Near-optimal separators in string graphs

Let G be a string graph (an intersection graph of continuous arcs in the plane) with m edges. Fox and Pach proved that G has a separator consisting of O(m^{3/4}\sqrt{log m})$ vertices, and they conjectured that the bound of O(\sqrt m) actually holds. We obtain separators with O(\sqrt m \log m) vertices.Comment: 4 pages; minor corrections and updates compared to version

Measurement of qTq_T-weighted TSAs in 2015 COMPASS Drell-Yan data

In the polarised Drell-Yan experiment at the COMPASS facility at CERN the beam of negatively-charged pions with 190 GeV/c momentum and intensity about $10^8$ pions/s interacted with transversely polarised NH$_3$ target. Muon pairs produced in Drell-Yan process (DY) were detected. Recently, the first ever Transverse Spin Asymmetries (TSAs) measurement in DY has been presented by COMPASS. A complementary analysis of the TSAs weighted by powers of the dimuon transverse momentum $q_T$ are presented. In the Transverse Momentum Dependent (TMD) PDF formalism, the $q_T$-weighted TSAs can be written in terms of products of the TMD PDFs of two colliding hadrons, unlike the conventional TSAs, which are their convolutions over quarks transverse momenta. The results are compared in a straightforward way with the weighted Sivers asymmetry in the SIDIS process, released by COMPASS in 2016.Comment: 4 pages, 7 figures. In Proceedings of the 17th Workshop on High Energy Spin Physics (DSPIN-17), Dubna, Russia, September 11-15, 201

Trajectory and navigation system design for robotic and piloted missions to Mars

Future Mars exploration missions, both robotic and piloted, may utilize Earth to Mars transfer trajectories that are significantly different from one another, depending upon the type of mission being flown and the time period during which the flight takes place. The use of new or emerging technologies for future missions to Mars, such as aerobraking and nuclear rocket propulsion, may yield navigation requirements that are much more stringent than those of past robotic missions, and are very difficult to meet for some trajectories. This article explores the interdependencies between the properties of direct Earth to Mars trajectories and the Mars approach navigation accuracy that can be achieved using different radio metric data types, such as ranging measurements between an approaching spacecraft and Mars orbiting relay satellites, or Earth based measurements such as coherent Doppler and very long baseline interferometry. The trajectory characteristics affecting navigation performance are identified, and the variations in accuracy that might be experienced over the range of different Mars approach trajectories are discussed. The results predict that three sigma periapsis altitude navigation uncertainties of 2 to 10 km can be achieved when a Mars orbiting satellite is used as a navigation aid

Topological lower bounds for the chromatic number: A hierarchy

This paper is a study of ``topological'' lower bounds for the chromatic number of a graph. Such a lower bound was first introduced by Lov\'asz in 1978, in his famous proof of the \emph{Kneser conjecture} via Algebraic Topology. This conjecture stated that the \emph{Kneser graph} \KG_{m,n}, the graph with all $k$-element subsets of $\{1,2,...,n\}$ as vertices and all pairs of disjoint sets as edges, has chromatic number $n-2k+2$. Several other proofs have since been published (by B\'ar\'any, Schrijver, Dolnikov, Sarkaria, Kriz, Greene, and others), all of them based on some version of the Borsuk--Ulam theorem, but otherwise quite different. Each can be extended to yield some lower bound on the chromatic number of an arbitrary graph. (Indeed, we observe that \emph{every} finite graph may be represented as a generalized Kneser graph, to which the above bounds apply.) We show that these bounds are almost linearly ordered by strength, the strongest one being essentially Lov\'asz' original bound in terms of a neighborhood complex. We also present and compare various definitions of a \emph{box complex} of a graph (developing ideas of Alon, Frankl, and Lov\'asz and of \kriz). A suitable box complex is equivalent to Lov\'asz' complex, but the construction is simpler and functorial, mapping graphs with homomorphisms to $\Z_2$-spaces with $\Z_2$-maps.Comment: 16 pages, 1 figure. Jahresbericht der DMV, to appea