@article{ArenasBorgeHolthoeferGomezetal.2010, author = {Arenas, Alexandre and Borge-Holthoefer, Javier and Gomez, Sergio and Zamora-Lopez, Gorka}, title = {Optimal map of the modular structure of complex networks}, issn = {1367-2630}, doi = {10.1088/1367-2630/12/5/053009}, year = {2010}, abstract = {The modular structure is pervasive in many complex networks of interactions observed in natural, social and technological sciences. Its study sheds light on the relation between the structure and the function of complex systems. Generally speaking, modules are islands of highly connected nodes separated by a relatively small number of links. Every module can have the contributions of links from any node in the network. The challenge is to disentangle these contributions to understand how the modular structure is built. The main problem is that the analysis of a certain partition into modules involves, in principle, as much data as the number of modules times the number of nodes. To confront this challenge, here we first define the contribution matrix, the mathematical object containing all the information about the partition of interest, and then we use truncated singular value decomposition to extract the best representation of this matrix in a plane. The analysis of this projection allows us to scrutinize the skeleton of the modular structure, revealing the structure of individual modules and their interrelations.}, language = {en} } @book{BlechmanLandaRosenblum1995, author = {Blechman, Ilja I. and Landa, Polina S. and Rosenblum, Michael}, title = {Synchronization and chaotization in interacting dynamical systems}, series = {Preprint NLD}, volume = {24}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {40 S.}, year = {1995}, language = {en} } @article{BraunDitlevsenKurthsetal.2010, author = {Braun, Holger and Ditlevsen, Peter D. and Kurths, J{\"u}rgen and Mudelsee, Manfred}, title = {Limitations of red noise in analysing Dansgaard-Oeschger events}, issn = {1814-9324}, doi = {10.5194/cp-6-85-2010}, year = {2010}, abstract = {During the last glacial period, climate records from the North Atlantic region exhibit a pronounced spectral component corresponding to a period of about 1470 years, which has attracted much attention. This spectral peak is closely related to the recurrence pattern of Dansgaard-Oeschger (DO) events. In previous studies a red noise random process, more precisely a first-order autoregressive (AR1) process, was used to evaluate the statistical significance of this peak, with a reported significance of more than 99\%. Here we use a simple mechanistic two-state model of DO events, which itself was derived from a much more sophisticated ocean-atmosphere model of intermediate complexity, to numerically evaluate the spectral properties of random (i.e., solely noise-driven) events. This way we find that the power spectral density of random DO events differs fundamentally from a simple red noise random process. These results question the applicability of linear spectral analysis for estimating the statistical significance of highly non-linear processes such as DO events. More precisely, to enhance our scientific understanding about the trigger of DO events, we must not consider simple "straw men" as, for example, the AR1 random process, but rather test against realistic alternative descriptions.}, language = {en} } @unpublished{BraunFeudel1996, author = {Braun, Robert and Feudel, Fred}, title = {Supertransient chaos in the two-dimensional complex Ginzburg-Landau equation}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14099}, year = {1996}, abstract = {We have shown that the two-dimensional complex Ginzburg-Landau equation exhibits supertransient chaos in a certain parameter range. Using numerical methods this behavior is found near the transition line separating frozen spiral solutions from turbulence. Supertransient chaos seems to be a common phenomenon in extended spatiotemporal systems. These supertransients are characterized by an average transient lifetime which depends exponentially on the size of the system and are due to an underlying nonattracting chaotic set.}, language = {en} } @book{BraunFeudel1996, author = {Braun, Robert and Feudel, Fred}, title = {Supertransient chaos in the two-dimensional complex Ginzburg-Landau equation}, series = {Preprint NLD}, volume = {29}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, pages = {8 S.}, year = {1996}, language = {en} } @unpublished{BraunFeudelGuzdar1998, author = {Braun, Robert and Feudel, Fred and Guzdar, Parvez}, title = {The route to chaos for a two-dimensional externally driven flow}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14717}, year = {1998}, abstract = {We have numerically studied the bifurcations and transition to chaos in a two-dimensional fluid for varying values of the Reynolds number. These investigations have been motivated by experiments in fluids, where an array of vortices was driven by an electromotive force. In these experiments, successive changes leading to a complex motion of the vortices, due to increased forcing, have been explored [Tabeling, Perrin, and Fauve, J. Fluid Mech. 213, 511 (1990)]. We model this experiment by means of two-dimensional Navier-Stokes equations with a special external forcing, driving a linear chain of eight counter-rotating vortices, imposing stress-free boundary conditions in the vertical direction and periodic boundary conditions in the horizontal direction. As the strength of the forcing or the Reynolds number is raised, the original stationary vortex array becomes unstable and a complex sequence of bifurcations is observed. Several steady states and periodic branches and a period doubling cascade appear on the route to chaos. For increasing values of the Reynolds number, shear flow develops, for which the spatial scale is large compared to the scale of the forcing. Furthermore, we have investigated the influence of the aspect ratio of the container as well as the effect of no-slip boundary conditions at the top and bottom, on the bifurcation scenario.}, language = {en} } @unpublished{BraunFeudelSeehafer1997, author = {Braun, Robert and Feudel, Fred and Seehafer, Norbert}, title = {Bifurcations and chaos in an array of forced vortices}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14564}, year = {1997}, abstract = {We have studied the bifurcation structure of the incompressible two-dimensional Navier-Stokes equations with a special external forcing driving an array of 8×8 counterrotating vortices. The study has been motivated by recent experiments with thin layers of electrolytes showing, among other things, the formation of large-scale spatial patterns. As the strength of the forcing or the Reynolds number is raised the original stationary vortex array becomes unstable and a complex sequence of bifurcations is observed. The bifurcations lead to several periodic branches, torus and chaotic solutions, and other stationary solutions. Most remarkable is the appearance of solutions characterized by structures on spatial scales large compared to the scale of the forcing. We also characterize the different dynamic regimes by means of tracers injected into the fluid. Stretching rates and Hausdorff dimensions of convected line elements are calculated to quantify the mixing process. It turns out that for time-periodic velocity fields the mixing can be very effective.}, language = {en} } @unpublished{BoeckmannBieleNeuberetal.1997, author = {B{\"o}ckmann, Christine and Biele, Jens and Neuber, Roland and Niebsch, Jenny}, title = {Retrieval of multimodal aerosol size distribution by inversion of multiwavelength data}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14360}, year = {1997}, abstract = {The ill-posed problem of aerosol size distribution determination from a small number of backscatter and extinction measurements was solved successfully with a mollifier method which is advantageous since the ill-posed part is performed on exactly given quantities, the points r where n(r) is evaluated may be freely selected. A new twodimensional model for the troposphere is proposed.}, language = {en} } @unpublished{BoeckmannNiebsch1998, author = {B{\"o}ckmann, Christine and Niebsch, Jenny}, title = {Examination of the nonlinear LIDAR-operator : the influence of inhomogeneous absorbing spheres on the operator}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14725}, year = {1998}, abstract = {The determination of the atmospheric aerosol size distribution is an inverse illposed problem. The shape and the material composition of the air-carried particles are two substantial model parameters. Present evaluation algorithms only used an approximation with spherical homogeneous particles. In this paper we propose a new numerically efficient recursive algorithm for inhomogeneous multilayered coated and absorbing particles. Numerical results of real existing particles show that the influence of the two parameters on the model is very important and therefore cannot be ignored.}, language = {en} } @book{BoeckmannNiebsch1998, author = {B{\"o}ckmann, Christine and Niebsch, Jenny}, title = {Examination of the nonlinear LIDAR-operator : the influence of inhomogeneous absorbing spheres on operator}, series = {Preprint NLD}, volume = {47}, journal = {Preprint NLD}, publisher = {Univ. Potsdam}, address = {Potsdam}, issn = {1432-2935}, pages = {16 S. : Abb.}, year = {1998}, language = {en} } @unpublished{BoeckmannSarkoezi1999, author = {B{\"o}ckmann, Christine and Sark{\"o}zi, Janos}, title = {The ill-posed inversion of multiwavelength lidar data by a hybrid method of variable projection}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14847}, year = {1999}, abstract = {The ill-posed problem of aerosol distribution determination from a small number of backscatter and extinction lidar measurements was solved successfully via a hybrid method by a variable dimension of projection with B-Splines. Numerical simulation results with noisy data at different measurement situations show that it is possible to derive a reconstruction of the aerosol distribution only with 4 measurements.}, language = {en} } @book{BoeckmannSarkoezi1999, author = {B{\"o}ckmann, Christine and Sark{\"o}zi, Janos}, title = {The ill-posed inversion of multiwavelength lidar data by a hybrid method of variable projection}, series = {Preprint NLD}, volume = {53}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, issn = {1432-2935}, pages = {[7] S. : graph. Darst.}, year = {1999}, language = {en} } @article{CserDonnerSchwarzetal.2001, author = {Cser, Adrienn and Donner, Reik Volker and Schwarz, Udo and Feudel, Ulrike and Otto, Andreas H.}, title = {Statistical parameters of a control strategy of laser beam melt ablation}, year = {2001}, abstract = {Laser beam melt ablation - a contact-free machining process - offers several advantages compared to conventional processing mechanisms: there exists no tool wear and even extremely hard or brittle materials can be processed. During ablation the workpiece is molten by a CO2-laser beam, this melt is then driven out by the impulse of a process gas. The idea behind laser ablation is rather simple, but it has a major limitation in practical applications: with increasing ablation rates surface quality of the workpiece processed declines rapidly. At high ablation rates, depending on the process parameters different periodic-like structures can be observed on the ablated surface. These structures show a dependence on the line energy, which has been identified as a fundamental control parameter. In dependence on this parameter several regimes with different behaviours of the process have been separated. These regimes are distinguishable as well in the surfaces obtained as in the signals gained by the measurement of the process emissions. Further aim is to identify the different modes of the system and reach a deeper understanding of the dynamics of the molten material in order to understand the formation of these surface structures. With this it should be possible to influence the system in the direction of avoiding structure formation even at high ablation rates. Relying on the results on-line monitoring and control of the process should be studied.}, language = {en} } @unpublished{DemircanScheelSeehafer1999, author = {Demircan, Ayhan and Scheel, Stefan and Seehafer, Norbert}, title = {Heteroclinic behavior in rotating Rayleigh-B{\´e}nard convection}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14914}, year = {1999}, abstract = {We investigate numerically the appearance of heteroclinic behavior in a three-dimensional, buoyancy-driven fluid layer with stress-free top and bottom boundaries, a square horizontal periodicity with a small aspect ratio, and rotation at low to moderate rates about a vertical axis. The Prandtl number is 6.8. If the rotation is not too slow, the skewed-varicose instability leads from stationary rolls to a stationary mixed-mode solution, which in turn loses stability to a heteroclinic cycle formed by unstable roll states and connections between them. The unstable eigenvectors of these roll states are also of the skewed-varicose or mixed-mode type and in some parameter regions skewed-varicose like shearing oscillations as well as square patterns are involved in the cycle. Always present weak noise leads to irregular horizontal translations of the convection pattern and makes the dynamics chaotic, which is verified by calculating Lyapunov exponents. In the nonrotating case, the primary rolls lose, depending on the aspect ratio, stability to traveling waves or a stationary square pattern. We also study the symmetries of the solutions at the intermittent fixed points in the heteroclinic cycle.}, language = {en} } @unpublished{DemircanSeehafer2000, author = {Demircan, Ayhan and Seehafer, Norbert}, title = {Nonlinear square patterns in Rayleigh-B{\´e}nard convection}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14986}, year = {2000}, abstract = {We numerically investigate nonlinear asymmetric square patterns in a horizontal convection layer with up-down reflection symmetry. As a novel feature we find the patterns to appear via the skewed varicose instability of rolls. The time-independent nonlinear state is generated by two unstable checkerboard (symmetric square) patterns and their nonlinear interaction. As the bouyancy forces increase, the interacting modes give rise to bifurcations leading to a periodic alternation between a nonequilateral hexagonal pattern and the square pattern or to different kinds of standing oscillations.}, language = {en} } @unpublished{Dicken1998, author = {Dicken, Volker}, title = {Simultaneous activity and attenuation reconstruction in emission tomography}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14747}, year = {1998}, abstract = {In single photon emission computed tomography (SPECT) one is interested in reconstructing the activity distribution f of some radiopharmaceutical. The data gathered suffer from attenuation due to the tissue density µ. Each imaged slice incorporates noisy sample values of the nonlinear attenuated Radon transform (formular at this place in the original abstract) Traditional theory for SPECT reconstruction treats µ as a known parameter. In practical applications, however, µ is not known, but either crudely estimated, determined in costly additional measurements or plainly neglected. We demonstrate that an approximation of both f and µ from SPECT data alone is feasible, leading to quantitatively more accurate SPECT images. The result is based on nonlinear Tikhonov regularization techniques for parameter estimation problems in differential equations combined with Gauss-Newton-CG minimization.}, language = {en} } @book{Dicken1998, author = {Dicken, Volker}, title = {Simultaneous activity and attenuation reconstruction in emission tomography}, series = {Preprint NLD}, volume = {50}, journal = {Preprint NLD}, publisher = {Univ.}, address = {Potsdam}, issn = {1432-2935}, pages = {27 S. : graph. Darst.}, year = {1998}, language = {en} } @unpublished{DickenMaass1995, author = {Dicken, Volker and Maaß, Peter}, title = {Wavelet-Galerkin methods for ill-posed problems}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13890}, year = {1995}, abstract = {Projection methods based on wavelet functions combine optimal convergence rates with algorithmic efficiency. The proofs in this paper utilize the approximation properties of wavelets and results from the general theory of regularization methods. Moreover, adaptive strategies can be incorporated still leading to optimal convergence rates for the resulting algorithms. The so-called wavelet-vaguelette decompositions enable the realization of especially fast algorithms for certain operators.}, language = {en} } @article{EbelingMolgedeyKurthsetal.2002, author = {Ebeling, Werner and Molgedey, Lutz and Kurths, J{\"u}rgen and Schwarz, Udo}, title = {Entropy, complexity, predictability, and data analysis of time series and letter sequences}, isbn = {3-540-41324-3}, year = {2002}, abstract = {The structure of time series and letter sequences is investigated using the concepts of entropy and complexity. First conditional entropy and transinformation are introduced and several generalizations are discussed. Further several measures of complexity are introduced and discussed. The capability of these concepts to describe the structure of time series and letter sequences generated by nonlinear maps, data series from meteorology, astrophysics, cardiology, cognitive psychology and finance is investigated. The relation between the complexity and the predictability of informational strings is discussed. The relation between local order and the predictability of time series is investigated.}, language = {en} } @unpublished{EngbertScheffczykKrampeetal.1997, author = {Engbert, Ralf and Scheffczyk, Christian and Krampe, Ralf-Thomas and Rosenblum, Mikhael and Kurths, J{\"u}rgen and Kliegl, Reinhold}, title = {Tempo-induced transitions in polyrhythmic hand movements}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14380}, year = {1997}, abstract = {We investigate the cognitive control in polyrhythmic hand movements as a model paradigm for bimanual coordination. Using a symbolic coding of the recorded time series, we demonstrate the existence of qualitative transitions induced by experimental manipulation of the tempo. A nonlinear model with delayed feedback control is proposed, which accounts for these dynamical transitions in terms of bifurcations resulting from variation of the external control parameter. Furthermore, it is shown that transitions can also be observed due to fluctuations in the timing control level. We conclude that the complexity of coordinated bimanual movements results from interactions between nonlinear control mechanisms with delayed feedback and stochastic timing components.}, language = {en} }