow-up period of 25 ± 19 months). Surgery was performed exclusively by one experienced glaucoma specialist using a standardized technique. Patients in group 1 received subconjunctival applications of 5-FU postoperatively. Patients in group 2 received 5-FU and subconjunctival injection of bevacizumab. Results: Group 1 had 6.4 ± 3.3 (0-15) (mean ± standard deviation and range, respectively) 5-FU injections. Group 2 had 4.0 ± 2.8 (0-12) (mean ± standard deviation and range, respectively) 5-FU injections. The added injection of bevacizumab significantly reduced the mean number of 5-FU injections by 2.4 ± 3.08 (P ≤ 0.005). There was no significantly lower IOP in group 2 when compared to group 1. A significant reduction in vascularization and in cork screw vessels could be found in both groups (P < 0.0001, 7 days to last 5-FU), yet there was no difference between the two groups at the last follow-up. Postoperative complications were significantly higher for both groups when more 5-FU injections were applied. (P = 0.008). No significant difference in best corrected visual acuity (P = 0.852) and visual field testing (P = 0.610) between preoperative to last follow-up could be found between the two groups. Conclusion: The postoperative injection of bevacizumab reduced the number of subconjunctival 5-FU injections significantly by 2.4 injections. A significant difference in postoperative IOP reduction, bleb morphology, and postoperative medication was not detected.}, language = {en} } @article{Harrach2013, author = {Harrach, Bastian}, title = {Recent Progress on the Factorization Method for Electrical Impedance Tomography}, series = {Computational and Mathematical Methods in Medicine}, journal = {Computational and Mathematical Methods in Medicine}, doi = {10.1155/2013/425184}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-96229}, year = {2013}, abstract = {The Factorization Method is a noniterative method to detect the shape and position of conductivity anomalies inside an object. The method was introduced by Kirsch for inverse scattering problems and extended to electrical impedance tomography (EIT) by Br{\"u}hl and Hanke. Since these pioneering works, substantial progress has been made on the theoretical foundations of the method. The necessary assumptions have been weakened, and the proofs have been considerably simplified. In this work, we aim to summarize this progress and present a state-of-the-art formulation of the Factorization Method for EIT with continuous data. In particular, we formulate the method for general piecewise analytic conductivities and give short and self-contained proofs.}, language = {en} } @article{ChenchiahSchloemerkemper2012, author = {Chenchiah, Isaac and Schl{\"o}merkemper, Anja}, title = {Non-laminate microstructures in monoclinic-I martensite}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-72134}, year = {2012}, abstract = {We study the symmetrised rank-one convex hull of monoclinic-I martensite (a twelve-variant material) in the context of geometrically-linear elasticity. We construct sets of T3s, which are (non-trivial) symmetrised rank-one convex hulls of 3-tuples of pairwise incompatible strains. Moreover we construct a five-dimensional continuum of T3s and show that its intersection with the boundary of the symmetrised rank-one convex hull is four-dimensional. We also show that there is another kind of monoclinic-I martensite with qualitatively different semi-convex hulls which, so far as we know, has not been experimentally observed. Our strategy is to combine understanding of the algebraic structure of symmetrised rank-one convex cones with knowledge of the faceting structure of the convex polytope formed by the strains.}, subject = {Martensit}, language = {en} } @article{BallesterBolinchesBeidlemanHeinekenetal.2010, author = {Ballester-Bolinches, A. and Beidleman, J. C. and Heineken, H. and Pedraza-Aguilera, M. C.}, title = {Local Classes and Pairwise Mutually Permutable Products of Finite Groups}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-68062}, year = {2010}, abstract = {The main aim of the paper is to present some results about products of pairwise mutually permutable subgroups and local classes.}, subject = {Mathematik}, language = {en} } @article{FerranteWimmer2010, author = {Ferrante, Augusto and Wimmer, Harald K.}, title = {Reachability matrices and cyclic matrices}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-68074}, year = {2010}, abstract = {We study reachability matrices R(A, b) = [b,Ab, . . . ,An-1b], where A is an n × n matrix over a field K and b is in Kn. We characterize those matrices that are reachability matrices for some pair (A, b). In the case of a cyclic matrix A and an n-vector of indeterminates x, we derive a factorization of the polynomial det(R(A, x)).}, subject = {Mathematik}, language = {en} } @article{JanssenMarohn1994, author = {Janssen, A. and Marohn, Frank}, title = {On statistical information of extreme order statistics, local extreme value alternatives, and Poisson point processes}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-45816}, year = {1994}, abstract = {The aim of the present paper is to clarify the role of extreme order statistics in general statistical models. This is done within the general setup of statistical experiments in LeCam's sense. Under the assumption of monotone likelihood ratios, we prove that a sequence of experiments is asymptotically Gaussian if, and only if, a fixed number of extremes asymptotically does not contain any information. In other words: A fixed number of extremes asymptotically contains information iff the Poisson part of the limit experiment is non-trivial. Suggested by this result, we propose a new extreme value model given by local alternatives. The local structure is described by introducing the space of extreme value tangents. It turns out that under local alternatives a new class of extreme value distributions appears as limit distributions. Moreover, explicit representations of the Poisson limit experiments via Poisson point processes are found. As a concrete example nonparametric tests for Frechet type distributions against stochastically larger alternatives are treated. We find asymptotically optimal tests within certain threshold models.}, language = {en} } @article{Marohn1994, author = {Marohn, Frank}, title = {Asymptotic sufficiency of order statistics for almost regular Weibull type densities}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-45837}, year = {1994}, abstract = {Consider a location family which is defined via a Weibull type density having shape parameter a = 1. We treat the problem, which portion of the order statistics is asymptotically sufficient. It turns out that the intermediate order statistics are relevant.}, language = {en} } @article{FalkMarohn1993, author = {Falk, Michael and Marohn, Frank}, title = {Von Mises condition revisited}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-45790}, year = {1993}, abstract = {It is shown that the rate of convergence in the von Mises conditions of extreme value theory determines the distance of the underlying distribution function F from a generalized Pareto distribution. The distance is measured in terms of the pertaining densities with the limit being ultimately attained if and only if F is ultimately a generalized Pareto distribution. Consequently, the rate of convergence of the extremes in an lid sample, whether in terms of the distribution of the largest order statistics or of corresponding empirical truncated point processes, is determined by the rate of convergence in the von Mises condition. We prove that the converse is also true.}, language = {en} } @article{FalkMarohn1993, author = {Falk, Michael and Marohn, Frank}, title = {Asymptotically optimal tests for conditional distributions}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-45823}, year = {1993}, abstract = {No abstract available}, language = {en} } @article{Zillober1993, author = {Zillober, Christian}, title = {A globally convergent version of the method of moving asymptotes}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-31984}, year = {1993}, abstract = {No abstract available}, language = {en} } @article{KredlerZilloberJohannesetal.1993, author = {Kredler, Christian and Zillober, Christian and Johannes, Frank and Sigl, Georg}, title = {An application of preconditioned conjugate gradients to relative placement in chip design}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-31996}, year = {1993}, abstract = {In distance geometry problems and many other applications, we are faced with the optimization of high-dimensional quadratic functions subject to linear equality constraints. A new approach is presented that projects the constraints, preserving sparsity properties of the original quadratic form such that well-known preconditioning techniques for the conjugate gradient method remain applicable. Very-largescale cell placement problems in chip design have been solved successfully with diagonal and incomplete Cholesky preconditioning. Numerical results produced by a FORTRAN 77 program illustrate the good behaviour of the algorithm.}, language = {en} } @article{Marohn1991, author = {Marohn, Frank}, title = {Global sufficiency of extreme order statistics in location models of Weibull type}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-47874}, year = {1991}, abstract = {In Janssen and Reiss (1988) it was shown that in a location model of a Weibull type sample with shape parameter -1 < a < 1 the k(n) lower extremes are asymptotically local sufficient. In the present paper we show that even global sufficiency holds. Moreover, it turns out that convergence of the given statistical experiments in the deficiency metric does not only hold for compact parameter sets but for the whole real line.}, subject = {Extremwertstatistik}, language = {de} }