Equivalences of Smooth and Continuous Principal Bundles with Infinite-Dimensional Structure Group

Let K be a a Lie group, modeled on a locally convex space, and M a finite-dimensional paracompact manifold with corners. We show that each continuous principal K-bundle over M is continuously equivalent to a smooth one and that two smooth principal K-bundles over M which are continuously equivalent are also smoothly equivalent. In the concluding section, we relate our results to neighboring topics.Comment: 18 pages, final versio

Measuring spin and CP from semi-hadronic ZZ decays using jet substructure

We apply novel jet techniques to investigate the spin and CP quantum numbers of a heavy resonance X, singly produced in pp -> X -> ZZ -> l(+)l(-)jj at the LHC. We take into account all dominant background processes to show that this channel, which has been considered unobservable until now, can qualify under realistic conditions to supplement measurements of the purely leptonic decay channels X -> ZZ -> 4l. We perform a detailed investigation of spin- and CP-sensitive angular observables on the fully-simulated final state for various spin and CP quantum numbers of the state X, tracing how potential sensitivity communicates through all the steps of a subjet analysis. This allows us to elaborate on the prospects and limitations of performing such measurements with the semihadronic final state. We find our analysis particularly sensitive to a CP-even or CP-odd scalar resonance, while, for tensorial and vectorial resonances, discriminative features are diminished in the boosted kinematical regime.Comment: 12 pages, 7 figures, 2 tables, published versio

The turbulent formation of stars

How stars are born from clouds of gas is a rich physics problem whose solution will inform our understanding of not just stars but also planets, galaxies, and the universe itself. Star formation is stupendously inefficient. Take the Milky Way. Our galaxy contains about a billion solar masses of fresh gas available to form stars-and yet it produces only one solar mass of new stars a year. Accounting for that inefficiency is one of the biggest challenges of modern astrophysics. Why should we care about star formation? Because the process powers the evolution of galaxies and sets the initial conditions for planet formation and thus, ultimately, for life.Comment: published in Physics Today, cover story, see http://www.mso.anu.edu.au/~chfeder/pubs/physics_today/physics_today.htm

R\'enyi Bounds on Information Combining

Bounds on information combining are entropic inequalities that determine how the information, or entropy, of a set of random variables can change when they are combined in certain prescribed ways. Such bounds play an important role in information theory, particularly in coding and Shannon theory. The arguably most elementary kind of information combining is the addition of two binary random variables, i.e. a CNOT gate, and the resulting quantities are fundamental when investigating belief propagation and polar coding. In this work we will generalize the concept to R\'enyi entropies. We give optimal bounds on the conditional R\'enyi entropy after combination, based on a certain convexity or concavity property and discuss when this property indeed holds. Since there is no generally agreed upon definition of the conditional R\'enyi entropy, we consider four different versions from the literature. Finally, we discuss the application of these bounds to the polarization of R\'enyi entropies under polar codes.Comment: 14 pages, accepted for presentation at ISIT 202