Continuous-time mean field Markov decision models

We consider a finite number of $N$ statistically equal individuals, each moving on a finite set of states according to a continuous-time Markov Decision Process. Transition intensities of the individuals and generated rewards depend not only on the state and action of the individual itself, but also on the states of the other individuals as well as the chosen action. Interactions like this are typical for a wide range of models in e.g.\ biology, epidemics, finance, social science and queueing systems among others. The aim is to maximize the expected discounted reward of the system, i.e. the individuals have to cooperate as a team. Computationally this is a difficult task when $N$ is large. Thus, we consider the limit for $N\to\infty.$ In contrast to other papers we do not consider the so-called Master equation. Instead we define a 'limiting' (deterministic) optimization problem from the limiting differential equation for the path trajectories. This has the advantage that we need less assumptions and can apply Pontryagin's maximum principle in order to construct asymptotically optimal strategies. We show how to apply our results using two examples: a machine replacement problem and a problem from epidemics. We also show that optimal feedback policies are not necessarily asymptotically optimal

Zeitaufgelöste Röntgenbeugung an einkristallinem Indiumantimonid

Die vorliegende Arbeit behandelt die experimentelle Untersuchung der strukturellen Änderung des Halbleiters Indiumantimonid (InSB) nach der Anregung durch einen ultrakurzen Laserpuls (60 fs). Die Untersuchung erfolgt durch ultrakurze Röntgenpulse (rund 100 fs). Als Quelle der ultrakurzen Röntgenpulse dient eine Laser-Plasma Röntgenquelle. Bei dieser Quelle wird ein ultrakurzer intensiver optischer Laserpuls auf eine Metallfolie fokussiert (Intensität bis 8*10^16 W/cm^2), durch das entstehende Plasma kommt es zu einer Emission von Röntgenstrahlung. Zur Charakterisierung der Röntgenquelle stand ein neuartiger Timepix- Detektor zu Verfügung, der es ermöglichte, Bremsstrahlung bis zu Photonenenergien von 700 keV zu detektieren. Die Eindringtiefe von Röntgenstrahlung ist meist mehrere Mikrometer und damit viel größer als die Eindringtiefe des zur Anregung verwendeten Laserpulses von 100 nm. Durch die Benutzung eines stark asymmetrischen Bragg-Reflexes konnte die Eindringtiefe der Röntgenstrahlung an die Eindringtiefe des Anregepulses angepasst werden. Durch die geringe Eindringtiefe ist bereits 2 ps nach der Anregung eine Expansion von 4% einer 4 nm dünnen Schicht an der Oberfläche messbar. Die Anregung des Halbleiters wird mit verschiedenen Modellen theoretisch beschrieben, die daraus gewonnene zeitliche Entwicklung der Deformation wird mit den durchgeführten Messungen verglichen

Untersuchung diffus spiegelnder Oberflächen mittels Infrarotdeflektometrie

Die Deflektometrie ist ein optisches Inspektionsverfahren für spiegelnde Oberflächen, welches eine hohe Empfindlichkeit gegenüber Neigungsänderungen der Oberfläche bietet. In dieser Arbeit werden mehrere Ansätze vorgestellt, um Deflektometrie im thermischen Infrarotspektrum umzusetzen. Viele technische Oberflächen, die im sichtbaren Spektrum diffus erscheinen, weisen im langwelligen Infrarot eine spiegelnde Reflexion auf, sodass hier das Verfahren der Infrarotdeflektometrie anwendbar ist

Satellitengestütze Schwerewellenmessungen in der Atmosphäre und Perspektiven einer zukünftigen ESA Mission (PREMIER)

Gravity waves play a key role in middle atmosphere dynamics. For an improved understanding of gravity waves and their interactions with the atmosphere, global modeling and measurements with high resolution are required. In this work we validate the gravity waves resolved in ECMWF ($\textbf{E}$uropean $\textbf{C}$entre for $\textbf{M}$edium-Range $\textbf{W}$eather $\textbf{F}$orecasts) model-data by comparison with gravity wave analysis of global satellite observations by SABER ($\textbf{S}$ounding of the $\textbf{A}$tmosphere using $\textbf{B}$roadband $\textbf{E}$mission $\textbf{R}$adiometry). The validation of the model-data shows that the modeled wave amplitudes are lowered by a factor of two in the troposphere and lower stratosphere. Above 50km altitude, the vertical resolution of ECMWF is reduced and accordingly the gravity waves are strongly damped. It is also shown that gravity waves with orographic sources are better represented in the model-data than convectively exited waves. Gravity waves with convective sources are suppressed by the resolution of the model and are only represented with small amplitudes. The validated ECMWF-data set can be used to simulate measurements of a future $\textbf{I}$nfrared $\textbf{L}$imb $\textbf{I}$mager (ILI). The investigation of the ILI-data shows that the measurement resolution is sufficient to calculate gravity wave momentum flux in both horizontal directions and that it will be possible to receive information about the propagation direction of the waves. The validated model-data are also used to improve the assumptions made by using temperature data to receive gravity wave momentum flux. The results of this study shows clearly the high potential of ILI-data for global measurements of gravity waves and the retrieval of gravity wave parameters. In particular momentum flux depending on the propagation direction of the waves will improve global circulation models

Cavlectometry: Towards Holistic Reconstruction of Large Mirror Objects

We introduce a method based on the deflectometry principle for the reconstruction of specular objects exhibiting significant size and geometric complexity. A key feature of our approach is the deployment of an Automatic Virtual Environment (CAVE) as pattern generator. To unfold the full power of this extraordinary experimental setup, an optical encoding scheme is developed which accounts for the distinctive topology of the CAVE. Furthermore, we devise an algorithm for detecting the object of interest in raw deflectometric images. The segmented foreground is used for single-view reconstruction, the background for estimation of the camera pose, necessary for calibrating the sensor system. Experiments suggest a significant gain of coverage in single measurements compared to previous methods. To facilitate research on specular surface reconstruction, we will make our data set publicly available

Probabilistic multi-class segmentation for the Amazon picking challenge

We present a method for multi-class segmentation from RGB-D data in a realistic warehouse picking setting. The method computes pixel-wise probabilities and combines them to find a coherent object segmentation. It reliably segments objects in cluttered scenarios, even when objects are translucent, reflective, highly deformable, have fuzzy surfaces, or consist of loosely coupled components. The robust performance results from the exploitation of problem structure inherent to the warehouse setting. The proposed method proved its capabilities as part of our winning entry to the 2015 Amazon Picking Challenge. We present a detailed experimental analysis of the contribution of different information sources, compare our method to standard segmentation techniques, and assess possible extensions that further enhance the algorithm’s capabilities. We release our software and data sets as open source

Sub-mm/mm optical properties of real protoplanetary matter derived from Rosetta/MIRO observations of comet 67P

Optical properties are required for the correct understanding and modelling of protoplanetary and debris discs. By assuming that comets are the most pristine bodies in the solar system, our goal is to derive optical constants of real protoplanetary material. We determine the complex index of refraction of the near-surface material of comet 67P/Churyumov-Gerasimenko by fitting the sub-millimetre/millimetre observations of the thermal emission of the comet's sub-surface made by the Microwave Instrument for the Rosetta Orbiter (MIRO) with synthetic temperatures derived from a thermophysical model and radiative-transfer models. According to the two major formation scenarios of comets, we model the sub-surface layers to consist of pebbles as well as of homogeneously packed dust grains. In the case of a homogeneous dusty surface material, we find a solution for the length-absorption coefficient of $\alpha \approx 0.22~\mathrm{cm^{-1}}$ for a wavelength of 1.594 mm and $\alpha \geq 3.84~\mathrm{cm^{-1}}$ for a wavelength of 0.533 mm and a constant thermal conductivity of $0.006~\mathrm{Wm^{-1}K^{-1}}$. For the pebble scenario, we find for the pebbles and a wavelength of 1.594 mm a complex refractive index of $n = (1.074 - 1.256) + \mathrm{i} \, (2.580 - 7.431)\cdot 10^{-3}$ for pebble radii between 1 mm and 6 mm. Taking into account other constraints, our results point towards a pebble makeup of the cometary sub-surface with pebble radii between 3 mm and 6 mm. The derived real part of the refractive index is used to constrain the composition of the pebbles and their volume filling factor. The optical and physical properties are discussed in the context of protoplanetary and debris disc observations.Comment: Accepted for publication in MNRA