@article{Menne2016, author = {Menne, Ulrich}, title = {Weakly Differentiable Functions on Varifolds}, series = {Indiana University mathematics journal}, volume = {65}, journal = {Indiana University mathematics journal}, publisher = {Indiana University, Department of Mathematics}, address = {Bloomington}, issn = {0022-2518}, doi = {10.1512/iumj.2016.65.5829}, pages = {977 -- 1088}, year = {2016}, abstract = {The present paper is intended to provide the basis for the study of weakly differentiable functions on rectifiable varifolds with locally bounded first variation. The concept proposed here is defined by means of integration-by-parts identities for certain compositions with smooth functions. In this class, the idea of zero boundary values is realised using the relative perimeter of superlevel sets. Results include a variety of Sobolev Poincare-type embeddings, embeddings into spaces of continuous and sometimes Holder-continuous functions, and point wise differentiability results both of approximate and integral type as well as coarea formulae. As a prerequisite for this study, decomposition properties of such varifolds and a relative isoperimetric inequality are established. Both involve a concept of distributional boundary of a set introduced for this purpose. As applications, the finiteness of the geodesic distance associated with varifolds with suitable summability of the mean curvature and a characterisation of curvature varifolds are obtained.}, language = {en} } @unpublished{Alsaedy2016, author = {Alsaedy, Ammar}, title = {Variational primitive of a differential form}, volume = {5}, number = {4}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-89223}, pages = {8}, year = {2016}, abstract = {In this paper we specify the Dirichlet to Neumann operator related to the Cauchy problem for the gradient operator with data on a part of the boundary. To this end, we consider a nonlinear relaxation of this problem which is a mixed boundary problem of Zaremba type for the p-Laplace equation.}, language = {en} } @article{KretschmerCoumouDongesetal.2016, author = {Kretschmer, Marlene and Coumou, Dim and Donges, Jonathan and Runge, Jakob}, title = {Using Causal Effect Networks to Analyze Different Arctic Drivers of Midlatitude Winter Circulation}, series = {Journal of climate}, volume = {29}, journal = {Journal of climate}, publisher = {American Meteorological Soc.}, address = {Boston}, issn = {0894-8755}, doi = {10.1175/JCLI-D-15-0654.1}, pages = {4069 -- 4081}, year = {2016}, abstract = {In recent years, the Northern Hemisphere midlatitudes have suffered from severe winters like the extreme 2012/13 winter in the eastern United States. These cold spells were linked to a meandering upper-tropospheric jet stream pattern and a negative Arctic Oscillation index (AO). However, the nature of the drivers behind these circulation patterns remains controversial. Various studies have proposed different mechanisms related to changes in the Arctic, most of them related to a reduction in sea ice concentrations or increasing Eurasian snow cover. Here, a novel type of time series analysis, called causal effect networks (CEN), based on graphical models is introduced to assess causal relationships and their time delays between different processes. The effect of different Arctic actors on winter circulation on weekly to monthly time scales is studied, and robust network patterns are found. Barents and Kara sea ice concentrations are detected to be important external drivers of the midlatitude circulation, influencing winter AO via tropospheric mechanisms and through processes involving the stratosphere. Eurasia snow cover is also detected to have a causal effect on sea level pressure in Asia, but its exact role on AO remains unclear. The CEN approach presented in this study overcomes some difficulties in interpreting correlation analyses, complements model experiments for testing hypotheses involving teleconnections, and can be used to assess their validity. The findings confirm that sea ice concentrations in autumn in the Barents and Kara Seas are an important driver of winter circulation in the midlatitudes.}, language = {en} } @unpublished{GairingHoegeleKosenkova2016, author = {Gairing, Jan and H{\"o}gele, Michael and Kosenkova, Tetiana}, title = {Transportation distances and noise sensitivity of multiplicative L{\´e}vy SDE with applications}, volume = {5}, number = {2}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-86693}, pages = {24}, year = {2016}, abstract = {This article assesses the distance between the laws of stochastic differential equations with multiplicative L{\´e}vy noise on path space in terms of their characteristics. The notion of transportation distance on the set of L{\´e}vy kernels introduced by Kosenkova and Kulik yields a natural and statistically tractable upper bound on the noise sensitivity. This extends recent results for the additive case in terms of coupling distances to the multiplicative case. The strength of this notion is shown in a statistical implementation for simulations and the example of a benchmark time series in paleoclimate.}, language = {en} } @article{AcevedoReichCubasch2016, author = {Acevedo, Walter and Reich, Sebastian and Cubasch, Ulrich}, title = {Towards the assimilation of tree-ring-width records using ensemble Kalman filtering techniques}, series = {Climate dynamics : observational, theoretical and computational research on the climate system}, volume = {46}, journal = {Climate dynamics : observational, theoretical and computational research on the climate system}, publisher = {Springer}, address = {New York}, issn = {0930-7575}, doi = {10.1007/s00382-015-2683-1}, pages = {1909 -- 1920}, year = {2016}, abstract = {This paper investigates the applicability of the Vaganov-Shashkin-Lite (VSL) forward model for tree-ring-width chronologies as observation operator within a proxy data assimilation (DA) setting. Based on the principle of limiting factors, VSL combines temperature and moisture time series in a nonlinear fashion to obtain simulated TRW chronologies. When used as observation operator, this modelling approach implies three compounding, challenging features: (1) time averaging, (2) "switching recording" of 2 variables and (3) bounded response windows leading to "thresholded response". We generate pseudo-TRW observations from a chaotic 2-scale dynamical system, used as a cartoon of the atmosphere-land system, and attempt to assimilate them via ensemble Kalman filtering techniques. Results within our simplified setting reveal that VSL's nonlinearities may lead to considerable loss of assimilation skill, as compared to the utilization of a time-averaged (TA) linear observation operator. In order to understand this undesired effect, we embed VSL's formulation into the framework of fuzzy logic (FL) theory, which thereby exposes multiple representations of the principle of limiting factors. DA experiments employing three alternative growth rate functions disclose a strong link between the lack of smoothness of the growth rate function and the loss of optimality in the estimate of the TA state. Accordingly, VSL's performance as observation operator can be enhanced by resorting to smoother FL representations of the principle of limiting factors. This finding fosters new interpretations of tree-ring-growth limitation processes.}, language = {en} } @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} } @unpublished{MeraTarkhanov2016, author = {Mera, Azal and Tarkhanov, Nikolai Nikolaevich}, title = {The Neumann problem after Spencer}, volume = {5}, number = {6}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-90631}, pages = {21}, year = {2016}, abstract = {When trying to extend the Hodge theory for elliptic complexes on compact closed manifolds to the case of compact manifolds with boundary one is led to a boundary value problem for the Laplacian of the complex which is usually referred to as Neumann problem. We study the Neumann problem for a larger class of sequences of differential operators on a compact manifold with boundary. These are sequences of small curvature, i.e., bearing the property that the composition of any two neighbouring operators has order less than two.}, language = {en} } @article{ZoellerHolschneider2016, author = {Z{\"o}ller, Gert and Holschneider, Matthias}, title = {The Maximum Possible and the Maximum Expected Earthquake Magnitude for Production-Induced Earthquakes at the Gas Field in Groningen, The Netherlands}, series = {Bulletin of the Seismological Society of America}, volume = {106}, journal = {Bulletin of the Seismological Society of America}, publisher = {Seismological Society of America}, address = {Albany}, issn = {0037-1106}, doi = {10.1785/0120160220}, pages = {2917 -- 2921}, year = {2016}, abstract = {The Groningen gas field serves as a natural laboratory for production-induced earthquakes, because no earthquakes were observed before the beginning of gas production. Increasing gas production rates resulted in growing earthquake activity and eventually in the occurrence of the 2012M(w) 3.6 Huizinge earthquake. At least since this event, a detailed seismic hazard and risk assessment including estimation of the maximum earthquake magnitude is considered to be necessary to decide on the future gas production. In this short note, we first apply state-of-the-art methods of mathematical statistics to derive confidence intervals for the maximum possible earthquake magnitude m(max). Second, we calculate the maximum expected magnitude M-T in the time between 2016 and 2024 for three assumed gas-production scenarios. Using broadly accepted physical assumptions and 90\% confidence level, we suggest a value of m(max) 4.4, whereas M-T varies between 3.9 and 4.3, depending on the production scenario.}, 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{ZoellerHolschneider2016, author = {Z{\"o}ller, Gert and Holschneider, Matthias}, title = {The Earthquake History in a Fault Zone Tells Us Almost Nothing about m(max)}, series = {Seismological research letters}, volume = {87}, journal = {Seismological research letters}, publisher = {Seismological Society of America}, address = {Albany}, issn = {0895-0695}, doi = {10.1785/0220150176}, pages = {132 -- 137}, year = {2016}, abstract = {In the present study, we summarize and evaluate the endeavors from recent years to estimate the maximum possible earthquake magnitude m(max) from observed data. In particular, we use basic and physically motivated assumptions to identify best cases and worst cases in terms of lowest and highest degree of uncertainty of m(max). In a general framework, we demonstrate that earthquake data and earthquake proxy data recorded in a fault zone provide almost no information about m(max) unless reliable and homogeneous data of a long time interval, including several earthquakes with magnitude close to m(max), are available. Even if detailed earthquake information from some centuries including historic and paleoearthquakes are given, only very few, namely the largest events, will contribute at all to the estimation of m(max), and this results in unacceptably high uncertainties. As a consequence, estimators of m(max) in a fault zone, which are based solely on earthquake-related information from this region, have to be dismissed.}, language = {en} } @article{LevyJimenezPaycha2016, author = {Levy, Cyril and Jimenez, Carolina Neira and Paycha, Sylvie}, title = {THE CANONICAL TRACE AND THE NONCOMMUTATIVE RESIDUE ON THE NONCOMMUTATIVE TORUS}, series = {Transactions of the American Mathematical Society}, volume = {368}, journal = {Transactions of the American Mathematical Society}, publisher = {American Mathematical Soc.}, address = {Providence}, issn = {0002-9947}, doi = {10.1090/tran/6369}, pages = {1051 -- 1095}, year = {2016}, abstract = {Using a global symbol calculus for pseudodifferential operators on tori, we build a canonical trace on classical pseudodifferential operators on noncommutative tori in terms of a canonical discrete sum on the underlying toroidal symbols. We characterise the canonical trace on operators on the noncommutative torus as well as its underlying canonical discrete sum on symbols of fixed (resp. any) noninteger order. On the grounds of this uniqueness result, we prove that in the commutative setup, this canonical trace on the noncommutative torus reduces to Kontsevich and Vishik's canonical trace which is thereby identified with a discrete sum. A similar characterisation for the noncommutative residue on noncommutative tori as the unique trace which vanishes on trace-class operators generalises Fathizadeh and Wong's characterisation in so far as it includes the case of operators of fixed integer order. By means of the canonical trace, we derive defect formulae for regularized traces. The conformal invariance of the \$ \zeta \$-function at zero of the Laplacian on the noncommutative torus is then a straightforward consequence.}, language = {en} } @article{HackHanischSchenkel2016, author = {Hack, Thomas-Paul and Hanisch, Florian and Schenkel, Alexander}, title = {Supergeometry in Locally Covariant Quantum Field Theory}, series = {Communications in mathematical physics}, volume = {342}, journal = {Communications in mathematical physics}, publisher = {Springer}, address = {New York}, issn = {0010-3616}, doi = {10.1007/s00220-015-2516-4}, pages = {615 -- 673}, year = {2016}, abstract = {In this paper we analyze supergeometric locally covariant quantum field theories. We develop suitable categories SLoc of super-Cartan supermanifolds, which generalize Lorentz manifolds in ordinary quantum field theory, and show that, starting from a few representation theoretic and geometric data, one can construct a functor U : SLoc -> S*Alg to the category of super-*-algebras, which can be interpreted as a non-interacting super-quantum field theory. This construction turns out to disregard supersymmetry transformations as the morphism sets in the above categories are too small. We then solve this problem by using techniques from enriched category theory, which allows us to replace the morphism sets by suitable morphism supersets that contain supersymmetry transformations as their higher superpoints. We construct superquantum field theories in terms of enriched functors eU : eSLoc -> eS*Alg between the enriched categories and show that supersymmetry transformations are appropriately described within the enriched framework. As examples we analyze the superparticle in 1 vertical bar 1-dimensions and the free Wess-Zumino model in 3 vertical bar 2-dimensions.}, language = {en} } @article{ShtrakovKoppitz2016, author = {Shtrakov, Slavcho and Koppitz, J{\"o}rg}, title = {Stable varieties of semigroups and groupoids}, series = {Algebra universalis}, volume = {75}, journal = {Algebra universalis}, publisher = {Springer}, address = {Basel}, issn = {0002-5240}, doi = {10.1007/s00012-015-0359-7}, pages = {85 -- 106}, year = {2016}, abstract = {The paper deals with Sigma-composition and Sigma-essential composition of terms which lead to stable and s-stable varieties of algebras. A full description of all stable varieties of semigroups, commutative and idempotent groupoids is obtained. We use an abstract reduction system which simplifies the presentations of terms of type tau - (2) to study the variety of idempotent groupoids and s-stable varieties of groupoids. S-stable varieties are a variation of stable varieties, used to highlight replacement of subterms of a term in a deductive system instead of the usual replacement of variables by terms.}, language = {en} } @article{NehringRaflerZessin2016, author = {Nehring, Benjamin and Rafler, Mathias and Zessin, Hans}, title = {Splitting-characterizations of the Papangelou process}, series = {Mathematische Nachrichten}, volume = {289}, journal = {Mathematische Nachrichten}, publisher = {Wiley-VCH}, address = {Weinheim}, issn = {0025-584X}, doi = {10.1002/mana.201400384}, pages = {85 -- 96}, year = {2016}, abstract = {For point processes we establish a link between integration-by-parts-and splitting-formulas which can also be considered as integration-by-parts-formulas of a new type. First we characterize finite Papangelou processes in terms of their splitting kernels. The main part then consists in extending these results to the case of infinitely extended Papangelou and, in particular, Polya and Gibbs processes. (C) 2015 WILEY-VCH Verlag GmbH \& Co. KGaA, Weinheim}, language = {en} } @article{Menne2016, author = {Menne, Ulrich}, title = {Sobolev functions on varifolds}, series = {Proceedings of the London Mathematical Society}, volume = {113}, journal = {Proceedings of the London Mathematical Society}, publisher = {Oxford Univ. Press}, address = {Oxford}, issn = {0024-6115}, doi = {10.1112/plms/pdw023}, pages = {725 -- 774}, year = {2016}, abstract = {This paper introduces first-order Sobolev spaces on certain rectifiable varifolds. These complete locally convex spaces are contained in the generally non-linear class of generalised weakly differentiable functions and share key functional analytic properties with their Euclidean counterparts. Assuming the varifold to satisfy a uniform lower density bound and a dimensionally critical summability condition on its mean curvature, the following statements hold. Firstly, continuous and compact embeddings of Sobolev spaces into Lebesgue spaces and spaces of continuous functions are available. Secondly, the geodesic distance associated to the varifold is a continuous, not necessarily Holder continuous Sobolev function with bounded derivative. Thirdly, if the varifold additionally has bounded mean curvature and finite measure, then the present Sobolev spaces are isomorphic to those previously available for finite Radon measures yielding many new results for those classes as well. Suitable versions of the embedding results obtained for Sobolev functions hold in the larger class of generalised weakly differentiable functions.}, language = {en} } @article{Kroencke2016, author = {Kr{\"o}ncke, Klaus}, title = {Rigidity and Infinitesimal Deformability of Ricci Solitons}, series = {The journal of geometric analysis}, volume = {26}, journal = {The journal of geometric analysis}, publisher = {Springer}, address = {New York}, issn = {1050-6926}, doi = {10.1007/s12220-015-9608-4}, pages = {1795 -- 1807}, year = {2016}, abstract = {In this paper, an obstruction against the integrability of certain infinitesimal solitonic deformations is given. Using this obstruction, we show that the complex projective spaces of even complex dimension are rigid as Ricci solitons although they have infinitesimal solitonic deformations.}, 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} } @phdthesis{Cheng2016, author = {Cheng, Yuan}, title = {Recursive state estimation in dynamical systems}, school = {Universit{\"a}t Potsdam}, pages = {84}, year = {2016}, 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} }