Numerical and experimental study of the effects of noise on the permutation entropy

We analyze the effects of noise on the permutation entropy of dynamical systems. We take as numerical examples the logistic map and the R\"ossler system. Upon varying the noise strengthfaster, we find a transition from an almost-deterministic regime, where the permutation entropy grows slower than linearly with the pattern dimension, to a noise-dominated regime, where the permutation entropy grows faster than linearly with the pattern dimension. We perform the same analysis on experimental time-series by considering the stochastic spiking output of a semiconductor laser with optical feedback. Because of the experimental conditions, the dynamics is found to be always in the noise-dominated regime. Nevertheless, the analysis allows to detect regularities of the underlying dynamics. By comparing the results of these three different examples, we discuss the possibility of determining from a time series whether the underlying dynamics is dominated by noise or not

Green's function based unparameterised multi-dimensional kernel density and likelihood ratio estimator

This paper introduces a probability density estimator based on Green's function identities. A density model is constructed under the sole assumption that the probability density is differentiable. The method is implemented as a binary likelihood estimator for classification purposes, so issues such as mis-modeling and overtraining are also discussed. The identity behind the density estimator can be interpreted as a real-valued, non-scalar kernel method which is able to reconstruct differentiable density functions.Comment: 7 pages, 4 figures. JPCS accepted it as a proceedings to the ACAT worksho

Soft-pulse dynamical decoupling in a cavity

Dynamical decoupling is a coherent control technique where the intrinsic and extrinsic couplings of a quantum system are effectively averaged out by application of specially designed driving fields (refocusing pulse sequences). This entails pumping energy into the system, which can be especially dangerous when it has sharp spectral features like a cavity mode close to resonance. In this work we show that such an effect can be avoided with properly constructed refocusing sequences. To this end we construct the average Hamiltonian expansion for the system evolution operator associated with a single ``soft'' pi-pulse. To second order in the pulse duration, we characterize a symmetric pulse shape by three parameters, two of which can be turned to zero by shaping. We express the effective Hamiltonians for several pulse sequences in terms of these parameters, and use the results to analyze the structure of error operators for controlled Jaynes-Cummings Hamiltonian. When errors are cancelled to second order, numerical simulations show excellent qubit fidelity with strongly-suppressed oscillator heating.Comment: 9pages, 5eps figure

Soft-Pulse Dynamical Decoupling with Markovian Decoherence

We consider the effect of broadband decoherence on the performance of refocusing sequences, having in mind applications of dynamical decoupling in concatenation with quantum error correcting codes as the first stage of coherence protection. Specifically, we construct cumulant expansions of effective decoherence operators for a qubit driven by a pulse of a generic symmetric shape, and for several sequences of $\pi$- and $\pi/2$-pulses. While, in general, the performance of soft pulses in decoupling sequences in the presence of Markovian decoherence is worse than that of the ideal $\delta$-pulses, it can be substantially improved by shaping.Comment: New version contains minor content clarification

Blockade of adenosine A2A receptors prevents protein phosphorylation in the striatum induced by cortical stimulation

©2006 Society for NeurosciencePrevious studies have shown that cortical stimulation selectively activates extracellular signal-regulated kinase 1/2 (ERK1/2) phosphorylation and immediate early gene expression in striatal GABAergic enkephalinergic neurons. In the present study, we demonstrate that blockade of adenosine A2A receptors with caffeine or a selective A2A receptor antagonist counteracts the striatal activation of cAMP– protein kinase A cascade (phosphorylation of the Ser845 residue of the glutamate receptor 1 subunit of the AMPA receptor) and mitogenactivated protein kinase (ERK1/2 phosphorylation) induced by the in vivo stimulation of corticostriatal afferents. The results indicate that A2A receptors strongly modulate the efficacy of glutamatergic synapses on striatal enkephalinergic neurons.This work was supported by the Intramural Research Program of the National Institutes of Health, National Institute on Drug Abuse, Department of Health and Human Services

On the order of BEC transition in weakly interacting gases predicted by mean-field theory

Predictions from Hartree-Fock (HF), Popov (P), Yukalov-Yukalova (YY) and $t$-matrix approximations regarding the thermodynamics from the normal to the BEC phase in weakly interacting Bose gases are considered. By analyzing the dependence of the chemical potential $\mu$ on temperature $T$ and particle density $\rho$ we show that none of them predicts a second-order phase transition as required by symmetry-breaking general considerations. In this work we find that the isothermal compressibility $\kappa_{T}$ predicted by these theories does not diverge at criticality as expected in a true second-order phase transition. Moreover the isotherms $\mu=\mu(\rho,T)$ typically exhibit a non-singled valued behavior in the vicinity of the BEC transition, a feature forbidden by general thermodynamic principles. This behavior can be avoided if a first order phase transition is appealed. The facts described above show that although these mean field approximations give correct results near zero temperature they are endowed with thermodynamic anomalies in the vicinity of the BEC transition. We address the implications of these results in the interpretation of current experiments with ultracold trapped alkali gases.Comment: 16 pages, 5 figure