Make a graph singly connected by edge orientations

A directed graph $D$ is singly connected if for every ordered pair of vertices $(s,t)$, there is at most one path from $s$ to $t$ in $D$. Graph orientation problems ask, given an undirected graph $G$, to find an orientation of the edges such that the resultant directed graph $D$ has a certain property. In this work, we study the graph orientation problem where the desired property is that $D$ is singly connected. Our main result concerns graphs of a fixed girth $g$ and coloring number $c$. For every $g,c\geq 3$, the problem restricted to instances of girth $g$ and coloring number $c$, is either NP-complete or in P. As further algorithmic results, we show that the problem is NP-hard on planar graphs and polynomial time solvable distance-hereditary graphs

Towards bio-inspired unsupervised representation learning for indoor aerial navigation

Aerial navigation in GPS-denied, indoor environments, is still an open challenge. Drones can perceive the environment from a richer set of viewpoints, while having more stringent compute and energy constraints than other autonomous platforms. To tackle that problem, this research displays a biologically inspired deep-learning algorithm for simultaneous localization and mapping (SLAM) and its application in a drone navigation system. We propose an unsupervised representation learning method that yields low-dimensional latent state descriptors, that mitigates the sensitivity to perceptual aliasing, and works on power-efficient, embedded hardware. The designed algorithm is evaluated on a dataset collected in an indoor warehouse environment, and initial results show the feasibility for robust indoor aerial navigation

Emission-line profile modelling of structured T Tauri magnetospheres

We present hydrogen emission line profile models of magnetospheric accretion onto Classical T Tauri stars. The models are computed under the Sobolev approximation using the three-dimensional Monte Carlo radiative-transfer code TORUS. We have calculated four illustrative models in which the accretion flows are confined to azimuthal curtains - a geometry predicted by magneto-hydrodynamical simulations. Properties of the line profile variability of our models are discussed, with reference to dynamic spectra and cross-correlation images. We find that some gross characteristics of observed line profile variability are reproduced by our models, although in general the level of variability predicted is larger than that observed. We conclude that this excessive variability probably excludes dynamical simulations that predict accretion flows with low degrees of axisymmetry.Comment: 14 pages, 12 figures. Published in MNRA

Compensation for geometrical deviations in additive manufacturing

The design of additive manufacturing processes, especially for batch production in industrial practice, is of high importance for the propagation of new additive manufacturing technology. Manual redesign procedures of the additive manufactured parts based on discrete measurement data or numerical meshes are error prone and hardly automatable. To achieve the required final accuracy of the parts, often, various iterations are necessary. To address these issues, a data-driven geometrical compensation approach is proposed that adapts concepts from forming technology. The measurement information of a first calibration cycle of manufactured parts is the basis of the approach. Through non-rigid transformations of the part geometry, a new shape for the subsequent additive manufacturing process was derived in a systematic way. Based on a purely geometrical approach, the systematic portion of part deviations can be compensated. The proposed concept is presented first and was applied to a sample fin-shaped part. The deviation data of three manufacturing cycles was utilised for validation and verification