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Abstract-This paper presents a novel method to generate the time-optimal trajectory that exactly follows a given differentiable joint-space path within given bounds on joint accelerations and velocities. We also present a path preprocessing method to make nondifferentiable paths differentiable by adding circular blends. We introduce improvements to existing work that make the algorithm more robust in the presence of numerical inaccuracies. Furthermore we validate our methods on hundreds of randomly generated test cases on simulated and real 7-DOF robot arms. Finally, we provide open source software that implements our algorithms.

Employing the Bonn-Gatchina partial wave analysis framework (PWA), we have analyzed HADES data of the reaction p(3.5 GeV) + p → pK + Λ. This reaction might contain information about the kaonic cluster "pp K − " (with quantum numbers J P = 0 − and total isospin I = 1/2) via its decay into pΛ. Due to interference effects in our coherent description of the data, a hypothetical K N N (or, specifically "pp K − ") cluster signal need not necessarily show up as a pronounced feature (e.g. a peak) in an invariant mass spectrum like pΛ. Our PWA analysis includes a variety of resonant and non-resonant intermediate states and delivers a good description of our data (various angular distributions and two-hadron invariant mass spectra) without a contribution of a K N N cluster. At a confidence level of CL s = 95% such a cluster cannot contribute more than 2-12% to the total cross section with a pK + Λ final state, which translates into a production cross-section between 0.7 μb and 4.2 μb, respectively. The range of the upper limit depends on the assumed cluster mass, width and production process.

The centrality determination for Au + Au collisions at 1.23A GeV, as measured with HADES at the GSI-SIS18, is described. In order to extract collision geometry related quantities, such as the average impact parameter or number of participating nucleons, a Glauber Monte Carlo approach is employed. For the application of this model to collisions at this relatively low centre-of-mass energy of √ s NN = 2.42 GeV special investigations were performed. As a result a well defined procedure to determine centrality classes for ongoing analyses of heavy-ion data is established.

Expansion microscopy (ExM) enables super-resolution imaging of proteins and nucleic acids on conventional microscopes. However, imaging of details of the organization of lipid bilayers by light microscopy remains challenging. We introduce an unnatural short-chain azide- and amino-modified sphingolipid ceramide, which upon incorporation into membranes can be labeled by click chemistry and linked into hydrogels, followed by 4× to 10× expansion. Confocal and structured illumination microscopy (SIM) enable imaging of sphingolipids and their interactions with proteins in the plasma membrane and membrane of intracellular organelles with a spatial resolution of 10–20 nm. As our functionalized sphingolipids accumulate efficiently in pathogens, we use sphingolipid ExM to investigate bacterial infections of human HeLa229 cells by Neisseria gonorrhoeae, Chlamydia trachomatis and Simkania negevensis with a resolution so far only provided by electron microscopy. In particular, sphingolipid ExM allows us to visualize the inner and outer membrane of intracellular bacteria and determine their distance to 27.6 ± 7.7 nm.