Generalized decision rule approximations for stochastic programming via liftings

Stochastic programming provides a versatile framework for decision-making under uncertainty, but the resulting optimization problems can be computationally demanding. It has recently been shown that, primal and dual linear decision rule approximations can yield tractable upper and lower bounds on the optimal value of a stochastic program. Unfortunately, linear decision rules often provide crude approximations that result in loose bounds. To address this problem, we propose a lifting technique that maps a given stochastic program to an equivalent problem on a higher-dimensional probability space. We prove that solving the lifted problem in primal and dual linear decision rules provides tighter bounds than those obtained from applying linear decision rules to the original problem. We also show that there is a one-to-one correspondence between linear decision rules in the lifted problem and families of non-linear decision rules in the original problem. Finally, we identify structured liftings that give rise to highly flexible piecewise linear decision rules and assess their performance in the context of a stylized investment planning problem

Plasma-wall-interaction in ECRIS II

In an ECR-discharge, where the plasma is confined inside a copper-resonator by a simple magnetic mirror, it could be shown that sputtering of wall material has an important influence upon the plasma [1]. Spectroscopic measurements in ECRIS II with a copper vessel confirmed this model. Evidence for the presence of copper atoms and ions in the plasma could be found by ion extraction as well as with VUV-spectrometry. In a nitrogen discharge by adding helium as a mixing-gas we found that the extracted current of Cu-ions decreased and measured line intensities of copper emission lines dropped down. [1] D. Meyer, "Einfluss der Plasmainstabilitaet auf die Produktion hochgeladener Ionen in einer ECR-Entladung", Dissertation, Bochum, 199

Planning with Information-Processing Constraints and Model Uncertainty in Markov Decision Processes

Information-theoretic principles for learning and acting have been proposed to solve particular classes of Markov Decision Problems. Mathematically, such approaches are governed by a variational free energy principle and allow solving MDP planning problems with information-processing constraints expressed in terms of a Kullback-Leibler divergence with respect to a reference distribution. Here we consider a generalization of such MDP planners by taking model uncertainty into account. As model uncertainty can also be formalized as an information-processing constraint, we can derive a unified solution from a single generalized variational principle. We provide a generalized value iteration scheme together with a convergence proof. As limit cases, this generalized scheme includes standard value iteration with a known model, Bayesian MDP planning, and robust planning. We demonstrate the benefits of this approach in a grid world simulation.Comment: 16 pages, 3 figure

Angular Forces Around Transition Metals in Biomolecules

Quantum-mechanical analysis based on an exact sum rule is used to extract an semiclassical angle-dependent energy function for transition metal ions in biomolecules. The angular dependence is simple but different from existing classical potentials. Comparison of predicted energies with a computer-generated database shows that the semiclassical energy function is remarkably accurate, and that its angular dependence is optimal.Comment: Tex file plus 4 postscript figure

An iterative decision-making scheme for Markov decision processes and its application to self-adaptive systems

Software is often governed by and thus adapts to phenomena that occur at runtime. Unlike traditional decision problems, where a decision-making model is determined for reasoning, the adaptation logic of such software is concerned with empirical data and is subject to practical constraints. We present an Iterative Decision-Making Scheme (IDMS) that infers both point and interval estimates for the undetermined transition probabilities in a Markov Decision Process (MDP) based on sampled data, and iteratively computes a confidently optimal scheduler from a given finite subset of schedulers. The most important feature of IDMS is the flexibility for adjusting the criterion of confident optimality and the sample size within the iteration, leading to a tradeoff between accuracy, data usage and computational overhead. We apply IDMS to an existing self-adaptation framework Rainbow and conduct a case study using a Rainbow system to demonstrate the flexibility of IDMS

Jet-veto in bottom-quark induced Higgs production at next-to-next-to-leading order

We present results for associated Higgs+n-jet production in bottom quark annihilation, for n=0 and n>=1 at NNLO and NLO accuracy, respectively. We consider both the cases with and without b-tagging. Numerical results are presented for parameters relevant for experiments at the LHC.Comment: 27 pages, 13 figures, 8 table

Top-mass effects in differential Higgs production through gluon fusion at order \alpha_s^4

Effects from a finite top quark mass on differential distributions in the Higgs+jet production cross section through gluon fusion are studied at next-to-leading order in the strong coupling, i.e. $O(\alpha_s^4)$. Terms formally subleading in $1/m_t$ are calculated, and their influence on the transverse momentum and rapidity distribution of the Higgs boson are evaluated. We find that, for the differential K-factor, the heavy-top limit is valid at the 2-3% level as long as the transverse momentum of the Higgs remains below about 150 GeV.Comment: 21 pages, 12 figure

A multi-vendor, multi-center study on reproducibility and comparability of fast strain-encoded cardiovascular magnetic resonance imaging

Myocardial strain is a convenient parameter to quantify left ventricular (LV) function. Fast strain-encoding (fSENC) enables the acquisition of cardiovascular magnetic resonance images for strain-measurement within a few heartbeats during free-breathing. It is necessary to analyze inter-vendor agreement of techniques to determine strain, such as fSENC, in order to compare existing studies and plan multi-center studies. Therefore, the aim of this study was to investigate inter-vendor agreement and test-retest reproducibility of fSENC for three major MRI-vendors. fSENC-images were acquired three times in the same group of 15 healthy volunteers using 3 Tesla scanners from three different vendors: at the German Heart Institute Berlin, the Charité University Medicine Berlin-Campus Buch and the Theresien-Hospital Mannheim. Volunteers were scanned using the same imaging protocol composed of two fSENC-acquisitions, a 15-min break and another two fSENC-acquisitions. LV global longitudinal and circumferential strain (GLS, GCS) were analyzed by a trained observer (Myostrain 5.0, Myocardial Solutions) and for nine volunteers repeatedly by another observer. Inter-vendor agreement was determined using Bland-Altman analysis. Test-retest reproducibility and intra- and inter-observer reproducibility were analyzed using intraclass correlation coefficient (ICC) and coefficients of variation (CoV). Inter-vendor agreement between all three sites was good for GLS and GCS, with biases of 0.01-1.88%. Test-retest reproducibility of scans before and after the break was high, shown by ICC- and CoV values of 0.63-0.97 and 3-9% for GLS and 0.69-0.82 and 4-7% for GCS, respectively. Intra- and inter-observer reproducibility were excellent for both parameters (ICC of 0.77-0.99, CoV of 2-5%). This trial demonstrates good inter-vendor agreement and test-retest reproducibility of GLS and GCS measurements, acquired at three different scanners from three different vendors using fSENC. The results indicate that it is necessary to account for a possible bias (< 2%) when comparing strain measurements of different scanners. Technical differences between scanners, which impact inter-vendor agreement, should be further analyzed and minimized.DRKS Registration Number: 00013253. Universal Trial Number (UTN): U1111-1207-5874