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Erscheinungsjahr
- 2010 (70) (entfernen)
Sprache
- Englisch (70)
Schlagworte
- dissipativity (3)
- optimal control (3)
- backward error (2)
- behavior approach (2)
- even pencil (2)
- even polynomial (2)
- finite elements (2)
- linear quadratic optimal control (2)
- problem (2)
- structured eigenvalue problem (2)
Projekt
Boolean modeling frameworks have long since proved their worth for capturing and analyzing essential characteristics of complex systems.
Hybrid approaches aim at exploiting the advantages of Boolean formalisms while refining expressiveness. In this paper, we present a formalism that augments Boolean models with stochastic aspects. More specifically, biological reactions effecting a system in a given state are associated
with probabilities, resulting in dynamical behavior represented as a Markov chain. Using this approach, we model and analyze the cytokinin
response network of Arabidopsis thaliana with a focus on clarifying the character of an important feedback mechanism.
Modeling the orientation distribution function by mixtures of angular central Gaussian distributions
(2010)
In this paper we develop a tensor mixture model for diffusion weighted imaging
data using an automatic model selection criterion for the order of tensor
components in a voxel. We show that the weighted orientation distribution
function for this model can be expanded into a mixture of angular central
Gaussian distributions. We show properties of this model in extensive
simulations and in a high angular resolution experimental data set. The results
suggest that the model may improve imaging of cerebral fiber tracts. We
demonstrate how inference on canonical model parameters may give rise to new
clinical applications.
The package fmri is provided for analysis of single run functional
Magnetic Resonance Imaging data. It implements structural adaptive smoothing
methods with signal detection for adaptive noise reduction which avoids blurring
of edges of activation areas. fmri provides fmri analysis from time series
modeling to signal detection and publication-ready images.
We consider the numerical solution of projected Lyapunov equations using Krylov subspace iterative methods. Such equations
play a fundamental role in balanced truncation model reduction of descriptor systems. We present generalizations of
the extended block and global Arnoldi methods to projected Lyapunov equations and compare these methods with the alternating direction implicit method with respect to performance on different examples.
A deflation strategy is also proposed to overcome possible breakdown in the
recurrence.
Recently, the format of TT tensors
\cite{hackbuschHT,osele1,tyrtosele2,tyrtosele3} has turned out to be
a promising new format for the approximation of solutions of high
dimensional problems. In this paper, we prove some new results for
the TT representation of a tensor $U \in \R^{n_1\times \ldots\times
n_d}$ and for the manifold of tensors of TT-rank $\underline{r}$.\As a first result, we prove that the TT (or compression) ranks $r_i$
of a tensor $U$ are unique and equal to the respective separation
ranks of $U$ if the components of the TT decomposition are required to
fulfil a certain maximal rank condition. We then show that the set
$\mathcal{T}$ of TT tensors of fixed rank $\underline{r}$ forms an embedded
manifold in $\R^{n^d}$, therefore preserving the essential theoretical
properties of the Tucker format, but often showing an improved scaling
behaviour. Extending a similar approach for matrices \cite{conte_lub},
we introduce certain gauge conditions to obtain a unique
representation of the tangent space $\cT_U\mathcal{T}$ of $\mathcal{T}$
and deduce a
local parametrization of the TT manifold. The parametrisation of
$\cT_{U}\mathcal{T}$ is often crucial for an algorithmic treatment of
high-dimensional time-dependent PDEs and minimisation problems
\cite{lubuch_blau}. We conclude with remarks on those applications and
present some numerical examples.
The PSurface Library
(2010)
We describe psurface, a C++ library that allows to store and access piecewise linear mappings between simplicial surfaces in $\R^2$ and $\R^3$. These mappings are stored in a graph data structure and can be constructed explicitly, by projection, or by surface simplification. Piecewise linear maps can be used, e.g., to construct boundary
approximations for finite element grids, and grid intersections for domain decomposition methods. In computer graphics the mappings allow to build level-of-detail representations as well as texture- and bump maps. We document the data structures and algorithms used and show how \psurface is used in the numerical analysis framework Dune
and the visualization software Amira.
We define a risk averse nonanticipative feasible policy for multistage stochastic programs and propose a methodology to implement it. The approach is based on dynamic programming equations written for a risk averse formulation of the problem.
This formulation relies on a new class of multiperiod risk functionals called extended polyhedral risk measures. Dual representations of such risk functionals are given and used to derive conditions of coherence. In the one-period case, conditions for convexity and consistency with second order stochastic dominance are also provided. The risk averse dynamic programming equations are specialized considering convex combinations of one-period extended polyhedral risk measures such as spectral risk measures.
To implement the proposed policy, the approximation of the risk averse recourse functions for stochastic linear programs is discussed. In this context, we detail a stochastic dual dynamic programming algorithm which converges to the optimal value of the risk averse problem.
We prove central and non-central limit theorems for the
Hermite variations of the anisotropic fractional Brownian sheet
$W^{\alpha, \beta}$
with Hurst parameter $(\alpha, \beta) \in (0,1)2$. When $0<\alpha \leq
1-\frac{1}{2q}$ or $0<\beta \leq 1-\frac{1}{2q}$ a central limit theorem
holds for the renormalized Hermite variations of order $q\geq 2$, while
for $1-\frac{1}{2q}<\alpha, \beta < 1$ we prove that these variations
satisfy a non-central limit theorem. In fact, they converge to a random
variable which is the value of a two-parameter Hermite process at time
$(1,1)$.
In this Note we consider a Lipschitz backward stochastic
differential equation (BSDE) driven by a continuous martingale $M$. We
prove (in Theorem \ref{theorem:main}) that if $M$ is a strong Markov
process and if the BSDE has regular data then the unique solution
$(Y,Z,N)$ of the BSDE is reduced to $(Y,Z)$, \textit{i.e.} the
orthogonal martingale $N$ is equal to zero, showing that in a Markovian
setting the "usual" solution $(Y,Z)$ (of a BSDE with regular data) has
not to be completed by a strongly orthogonal component even if $M$ does
not enjoy the martingale representation property.