Estimating Mutual Information

We present two classes of improved estimators for mutual information $M(X,Y)$, from samples of random points distributed according to some joint probability density $\mu(x,y)$. In contrast to conventional estimators based on binnings, they are based on entropy estimates from $k$-nearest neighbour distances. This means that they are data efficient (with $k=1$ we resolve structures down to the smallest possible scales), adaptive (the resolution is higher where data are more numerous), and have minimal bias. Indeed, the bias of the underlying entropy estimates is mainly due to non-uniformity of the density at the smallest resolved scale, giving typically systematic errors which scale as functions of $k/N$ for $N$ points. Numerically, we find that both families become {\it exact} for independent distributions, i.e. the estimator $\hat M(X,Y)$ vanishes (up to statistical fluctuations) if $\mu(x,y) = \mu(x) \mu(y)$. This holds for all tested marginal distributions and for all dimensions of $x$ and $y$. In addition, we give estimators for redundancies between more than 2 random variables. We compare our algorithms in detail with existing algorithms. Finally, we demonstrate the usefulness of our estimators for assessing the actual independence of components obtained from independent component analysis (ICA), for improving ICA, and for estimating the reliability of blind source separation.Comment: 16 pages, including 18 figure

Mutual information rate and bounds for it

The amount of information exchanged per unit of time between two nodes in a dynamical network or between two data sets is a powerful concept for analysing complex systems. This quantity, known as the mutual information rate (MIR), is calculated from the mutual information, which is rigorously defined only for random systems. Moreover, the definition of mutual information is based on probabilities of significant events. This work offers a simple alternative way to calculate the MIR in dynamical (deterministic) networks or between two data sets (not fully deterministic), and to calculate its upper and lower bounds without having to calculate probabilities, but rather in terms of well known and well defined quantities in dynamical systems. As possible applications of our bounds, we study the relationship between synchronisation and the exchange of information in a system of two coupled maps and in experimental networks of coupled oscillators

The adaptive optics simulation analysis tool(kit) (AOSAT)

AOSAT is a python package for the analysis of single-conjugate adaptive optics (SCAO) simulation results. Python is widely used in the astronomical community these days, and AOSAT may be used stand-alone, integrated into a simulation environment, or can easily be extended according to a user's needs. Standalone operation requires the user to provide the residual wavefront frames provided by the SCAO simulation package used, the aperture mask (pupil) used for the simulation, and a custom setup file describing the simulation/analysis configuration. In its standard form, AOSAT's "tearsheet" functionality will then run all standard analyzers, providing an informative plot collection on properties such as the point-spread function (PSF) and its quality, residual tip-tilt, the impact of pupil fragmentation, residual optical aberration modes both static and dynamic, the expected high-contrast performance of suitable instrumentation with and without coronagraphs, and the power spectral density of residual wavefront errors. AOSAT fills the gap between the simple numerical outputs provided by most simulation packages, and the full-scale deployment of instrument simulators and data reduction suites operating on SCAO residual wavefronts. It enables instrument designers and end-users to quickly judge the impact of design or configuration decisions on the final performance of down-stream instrumentation.EPI

Protons in near earth orbit

The proton spectrum in the kinetic energy range 0.1 to 200 GeV was measured by the Alpha Magnetic Spectrometer (AMS) during space shuttle flight STS-91 at an altitude of 380 km. Above the geomagnetic cutoff the observed spectrum is parameterized by a power law. Below the geomagnetic cutoff a substantial second spectrum was observed concentrated at equatorial latitudes with a flux ~ 70 m^-2 sec^-1 sr^-1. Most of these second spectrum protons follow a complicated trajectory and originate from a restricted geographic region.Comment: 19 pages, Latex, 7 .eps figure

Search for antihelium in cosmic rays

The Alpha Magnetic Spectrometer (AMS) was flown on the space shuttle Discovery during flight STS-91 in a 51.7 degree orbit at altitudes between 320 and 390 km. A total of 2.86 * 10^6 helium nuclei were observed in the rigidity range 1 to 140 GV. No antihelium nuclei were detected at any rigidity. An upper limit on the flux ratio of antihelium to helium of < 1.1 * 10^-6 is obtained.Comment: 18 pages, Latex, 9 .eps figure

Study of Z Boson Pair Production in e+e- Collisions at LEP at \sqrt{s}=189 GeV

The pair production of Z bosons is studied using the data collected by the L3 detector at LEP in 1998 in e+e- collisions at a centre-of-mass energy of 189 GeV. All the visible final states are considered and the cross section of this process is measured to be 0.74 +0.15 -0.14 (stat.) +/- 0.04 (syst.) pb. Final states containing b quarks are enhanced by a dedicated selection and their production cross section is found to be 0.18 +0.09 -0.07 (stat.) +/- 0.02 (syst.) pb. Both results are in agreement with the Standard Model predictions. Limits on anomalous couplings between neutral gauge bosons are derived from these measurements

Search for Scalar Leptons in e+e- collisions at \sqrt{s}=189 GeV

We report the result of a search for scalar leptons in e+e- collisions at 189 GeV centre-of-mass energy at LEP. No evidence for such particles is found in a data sample of 176 pb^{-1}. Improved upper limits are set on the production cross sections for these new particles. New exclusion contours in the parameter space of the Minimal Supersymmetric Standard Model are derived, as well as new lower limits on the masses of these supersymmetric particles. Under the assumptions of common gaugino and scalar masses at the GUT scale, we set an absolute lower limit on the mass of the lightest scalar electron of 65.5 Ge

Search for Low Scale Gravity Effects in e+e- Collisions at LEP

Recent theories propose that quantum gravity effects may be observable at LEP energies via gravitons that couple to Standard Model particles and propagate into extra spatial dimensions. The associated production of a graviton and a photon is searched for as well as the effects of virtual graviton exchange in the processes: e+e- -> gamma gamma, ZZ, WW, mu mu, tau tau, qq and ee No evidence for this new interaction is found in the data sample collected by the L3 detector at LEP at centre-of-mass energies up to 183 GeV. Limits close to 1 TeV on the scale of this new scenario of quantum gravity are set

Direct Observation of Longitudinally Polarised W Bosons

The three different helicity states of W bosons, produced in the reaction e+e- -> W+W- -> l nu q q~ are studied using leptonic and hadronic W decays at sqrt{s}=183GeV and 189GeV. The W polarisation is also measured as a function of the scattering angle between the W- and the direction of the e- beam. The analysis demonstrates that W bosons are produced with all three helicities, the longitudinal and the two transverse states. Combining the results from the two center-of-mass energies and with leptonic and hadronic W decays, the fraction of longitudinally polarised W bosons is measured to be 0.261 +/- 0.051(stat.) +/- 0.016(syst.) in agreement with the expectation from the Standard Model