Slalom numbers

The paper is an extensive and systematic study of cardinal invariants we call slalom numbers, describing the combinatorics of sequences of sets of natural numbers. Our general approach, based on relational systems, covers many such cardinal characteristics, including localization and anti-localization cardinals. We show that most of the slalom numbers are connected to topological selection principles, in particular, we obtain the representation of the uniformity of meager and the cofinality of measure. Considering instances of slalom numbers parametrized by ideals on natural numbers, we focus on monotonicity properties with respect to ideal orderings and computational formulas for the disjoint sum of ideals. Hence, we get such formulas for several pseudo-intersection numbers as well as for the bounding and dominating numbers parametrized with ideals. Based on the effect of adding a Cohen real, we get many consistent constellations of different values of slalom numbers

Observation of Skyrmion Bubbles in Multilayer [Pt/Co/Cu]n using spin-polarized STM

Magnetic multilayers are a promising platform for storage and logic devices based on skyrmion spin textures, due to the large materials phase space for tuning properties. Epitaxial superlattice structures of [Pt/Co/Cu]n thin films were grown by molecular beam epitaxy at room temperature. Spin-polarized scanning tunneling microscopy (SP-STM) of these samples was used to probe the connection between surface structure and skyrmion morphology with nanoscale spatial resolution. Irregular-shaped skyrmion bubbles were observed, with effective diameters from 20-200 nm that are much larger than the nanoscale grain structure of the surface topography. Nucleation, annihilation, and motion of skyrmion bubbles could be driven using the stray field of the ferromagnetic tip in repeated imaging, and spin-polarized current/voltage pulses. Our detailed comparison of STM topography and differential conductance images shows that there are no surface defects or inhomogeneities at length scales that could account for the range in skyrmion bubble size or shape observed in the measurements.Comment: 11 pages, 5 figure

Computational exploration of molecular receptive fields in the olfactory bulb reveals a glomerulus-centric chemical map

© The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.Progress in olfactory research is currently hampered by incomplete knowledge about chemical receptive ranges of primary receptors. Moreover, the chemical logic underlying the arrangement of computational units in the olfactory bulb has still not been resolved. We undertook a large-scale approach at characterising molecular receptive ranges (MRRs) of glomeruli in the dorsal olfactory bulb (dOB) innervated by the MOR18-2 olfactory receptor, also known as Olfr78, with human ortholog OR51E2. Guided by an iterative approach that combined biological screening and machine learning, we selected 214 odorants to characterise the response of MOR18-2 and its neighbouring glomeruli. We found that a combination of conventional physico-chemical and vibrational molecular descriptors performed best in predicting glomerular responses using nonlinear Support-Vector Regression. We also discovered several previously unknown odorants activating MOR18-2 glomeruli, and obtained detailed MRRs of MOR18-2 glomeruli and their neighbours. Our results confirm earlier findings that demonstrated tunotopy, that is, glomeruli with similar tuning curves tend to be located in spatial proximity in the dOB. In addition, our results indicate chemotopy, that is, a preference for glomeruli with similar physico-chemical MRR descriptions being located in spatial proximity. Together, these findings suggest the existence of a partial chemical map underlying glomerular arrangement in the dOB. Our methodology that combines machine learning and physiological measurements lights the way towards future high-throughput studies to deorphanise and characterise structure-activity relationships in olfaction.Peer reviewe