Updating Neighbour Cell List via Crowdsourced User Reports: A Framework for Measuring Time Performance

In modern wireless networks deployments, each serving node needs to keep its Neighbour Cell List (NCL) constantly up to date to keep track of network changes. The time needed by each serving node to update its NCL is an important parameter of the network’s reliability and performance. An adequate estimate of such parameter enables a significant improvement of self-configuration functionalities. This paper focuses on the update time of NCLs when an approach of crowdsourced user reports is adopted. In this setting, each user periodically reports to the serving node information about the set of nodes sensed by the user itself. We show that, by mapping the local topological structure of the network onto states of increasing knowledge, a crisp mathematical framework can be obtained, which allows in turn for the use of a variety of user mobility models. Further, using a simplified mobility model we show how to obtain useful upper bounds on the expected time for a serving node to gain Full Knowledge of its local neighbourhood

Characterization of a periodically driven chaotic dynamical system

We discuss how to characterize the behavior of a chaotic dynamical system depending on a parameter that varies periodically in time. In particular, we study the predictability time, the correlations and the mean responses, by defining a local--in--time version of these quantities. In systems where the time scale related to the time periodic variation of the parameter is much larger than the ``internal'' time scale, one has that the local quantities strongly depend on the phase of the cycle. In this case, the standard global quantities can give misleading information.Comment: 15 pages, Revtex 2.0, 8 figures, included. All files packed with uufile

Type Ia supernovae tests of fractal bubble universe with no cosmic acceleration

The unexpected dimness of Type Ia supernovae at redshifts z >~ 1 has over the past 7 years been seen as an indication that the expansion of the universe is accelerating. A new model cosmology, the "fractal bubble model", has been proposed by one of us [gr-qc/0503099], based on the idea that our observed universe resides in an underdense bubble remnant from a primordial epoch of cosmic inflation, together with a new solution for averaging in an inhomogeneous universe. Although there is no cosmic acceleration, it is claimed that the luminosity distance of type Ia supernovae data will nonetheless fit the new model, since it mimics a Milne universe at low redshifts. In this paper the hypothesis is tested statistically against the available type Ia supernovae data by both chi-square and Bayesian methods. While the standard model with cosmological constant Omega_Lambda = 1-Omega_m is favoured by a Bayesian analysis with wide priors, the comparison depends strongly on the priors chosen for the density parameter, Omega_m. The fractal bubble model gives better agreement generally for Omega_m<0.2. It also gives reasonably good fits for all the range, Omega_m=0.01-0.55, allowing the possibility of a viable cosmology with just baryonic matter, or alternatively with both baryonic matter and additional cold dark matter.Comment: 10 pages, 5 figures, aastex. v3: Corrected volume factor changes parameter estimates and discussion, figures redrawn, references adde

Modeling Kelvin wave cascades in superfluid helium

We study two different types of simplified models for Kelvin wave turbulence on quantized vortex lines in superfluids near zero temperature. Our first model is obtained from a truncated expansion of the Local Induction Approximation (Truncated-LIA) and it is shown to possess the same scalings and the essential behaviour as the full Biot-Savart model, being much simpler than the later and, therefore, more amenable to theoretical and numerical investigations. The Truncated-LIA model supports six-wave interactions and dual cascades, which are clearly demonstrated via the direct numerical simulation of this model in the present paper. In particular, our simulations confirm presence of the weak turbulence regime and the theoretically predicted spectra for the direct energy cascade and the inverse wave action cascade. The second type of model we study, the Differential Approximation Model (DAM), takes a further drastic simplification by assuming locality of interactions in k-space via using a differential closure that preserves the main scalings of the Kelvin wave dynamics. DAMs are even more amenable to study and they form a useful tool by providing simple analytical solutions in the cases when extra physical effects are present, e.g. forcing by reconnections, friction dissipation and phonon radiation. We study these models numerically and test their theoretical predictions, in particular the formation of the stationary spectra, and closeness of numerics for the higher-order DAM to the analytical predictions for the lower-order DAM

Interference in Exclusive Vector Meson Production in Heavy Ion Collisions

Photons emitted from the electromagnetic fields of relativistic heavy ions can fluctuate into quark anti-quark pairs and scatter from a target nucleus, emerging as vector mesons. These coherent interactions are identifiable by final states consisting of the two nuclei and a vector meson with a small transverse momentum. The emitters and targets can switch roles, and the two possibilities are indistinguishable, so interference may occur. Vector mesons are negative parity so the amplitudes have opposite signs. When the meson transverse wavelength is larger than the impact parameter, the interference is large and destructive. The short-lived vector mesons decay before amplitudes from the two sources can overlap, and so cannot interfere directly. However, the decay products are emitted in an entangled state, and the interference depends on observing the complete final state. The non-local wave function is an example of the Einstein-Podolsky-Rosen paradox.Comment: 13 pages with 3 figures; submitted to Physical Review Letter

Dark energy from scalar field with Gauss Bonnet and non-minimal kinetic coupling

We study a model of scalar field with a general non-minimal kinetic coupling to itself and to the curvature, and additional coupling to the Gauss Bonnet 4-dimensional invariant. The model presents rich cosmological dynamics and some of its solutions are analyzed. A variety of scalar fields and potentials giving rise to power-law expansion have been found. The dynamical equation of state is studied for two cases, with and without free kinetic term . In both cases phenomenologically acceptable solutions have been found. Some solutions describe essentially dark energy behavior, and and some solutions contain the decelerated and accelerated phases.Comment: 21 page

Improved linear response for stochastically driven systems

The recently developed short-time linear response algorithm, which predicts the average response of a nonlinear chaotic system with forcing and dissipation to small external perturbation, generally yields high precision of the response prediction, although suffers from numerical instability for long response times due to positive Lyapunov exponents. However, in the case of stochastically driven dynamics, one typically resorts to the classical fluctuation-dissipation formula, which has the drawback of explicitly requiring the probability density of the statistical state together with its derivative for computation, which might not be available with sufficient precision in the case of complex dynamics (usually a Gaussian approximation is used). Here we adapt the short-time linear response formula for stochastically driven dynamics, and observe that, for short and moderate response times before numerical instability develops, it is generally superior to the classical formula with Gaussian approximation for both the additive and multiplicative stochastic forcing. Additionally, a suitable blending with classical formula for longer response times eliminates numerical instability and provides an improved response prediction even for long response times

Predictability in Systems with Many Characteristic Times: The Case of Turbulence

In chaotic dynamical systems, an infinitesimal perturbation is exponentially amplified at a time-rate given by the inverse of the maximum Lyapunov exponent $\lambda$. In fully developed turbulence, $\lambda$ grows as a power of the Reynolds number. This result could seem in contrast with phenomenological arguments suggesting that, as a consequence of `physical' perturbations, the predictability time is roughly given by the characteristic life-time of the large scale structures, and hence independent of the Reynolds number. We show that such a situation is present in generic systems with many degrees of freedom, since the growth of a non-infinitesimal perturbation is determined by cumulative effects of many different characteristic times and is unrelated to the maximum Lyapunov exponent. Our results are illustrated in a chain of coupled maps and in a shell model for the energy cascade in turbulence.Comment: 24 pages, 10 Postscript figures (included), RevTeX 3.0, files packed with uufile

Growth of non-infinitesimal perturbations in turbulence

We discuss the effects of finite perturbations in fully developed turbulence by introducing a measure of the chaoticity degree associated to a given scale of the velocity field. This allows one to determine the predictability time for non-infinitesimal perturbations, generalizing the usual concept of maximum Lyapunov exponent. We also determine the scaling law for our indicator in the framework of the multifractal approach. We find that the scaling exponent is not sensitive to intermittency corrections, but is an invariant of the multifractal models. A numerical test of the results is performed in the shell model for the turbulent energy cascade.Comment: 4 pages, 2 Postscript figures (included), RevTeX 3.0, files packed with uufile