Extrapolation of K to \pi\pi decay amplitude

We examine the uncertainties involved in the off-mass-shell extrapolation of the $K\rightarrow \pi\pi$ decay amplitude with emphasis on those aspects that have so far been overlooked or ignored. Among them are initial-state interactions, choice of the extrapolated kaon field, and the relation between the asymptotic behavior and the zeros of the decay amplitude. In the inelastic region the phase of the decay amplitude cannot be determined by strong interaction alone and even its asymptotic value cannot be deduced from experiment. More a fundamental issue is intrinsic nonuniqueness of off-shell values of hadronic matrix elements in general. Though we are hampered with complexity of intermediate-energy meson interactions, we attempt to obtain a quantitative idea of the uncertainties due to the inelastic region and find that they can be much larger than more optimistic views portray.Comment: 16 pages with 5 eps figures in REVTE

Complexity Measures from Interaction Structures

We evaluate new complexity measures on the symbolic dynamics of coupled tent maps and cellular automata. These measures quantify complexity in terms of $k$-th order statistical dependencies that cannot be reduced to interactions between $k-1$ units. We demonstrate that these measures are able to identify complex dynamical regimes.Comment: 11 pages, figures improved, minor changes to the tex

A Bayesian approach to the estimation of maps between riemannian manifolds

Let \Theta be a smooth compact oriented manifold without boundary, embedded in a euclidean space and let \gamma be a smooth map \Theta into a riemannian manifold \Lambda. An unknown state \theta \in \Theta is observed via X=\theta+\epsilon \xi where \epsilon>0 is a small parameter and \xi is a white Gaussian noise. For a given smooth prior on \Theta and smooth estimator g of the map \gamma we derive a second-order asymptotic expansion for the related Bayesian risk. The calculation involves the geometry of the underlying spaces \Theta and \Lambda, in particular, the integration-by-parts formula. Using this result, a second-order minimax estimator of \gamma is found based on the modern theory of harmonic maps and hypo-elliptic differential operators.Comment: 20 pages, no figures published version includes correction to eq.s 31, 41, 4

Anisotropic and strong negative magneto-resistance in the three-dimensional topological insulator Bi2Se3

We report on high-field angle-dependent magneto-transport measurements on epitaxial thin films of Bi2Se3, a three-dimensional topological insulator. At low temperature, we observe quantum oscillations that demonstrate the simultaneous presence of bulk and surface carriers. The magneto- resistance of Bi2Se3 is found to be highly anisotropic. In the presence of a parallel electric and magnetic field, we observe a strong negative longitudinal magneto-resistance that has been consid- ered as a smoking-gun for the presence of chiral fermions in a certain class of semi-metals due to the so-called axial anomaly. Its observation in a three-dimensional topological insulator implies that the axial anomaly may be in fact a far more generic phenomenon than originally thought.Comment: 6 pages, 4 figure

Online Meta-learning by Parallel Algorithm Competition

The efficiency of reinforcement learning algorithms depends critically on a few meta-parameters that modulates the learning updates and the trade-off between exploration and exploitation. The adaptation of the meta-parameters is an open question in reinforcement learning, which arguably has become more of an issue recently with the success of deep reinforcement learning in high-dimensional state spaces. The long learning times in domains such as Atari 2600 video games makes it not feasible to perform comprehensive searches of appropriate meta-parameter values. We propose the Online Meta-learning by Parallel Algorithm Competition (OMPAC) method. In the OMPAC method, several instances of a reinforcement learning algorithm are run in parallel with small differences in the initial values of the meta-parameters. After a fixed number of episodes, the instances are selected based on their performance in the task at hand. Before continuing the learning, Gaussian noise is added to the meta-parameters with a predefined probability. We validate the OMPAC method by improving the state-of-the-art results in stochastic SZ-Tetris and in standard Tetris with a smaller, 10$\times$10, board, by 31% and 84%, respectively, and by improving the results for deep Sarsa($\lambda$) agents in three Atari 2600 games by 62% or more. The experiments also show the ability of the OMPAC method to adapt the meta-parameters according to the learning progress in different tasks.Comment: 15 pages, 10 figures. arXiv admin note: text overlap with arXiv:1702.0311

Euclidean versus hyperbolic congestion in idealized versus experimental networks

This paper proposes a mathematical justification of the phenomenon of extreme congestion at a very limited number of nodes in very large networks. It is argued that this phenomenon occurs as a combination of the negative curvature property of the network together with minimum length routing. More specifically, it is shown that, in a large n-dimensional hyperbolic ball B of radius R viewed as a roughly similar model of a Gromov hyperbolic network, the proportion of traffic paths transiting through a small ball near the center is independent of the radius R whereas, in a Euclidean ball, the same proportion scales as 1/R^{n-1}. This discrepancy persists for the traffic load, which at the center of the hyperbolic ball scales as the square of the volume, whereas the same traffic load scales as the volume to the power (n+1)/n in the Euclidean ball. This provides a theoretical justification of the experimental exponent discrepancy observed by Narayan and Saniee between traffic loads in Gromov-hyperbolic networks from the Rocketfuel data base and synthetic Euclidean lattice networks. It is further conjectured that for networks that do not enjoy the obvious symmetry of hyperbolic and Euclidean balls, the point of maximum traffic is near the center of mass of the network.Comment: 23 pages, 4 figure

Remarks on the naturality of quantization

Hamiltonian quantization of an integral compact symplectic manifold M depends on a choice of compatible almost complex structure J. For open sets U in the set of compatible almost complex structures and small enough values of Planck's constant, the Hilbert spaces of the quantization form a bundle over U with a natural connection. In this paper we examine the dependence of the Hilbert spaces on the choice of J, by computing the semi-classical limit of the curvature of this connection. We also show that parallel transport provides a link between the action of the group Symp(M) of symplectomorphisms of M and the Schrodinger equation.Comment: 20 page

CFD code comparison for 2D airfoil flows

The current paper presents the effort, in the EU AVATAR project, to establish the necessary requirements to obtain consistent lift over drag ratios among seven CFD codes. The flow around a 2D airfoil case is studied, for both transitional and fully turbulent conditions at Reynolds numbers of 3 × 106 and 15 × 106. The necessary grid resolution, domain size, and iterative convergence criteria to have consistent results are discussed, and suggestions are given for best practice. For the fully turbulent results four out of seven codes provide consistent results. For the laminar-turbulent transitional results only three out of seven provided results, and the agreement is generally lower than for the fully turbulent case

On the monodromy of the moduli space of Calabi-Yau threefolds coming from eight planes in P3\mathbb{P}^3

It is a fundamental problem in geometry to decide which moduli spaces of polarized algebraic varieties are embedded by their period maps as Zariski open subsets of locally Hermitian symmetric domains. In the present work we prove that the moduli space of Calabi-Yau threefolds coming from eight planes in $\mathbb{P}^3$ does {\em not} have this property. We show furthermore that the monodromy group of a good family is Zariski dense in the corresponding symplectic group. Moreover, we study a natural sublocus which we call hyperelliptic locus, over which the variation of Hodge structures is naturally isomorphic to wedge product of a variation of Hodge structures of weight one. It turns out the hyperelliptic locus does not extend to a Shimura subvariety of type III (Siegel space) within the moduli space. Besides general Hodge theory, representation theory and computational commutative algebra, one of the proofs depends on a new result on the tensor product decomposition of complex polarized variations of Hodge structures.Comment: 26 page