We propose a new, nonparametric approach to learning and representing transition dynamics in Markov decision processes (MDPs), which can be combined easily with dynamic programming methods for policy optimisation and value estimation. This approach m
akes use of a recently developed representation of conditional distributions as emph{embeddings} in a reproducing kernel Hilbert space (RKHS). Such representations bypass the need for estimating transition probabilities or densities, and apply to any domain on which kernels can be defined. This avoids the need to calculate intractable integrals, since expectations are represented as RKHS inner products whose computation has linear complexity in the number of points used to represent the embedding. We provide guarantees for the proposed applications in MDPs: in the context of a value iteration algorithm, we prove convergence to either the optimal policy, or to the closest projection of the optimal policy in our model class (an RKHS), under reasonable assumptions. In experiments, we investigate a learning task in a typical classical control setting (the under-actuated pendulum), and on a navigation problem where only images from a sensor are observed. For policy optimisation we compare with least-squares policy iteration where a Gaussian process is used for value function estimation. For value estimation we also compare to the NPDP method. Our approach achieves better performance in all experiments.
We investigate the entanglement properties of the Kondo spin chain when it is prepared in its ground state as well as its dynamics following a single bond quench. We show that a true measure of entanglement such as negativity enables to characterize
the unique features of the gapless Kondo regime. We determine the spatial extent of the Kondo screening cloud and propose an ansatz for the ground state in the Kondo regime accessible to this spin chain; we also demonstrate that the impurity spin is indeed maximally entangled with the Kondo cloud. We exploit these features of the entanglement in the gapless Kondo regime to show that a single local quench at one end of a Kondo spin chain may always induce a fast and long lived oscillatory dynamics, which establishes a high quality entanglement between the individual spins at the opposite ends of the chain. This entanglement is a footprint of the presence of the Kondo cloud and may be engineered so as to attain - even for very large chains- a constant high value independent of the length; in addition, it is thermally robust. To better evidence the remarkable peculiarities of the Kondo regime, we carry a parallel analysis of the entanglement properties of the Kondo spin chain model in the gapped dimerised regime where these remarkable features are absent.
We have studied the X-ray nuclear activity of 187 nearby (distance < 15 Mpc) galaxies observed with Chandra/ACIS. We found that 86 of them have a point-like X-ray core, consistent with an accreting black hole (BH). We argue that the majority of them
are nuclear BHs, rather than X-ray binaries. The fraction of galaxies with an X-ray detected nuclear BH is higher (~60 per cent) for ellipticals and early-type spirals (E to Sb), and lower (~30 per cent) for late-type spirals (Sc to Sm). There is no preferential association of X-ray cores with a large-scale bar; in fact, strongly barred galaxies appear to have slightly lower detection fraction and luminosity for their nuclear X-ray sources, compared with non-barred or weakly barred galaxies of similar Hubble types. The cumulative luminosity distribution of the nuclear sources in the 0.3-8 keV band is a power-law with slope ~-0.5, from ~2 x 10^{38} erg/s to ~10^{42} erg/s. The Eddington ratio is lower for ellipticals (L_{X}/L_{Edd} ~ 10^{-8}) and higher for late-type spirals (up to L_{X}/L_{Edd} ~ 10^{-4}), but in all cases, the accretion rate is low enough to be in the radiatively-inefficient regime. The intrinsic NH is generally low, especially for the less luminous sources: there appear to be no Type-2 nuclear BHs at luminosities <~ 10^{39} erg/s. The lack of a dusty torus or of other sources of intrinsic absorption (e.g., an optically-thick disk wind) may be directly related to the lack of a standard accretion disk around those faint nuclear BHs. The fraction of obscured sources increases with the nuclear BH luminosity: 2/3 of the sources with L_{X} > 10^{40} erg/s have a fitted NH > 10^{22} cm^{-2}. This is contrary to the declining trend of the obscured fraction with increasing luminosities, observed in more luminous AGN and quasars.
The determination of atmospheric parameters is the first and most fundamental step in the analysis of a stellar spectrum. Current and forthcoming surveys involve samples of up to several million stars, and therefore fully automated approaches are req
uired to handle not just data reduction but also the analysis, and in particular the determination of atmospheric parameters. We propose that a successful methodology needs, at the very least, to pass a series of consistency tests that we dub the four-step program. This and related issues are discussed in some detail in the context of the massive data set to be obtained with the Radial Velocity Spectrometer onboard Gaia
(Abridged) Combining cosmic shear power spectra and cluster counts is powerful to improve cosmological parameter constraints and/or test inherent systematics. However they probe the same cosmic mass density field, if the two are drawn from the same s
urvey region, and therefore the combination may be less powerful than first thought. We investigate the cross-covariance between the cosmic shear power spectra and the cluster counts based on the halo model approach, where the cross-covariance arises from the three-point correlations of the underlying mass density field. Fully taking into account the cross-covariance as well as non-Gaussian errors on the lensing power spectrum covariance, we find a significant cross-correlation between the lensing power spectrum signals at multipoles l~10^3 and the cluster counts containing halos with masses M>10^{14}Msun. Including the cross-covariance for the combined measurement degrades and in some cases improves the total signal-to-noise ratios up to plus or minus 20% relative to when the two are independent. For cosmological parameter determination, the cross-covariance has a smaller effect as a result of working in a multi-dimensional parameter space, implying that the two observables can be considered independent to a good approximation. We also discuss that cluster count experiments using lensing-selected mass peaks could be more complementary to cosmic shear tomography than mass-selected cluster counts of the corresponding mass threshold. Using lensing selected clusters with a realistic usable detection threshold (S/N~6 for a ground-based survey), the uncertainty on each dark energy parameter may be roughly halved by the combined experiments, relative to using the power spectra alone.
