Bayesian multitask inverse reinforcement learning

We generalise the problem of inverse reinforcement learning to multiple tasks, from multiple demonstrations. Each one may represent one expert trying to solve a different task, or as different experts trying to solve the same task. Our main contribution is to formalise the problem as statistical preference elicitation, via a number of structured priors, whose form captures our biases about the relatedness of different tasks or expert policies. In doing so, we introduce a prior on policy optimality, which is more natural to specify. We show that our framework allows us not only to learn to efficiently from multiple experts but to also effectively differentiate between the goals of each. Possible applications include analysing the intrinsic motivations of subjects in behavioural experiments and learning from multiple teachers.Comment: Corrected version. 13 pages, 8 figure

Probing the energy bands of a Bose-Einstein condensate in an optical lattice

We simulate three experimental methods which could be realized in the laboratory to probe the band excitation energies and the momentum distribution of a Bose-Einstein condensate inside an optical lattice. The values of the excitation energies obtained in these different methods agree within the accuracy of the simulation. The meaning of the results in terms of density and phase deformations is tested by studying the relaxation of a phase-modulated condensate towards the ground state.Comment: 5 pages, 5 figure

Neutrino Masses, Baryon Asymmetry, Dark Matter and the Moduli Problem : A Complete Framework

Recent developments in string theory have led to "realistic" string compactifications which lead to moduli stabilization while generating a hierarchy between the Electroweak and Planck scales at the same time. However, this seems to suggest a rethink of our standard notions of cosmological evolution after the end of inflation and before the beginning of BBN. We argue that within classes of realistic string compactifications, there generically exists a light modulus with a mass comparable to that of the gravitino which generates a large late-time entropy when it decays. Therefore, all known mechanisms of generating the baryon asymmetry of the Universe in the literature have to take this fact into account. In this work, we find that it is still possible to naturally generate the observed baryon asymmetry of the Universe as well as light left-handed neutrino masses from a period of Affleck-Dine(AD) leptogenesis shortly after the end of inflation, in classes of realistic string constructions with a minimal extension of the MSSM below the unification scale (consisting only of right-handed neutrinos) and satisfying certain microscopic criteria described in the text. The consequences are as follows. The lightest left-handed neutrino is required to be virtually massless. The moduli (gravitino) problem can be naturally solved in this framework both within gravity and gauge mediation. The observed upper bound on the relic abundance constrains the moduli-matter and moduli-gravitino couplings since the DM is produced non-thermally within this framework. Finally, although not a definite prediction, the framework naturally allows a light right-handed neutrino and sneutrinos around the electroweak scale which could have important implications for DM as well as the LHC.Comment: 41 pages, no figures, journal version adde

Granular discharge and clogging for tilted hoppers

We measure the flux of spherical glass beads through a hole as a systematic function of both tilt angle and hole diameter, for two different size beads. The discharge increases with hole diameter in accord with the Beverloo relation for both horizontal and vertical holes, but in the latter case with a larger small-hole cutoff. For large holes the flux decreases linearly in cosine of the tilt angle, vanishing smoothly somewhat below the angle of repose. For small holes it vanishes abruptly at a smaller angle. The conditions for zero flux are discussed in the context of a {\it clogging phase diagram} of flow state vs tilt angle and ratio of hole to grain size

Generalised quantum weakest preconditions

Generalisation of the quantum weakest precondition result of D'Hondt and Panangaden is presented. In particular the most general notion of quantum predicate as positive operator valued measure (POVM) is introduced. The previously known quantum weakest precondition result has been extended to cover the case of POVM playing the role of a quantum predicate. Additionally, our result is valid in infinite dimension case and also holds for a quantum programs defined as a positive but not necessary completely positive transformations of a quantum states.Comment: 7 pages, no figures, added references, changed conten

Stability of Repulsive Bose-Einstein Condensates in a Periodic Potential

The cubic nonlinear Schr\"odinger equation with repulsive nonlinearity and an elliptic function potential models a quasi-one-dimensional repulsive dilute gas Bose-Einstein condensate trapped in a standing light wave. New families of stationary solutions are presented. Some of these solutions have neither an analog in the linear Schr\"odinger equation nor in the integrable nonlinear Schr\"odinger equation. Their stability is examined using analytic and numerical methods. All trivial-phase stable solutions are deformations of the ground state of the linear Schr\"odinger equation. Our results show that a large number of condensed atoms is sufficient to form a stable, periodic condensate. Physically, this implies stability of states near the Thomas-Fermi limit.Comment: 12 pages, 17 figure

Sparticle Spectra and LHC Signatures for Large Volume String Compactifications

We study the supersymmetric particle spectra and LHC collider observables for the large-volume string models with a fundamental scale of 10^{11} GeV that arise in moduli-fixed string compactifications with branes and fluxes. The presence of magnetic fluxes on the brane world volume, required for chirality, perturb the soft terms away from those previously computed in the dilute-flux limit. We use the difference in high-scale gauge couplings to estimate the magnitude of this perturbation and study the potential effects of the magnetic fluxes by generating many random spectra with the soft terms perturbed around the dilute flux limit. Even with a 40% variation in the high-scale soft terms the low-energy spectra take a clear and predictive form. The resulting spectra are broadly similar to those arising on the SPS1a slope, but more degenerate. In their minimal version the models predict the ratios of gaugino masses to be M_1 : M_2 : M_3=(1.5 - 2) : 2 : 6, different to both mSUGRA and mirage mediation. Among the scalars, the squarks tend to be lighter and the sleptons heavier than for comparable mSUGRA models. We generate 10 fb^{-1} of sample LHC data for the random spectra in order to study the range of collider phenomenology that can occur. We perform a detailed mass reconstruction on one example large-volume string model spectrum. 100 fb^{-1} of integrated luminosity is sufficient to discriminate the model from mSUGRA and aspects of the sparticle spectrum can be accurately reconstructed.Comment: 42 pages, 21 figures. Added references and discussion for section 3. Slight changes in the tex

Pair Production of the Lightest Chargino via Gluon-Gluon Collisions

The production of the lightest chargino pair from gluon-gluon fusion is studied in the minimal supersymmetric model(MSSM) at proton-proton colliders. We find that with the chosen parameters, the production rate of the subprocess can be over 2.7 femto barn when the chargino is higgsino-like, and the corresponding total cross section in proton-proton collider can reach 56 femto barn at the LHC in the CP-conserving MSSM. It shows that this loop mediated subprocess can be competitive with the standard Drell-Yan subprocess in proton-proton colliders, especially at the LHC. Furthermore, our calculation shows it would be possible to extract information about some CP-violating phase parameters, if we collected enough chargino pair events.Comment: 39 pages, LaTex, 8 figure