Path integrals and wavepacket evolution for damped mechanical systems

Damped mechanical systems with various forms of damping are quantized using the path integral formalism. In particular, we obtain the path integral kernel for the linearly damped harmonic oscillator and a particle in a uniform gravitational field with linearly or quadratically damped motion. In each case, we study the evolution of Gaussian wavepackets and discuss the characteristic features that help us distinguish between different types of damping. For quadratic damping, we show that the action and equation of motion of such a system has a connection with the zero dimensional version of a currently popular scalar field theory. Furthermore we demonstrate that the equation of motion (for quadratic damping) can be identified as a geodesic equation in a fictitious two-dimensional space.Comment: 15 pages, 6 figure

Bayesian Networks for Max-linear Models

We study Bayesian networks based on max-linear structural equations as introduced in Gissibl and Kl\"uppelberg [16] and provide a summary of their independence properties. In particular we emphasize that distributions for such networks are generally not faithful to the independence model determined by their associated directed acyclic graph. In addition, we consider some of the basic issues of estimation and discuss generalized maximum likelihood estimation of the coefficients, using the concept of a generalized likelihood ratio for non-dominated families as introduced by Kiefer and Wolfowitz [21]. Finally we argue that the structure of a minimal network asymptotically can be identified completely from observational data.Comment: 18 page

Debris and micrometeorite impact measurements in the laboratory

A method was developed to simulate space debris in the laboratory. This method, which is an outgrowth of research in inertial confinement fusion (ICF), uses laser ablation to accelerate material. Using this method, single 60 micron aluminum spheres were accelerated to 15 km/sec and larger 500 micron aluminum spheres were accelerated to 2 km/sec. Also, many small (less than 10 micron diameter) irregularly shaped particles were accelerated to speeds of 100 km/sec

Responding to class theft: Theoretical and empirical links to critical management studies

Redrafted submission for inclusion in Remarx Section of Rethinking MarxismThis paper suggests closer linkages between the fields of Postmodern Class Analysis (PCA) and Critical Management Studies (CMS)2 are possible. It argues that CMS might contribute to the empirical engagement with the over-determined relations between class and non-class processes in work organizations (this appears to have received relatively little attention in PCA) and that PCA's theoretical and conceptual commitments may provide one means for CMS to engage in class analysis. CMS's focus on power and symbolic relations has led to the relative neglect of exploitation and class, in surplus terms. Both fields share similar although not identical political and ethical commitments

RAFCON: a Graphical Tool for Task Programming and Mission Control

There are many application fields for robotic systems including service robotics, search and rescue missions, industry and space robotics. As the scenarios in these areas grow more and more complex, there is a high demand for powerful tools to efficiently program heterogeneous robotic systems. Therefore, we created RAFCON, a graphical tool to develop robotic tasks and to be used for mission control by remotely monitoring the execution of the tasks. To define the tasks, we use state machines which support hierarchies and concurrency. Together with a library concept, even complex scenarios can be handled gracefully. RAFCON supports sophisticated debugging functionality and tightly integrates error handling and recovery mechanisms. A GUI with a powerful state machine editor makes intuitive, visual programming and fast prototyping possible. We demonstrated the capabilities of our tool in the SpaceBotCamp national robotic competition, in which our mobile robot solved all exploration and assembly challenges fully autonomously. It is therefore also a promising tool for various RoboCup leagues.Comment: 8 pages, 5 figure

Learning Implicit Brain MRI Manifolds with Deep Learning

An important task in image processing and neuroimaging is to extract quantitative information from the acquired images in order to make observations about the presence of disease or markers of development in populations. Having a lowdimensional manifold of an image allows for easier statistical comparisons between groups and the synthesis of group representatives. Previous studies have sought to identify the best mapping of brain MRI to a low-dimensional manifold, but have been limited by assumptions of explicit similarity measures. In this work, we use deep learning techniques to investigate implicit manifolds of normal brains and generate new, high-quality images. We explore implicit manifolds by addressing the problems of image synthesis and image denoising as important tools in manifold learning. First, we propose the unsupervised synthesis of T1-weighted brain MRI using a Generative Adversarial Network (GAN) by learning from 528 examples of 2D axial slices of brain MRI. Synthesized images were first shown to be unique by performing a crosscorrelation with the training set. Real and synthesized images were then assessed in a blinded manner by two imaging experts providing an image quality score of 1-5. The quality score of the synthetic image showed substantial overlap with that of the real images. Moreover, we use an autoencoder with skip connections for image denoising, showing that the proposed method results in higher PSNR than FSL SUSAN after denoising. This work shows the power of artificial networks to synthesize realistic imaging data, which can be used to improve image processing techniques and provide a quantitative framework to structural changes in the brain.Comment: SPIE Medical Imaging 201

Incompressible flow in porous media with fractional diffusion

In this paper we study the heat transfer with a general fractional diffusion term of an incompressible fluid in a porous medium governed by Darcy's law. We show formation of singularities with infinite energy and for finite energy we obtain existence and uniqueness results of strong solutions for the sub-critical and critical cases. We prove global existence of weak solutions for different cases. Moreover, we obtain the decay of the solution in $L^p$, for any $p\geq2$, and the asymptotic behavior is shown. Finally, we prove the existence of an attractor in a weak sense and, for the sub-critical dissipative case with $\alpha\in (1,2]$, we obtain the existence of the global attractor for the solutions in the space $H^s$ for any $s > (N/2)+1-\alpha$