Prof. Dr. Christof Schütte

Projects as a project leader

• CH14

  Understanding cell trajectories with sparse similarity learning

  Prof. Dr. Tim Conrad / Prof. Dr. Gitta Kutyniok / Prof. Dr. Christof Schütte

  Project heads: Prof. Dr. Tim Conrad / Prof. Dr. Gitta Kutyniok / Prof. Dr. Christof Schütte
  Project members: Nada Cvetkovic
  Duration: 01.06.2017 - 31.12.2019
  Status: running
  Located at: Freie Universität Berlin / Technische Universität Berlin / Konrad-Zuse-Zentrum für Informationstechnik Berlin
  

  Description

  In living organisms, biological cells transition from one state to another. This happens during normal cell development (e.g. aging) or is triggered by events, such as diseases. The time-ordered set of state changes is called a trajectory. Identifying these cell trajectories is a crucial part in bio-medical research to understand changes on a gene and molecular level. It allows to derive biological insights such as disease mechanisms and can lead to new biomedical discoveries and to advances in health-care. With the advent of single cell experiments such as Drop-Seq or inDrop, individual gene expression profiles of thousands of cells can be measured in a single experiment. These large data-sets allow to determine a cell's state based on its gene activity (cell expression profiles, CEPs), which can be expressed as a large feature vector representing its location in some large state space. The main problem with these experiments is that the actual time-information is lost, and needs to be recovered. The state-of-the art solution is to introduce the concept of pseudo-time in which the cells are ordered by CEP similarity. To find robust and biological meaningful trajectories based on CEPs, two main tasks have to be performed: (1) A CEP-based metric has to be learned to define pair-wise distances between CEPs. (2) Given this metric, similar CEP groups and transition paths between those groups should be identified and analysed.
  
  http://medicalbioinformatics.de/research/projects/ecmath-ch14

• CH17

  Hybrid reaction-diffusion / Markov-state model of systems with many interacting molecules

  Prof. Dr. Frank Noé / Prof. Dr. Christof Schütte

  Project heads: Prof. Dr. Frank Noé / Prof. Dr. Christof Schütte
  Project members: Dr. Mauricio del Razo Sarmina
  Duration: 01.06.2017 - 31.12.2019
  Status: running
  Located at: Freie Universität Berlin
  

  Description

  While simulations of detailed molecular structure, e.g. using atomistic or coarse- grained MD simulation is able to describe the evolution of molecular systems at length/timescales of nanometers/milliseconds, we require a way to bridge from the molecular scale to large-scale/long-time evolutions of molecular superstructures such as actin networks on the scale of micrometers/hours. Such time- and lengthscales while still maintaining some structural, and importantly single-molecule resolution, can be covered by particle-based reaction-diffusion simulations. Molecular kinetic models of small parts of the overall machinery (single molecules and small complexes) can be parametrized with high-throughput MD simulations, enhanced sampling simu- lations, possibly by incorporating constraints from experimental data. In order to ex- plore the long-range and long-time behavior of mixtures and superstructures of many molecules, we set out ot develop a rigorous and computationally efficient coupling be- tween molecular kinetics models and particle-based reaction-diffusion dynamics (Fig. 1).
  
  https://www.mi.fu-berlin.de/en/math/groups/mathlife/projects_neu/SE16/index.html

• CH21

  Data-Driven Modelling of Cellular Processes and beyond

  Prof. Dr. Tim Conrad / Dr. Stefan Klus / Prof. Dr. Christof Schütte

  Project heads: Prof. Dr. Tim Conrad / Dr. Stefan Klus / Prof. Dr. Christof Schütte
  Project members: Dr. Wei Zhang
  Duration: 01.06.2017 - 31.12.2019
  Status: running
  Located at: Konrad-Zuse-Zentrum für Informationstechnik Berlin
  

  Description

  Cellular processes are governed by diffusion, transport, and interactions of its constituents. For many processes the spatial inhomogeneity of cells is of secondary importance; modelling such processes means finding appropriate kinetic models of the underlying cellular reaction networks (CRNs). The availability of such models is key to many areas of the life sciences ranging from computational biology to system medicine and is essential for understanding the fundamentals of cellular behavior, its malfunction under external stress and its restoration by regenerative interventions.
  
  http://medicalbioinformatics.de/research/projects/ecmath-ch21

• CH-AP8

  Probing scales in equilibrated systems by optimal nonequilibrium forcing

  Prof. Dr. Christof Schütte / PD Dr. Marcus Weber

  Project heads: Prof. Dr. Christof Schütte / PD Dr. Marcus Weber
  Project members: -
  Duration: 01.10.2014 - 30.06.2022
  Status: running
  Located at: Freie Universität Berlin
  

  Description

  The dynamics of biomolecules show an inherent multiscale behaviour with cascades of time scales and strong interaction between them. Molecular dynamics (MD) simulations allow for analysis and, at least partly, understanding of this dynamical behaviour. However realistic simulations on timescales beyond milliseconds are still infeasible even on the most powerful computers, which renders the MD-based analysis of many important equilibrium processes – often processes that are related to biological function and require much longer simulation timescales – impossible. Driven by the recent progress in experimental techniques to manipulate single molecules, numerical nonequilibrium methods that attempt to bridge the timescale gap between the fastest random oscillations and the rare events that are related to the slowest function-related processes have gained enormous popularity. These methods are yet lacking both theoretical foundation and practicability, first and foremost due to the poor convergence of the corresponding numerical estimators. This project aims at exploiting ideas from stochastic control, in order (1) to analyse the influence of nonequilibrium perturbation on the statistics of a system when it is driven out of thermodynamic equilibrium and (2) to devise novel efficient importance sampling strategies based on optimal controls that speed up the sampling of the relevant rare events while giving statistical estimators with small variance and good convergence properties, beyond the asymptotic regime of large deviations theory.
  
  http://sfb1114.imp.fu-berlin.de/research/index.php?option=com_projectlog&view=project&id=1

• CH-AP10

  Multiscale modeling and simulation for spatiotemporal master equations

  Prof. Dr. Frank Noé / Prof. Dr. Christof Schütte

  Project heads: Prof. Dr. Frank Noé / Prof. Dr. Christof Schütte
  Project members: -
  Duration: 01.10.2014 - 30.06.2022
  Status: running
  Located at: Freie Universität Berlin
  

  Description

  Accurate modeling of reaction kinetics is important for understanding the functionality of biological cells and the design of chemical reactors. Depending on the particle con­centrations and on the relation between particle mobility and reaction rate constants, different mathematical models are appropriate. In the limit of slow diffusion and small concentrations, both discrete particle numbers and spatial inhomogeneities must be taken into account. The most detailed root model consists of particle-based reaction-diffusion dynamics (PBRD), where all individual par­ticles are explicitly resolved in time and space, and particle positions are propagated by some equation of motion, and reaction events may occur only when reactive species are adjacent.
  For rapid diffusion or large concentrations, the model may be coarse-grained in dif­ferent ways. Rapid diffusion leads to mixing and implies that spatial resolution is not needed below a certain lengthscale. This permits the system to be modeled via a spa­tiotemporal chemical Master equation (STCME), i.e. a coupled set of chemical Master equations acting on spatial subvolumes. The STCME becomes a chemical Master equa­tion (CME) when diffusion is so fast that the entire system is well-mixed. When particle concentrations are large, populations may be described by concentrations rather than by discrete numbers, leading to a PDE or ODE formulation.
  
  Many biological processes call for detailed models (PBRD, ST-CME or CME), but these models are extremely costly to solve. Ef.cient mathematical and computational methods are needed in order to approximate the solutions of these models with some guaranteed accuracy level. An approach to optimal or ef.cient switching between different models is, as yet, missing.
  In this project, we will set out to develop a multiscale theory for reaction kinetics processes, starting from a consistent and well-de.ned formulation of PBRD models, and including spatial scaling (PBRD -> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored. In this project, we will set out to develop a multiscale theory for reaction kinetics processes, starting from a consistent and well-de.ned formulation of PBRD models, and including spatial scaling (PBRD -> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored.-> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored. In this project, we will set out to develop a multiscale theory for reaction kinetics processes, starting from a consistent and well-de.ned formulation of PBRD models, and including spatial scaling (PBRD -> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored. In this project, we will set out to develop a multiscale theory for reaction kinetics processes, starting from a consistent and well-de.ned formulation of PBRD models, and including spatial scaling (PBRD -> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored.-> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored.-> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored. In this project, we will set out to develop a multiscale theory for reaction kinetics processes, starting from a consistent and well-de.ned formulation of PBRD models, and including spatial scaling (PBRD -> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored. In this project, we will set out to develop a multiscale theory for reaction kinetics processes, starting from a consistent and well-de.ned formulation of PBRD models, and including spatial scaling (PBRD -> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored.-> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored. In this project, we will set out to develop a multiscale theory for reaction kinetics processes, starting from a consistent and well-de.ned formulation of PBRD models, and including spatial scaling (PBRD -> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored. In this project, we will set out to develop a multiscale theory for reaction kinetics processes, starting from a consistent and well-de.ned formulation of PBRD models, and including spatial scaling (PBRD -> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored.-> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored.-> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored.-> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored. In this project, we will set out to develop a multiscale theory for reaction kinetics processes, starting from a consistent and well-de.ned formulation of PBRD models, and including spatial scaling (PBRD -> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored. In this project, we will set out to develop a multiscale theory for reaction kinetics processes, starting from a consistent and well-de.ned formulation of PBRD models, and including spatial scaling (PBRD -> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored.-> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored. In this project, we will set out to develop a multiscale theory for reaction kinetics processes, starting from a consistent and well-de.ned formulation of PBRD models, and including spatial scaling (PBRD -> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored. In this project, we will set out to develop a multiscale theory for reaction kinetics processes, starting from a consistent and well-de.ned formulation of PBRD models, and including spatial scaling (PBRD -> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored.-> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored.-> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored. In this project, we will set out to develop a multiscale theory for reaction kinetics processes, starting from a consistent and well-de.ned formulation of PBRD models, and including spatial scaling (PBRD -> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored. In this project, we will set out to develop a multiscale theory for reaction kinetics processes, starting from a consistent and well-de.ned formulation of PBRD models, and including spatial scaling (PBRD -> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored.-> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored. In this project, we will set out to develop a multiscale theory for reaction kinetics processes, starting from a consistent and well-de.ned formulation of PBRD models, and including spatial scaling (PBRD -> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored. In this project, we will set out to develop a multiscale theory for reaction kinetics processes, starting from a consistent and well-de.ned formulation of PBRD models, and including spatial scaling (PBRD -> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored.-> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored.-> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored.-> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored.-> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored. In this project, we will set out to develop a multiscale theory for reaction kinetics processes, starting from a consistent and well-de.ned formulation of PBRD models, and including spatial scaling (PBRD -> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored. In this project, we will set out to develop a multiscale theory for reaction kinetics processes, starting from a consistent and well-de.ned formulation of PBRD models, and including spatial scaling (PBRD -> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored.-> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored. In this project, we will set out to develop a multiscale theory for reaction kinetics processes, starting from a consistent and well-de.ned formulation of PBRD models, and including spatial scaling (PBRD -> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored. In this project, we will set out to develop a multiscale theory for reaction kinetics processes, starting from a consistent and well-de.ned formulation of PBRD models, and including spatial scaling (PBRD -> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored.-> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored.-> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored. In this project, we will set out to develop a multiscale theory for reaction kinetics processes, starting from a consistent and well-de.ned formulation of PBRD models, and including spatial scaling (PBRD -> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored. In this project, we will set out to develop a multiscale theory for reaction kinetics processes, starting from a consistent and well-de.ned formulation of PBRD models, and including spatial scaling (PBRD -> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored.-> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored. In this project, we will set out to develop a multiscale theory for reaction kinetics processes, starting from a consistent and well-de.ned formulation of PBRD models, and including spatial scaling (PBRD -> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored. In this project, we will set out to develop a multiscale theory for reaction kinetics processes, starting from a consistent and well-de.ned formulation of PBRD models, and including spatial scaling (PBRD -> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored.-> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored.-> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored.-> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored. In this project, we will set out to develop a multiscale theory for reaction kinetics processes, starting from a consistent and well-de.ned formulation of PBRD models, and including spatial scaling (PBRD -> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored. In this project, we will set out to develop a multiscale theory for reaction kinetics processes, starting from a consistent and well-de.ned formulation of PBRD models, and including spatial scaling (PBRD -> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored.-> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored. In this project, we will set out to develop a multiscale theory for reaction kinetics processes, starting from a consistent and well-de.ned formulation of PBRD models, and including spatial scaling (PBRD -> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored. In this project, we will set out to develop a multiscale theory for reaction kinetics processes, starting from a consistent and well-de.ned formulation of PBRD models, and including spatial scaling (PBRD -> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored.-> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored.-> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored. In this project, we will set out to develop a multiscale theory for reaction kinetics processes, starting from a consistent and well-de.ned formulation of PBRD models, and including spatial scaling (PBRD -> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored. In this project, we will set out to develop a multiscale theory for reaction kinetics processes, starting from a consistent and well-de.ned formulation of PBRD models, and including spatial scaling (PBRD -> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored.-> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored. In this project, we will set out to develop a multiscale theory for reaction kinetics processes, starting from a consistent and well-de.ned formulation of PBRD models, and including spatial scaling (PBRD -> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored. In this project, we will set out to develop a multiscale theory for reaction kinetics processes, starting from a consistent and well-de.ned formulation of PBRD models, and including spatial scaling (PBRD -> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored.-> ST-CME -> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored.-> CME) coupled to population scaling (CME -> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored.-> ODE). In particular, we aim at providing solutions for the problematic cases of having particles at diverse copy numbers (CME . ODE) and at least some slowly diffusing particles (PBRD -> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored.-> CME -> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored.-> STCME). The cascades of scales in these scenarios and efficient approximation strategies will be explored.
  
  http://sfb1114.imp.fu-berlin.de/research/index.php?option=com_projectlog&view=project&id=12

• CH-AP16

  Projection theory of transfer operators

  Prof. Dr. Christof Schütte / PD Dr. Marcus Weber

  Project heads: Prof. Dr. Christof Schütte / PD Dr. Marcus Weber
  Project members: -
  Duration: 01.01.2014 - 31.12.2017
  Status: completed
  Located at: Konrad-Zuse-Zentrum für Informationstechnik Berlin
  

  Description

  The main object is analysing sufficent ways to compute a galerkin approximation of the transfer operator. This includes to study the theoretical properties of a galerkin approximation of specific systems and to development algorithms which guarantee those properties for the numerical approximation. Furthermore, one is interested in making this computation as cheap as possible.
  
  http://www.zib.de/projects/projection-theory-transfer-operators

• CH2

  Sparse compressed sensing based classifiers for -omics mass-data

  Prof. Dr. Tim Conrad / Prof. Dr. Gitta Kutyniok / Prof. Dr. Christof Schütte

  Project heads: Prof. Dr. Tim Conrad / Prof. Dr. Gitta Kutyniok / Prof. Dr. Christof Schütte
  Project members: Nada Cvetkovic / Martin Genzel
  Duration: -
  Status: completed
  Located at: Freie Universität Berlin / Technische Universität Berlin
  

  Description

  Tumor diseases rank among the most frequent causes of death in Western countries coinciding with an incomplete understanding of the underlying pathogenic mechanisms and a lack of individual treatment options. Hence, early diagnosis of the disease and early relapse monitoring are currently the best available options to improve patient survival. In this project, we aim for the identification of disease specific sets of biological signals that reliably indicate a disease outbreak (or status) in an individual. Such biological signals (e.g. proteomics or genomics data) are typically very large (millions of dimensions), which significantly increases the complexity of algorithms for analyzing the parameter space or makes them even infeasible. However, these types of data usually exhibit a very particular structure, and at the same time, the set of disease specific features is very small compared to the ambient dimension. Such a high-dimensional setting naturally calls for the application of the concept of sparse classifiers, which has been extensively studied in the fields of compressed sensing and statistical learning during the last decade. Our research focuses on both algorithmic improvements of available methods as well as theoretical results such as recovery guarantees for general data models.
  
  http://medicalbioinformatics.de/research/projects/ecmath-ch2

• CH6

  Uncertainty quantification for Bayesian inverse problems with applications to systems biology

  Prof. Dr. Susanna Röblitz / Prof. Dr. Christof Schütte

  Project heads: Prof. Dr. Susanna Röblitz / Prof. Dr. Christof Schütte
  Project members: Dr Ilja Klebanov
  Duration: -
  Status: completed
  Located at: Konrad-Zuse-Zentrum für Informationstechnik Berlin
  

  Description

  In biotechnology, systems biology, or reaction engineering one is faced with large systems of ordinary differential equations (ODE) that are used to describe the kinetics of the reaction network of interest. These ODE models contain a large number of mostly unknown kinetic parameters that one needs to infer from usually sparse and noisy experimental data. Typically, inverse problems like classical parameter identification are associated with ill-posed behaviour. However, Bayesian approaches can be used to recover joint parameter distributions and allow for the quantification of uncertainty and risk in a way demanded by the applications. In this project, we want to overcome the computational limitations of classical Markov-chain Monte-Carlo methods by developing new algorithmic approaches to Bayesian inverse problems using, e.g., sparse approximation results or empirical Bayes methods. The methods will directly be applied to large-scale networks in systems biology.
  
  http://www.zib.de/projects/UQ-systems-biology

• CH7

  Network-of-Network based -omics data integration

  Prof. Dr. Tim Conrad / Prof. Dr. Christof Schütte

  Project heads: Prof. Dr. Tim Conrad / Prof. Dr. Christof Schütte
  Project members: -
  Duration: -
  Status: completed
  Located at: Freie Universität Berlin
  

  Description

  Project Background

  Pancreatic cancer is the fifth leading cause of cancer death in Germany (see DKFZ Report, 2010). It is estimated that in 2030 it will be the second leading cause of cancer death incurring a cost of about 15,8 Billion US-Dollar worldwide to the public health systems.

  Cancer is a systems disease

  "Cancer is no more a disease of cells than a traffic jam is a disease of cars. A lifetime of study of the internal-combustion engine would not help anyone to understand our traffic problems.'" (Smithers1962). It is accepted that gene mutations are part of the process of cancer, but mutations alone are not enough. Cancer involves an interaction between neoplastic cells and surrounding tissue on many different levels, e.g. interaction of RNA molecules, proteins, and metabolites. But most available models are limited to only one or very few levels of interactions and describe a rather static view.

  From single to multi source: data integration on a systems level

  Current high-throughput -omics technologies have dramatically eased the production of part lists for a variety of organisms. What is still missing are the dynamic interactions among an organism's molecular parts, and the interactions between different biological levels, such as transcriptomics and proteomics. This is pivotal to better understanding of an organism's biology, and - in our case - to understand pancreas cancer.
  
  Therefore, the aim of this project is two-fold: (1) use data acquired in our earlier projects to create a holistic integration of the aforementioned sources and levels for modeling pancreas cancer, which we call Network-of-Networks or short: NoN (in our context networks of different -omics levels, such as genomics, transcriptomics, proteomics and metabolomics. (2) A NoN is a very large and complex object and its structure differs significantly from other biological networks. Thus, new methods for complexity reduction and analyzing NoNs will be developed in this project.

  The goal

  In this project we aim to develop a new method that can be used to solve this task: the identification of minimal, yet robust fingerprints from very high-dimensional, noisy -omics data. Our method will be based on ideas from the areas of compressed sensing and machine learning.
  
  http://medicalbioinformatics.de/research/projects/ecmath-ch7