Successful prediction of horse racing results using a neural network

Most application work within neural computing continues to employ multi-layer perceptrons (MLP). Though many variations of the fully interconnected feed-forward MLP, and even more variations of the back propagation learning rule, exist; the first section of the paper attempts to highlight several properties of these standard networks. The second section outlines an application-namely the prediction of horse racing result

Long-Term Evolution of Massive Black Hole Binaries. III. Binary Evolution in Collisional Nuclei

[Abridged] In galactic nuclei with sufficiently short relaxation times, binary supermassive black holes can evolve beyond their stalling radii via continued interaction with stars. We study this "collisional" evolutionary regime using both fully self-consistent N-body integrations and approximate Fokker-Planck models. The N-body integrations employ particle numbers up to 0.26M and a direct-summation potential solver; close interactions involving the binary are treated using a new implementation of the Mikkola-Aarseth chain regularization algorithm. Even at these large values of N, two-body scattering occurs at high enough rates in the simulations that they can not be simply scaled to the large-N regime of real galaxies. The Fokker-Planck model is used to bridge this gap; it includes, for the first time, binary-induced changes in the stellar density and potential. The Fokker-Planck model is shown to accurately reproduce the results of the N-body integrations, and is then extended to the much larger N regime of real galaxies. Analytic expressions are derived that accurately reproduce the time dependence of the binary semi-major axis as predicted by the Fokker-Planck model. Gravitational wave coalescence is shown to occur in <10 Gyr in nuclei with velocity dispersions below about 80 km/s. Formation of a core results from a competition between ejection of stars by the binary and re-supply of depleted orbits via two-body scattering. Mass deficits as large as ~4 times the binary mass are produced before coalescence. After the two black holes coalesce, a Bahcall-Wolf cusp appears around the single hole in one relaxation time, resulting in a nuclear density profile consisting of a flat core with an inner, compact cluster, similar to what is observed at the centers of low-luminosity spheroids.Comment: 21 page

Phase Space Transport in Noisy Hamiltonian Systems

This paper analyses the effect of low amplitude friction and noise in accelerating phase space transport in time-independent Hamiltonian systems that exhibit global stochasticity. Numerical experiments reveal that even very weak non-Hamiltonian perturbations can dramatically increase the rate at which an ensemble of orbits penetrates obstructions like cantori or Arnold webs, thus accelerating the approach towards an invariant measure, i.e., a near-microcanonical population of the accessible phase space region. An investigation of first passage times through cantori leads to three conclusions, namely: (i) that, at least for white noise, the detailed form of the perturbation is unimportant, (ii) that the presence or absence of friction is largely irrelevant, and (iii) that, overall, the amplitude of the response to weak noise scales logarithmically in the amplitude of the noise.Comment: 13 pages, 3 Postscript figures, latex, no macors. Annals of the New York Academy of Sciences, in pres

On the Importance of Registers for Computability

All consensus hierarchies in the literature assume that we have, in addition to copies of a given object, an unbounded number of registers. But why do we really need these registers? This paper considers what would happen if one attempts to solve consensus using various objects but without any registers. We show that under a reasonable assumption, objects like queues and stacks cannot emulate the missing registers. We also show that, perhaps surprisingly, initialization, shown to have no computational consequences when registers are readily available, is crucial in determining the synchronization power of objects when no registers are allowed. Finally, we show that without registers, the number of available objects affects the level of consensus that can be solved. Our work thus raises the question of whether consensus hierarchies which assume an unbounded number of registers truly capture synchronization power, and begins a line of research aimed at better understanding the interaction between read-write memory and the powerful synchronization operations available on modern architectures.Comment: 12 pages, 0 figure

Gravitational waves from galaxy encounters

We discuss the emission of gravitational radiation produced in encounters of dark matter galactic halos. To this aim we perform a number of numerical simulations of typical galaxy mergers, computing the associated gravitational radiation waveforms as well as the energy released in the processes. Our simulations yield dimensionless gravitational wave amplitudes of the order of $10^{-13}$ and gravitational wave frequencies of the order of $10^{-16}$ Hz, when the galaxies are located at a distance of 10 Mpc. These values are of the same order as those arising in the gravitational radiation originated by strong variations of the gravitational field in the early Universe, and therefore, such gravitational waves cannot be directly observed by ground-based detectors. We discuss the feasibility of an indirect detection by means of the B-mode polarization of the Cosmic Microwave Background (CMB) induced by such waves. Our results show that the gravitational waves from encounters of dark matter galactic halos leave much too small an imprint on the CMB polarization to be actually observed with ongoing and future missions.Comment: 9 pages with revtex style, 3 ps figures; to be published in Physical Review

The M(BH)-Sigma Relation for Supermassive Black Holes

We investigate the differences in the M(BH)-sigma relation derived recently by Ferrarese & Merritt (2000) and Gebhardt et al. (2000). The shallower slope found by the latter authors (3.75 vs. 4.8) is due partly to the use of a regression algorithm that ignores measurement errors, and partly to the value of the velocity dispersion adopted for a single galaxy, the Milky Way. A steeper relation is shown to provide a better fit to black hole masses derived from reverberation mapping studies. Combining the stellar dynamical, gas dynamical, and reverberation mapping mass estimates, we derive a best-fit relation M(BH) = 1.30 (+/- 0.36) X 10^8 (sigma_c/200)^{4.72(+/- 0.36)}, where M(BH) is in solar masses, and sigma in km/s.Comment: The Astrophysical Journal, in pres

Chaotic mixing in noisy Hamiltonian systems

This paper summarises an investigation of the effects of low amplitude noise and periodic driving on phase space transport in 3-D Hamiltonian systems, a problem directly applicable to systems like galaxies, where such perturbations reflect internal irregularities and.or a surrounding environment. A new diagnsotic tool is exploited to quantify how, over long times, different segments of the same chaotic orbit can exhibit very different amounts of chaos. First passage time experiments are used to study how small perturbations of an individual orbit can dramatically accelerate phase space transport, allowing `sticky' chaotic orbits trapped near regular islands to become unstuck on suprisingly short time scales. Small perturbations are also studied in the context of orbit ensembles with the aim of understanding how such irregularities can increase the efficacy of chaotic mixing. For both noise and periodic driving, the effect of the perturbation scales roughly in amplitude. For white noise, the details are unimportant: additive and multiplicative noise tend to have similar effects and the presence or absence of a friction related to the noise by a Fluctuation- Dissipation Theorem is largely irrelevant. Allowing for coloured noise can significantly decrease the efficacy of the perturbation, but only when the autocorrelation time, which vanishes for white noise, becomes so large that t here is little power at frequencies comparable to the natural frequencies of the unperturbed orbit. This suggests strongly that noise-induced extrinsic diffusion, like modulational diffusion associated with periodic driving, is a resonance phenomenon. Potential implications for galaxies are discussed.Comment: 15 pages including 18 figures, uses MNRAS LaTeX macro