Successfully completed projects

Financed by others

  • CH-AP1

    Interacting stochastic partial differential equations, combinatorial stochastic processes and duality in spatial population dynamics

    Prof. Dr. Jochen Blath

    Project heads: Prof. Dr. Jochen Blath
    Project members: -
    Duration: 01.03.2013 - 30.09.2015
    Status: completed
    Located at: Technische Universität Berlin

    Description

    The method of duality is a mathematical formalism that allows one to establish close connections between two stochastic Markov processes with respect to a class of `duality functions'. If a formal duality is established, it is often possible to study important properties of a `complicated' spatial stochastic system, such as longtime-behaviour or properties of its genealogy, by analysing the properties of a simpler, typically discreteor combinatorial, dual process. This method has been used with great success for many processes in the theory of interacting particle systems and interacting stochastic (P)DEs modeling the evolution of populations (e.g. the stepping stone or the Wright-Fisher model). In the last years, important progress has been achieved. However, there is still no systematic theory of duality (“finding dual processes is something of a black art", A. Etheridge [Eth06] p.519), and many systems of theoretical and practical importance await further analysis. This project has three main objectives. Firstly, we would like to transfer several concrete questions about certain SPDEs to questions about their dual processes (I). Secondly, we are interested in the long-term properties of the dual processes themselves (II). Finally, we aim towards a systematic analysis of the method of duality.

    http://www.dfg-spp1590.de/abstracts.php#27
  • CH-AP11

    Wear Simulation of Knee Implants and Shape Optimization for Patient-group specific Wear Minimization

    Prof. Dr. Ralf Kornhuber / Dr. Martin Weiser

    Project heads: Prof. Dr. Ralf Kornhuber / Dr. Martin Weiser
    Project members: -
    Duration: 01.07.2013 - 30.12.2016
    Status: completed
    Located at: Konrad-Zuse-Zentrum für Informationstechnik Berlin

    Description

    For the market admittance of joint implants, a standardized wear test has to be performed. During the design phase, similar tests are necessary as well. Those tests are very cost and time expensive. The project aims at the development of simulation and optimization methods for substituting some of the design phase tests by simulations. Additionally, the design process shall be accelerated by shape optimization, and the offered implants be tailored to the patient population by taking different patient groups into account.

    Focus of the work at ZIB is the long-time integration of wear trajectories. The implant geometry is modified due to wear, which in turn changes the wear rate. The evolution is determined by the wear of one load cycle, the simulation of which is computationally expensive. We develop adaptive methods for controlling tolerance, order, and time step for an efficient simulation of many load cycles.

    http://www.zib.de/projects/wear-simulation-knee-implants-and-shape-optimization-patient-group-specific-wear-minimization
  • CH-AP13

    Adaptive Konformationsdynamik mit Anwendung auf Rhodopsinaktivierung

    Prof. Dr. Frank Noé

    Project heads: Prof. Dr. Frank Noé
    Project members: -
    Duration: 01.07.2012 - 30.06.2015
    Status: completed
    Located at: Freie Universität Berlin

    Description

    Rare molecular events such as folding of proteins or nucleic acids, ligand binding, conformational changes or macromolecular aggregation are the basis of all life processes. Besides experimental techniques, molecular dynamics (MD) simulation is an established tool to analyze such processes. However, the usefulness of MD for investigating biological processes is limited by the sampling problem: Due to the high computational effort involved in simulating biomolecules at atomistic resolution, the accessible simulation times are much too short to find the biologically relevant conformations and make statistically reliable statements about transition rates. This problem also hinders the improvement of molecular models towards the reliable prediction of experimental observables. In the proposed work we will develop an adaptive conformation dynamics (ACD) which facilitates the simulation of slow biomolecular processes on small CPU clusters using atomistic models. This method will be applied in order to elucidate the detailed structural mechanism of the activation of the G-protein coupled receptor Rhodopsin.

    http://compmolbio.biocomputing-berlin.de/index.php/projects/93-dfg825-3-1
  • CH-AP15

    Generalized tensor methods in quantum chemistry

    Prof. Dr. Reinhold Schneider

    Project heads: Prof. Dr. Reinhold Schneider
    Project members: -
    Duration: 01.06.2013 - 31.05.2016
    Status: completed
    Located at: Technische Universität Berlin

    Description

    The computation of the electronic structure is of utmost importance for the task of molecular engineering in modern chemistry and material science. In this context, the accurate computation of the electron correlation is a fundamental and extremely difficult problem. In contrast to the tremendous progress made in calculating weakly correlated systems by Density Functional Theory (DFT) for extended systems or Coupled Cluster Methods for highly accurate calculations, there are two major types of systems for which current quantum chemical methods have deficiencies: (1) Open-shell systems with a large number of unpaired electrons, as they occur in multiple transition metal complexes or in molecular magnets; (2) Extended or periodic systems without a band gap, where the limit of the applicability of the available size consistent methods is reached.The aim of this proposal is to develop a general tensor network state (TNS) based algorithm that can be applied efficiently to these open problems of quantum chemistry. Realization of such an algorithm relies on carrying out a variety of complex tasks. Several new formal methods and methodological concepts of tensor decompositions will have to be designed to comply with the specific, nonlocal nature of the Hamiltonian, and to this end, the applicants will join their rather complementary expertise regarding the powerful DMRG method and similar recent developments from physics, mathematics and information technology. To arrive at an efficient implementation of the quantum chemistry TNS algorithm, our contributions will be implemented and tested based on existing program structures of the QC-DMRG- Budapest [Legeza-2011] and the TTNS-Vienna [Murg-2010c] codes.

    http://gepris.dfg.de/gepris/projekt/234056486?language=en
  • CH-AP17

    The mathematical analysis of interacting stochastic oscillators

    Prof. Dr. Wilhelm Stannat

    Project heads: Prof. Dr. Wilhelm Stannat
    Project members: -
    Duration: 01.11.2011 - 30.04.2016
    Status: completed
    Located at: Technische Universität Berlin

    Description

    State-the-art, own contribution: Rigorous mathematical models for spatialy extended neurons and neural systems under the influence of noise will be developed and analysed using the mathematical theory of stochastic evolution equations, in particular stochastic partial differential equations (see [6]). We will take into account thermal noise modelling local exterior forces acting on a couple of adjacent neurons but also parametric noise modelling uncertainties in the parameters. The impact of noise on the whole system will then be analyzed rigorously, to quantify, e.g., the probability for the propagation failure of an action potential. There are only few applications of the mathematical theory of stochastic evolution equations to neural systems subject to noise (see [1,2,8,10]). In particular, the recent developments of the theory based on the semigroup approach for mild solutions and the analysis of the associated Kolmogorov operator (see [9]) has so far only been applied to stochastic FitzHugh Nagumo systems in [4,5].

    Cited references:
    • [1] Albeverio S, Cebulla C (2007) Synchronizability of Stochastic Network Ensembles in a Model of Interacting Dynamical Units. Physica A Stat. Mech. Appl. 386, 503-512.
    • [2] Albeverio S, Cebulla C (2008) Synchronizability of a Stochastic Version of FitzHugh-Nagumo Type Neural Oscillator Networks, Preprint, SFB 611, Bonn.
    • [3] Blömker D (2007) Amplitude Equations for Stochastic Partial Differential Equations, World Scientific, New Jersey.
    • [4] Bonaccorsi S, Marinelli C, Ziglio G (2008) Stochastic FitzHugh-Nagumo equations on networks with impulsive noise, EJP 13, 1362-1379.
    • [5] Bonaccorsi S, Mastrogiacomo E (2007) Analysis of the stochastic FitzHugh-Nagumo system, Technical Report UTM 719, Mathematics, Trento, arXiv:0801.2325.
    • [6] Da Prato G, Zabczyk, J (1992) Stochastic Equations in Infinite Dimensions, Cambridge University Press, Cambridge.
    • [7] Es-Sarhir A Stannat W (2008) Invariant measures for Semilinear SPDE's with local Lipschitz Drift Coefficients and applications, Journal of Evolution Equations 8, 129-154.
    • [8] Kallianpur G, Wolpert R (1984) Infinite dimensional stochastic differential equation models for spatially distributed neurons, Appl. Math. Optim. 12, 125-172.


    https://www.bccn-berlin.de/Research/Projects_II/Branch_A/A11/
  • CH-AP18

    Numerical analysis and simulation of cooperative phenomena in interacting stochastic oscillators

    Prof. Dr. Wilhelm Stannat

    Project heads: Prof. Dr. Wilhelm Stannat
    Project members: -
    Duration: 01.05.2013 - 30.04.2016
    Status: completed
    Located at: Technische Universität Berlin

    Description

    State-the-art, own contribution: In contrast to the case of deterministic reaction diffusion systems there are only few publications on the numerical analysis of stochastic reaction diffusion systems arising in neuroscience, like e.g. stochastic FitzHugh Nagumo systems (see [2,6,7]). From the neuroscience perspective in particular the numerical analysis of stochastic reaction diffusion systems exhibiting various spatial patterns based e.g. on partial synchronization are of interest (see [8] and references therein). From the mathematical viewpoint a major difficulty comes from the fact that the coefficients of the systems typically only satisfy a one-sided Lipschitz condition that cannot be controlled easily if perturbed with stochastic forcing terms. Recent results in the numerical analysis of stochastic differential equations with non-Lipschitz coefficients show that their numerical approximation has to be carried out with additional care (see [3]) in order to validate simulation results. We will be therefore interested in development and rigorous mathematical analysis of the numerical approximation of stochastic reaction diffusion systems in the excitable regime. There is a considerable amount of work in the physics literature on the influence of noise in excitable reacton diffusion systems (see [5] for a survey). On the other hand there is only a limited quantitative understanding of the influence of the stochastic forcing terms on the various effects like wave speed or nucleation of wave patterns. Certainly, spatial correlation of the noise terms will play a crucial role, which will be studied also systematically within this project.

    Cited references:
    • [1] Dahlem M A, Graf R,Strong A J, Dreier J P, Dahlem Y A, Sieber M, Hanke W, Podoll K, Schöll E (2010) Two-dimensional wave patterns of spreading depolarization: Retracting, re-entrant, and stationary waves, Physica D 239, 889-903.
    • [2] DeVille R E L, Vanden-Eijnden E (2007) Wavetrain response of an excitable medium to local stochastic forcing, Nonlinearity 20, 51-74.
    • [3] Hutzenthaler M, Jentzen A, Kloeden P E (2011) Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 467, 1563–1576.
    • [4] Laing C, Lord G J (Eds.), Stochastic Methods in Neuroscience (2010) Oxford University Press, Oxford.
    • [5] Lindner B, Garcia-Ojalvo J, Neiman A, Schimansky-Geier L (2004), Effects of noise in excitable systems, Physics Reports 392, 321-424.
    • [6] Shardlow T (2005) Numerical simulation of stochastic PDEs for excitable media, J. Comput. Appl. Math. 175, 429-446.
    • [7] Shardlow T (2004) Nucleation of waves in excitable media, Multiscale Model. Simul. 3, 151-167.
    • [8] Tass P (1999) Phase Resetting in Medicine and Biology - Stochastic Modelling and Data Analys, Springer, Berlin.


    https://www.bccn-berlin.de/Research/Projects_II/Branch_A/A12/
  • CH-AP21

    pH-dependent opioids

    PD Dr. Marcus Weber

    Project heads: PD Dr. Marcus Weber
    Project members: -
    Duration: 01.10.2012 - 30.06.2016
    Status: completed
    Located at: Konrad-Zuse-Zentrum für Informationstechnik Berlin

    Description

    The goal of this project is design of pain relief drugs (opioids), which should be active only in inflamed tissue and therefore have reduced side effects compared to conventional opioids. We managed to develop a candidate, which was synthesized by the ASCA GmbH in Berlin. The opioid is currently undergoing in-vivo and in-vitro experiments at the Charité Berlin.

    http://www.zib.de/projects/ph-dependent-opioids
  • CH-AP22

    Transformation products of trace pollutants

    PD Dr. Marcus Weber

    Project heads: PD Dr. Marcus Weber
    Project members: -
    Duration: 01.11.2011 - 31.10.2014
    Status: completed
    Located at: Konrad-Zuse-Zentrum für Informationstechnik Berlin

    Description

    Das am 01. November 2011 gestartete Projekt TransRisk richtet den Blick besonders auf Transformationsprodukte, die durch oxidativen Abbau aus Spurenstoffen hervorgehen. Das daraus entstehende Risiko wird genauer analysiert und in ein handlungsorientiertes Risikomanagementkonzept integriert. Um einen weitergehenden Abbau von Spurenstoffen und eine Minimierung der Bildung von Transformationsprodukten zu erreichen, werden in TransRisk verschiedene Verfahrenskombinationen aus konventionellen Aufreinigungsverfahren wie z.B. Nitrifikation mit erweiterten Behandlungstechniken wie beispielsweise Ozonung und Aktivkohlefiltration kombiniert. Darüber hinaus werden aber auch neue Verfahren wie die Verwendung von Eisenbakterien in der biologischen Abwasserreinigung detailliert untersucht. Weitere Schwerpunkte von TransRisk sind neu aufkommende Krankheitserreger und die antibiotikaresistenten Keime. Hierbei werden neue Nachweismethoden entwickelt, um die Verbreitung dieser Bakterien besser zu verstehen und geeignete Maßnahmen einleiten zu können. Die erzielten Projektergebnisse werden in der Modellregion Donauried mit den Betroffenen vor Ort diskutiert und – soweit möglich – auch umgesetzt. TransRisk ist ein Verbundprojekt, welches sich aus insgesamt 15 Teilprojekten von 14 Institutionen wie Universitäten, Wasserversorgern, Verbänden, Industrie und Forschungseinrichtungen zusammensetzt. TransRisk wird durch das Bundesministerium für Bildung und Forschung (BMBF) im Förderschwerpunkt „NaWaM - Nachhaltiges Wassermanagement“ im Rahmen der Fördermaßnahme „RiSKWa - Risikomanagement von neuen Schadstoffen und Krankheitserregern im Wasserkreislauf“ gefördert. Der Förderschwerpunkt NaWaM bündelt die Aktivitäten des BMBF im Bereich der Wasserforschung innerhalb des BMBF-Rahmenprogramms „FONA - Forschung für nachhaltige Entwicklungen“.

    http://www.transrisk-projekt.de/TRANSRISK/DE/01_Home/home_node.html
  • CH-TU23

    Tractable recovery of multivariate functions from limited number of samples

    Dr. Jan Vybiral

    Project heads: Dr. Jan Vybiral
    Project members: Anton Kolleck
    Duration: 01.06.2014 - 30.04.2015
    Status: completed
    Located at: Technische Universität Berlin

    Description



  • CH-AP23

    Regularity, complexity, and approximability of electronic wavefunctions

    Prof. Dr. Harry Yserentant

    Project heads: Prof. Dr. Harry Yserentant
    Project members: -
    Duration: 01.10.2013 - 30.09.2016
    Status: completed
    Located at: Technische Universität Berlin

    Description

    The project considers the electronic Schrödinger equation of quantum chemistry that describes the motion of N electrons under Coulomb interaction forces in a field of clamped nuclei. Solutions of this equation depend on 3N variables, three spatial dimensions for each electron. Approximating the solutions is thus inordinately challenging. It is conventionally believed that the accuracy cannot be systematically improved without the effort truly exploding for larger numbers of electrons and that a reduction to simplified models, such as those of the Hartree-Fock method or density functional theory, is the only tenable approach for the approximation of the solutions. Results of the applicant indicate that this conventional wisdom need not be ironclad: the regularity of the solutions, which increases with the number of electrons, the decay behavior of their mixed derivatives, and the antisymmetry enforced by the Pauli principle contribute properties that allow these functions to be approximated with an order of complexity which comes arbitrarily close to that of a system of two electrons or even only one electron. Goal of the project is to extend and refine these results and to identify structural properties of the wavefunctions that could ideally enable breaking the curse of dimensionality and to develop the present approximation methods further to true discretications of the Schrödinger equation.

    http://www.dfg-spp1324.de/abstracts.php?lang=de#20
  • CH-AP26

    Branching random walks in random environment with a special focus on the intermittent behavior of the particle flow

    Prof. Dr. Wolfgang König

    Project heads: Prof. Dr. Wolfgang König
    Project members: -
    Duration: 01.04.2013 - 31.08.2016
    Status: completed
    Located at: Weierstraß-Institut

    Description

    We study the long-time behaviour of branching random walk in random environment (BRWRE) on the d-dimensional lattice. We consider one of the basic models, which includes migration and branching/killing of the particles, given a random potential of spatially dependent branching/killing rates. Based on the observation that the expectation of the population size over the migration and the branching and killing is equal to the solution to the well-known and much-studied parabolic Anderson model (PAM), we will use our understanding of the long-time behaviour of the PAM to develop a detailed picture of the BRWRE. Furthermore, we will exploit methods that were successful in the treatment of the PAM to prove at least part of this picture. Particular attention is payed to the study of the concentration of the population in sites that determine the long-time behaviour of the PAM, which shows a kind of intermittency. One fundamental thesis that we want to make precise and rigorous is that the overwhelming contribution to the total population size of the BRWRE comes from small islands where most of the particles travel to and have a extremely high reproduction activity. We aim at a detailed analysis for the case of the random potential being Pareto-distributed, in which case the rigorous study of the PAM has achieved a particularly clear picture. This project has the following four main goals. I. For a variety of random potentials, we derive large-time asymptotics for the n-th moments of the local and total population size, based on techniques from the study of the PAM. II. We want to understand and identify the limiting distributions of the global population size by a finer analysis for Pareto-distributed potentials. III. We want to investigate, for Pareto-distributed potentials, the long-time (de)correlation properties of the evolution of the particles such as aging, in particular, slow/fast evolution phenomena and what type of aging functions will appear. IV. We want to study, for Paretodistributed potentials, almost surely with respect to the potential, the particle flow of the BRWRE in a geometric sense by finding trajectories along which most of the particles travel and branch, in particular the sites and the time intervals where, respectively when, most of the particles show an extremely high reproduction activity.

    http://www.dfg-spp1590.de/abstracts.php#34
  • CH-AP27

    Application of rough path theory for filtering and numerical integration methods

    Prof. Dr. Peter Karl Friz / Prof. Dr. Wilhelm Stannat

    Project heads: Prof. Dr. Peter Karl Friz / Prof. Dr. Wilhelm Stannat
    Project members: -
    Duration: 01.11.2011 - 31.10.2014
    Status: completed
    Located at: Technische Universität Berlin

    Description

    In 1998 T. Lyons (Oxford) suggested a new approach for the robust pathwise solution of stochastic di fferential equations which is nowadays known as the rough path analysis. Based on this approach a new class of numerical algorithms for the solution of stochastic differential equations have been developed. Recently, the rough path approach has been successfully extended also to stochastic partial di fferential equations. In stochastic filtering, the (unnormalized) conditional distribution of a Markovian signal observed with additive noise is called the optimal fi lter and it can be described as the solution of a stochastic partial diff erential equation which is called the Zakai equation. In the proposed project we want to apply the rough path analysis to a robust pathwise solution of the Zakai equation in order to construct robust versions of the optimal filter. Subsequently, we want to apply known algorithms based on the rough path approach to the numerical approximation of these robust estimators and further investigate their properties.

    http://www.dfg-spp1324.de/abstracts.php?lang=de#8
  • CH-AP3

    Multiple testing under unspecified dependency structure

    Dr. Thorsten Dickhaus

    Project heads: Dr. Thorsten Dickhaus
    Project members: -
    Duration: 01.04.2012 - 31.03.2015
    Status: completed
    Located at: Humboldt Universität Berlin

    Description

    Multiple hypotheses testing has emerged as one of the most active research fields in statistics over the last 10-15 years, contributing at present approximately 8% of all articles in the four leading methodological statistics journals (data from Benjamini, 2010). This growing interest is especially driven by large-scale applications, such as in genomics, proteomics or cosmology. Many new multiple type I and type II error criteria like the meanwhile quite popular “false discovery rate” (FDR) have recently been propagated and published together with explicit algorithms for controlling them. A broad class of these methods employs marginal test statistics or p-values, respectively, for each individual hypothesis and a set of critical constants with which they have to be compared. Up to now, only under joint independence of all marginal p-values the behaviour of such methods is understood well. Moreover, under unspecified dependence the type I error level is often not kept accurately or not fully exhausted. This holds true especially for the FDR or related measures and offers room for improvements of those procedures with respect to type I error control and power. An adaptation to the dependency structure can therefore lead to a gain in validity (type I error rate is kept accurately) and efficiency (quantified by multiple power measures). In this project, a general theory of the usage of parametric copulae methods in this multiple testing shall be developed. This will be flanked by structural assumptions regarding the multivariate distribution of p-values reducing the complexity of the problem, for instance, the dimensionality of the copula parameter. Moreover, we will develop resampling techniques for empirical calibration of multiple testing thresholds in the case of unspecified dependency.

    https://www.mathematik.hu-berlin.de/de/for1735/projects_old/multipleTesting
  • CH-AP4

    Statistical inference methods for behavioral genetics and neuroeconomics

    Dr. Thorsten Dickhaus

    Project heads: Dr. Thorsten Dickhaus
    Project members: -
    Duration: 01.07.2013 - 31.03.2015
    Status: completed
    Located at: Humboldt Universität Berlin

    Description

    The proposed project contributes to fundamental research in behavioral genetics and neuroeconomics by developing refined statistical inference methods for data generated in these fields. In particular, techniques for multiple hypotheses testing will be refined, adapted and newly worked out. Multiple tests are needed in behavioral genetics in order to analyze associations between many genetic markers and behavioral phenotypes simultaneously. In neuroeconomics, high-dimensional and spatially clustered functional magnetic resonance imaging time series have to be analyzed with multiple testing techniques. We will apply the methods resulting from the research in this project to risk preference and genetics data that we have compiled in prior work. Furthermore, our methodological contributions will be applicable in many other fields, too: High-dimensional categorical data are also prevalent, for example, in genetic epidemiology and high-dimensional hierarchical data structures occur for instance in spatial statistics or in the context of the analysis of variance with many groups.

    http://gepris.dfg.de/gepris/projekt/239049500
  • CH-AP5

    EPILYZE - DNA Methylierungs-Signaturen als innovative Biomarker für die quantitative und qualitative Analyse von Immunzellen, Subproject C

    Dr. Thorsten Dickhaus

    Project heads: Dr. Thorsten Dickhaus
    Project members: -
    Duration: 01.12.2012 - 31.03.2015
    Status: completed
    Located at: Humboldt Universität Berlin

    Description



    http://foerderportal.bund.de/foekat/jsp/SucheAction.do?actionMode=view&fkz=031A191A#
  • CH-AP6

    Numerische Analysis Hamiltonscher partieller Differentialgleichungen und hochdimensionaler Probleme

    Dr. Ludwig Gauckler

    Project heads: Dr. Ludwig Gauckler
    Project members: -
    Duration: 01.06.2014 - 31.05.2016
    Status: completed
    Located at: Technische Universität Berlin

    Description

    Numerical discretizations of Hamiltonian partial differential equations and differential equations in high dimensions shall be analysed in the project. On the one hand, qualitative properties of numerical methods for the discretization in time such as splitting and Runge-Kutta methods will be investigated. In particular, we will pursue the question if and on which time intervals a numerical method is able to reproduce the stability of waves, which is studied in detail in the mathematical analysis of the equations. On the other hand, the analysis of approximations in high spatial dimensions will be the second key activity in the project. Approximations on tensor manifolds shall be analysed with respect to their approximation properties, but also their long-time behaviour. Such approximations are used successfully in quantum dynamics in the case of the high dimensional linear Schrödinger equation. In addition, the convergence of numerical methods for the chemical master equation, an important equation in biology and chemistry, will be studied on the basis of recent regularity results.

    http://www.tu-berlin.de/?id=149224

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