@article{StolleMichaelisRauberg2016, author = {Stolle, Claudia and Michaelis, Ingo and Rauberg, Jan}, title = {The role of high-resolution geomagnetic field models for investigating ionospheric currents at low Earth orbit satellites}, series = {Earth, planets and space}, volume = {68}, journal = {Earth, planets and space}, publisher = {Springer}, address = {Heidelberg}, issn = {1880-5981}, doi = {10.1186/s40623-016-0494-1}, pages = {10}, year = {2016}, abstract = {Low Earth orbiting geomagnetic satellite missions, such as the Swarm satellite mission, are the only means to monitor and investigate ionospheric currents on a global scale and to make in situ measurements of F region currents. High-precision geomagnetic satellite missions are also able to detect ionospheric currents during quiet-time geomagnetic conditions that only have few nanotesla amplitudes in the magnetic field. An efficient method to isolate the ionospheric signals from satellite magnetic field measurements has been the use of residuals between the observations and predictions from empirical geomagnetic models for other geomagnetic sources, such as the core and lithospheric field or signals from the quiet-time magnetospheric currents. This study aims at highlighting the importance of high-resolution magnetic field models that are able to predict the lithospheric field and that consider the quiet-time magnetosphere for reliably isolating signatures from ionospheric currents during geomagnetically quiet times. The effects on the detection of ionospheric currents arising from neglecting the lithospheric and magnetospheric sources are discussed on the example of four Swarm orbits during very quiet times. The respective orbits show a broad range of typical scenarios, such as strong and weak ionospheric signal (during day- and nighttime, respectively) superimposed over strong and weak lithospheric signals. If predictions from the lithosphere or magnetosphere are not properly considered, the amplitude of the ionospheric currents, such as the midlatitude Sq currents or the equatorial electrojet (EEJ), is modulated by 10-15 \% in the examples shown. An analysis from several orbits above the African sector, where the lithospheric field is significant, showed that the peak value of the signatures of the EEJ is in error by 5 \% in average when lithospheric contributions are not considered, which is in the range of uncertainties of present empirical models of the EEJ.}, language = {en} } @article{Denecke2016, author = {Denecke, Klaus-Dieter}, title = {The partial clone of linear terms}, series = {Siberian Mathematical Journal}, volume = {57}, journal = {Siberian Mathematical Journal}, publisher = {Pleiades Publ.}, address = {New York}, issn = {0037-4466}, doi = {10.1134/S0037446616040030}, pages = {589 -- 598}, year = {2016}, abstract = {Generalizing a linear expression over a vector space, we call a term of an arbitrary type tau linear if its every variable occurs only once. Instead of the usual superposition of terms and of the total many-sorted clone of all terms in the case of linear terms, we define the partial many-sorted superposition operation and the partial many-sorted clone that satisfies the superassociative law as weak identity. The extensions of linear hypersubstitutions are weak endomorphisms of this partial clone. For a variety V of one-sorted total algebras of type tau, we define the partial many-sorted linear clone of V as the partial quotient algebra of the partial many-sorted clone of all linear terms by the set of all linear identities of V. We prove then that weak identities of this clone correspond to linear hyperidentities of V.}, language = {en} } @article{KistnerVollmeyerBurnsetal.2016, author = {Kistner, Saskia and Vollmeyer, Regina and Burns, Bruce D. and Kortenkamp, Ulrich}, title = {Model development in scientific discovery learning with a computer-based physics task}, series = {Computers in human behavior}, volume = {59}, journal = {Computers in human behavior}, publisher = {Elsevier}, address = {Oxford}, issn = {0747-5632}, doi = {10.1016/j.chb.2016.02.041}, pages = {446 -- 455}, year = {2016}, abstract = {Based on theories of scientific discovery learning (SDL) and conceptual change, this study explores students' preconceptions in the domain of torques in physics and the development of these conceptions while learning with a computer-based SDL task. As a framework we used a three-space theory of SDL and focused on model space, which is supposed to contain the current conceptualization/model of the learning domain, and on its change through hypothesis testing and experimenting. Three questions were addressed: (1) What are students' preconceptions of torques before learning about this domain? To do this a multiple-choice test for assessing students' models of torques was developed and given to secondary school students (N = 47) who learned about torques using computer simulations. (2) How do students' models of torques develop during SDL? Working with simulations led to replacement of some misconceptions with physically correct conceptions. (3) Are there differential patterns of model development and if so, how do they relate to students' use of the simulations? By analyzing individual differences in model development, we found that an intensive use of the simulations was associated with the acquisition of correct conceptions. Thus, the three-space theory provided a useful framework for understanding conceptual change in SDL.}, language = {en} } @article{SinclairBussideVilliersetal.2016, author = {Sinclair, Nathalie and Bussi, Maria G. Bartolini and de Villiers, Michael and Jones, Keith and Kortenkamp, Ulrich and Leung, Allen and Owens, Kay}, title = {Recent research on geometry education: an ICME-13 survey team report}, series = {ZDM : The International Journal on Mathematics Education}, volume = {48}, journal = {ZDM : The International Journal on Mathematics Education}, publisher = {Springer}, address = {Heidelberg}, issn = {1863-9690}, doi = {10.1007/s11858-016-0796-6}, pages = {691 -- 719}, year = {2016}, abstract = {This survey on the theme of Geometry Education (including new technologies) focuses chiefly on the time span since 2008. Based on our review of the research literature published during this time span (in refereed journal articles, conference proceedings and edited books), we have jointly identified seven major threads of contributions that span from the early years of learning (pre-school and primary school) through to post-compulsory education and to the issue of mathematics teacher education for geometry. These threads are as follows: developments and trends in the use of theories; advances in the understanding of visuo spatial reasoning; the use and role of diagrams and gestures; advances in the understanding of the role of digital technologies; advances in the understanding of the teaching and learning of definitions; advances in the understanding of the teaching and learning of the proving process; and, moving beyond traditional Euclidean approaches. Within each theme, we identify relevant research and also offer commentary on future directions.}, language = {en} } @article{KistnerBurnsVollmeyeretal.2016, author = {Kistner, Saskia and Burns, Bruce D. and Vollmeyer, Regina and Kortenkamp, Ulrich}, title = {The importance of understanding: Model space moderates goal specificity effects}, series = {The quarterly journal of experimental psychology}, volume = {69}, journal = {The quarterly journal of experimental psychology}, publisher = {Optical Society of America}, address = {Abingdon}, issn = {1747-0218}, doi = {10.1080/17470218.2015.1076865}, pages = {1179 -- 1196}, year = {2016}, abstract = {The three-space theory of problem solving predicts that the quality of a learner's model and the goal specificity of a task interact on knowledge acquisition. In Experiment 1 participants used a computer simulation of a lever system to learn about torques. They either had to test hypotheses (nonspecific goal), or to produce given values for variables (specific goal). In the good- but not in the poor-model condition they saw torque depicted as an area. Results revealed the predicted interaction. A nonspecific goal only resulted in better learning when a good model of torques was provided. In Experiment 2 participants learned to manipulate the inputs of a system to control its outputs. A nonspecific goal to explore the system helped performance when compared to a specific goal to reach certain values when participants were given a good model, but not when given a poor model that suggested the wrong hypothesis space. Our findings support the three-space theory. They emphasize the importance of understanding for problem solving and stress the need to study underlying processes.}, language = {en} } @article{KortenkampMonaghanTrouche2016, author = {Kortenkamp, Ulrich and Monaghan, John and Trouche, Luc}, title = {Jonathan M Borwein (1951-2016): exploring, experiencing and experimenting in mathematics - an inspiring journey in mathematics}, series = {Educational studies in mathematics : an international journal}, volume = {93}, journal = {Educational studies in mathematics : an international journal}, publisher = {Springer}, address = {Dordrecht}, issn = {0013-1954}, doi = {10.1007/s10649-016-9729-0}, pages = {131 -- 136}, year = {2016}, language = {en} } @article{LyTarkhanov2016, author = {Ly, Ibrahim and Tarkhanov, Nikolai Nikolaevich}, title = {A Rado theorem for p-harmonic functions}, series = {Boletin de la Sociedad Matem{\~A}!'tica Mexicana}, volume = {22}, journal = {Boletin de la Sociedad Matem{\~A}!'tica Mexicana}, publisher = {Springer}, address = {Basel}, issn = {1405-213X}, doi = {10.1007/s40590-016-0109-7}, pages = {461 -- 472}, year = {2016}, abstract = {Let A be a nonlinear differential operator on an open set X subset of R-n and S a closed subset of X. Given a class F of functions in X, the set S is said to be removable for F relative to A if any weak solution of A(u) = 0 in XS of class F satisfies this equation weakly in all of X. For the most extensively studied classes F, we show conditions on S which guarantee that S is removable for F relative to A.}, language = {en} } @phdthesis{Ludewig2016, author = {Ludewig, Matthias}, title = {Path integrals on manifolds with boundary and their asymptotic expansions}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-94387}, school = {Universit{\"a}t Potsdam}, pages = {146}, year = {2016}, abstract = {It is "scientific folklore" coming from physical heuristics that solutions to the heat equation on a Riemannian manifold can be represented by a path integral. However, the problem with such path integrals is that they are notoriously ill-defined. One way to make them rigorous (which is often applied in physics) is finite-dimensional approximation, or time-slicing approximation: Given a fine partition of the time interval into small subintervals, one restricts the integration domain to paths that are geodesic on each subinterval of the partition. These finite-dimensional integrals are well-defined, and the (infinite-dimensional) path integral then is defined as the limit of these (suitably normalized) integrals, as the mesh of the partition tends to zero. In this thesis, we show that indeed, solutions to the heat equation on a general compact Riemannian manifold with boundary are given by such time-slicing path integrals. Here we consider the heat equation for general Laplace type operators, acting on sections of a vector bundle. We also obtain similar results for the heat kernel, although in this case, one has to restrict to metrics satisfying a certain smoothness condition at the boundary. One of the most important manipulations one would like to do with path integrals is taking their asymptotic expansions; in the case of the heat kernel, this is the short time asymptotic expansion. In order to use time-slicing approximation here, one needs the approximation to be uniform in the time parameter. We show that this is possible by giving strong error estimates. Finally, we apply these results to obtain short time asymptotic expansions of the heat kernel also in degenerate cases (i.e. at the cut locus). Furthermore, our results allow to relate the asymptotic expansion of the heat kernel to a formal asymptotic expansion of the infinite-dimensional path integral, which gives relations between geometric quantities on the manifold and on the loop space. In particular, we show that the lowest order term in the asymptotic expansion of the heat kernel is essentially given by the Fredholm determinant of the Hessian of the energy functional. We also investigate how this relates to the zeta-regularized determinant of the Jacobi operator along minimizing geodesics.}, language = {en} } @misc{Scharrer2016, type = {Master Thesis}, author = {Scharrer, Christian}, title = {Relating diameter and mean curvature for varifolds}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-97013}, school = {Universit{\"a}t Potsdam}, pages = {42}, year = {2016}, abstract = {The main results of this thesis are formulated in a class of surfaces (varifolds) generalizing closed and connected smooth submanifolds of Euclidean space which allows singularities. Given an indecomposable varifold with dimension at least two in some Euclidean space such that the first variation is locally bounded, the total variation is absolutely continuous with respect to the weight measure, the density of the weight measure is at least one outside a set of weight measure zero and the generalized mean curvature is locally summable to a natural power (dimension of the varifold minus one) with respect to the weight measure. The thesis presents an improved estimate of the set where the lower density is small in terms of the one dimensional Hausdorff measure. Moreover, if the support of the weight measure is compact, then the intrinsic diameter with respect to the support of the weight measure is estimated in terms of the generalized mean curvature. This estimate is in analogy to the diameter control for closed connected manifolds smoothly immersed in some Euclidean space of Peter Topping. Previously, it was not known whether the hypothesis in this thesis implies that two points in the support of the weight measure have finite geodesic distance.}, language = {en} } @unpublished{ShlapunovTarkhanov2016, author = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich}, title = {An open mapping theorem for the Navier-Stokes equations}, volume = {5}, number = {10}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-98687}, pages = {80}, year = {2016}, abstract = {We consider the Navier-Stokes equations in the layer R^n x [0,T] over R^n with finite T > 0. Using the standard fundamental solutions of the Laplace operator and the heat operator, we reduce the Navier-Stokes equations to a nonlinear Fredholm equation of the form (I+K) u = f, where K is a compact continuous operator in anisotropic normed H{\"o}lder spaces weighted at the point at infinity with respect to the space variables. Actually, the weight function is included to provide a finite energy estimate for solutions to the Navier-Stokes equations for all t in [0,T]. On using the particular properties of the de Rham complex we conclude that the Fr{\´e}chet derivative (I+K)' is continuously invertible at each point of the Banach space under consideration and the map I+K is open and injective in the space. In this way the Navier-Stokes equations prove to induce an open one-to-one mapping in the scale of H{\"o}lder spaces.}, language = {en} } @unpublished{BlanchardKraemer2016, author = {Blanchard, Gilles and Kr{\"a}mer, Nicole}, title = {Convergence rates of kernel conjugate gradient for random design regression}, volume = {5}, number = {8}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-94195}, pages = {31}, year = {2016}, abstract = {We prove statistical rates of convergence for kernel-based least squares regression from i.i.d. data using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping. This method is related to Kernel Partial Least Squares, a regression method that combines supervised dimensionality reduction with least squares projection. Following the setting introduced in earlier related literature, we study so-called "fast convergence rates" depending on the regularity of the target regression function (measured by a source condition in terms of the kernel integral operator) and on the effective dimensionality of the data mapped into the kernel space. We obtain upper bounds, essentially matching known minimax lower bounds, for the L^2 (prediction) norm as well as for the stronger Hilbert norm, if the true regression function belongs to the reproducing kernel Hilbert space. If the latter assumption is not fulfilled, we obtain similar convergence rates for appropriate norms, provided additional unlabeled data are available.}, language = {en} } @phdthesis{Chutsagulprom2016, author = {Chutsagulprom, Nawinda}, title = {Ensemble-based filters dealing with non-Gaussianity and nonlinearity}, school = {Universit{\"a}t Potsdam}, pages = {95}, year = {2016}, language = {en} } @unpublished{RoellyVallois2016, author = {Roelly, Sylvie and Vallois, Pierre}, title = {Convoluted Brownian motion}, volume = {5}, number = {9}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-96339}, pages = {37}, year = {2016}, abstract = {In this paper we analyse semimartingale properties of a class of Gaussian periodic processes, called convoluted Brownian motions, obtained by convolution between a deterministic function and a Brownian motion. A classical example in this class is the periodic Ornstein-Uhlenbeck process. We compute their characteristics and show that in general, they are neither Markovian nor satisfy a time-Markov field property. Nevertheless, by enlargement of filtration and/or addition of a one-dimensional component, one can in some case recover the Markovianity. We treat exhaustively the case of the bidimensional trigonometric convoluted Brownian motion and the higher-dimensional monomial convoluted Brownian motion.}, language = {en} } @phdthesis{Pirhayati2016, author = {Pirhayati, Mohammad}, title = {Edge operators and boundary value problems}, school = {Universit{\"a}t Potsdam}, pages = {VI, 119}, year = {2016}, language = {en} } @phdthesis{Lyu2016, author = {Lyu, Xiaojing}, title = {Operators on singular manifolds}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-103643}, school = {Universit{\"a}t Potsdam}, pages = {117}, year = {2016}, abstract = {We study the interplay between analysis on manifolds with singularities and complex analysis and develop new structures of operators based on the Mellin transform and tools for iterating the calculus for higher singularities. We refer to the idea of interpreting boundary value problems (BVPs) in terms of pseudo-differential operators with a principal symbolic hierarchy, taking into account that BVPs are a source of cone and edge operator algebras. The respective cone and edge pseudo-differential algebras in turn are the starting point of higher corner theories. In addition there are deep relationships between corner operators and complex analysis. This will be illustrated by the Mellin symbolic calculus.}, language = {en} } @phdthesis{Gopalakrishnan2016, author = {Gopalakrishnan, Sathej}, title = {Mathematical modelling of host-disease-drug interactions in HIV disease}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-100100}, school = {Universit{\"a}t Potsdam}, pages = {121}, year = {2016}, abstract = {The human immunodeficiency virus (HIV) has resisted nearly three decades of efforts targeting a cure. Sustained suppression of the virus has remained a challenge, mainly due to the remarkable evolutionary adaptation that the virus exhibits by the accumulation of drug-resistant mutations in its genome. Current therapeutic strategies aim at achieving and maintaining a low viral burden and typically involve multiple drugs. The choice of optimal combinations of these drugs is crucial, particularly in the background of treatment failure having occurred previously with certain other drugs. An understanding of the dynamics of viral mutant genotypes aids in the assessment of treatment failure with a certain drug combination, and exploring potential salvage treatment regimens. Mathematical models of viral dynamics have proved invaluable in understanding the viral life cycle and the impact of antiretroviral drugs. However, such models typically use simplified and coarse-grained mutation schemes, that curbs the extent of their application to drug-specific clinical mutation data, in order to assess potential next-line therapies. Statistical models of mutation accumulation have served well in dissecting mechanisms of resistance evolution by reconstructing mutation pathways under different drug-environments. While these models perform well in predicting treatment outcomes by statistical learning, they do not incorporate drug effect mechanistically. Additionally, due to an inherent lack of temporal features in such models, they are less informative on aspects such as predicting mutational abundance at treatment failure. This limits their application in analyzing the pharmacology of antiretroviral drugs, in particular, time-dependent characteristics of HIV therapy such as pharmacokinetics and pharmacodynamics, and also in understanding the impact of drug efficacy on mutation dynamics. In this thesis, we develop an integrated model of in vivo viral dynamics incorporating drug-specific mutation schemes learned from clinical data. Our combined modelling approach enables us to study the dynamics of different mutant genotypes and assess mutational abundance at virological failure. As an application of our model, we estimate in vivo fitness characteristics of viral mutants under different drug environments. Our approach also extends naturally to multiple-drug therapies. Further, we demonstrate the versatility of our model by showing how it can be modified to incorporate recently elucidated mechanisms of drug action including molecules that target host factors. Additionally, we address another important aspect in the clinical management of HIV disease, namely drug pharmacokinetics. It is clear that time-dependent changes in in vivo drug concentration could have an impact on the antiviral effect, and also influence decisions on dosing intervals. We present a framework that provides an integrated understanding of key characteristics of multiple-dosing regimens including drug accumulation ratios and half-lifes, and then explore the impact of drug pharmacokinetics on viral suppression. Finally, parameter identifiability in such nonlinear models of viral dynamics is always a concern, and we investigate techniques that alleviate this issue in our setting.}, language = {en} } @unpublished{VasilievTarkhanov2016, author = {Vasiliev, Serguei and Tarkhanov, Nikolai Nikolaevich}, title = {Construction of series of perfect lattices by layer superposition}, volume = {5}, number = {11}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-100591}, pages = {11}, year = {2016}, abstract = {We construct a new series of perfect lattices in n dimensions by the layer superposition method of Delaunay-Barnes.}, language = {en} } @article{HedayatMahmoudiSchulze2016, author = {Hedayat Mahmoudi, Mahdi and Schulze, Bert-Wolfgang}, title = {Corner boundary value problems}, series = {Asian-European journal of mathematics}, volume = {10}, journal = {Asian-European journal of mathematics}, number = {1}, publisher = {World Scientific}, address = {Singapore}, issn = {1793-5571}, doi = {10.1142/S1793557117500541}, pages = {45}, year = {2016}, abstract = {The paper develops some crucial steps in extending the first-order cone or edge calculus to higher singularity orders. We focus here on order 2, but the ideas are motivated by an iterative approach for higher singularities.}, language = {en} } @article{AntoniniAzzaliSkandalis2016, author = {Antonini, Paolo and Azzali, Sara and Skandalis, Georges}, title = {Bivariant K-theory with R/Z-coefficients and rho classes of unitary representations}, series = {Journal of functional analysis}, volume = {270}, journal = {Journal of functional analysis}, publisher = {Elsevier}, address = {San Diego}, issn = {0022-1236}, doi = {10.1016/j.jfa.2015.06.017}, pages = {447 -- 481}, year = {2016}, abstract = {We construct equivariant KK-theory with coefficients in and R/Z as suitable inductive limits over II1-factors. We show that the Kasparov product, together with its usual functorial properties, extends to KK-theory with real coefficients. Let Gamma be a group. We define a Gamma-algebra A to be K-theoretically free and proper (KFP) if the group trace tr of Gamma acts as the unit element in KKR Gamma (A, A). We show that free and proper Gamma-algebras (in the sense of Kasparov) have the (KFP) property. Moreover, if Gamma is torsion free and satisfies the KK Gamma-form of the Baum-Connes conjecture, then every Gamma-algebra satisfies (KFP). If alpha : Gamma -> U-n is a unitary representation and A satisfies property (KFP), we construct in a canonical way a rho class rho(A)(alpha) is an element of KKR/Z1,Gamma (A A) This construction generalizes the Atiyah-Patodi-Singer K-theory class with R/Z-coefficients associated to alpha. (C) 2015 Elsevier Inc. All rights reserved.}, language = {en} } @article{Benini2016, author = {Benini, Marco}, title = {Optimal space of linear classical observables for Maxwell k-forms via spacelike and timelike compact de Rham cohomologies}, series = {Journal of mathematical physics}, volume = {57}, journal = {Journal of mathematical physics}, publisher = {American Institute of Physics}, address = {Melville}, issn = {0022-2488}, doi = {10.1063/1.4947563}, pages = {1249 -- 1279}, year = {2016}, abstract = {Being motivated by open questions in gauge field theories, we consider non-standard de Rham cohomology groups for timelike compact and spacelike compact support systems. These cohomology groups are shown to be isomorphic respectively to the usual de Rham cohomology of a spacelike Cauchy surface and its counterpart with compact support. Furthermore, an analog of the usual Poincare duality for de Rham cohomology is shown to hold for the case with non-standard supports as well. We apply these results to find optimal spaces of linear observables for analogs of arbitrary degree k of both the vector potential and the Faraday tensor. The term optimal has to be intended in the following sense: The spaces of linear observables we consider distinguish between different configurations; in addition to that, there are no redundant observables. This last point in particular heavily relies on the analog of Poincare duality for the new cohomology groups. Published by AIP Publishing.}, language = {en} }