Composition Operators on the Dirichlet Space and Related Problems

In this paper we investigate the following problem: when a bounded analytic function $\phi$ on the unit disk $\mathbb{D}$, fixing 0, is such that $\{\phi^n : n = 0, 1, 2, . . . \}$ is orthogonal in $\mathbb{D}$?, and consider the problem of characterizing the univalent, full self-maps of $\mathbb{D}$ in terms of the norm of the composition operator induced. The first problem is analogous to a celebrated question asked by W. Rudin on the Hardy space setting that was answered recently ([3] and [15]). The second problem is analogous to a problem investigated by J. Shapiro in [14] about characterization of inner functions in the setting of $H^2$.Comment: 8 pages, 1 figure. See also http://webdelprofesor.ula.ve/nucleotachira/gchacon or http://webdelprofesor.ula.ve/humanidades/grchaco

Design and evaluation of an augmented reality head-mounted display user interface for controlling legged manipulators

Designing an intuitive User Interface (UI) for controlling assistive robots remains challenging. Most existing UIs leverage traditional control interfaces such as joysticks, hand-held controllers, and 2D UIs. Thus, users have limited availability to use their hands for other tasks. Furthermore, although there is extensive research regarding legged manipulators, comparatively little is on their UIs. Towards extending the state-of-art in this domain, we provide a user study comparing an Augmented Reality (AR) Head-Mounted Display (HMD) UI we developed for controlling a legged manipulator against off-the-shelf control methods for such robots. We made this comparison baseline across multiple factors relevant to a successful interaction. The results from our user study ( N=17 ) show that although the AR UI increases immersion, off-the-shelf control methods outperformed the AR UI in terms of time performance and cognitive workload. Nonetheless, a follow-up pilot study incorporating the lessons learned shows that AR UIs can outpace hand-held-based control methods and reduce the cognitive requirements when designers include hands-free interactions and cognitive offloading principles into the UI

A cross-linguistic database of phonetic transcription systems

Contrary to what non-practitioners might expect, the systems of phonetic notation used by linguists are highly idiosyncratic. Not only do various linguistic subfields disagree on the specific symbols they use to denote the speech sounds of languages, but also in large databases of sound inventories considerable variation can be found. Inspired by recent efforts to link cross-linguistic data with help of reference catalogues (Glottolog, Concepticon) across different resources, we present initial efforts to link different phonetic notation systems to a catalogue of speech sounds. This is achieved with the help of a database accompanied by a software framework that uses a limited but easily extendable set of non-binary feature values to allow for quick and convenient registration of different transcription systems, while at the same time linking to additional datasets with restricted inventories. Linking different transcription systems enables us to conveniently translate between different phonetic transcription systems, while linking sounds to databases allows users quick access to various kinds of metadata, including feature values, statistics on phoneme inventories, and information on prosody and sound classes. In order to prove the feasibility of this enterprise, we supplement an initial version of our cross-linguistic database of phonetic transcription systems (CLTS), which currently registers five transcription systems and links to fifteen datasets, as well as a web application, which permits users to conveniently test the power of the automatic translation across transcription systems

Controlling chaotic transport in two-dimensional periodic potentials

We uncover and characterize different chaotic transport scenarios in perfect two-dimensional periodic potentials by controlling the chaotic dynamics of particles subjected to periodic external forces in the absence of a ratchet effect i.e., with no directed transport by symmetry breaking of zero-mean forces . After identifying relevant symmetries of the equations of motion, analytical estimates in parameter space for the occurrence of different transport scenarios are provided and confirmed by numerical simulations. These scenarios are highly sensitive to variations of the system’s asymmetry parameters, including the eccentricity of the two-dimensional periodic potential and the direction of dc and ac forces, which could be useful for particle sorting purposes in those cases where chaos is unavoidablePostprint (published version

Bouncing states of a droplet on a liquid surface under generalized forcing

Droplets can exhibit complex dynamics when vertically and sinusoidally forced by a liquid surface from which they remain separated by a thin air cushion. Here we extend previous studies to include a family of periodic forcing functions that vary smoothly from sinusoidal to square wave by changing a single parameter. Through analytical and numerical work we find that the dynamics of the droplets and transitions between regular and chaotic regimes are effectively controlled by the impulse imparted on the droplets over a half-period. We also find that having nonsinusoidal forcing lowers the threshold amplitudes for most of the dynamical regimes. This is explained on the basis of a correlation between impulse increases and subsequent energy increases

Uniaxial pressure dependence of magnetic order in MnSi

We report comprehensive small angle neutron scattering (SANS) measurements complemented by ac susceptibility data of the helical order, conical phase and skyrmion lattice phase (SLP) in MnSi under uniaxial pressures. For all crystallographic orientations uniaxial pressure favours the phase for which a spatial modulation of the magnetization is closest to the pressure axis. Uniaxial pressures as low as 1kbar applied perpendicular to the magnetic field axis enhance the skyrmion lattice phase substantially, whereas the skyrmion lattice phase is suppressed for pressure parallel to the field. Taken together we present quantitative microscopic information how strain couples to magnetic order in the chiral magnet MnSi.Comment: 23 pages, includes supplemen