Refine
Year of publication
- 2010 (70) (remove)
Language
- English (70)
Keywords
- 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)
Project
We present a novel algorithm for automatic parameterization of tube-like surfaces of arbitrary genus such as the surfaces of knots, trees, blood vessels, neurons, or any tubular graph with a globally consistent stripe texture. We use the principal curvature frame field of the underlying tube-like surface to guide the creation of a global, topologically consistent stripe parameterization of the surface. Our algorithm extends the QuadCover algorithm and is based, first, on the use of so-called projective vector fields instead of frame fields, and second, on different types of branch points. That does not only simplify the mathematical theory, but also reduces computation time by the decomposition of the underlying stiffness matrices.
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.
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.
This paper presents concepts and implementation of the finite element toolbox Kaskade 7, a flexible C++ code for solving elliptic and parabolic PDE systems. Issues such as problem formulation, assembly and adaptivity are discussed at the example of optimal control problems. Trajectory compression for parabolic optimization problems is considered as a case study.
In this paper we study BSDEs arising from a special class of backward stochastic partial differential equations (BSPDEs) that is intimately related to utility maximization problems with respect to arbitrary utility functions. After providing existence and uniqueness we discuss the numerical realizability. Then we study utility maximization problems on incomplete financial markets whose dynamics are governed by continuous semimartingales. Adapting standard methods that solve the utility maximization problem using BSDEs, we give solutions for the portfolio optimization problem which involve the delivery of a liability at maturity. We illustrate our study by numerical simulations for selected examples. As a byproduct we prove existence of a solution to a very particular quadratic growth BSDE with unbounded terminal condition. This complements results on this topic obtained in [6,7,8].
Many applications give rise to matrix polynomials whose coefficients have
a kind of reversal symmetry, a structure we call palindromic.
Several properties of scalar palindromic polynomials are derived,
and together with properties of compound matrices, used to
establish the Smith form of regular and singular T-palindromic matrix polynomials,
over arbitrary fields.
The invariant polynomials are shown to
inherit palindromicity,
and their structure is described in detail.
Jordan structures of palindromic matrix polynomials are characterized,
and necessary conditions for the
existence of structured linearizations established.
In the odd degree case, a constructive procedure for building
palindromic linearizations shows that the necessary conditions are sufficient as well.
The Smith form for *-palindromic polynomials is also analyzed. Finally, results for palindromic matrix polynomials over fields of
characteristic two are presented.
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.
To address the plurality of interpretations of the subjective notion of risk, we describe it by means of a risk order and concentrate on the context invariant features of diversification and monotonicity. Our main results are uniquely characterized robust representations of lower semicontinuous risk orders on vector spaces and convex sets. This representation covers most instruments related to risk and allow for a differentiated interpretation depending on the underlying context which is illustrated in different settings: For random variables, risk perception can be interpreted as model risk, and we compute among others the robust representation of the economic index of riskiness. For lotteries, risk perception can be viewed as distributional risk and we study the "Value at Risk". For consumption patterns, which excerpt an intertemporality dimension in risk perception, we provide an interpretation in terms of discounting risk and discuss some examples.
We study the risk assessment of uncertain cash flows in terms of dynamic convex risk measures for processes as introduced in Cheridito, Delbaen, and Kupper (2006). These risk measures take into account not only the amounts but also the timing of a cash flow. We discuss their robust representation in terms of suitably penalized probability measures on the optional $\sigma$-field. This yields an explicit analysis both of model and discounting ambiguity. We focus on supermartingale criteria for time consistency. In particular we show how ``bubbles'' may appear in the dynamic penalization, and how they cause a breakdown of asymptotic safety of the risk assessment procedure.