MDL Convergence Speed for Bernoulli Sequences

The Minimum Description Length principle for online sequence estimation/prediction in a proper learning setup is studied. If the underlying model class is discrete, then the total expected square loss is a particularly interesting performance measure: (a) this quantity is finitely bounded, implying convergence with probability one, and (b) it additionally specifies the convergence speed. For MDL, in general one can only have loss bounds which are finite but exponentially larger than those for Bayes mixtures. We show that this is even the case if the model class contains only Bernoulli distributions. We derive a new upper bound on the prediction error for countable Bernoulli classes. This implies a small bound (comparable to the one for Bayes mixtures) for certain important model classes. We discuss the application to Machine Learning tasks such as classification and hypothesis testing, and generalization to countable classes of i.i.d. models.Comment: 28 page

Extreme State Aggregation Beyond MDPs

We consider a Reinforcement Learning setup where an agent interacts with an environment in observation-reward-action cycles without any (esp.\ MDP) assumptions on the environment. State aggregation and more generally feature reinforcement learning is concerned with mapping histories/raw-states to reduced/aggregated states. The idea behind both is that the resulting reduced process (approximately) forms a small stationary finite-state MDP, which can then be efficiently solved or learnt. We considerably generalize existing aggregation results by showing that even if the reduced process is not an MDP, the (q-)value functions and (optimal) policies of an associated MDP with same state-space size solve the original problem, as long as the solution can approximately be represented as a function of the reduced states. This implies an upper bound on the required state space size that holds uniformly for all RL problems. It may also explain why RL algorithms designed for MDPs sometimes perform well beyond MDPs.Comment: 28 LaTeX pages. 8 Theorem

On Martin-Löf convergence of Solomonoff’s mixture

We study the convergence of Solomonoff’s universal mixture on individual Martin-Löf random sequences. A new result is presented extending the work of Hutter and Muchnik (2004) by showing that there does not exist a universal mixture that converges on all Martin-Löf random sequences

A time-dependent Tsirelson's bound from limits on the rate of information gain in quantum systems

We consider the problem of distinguishing between a set of arbitrary quantum states in a setting in which the time available to perform the measurement is limited. We provide simple upper bounds on how well we can perform state discrimination in a given time as a function of either the average energy or the range of energies available during the measurement. We exhibit a specific strategy that nearly attains this bound. Finally, we consider several applications of our result. First, we obtain a time-dependent Tsirelson's bound that limits the extent of the Bell inequality violation that can be in principle be demonstrated in a given time t. Second, we obtain a Margolus-Levitin type bound when considering the special case of distinguishing orthogonal pure states.Comment: 15 pages, revtex, 1 figur

Decoupling with unitary approximate two-designs

Consider a bipartite system, of which one subsystem, A, undergoes a physical evolution separated from the other subsystem, R. One may ask under which conditions this evolution destroys all initial correlations between the subsystems A and R, i.e. decouples the subsystems. A quantitative answer to this question is provided by decoupling theorems, which have been developed recently in the area of quantum information theory. This paper builds on preceding work, which shows that decoupling is achieved if the evolution on A consists of a typical unitary, chosen with respect to the Haar measure, followed by a process that adds sufficient decoherence. Here, we prove a generalized decoupling theorem for the case where the unitary is chosen from an approximate two-design. A main implication of this result is that decoupling is physical, in the sense that it occurs already for short sequences of random two-body interactions, which can be modeled as efficient circuits. Our decoupling result is independent of the dimension of the R system, which shows that approximate 2-designs are appropriate for decoupling even if the dimension of this system is large.Comment: Published versio

Parsec-scale Magnetic-Field Structures in HEAO-1 BL Lacs

We present very long baseline interferometry polarization images of an X-ray selected sample of BL Lacertae objects belonging to the first High Energy Astronomy Observatory (HEAO-1) and the ROSAT-Green Bank (RGB) surveys. These are primarily high-energy-peaked BL Lacs (HBLs) and exhibit core-jet radio morphologies on pc-scales. They show moderately polarized jet components, similar to those of low-energy-peaked BL Lacs (LBLs). The fractional polarization in the unresolved cores of the HBLs is, on average, lower than in the LBLs, while the fractional polarizations in the pc-scale jets of HBLs and LBLs are comparable. However a difference is observed in the orientation of the inferred jet magnetic fields -- while LBL jets are well-known to preferentially exhibit transverse magnetic fields, the HBL jets tend to display longitudinal magnetic fields. Although a `spine-sheath' jet velocity structure, along with larger viewing angles for HBLs could produce the observed magnetic field configuration, differences in other properties of LBLs and HBLs, such as their total radio power, cannot be fully reconciled with the different-angle scenario alone. Instead it appears that LBLs and HBLs differ intrinsically, perhaps in the spin rates of their central black holes.Comment: 41 pages, 21 figures, accepted for publication in MNRA

A theory of metamaterials based on periodically loaded transmission lines: Interaction between magnetoinductive and electromagnetic waves

Published versio

Relativistic separable dual-space Gaussian Pseudopotentials from H to Rn

We generalize the concept of separable dual-space Gaussian pseudopotentials to the relativistic case. This allows us to construct this type of pseudopotential for the whole periodic table and we present a complete table of pseudopotential parameters for all the elements from H to Rn. The relativistic version of this pseudopotential retains all the advantages of its nonrelativistic version. It is separable by construction, it is optimal for integration on a real space grid, it is highly accurate and due to its analytic form it can be specified by a very small number of parameters. The accuracy of the pseudopotential is illustrated by an extensive series of molecular calculations

Properties of the H-alpha-emitting Circumstellar Regions of Be Stars

Long-baseline interferometric observations obtained with the Navy Prototype Optical Interferometer of the H-alpha-emitting envelopes of the Be stars eta Tauri and beta Canis Minoris are presented. For compatibility with the previously published interferometric results in the literature of other Be stars, circularly symmetric and elliptical Gaussian models were fitted to the calibrated H-alpha observations. The models are sufficient in characterizing the angular distribution of the H-alpha-emitting circumstellar material associated with these Be stars. To study the correlations between the various model parameters and the stellar properties, the model parameters for eta Tau and beta CMi were combined with data for other Be stars from the literature. After accounting for the different distances to the sources and stellar continuum flux levels, it was possible to study the relationship between the net H-alpha emission and the physical extent of the H-alpha-emitting circumstellar region. A clear dependence of the net H-alpha emission on the linear size of the emitting region is demonstrated and these results are consistent with an optically thick line emission that is directly proportional to the effective area of the emitting disk. Within the small sample of stars considered in this analysis, no clear dependence on the spectral type or stellar rotation is found, although the results do suggest that hotter stars might have more extended H-alpha-emitting regions.Comment: 24 pages, 16 figures, accepted for publication in Ap

Construction and Expected Performance of the Hadron Blind Detector for the PHENIX Experiment at RHIC

A new Hadron Blind Detector (HBD) for electron identification in high density hadron environment has been installed in the PHENIX detector at RHIC in the fall of 2006. The HBD will identify low momentum electron-positron pairs to reduce the combinatorial background in the $e^{+}e^{-}$ mass spectrum, mainly in the low-mass region below 1 GeV/c$^{2}$. The HBD is a windowless proximity-focusing Cherenkov detector with a radiator length of 50 cm, a CsI photocathode and three layers of Gas Electron Multipliers (GEM). The HBD uses pure CF$_{4}$ as a radiator and a detector gas. Construction details and the expected performance of the detector are described.Comment: QM2006 proceedings, 4 pages 3 figure