ZIB-Report
Refine
Year of publication
Document Type
- ZIB-Report (1754)
- Doctoral Thesis (10)
- Habilitation (10)
- Article (5)
- In Proceedings (1)
Keywords
- integer programming (33)
- mixed integer programming (32)
- optimal control (29)
- KOBV (28)
- Kooperativer Bibliotheksverbund Berlin-Brandenburg (24)
- Bibliotheksverbund (20)
- Mixed Integer Programming (20)
- Integer Programming (17)
- line planning (14)
- mixed-integer programming (14)
Institute
- ZIB Allgemein (909)
- Mathematical Optimization (429)
- Numerical Mathematics (196)
- Visual and Data-centric Computing (92)
- Visual Data Analysis (88)
- Mathematical Optimization Methods (71)
- Mathematics of Transportation and Logistics (66)
- Computational Medicine (62)
- Digital Data and Information for Society, Science, and Culture (55)
- Applied Algorithmic Intelligence Methods (47)
19-45
Following axon pathfinding, growth cones transition from stochastic filopodial exploration to the formation of a limited number of synapses. How the interplay of filopodia and synapse assembly ensures robust connectivity in the brain has remained a challenging problem. Here, we developed a new 4D analysis method for filopodial dynamics and a data-driven computational model of synapse formation for R7 photoreceptor axons in developing Drosophila brains. Our live data support a 'serial synapse formation' model, where at any time point only a single 'synaptogenic' filopodium suppresses the synaptic competence of other filopodia through competition for synaptic seeding factors. Loss of the synaptic seeding factors Syd-1 and Liprin-α leads to a loss of this suppression, filopodial destabilization and reduced synapse formation, which is sufficient to cause the destabilization of entire axon terminals. Our model provides a filopodial 'winner-takes-all' mechanism that ensures the formation of an appropriate number of synapses.
SC-99-33
We describe a novel method for continuously transforming two triangulated models of arbitrary topology into each other. Equal global topology for both objects is assumed, extensions for genus changes during metamorphosis are provided. The proposed method addresses the major challenge in 3D metamorphosis, namely specifying the morphing process intuitively, with minimal user interaction and sufficient detail. Corresponding regions and point features are interactively identified. These regions are parametrized automatically and consistently, providing a basis for smooth interpolation. Utilizing suitable 3D interaction techniques a simple and intuitive control over the whole morphing process is offered.
01-32
By combining techniques of preparation, histology, confocal microscopy, data visualization and data processing, we have created and recently published a standard brain model for drosophila and honey bee brains. This report describes the algorithms and implementation of the corresponding software modules. At the same time it serves as a user's guide for scientist who want to reproduce the results for differerent species or mutants.
02-34
We consider the design of transparent optical networks from a practical perspective. Network operators aim at satisfying the communication demands at minimum cost. Such an optimization involves three interdependent planning issues: the dimensioning of the physical topology, the routing of lightpaths, and the wavelength assignment. Further topics include the reliability of the configuration and sparse wavelength conversion for efficient use of the capacities. In this paper, we investigate this extensive optical network design task. Using a flexible device-based model, we present an integer programming formulation that supports greenfield planning as well as expansion planning on top of an existing network. As solution method, we propose a suitable decomposition approach that separates the wavelength assignment from the dimensioning and routing. Our method in particular provides a lower bound on the total cost which allows to rate the solution quality. Computational experiments on realistic networks approve the solution approach to be appropriate.
TR-93-12
TR-94-10
The first part of the report contains a lecture presented at ``Scientific Computing in der Theoretischen Physik'', a workshop organized by the DMV-Fachgruppe Scientific Computing in cooperation with the GAMM-Fachauschuß Scientific Computing at Freie Universit{ä}t Berlin in March 1994. To complete this lecture, a slightly modified version of TR 93-12 is appended.
TR-94-05
Results from finite-element-calculations are usually visualized by colored surface- and contour-line-plots or polygonal patches or simply displaced lines and grids. In computer graphics however more advanced techniques like texture-mapping and NURBS are well established and there exist efficient algorithms and implementations. We show that these techniques are not only easy to use, but form a very natural and far more efficient approach for visualization of higher order finite-element's solutions like in $p$- and $h$-$p$-version. Texture-mapping is useful for displaying vector-valued data, too.
SC-95-18
The $h$-$p$-version of finite-elements delivers a sub-exponential convergence in the energy norm. A step towards a full adaptive implementation is taken in the context of unstructured meshes of simplices with variable order $p$ in space. Both assumptions lead to desirable properties of shape functions like symmetry, $p$-hierarchy and simple coupling of elements. In a first step it is demonstrated that for standard polynomial vector spaces on simplices not all of these features can be obtained simultaneously. However, this is possible if these spaces are slightly extended or reduced. Thus a new class of polynomial shape functions is derived, which are especially well suited for three dimensional tetrahedra. The construction is completed by directly minimizing the condition numbers of the arising preconditioned local finite element matrices. The preconditioner is based on two-step domain decomposition techniques using a multigrid solver for the global linear problem $p=1$ and direct solvers for local higher order problems. Some numerical results concerning an adaptive (feedback) version of $h$-$p$ finite elements are presented.
SC-95-24
A set of adaptive algorithms for quadrature on multi-dimensional polyhedral domains is presented. Several kinds of refinement are discussed, covering local improvement of quadrature order and splitting the domain into sub-domains, resulting in isotropic, graded or anisotropic grids. The algorithms are pure local heuristics using no a priori knowledge or tuning parameters. This approach was motivated by results from finite element theory for optimal approximation results. Numerical experiments show the optimality of pure local greedy-like algorithms for singularity-type functions typically occurring in finite element computations.