Poissonian bursts in e-mail correspondence

Recent work has shown that the distribution of inter-event times for e-mail communication exhibits a heavy tail which is statistically consistent with a cascading Poisson process. In this work we extend the analysis to higher-order statistics, using the Fano and Allan factors to quantify the extent to which the empirical data depart from the known correlations of Poissonian statistics. The analysis shows that the higher-order statistics from the empirical data is indistinguishable from that of randomly reordered time series, thus demonstrating that e-mail correspondence is no more bursty or correlated than a Poisson process. Furthermore synthetic data sets generated by a cascading Poisson process replicate the burstiness and correlations observed in the empirical data. Finally, a simple rescaling analysis using the best-estimate rate of activity, confirms that the empirically observed correlations arise from a non-homogeneus Poisson process

Physics of Psychophysics: Stevens and Weber-Fechner laws are transfer functions of excitable media

Sensory arrays made of coupled excitable elements can improve both their input sensitivity and dynamic range due to collective non-linear wave properties. This mechanism is studied in a neural network of electrically coupled (e.g. via gap junctions) elements subject to a Poisson signal process. The network response interpolates between a Weber-Fechner logarithmic law and a Stevens power law depending on the relative refractory period of the cell. Therefore, these non-linear transformations of the input level could be performed in the sensory periphery simply due to a basic property: the transfer function of excitable media.Comment: 4 pages, 5 figure

Brownian rectifiers in the presence of temporally asymmetric unbiased forces

The efficiency of energy transduction in a temporally asymmetric rocked ratchet is studied. Time asymmetry favours current in one direction and suppresses it in the opposite direction due to which large efficiency ~ 50% is readily obtained. The spatial asymmetry in the potential together with system inhomogeneity may help in further enhancing the efficiency. Fine tuning of system parameters considered leads to multiple current reversals even in the adiabatic regime

Self Tuned Criticality: Controlling a neuron near its bifurcation point via temporal correlations

Previous work showed that the collective activity of large neuronal networks can be tamed to remain near its critical point by a feedback control that maximizes the temporal correlations of the mean-field fluctuations. Since such correlations behave similarly near instabilities across nonlinear dynamical systems, it is expected that the principle should control also low dimensional dynamical systems exhibiting continuous or discontinuous bifurcations from fixed points to limit cycles. Here we present numerical evidence that the dynamics of a single neuron can be controlled in the vicinity of its bifurcation point. The approach is tested in two models: a 2D generic excitable map and the paradigmatic FitzHugh-Nagumo neuron model. The results show that in both cases, the system can be self-tuned to its bifurcation point by modifying the control parameter according to the first coefficient of the autocorrelation function

Rate-dependent propagation of cardiac action potentials in a one-dimensional fiber

Action potential duration (APD) restitution, which relates APD to the preceding diastolic interval (DI), is a useful tool for predicting the onset of abnormal cardiac rhythms. However, it is known that different pacing protocols lead to different APD restitution curves (RCs). This phenomenon, known as APD rate-dependence, is a consequence of memory in the tissue. In addition to APD restitution, conduction velocity restitution also plays an important role in the spatiotemporal dynamics of cardiac tissue. We present new results concerning rate-dependent restitution in the velocity of propagating action potentials in a one-dimensional fiber. Our numerical simulations show that, independent of the amount of memory in the tissue, waveback velocity exhibits pronounced rate-dependence and the wavefront velocity does not. Moreover, the discrepancy between waveback velocity RCs is most significant for small DI. We provide an analytical explanation of these results, using a system of coupled maps to relate the wavefront and waveback velocities. Our calculations show that waveback velocity rate-dependence is due to APD restitution, not memory.Comment: 17 pages, 7 figure

Motion in a rocked ratchet with spatially periodic friction

We present a detailed study of the transport and energetics of a Brownian particle moving in a periodic potential in the presence of an adiabatic external periodic drive. The particle is considered to move in a medium with periodic space dependent friction with the same periodicity as that of the potential but with a phase lag. We obtain several results, most of them arising due to the medium being inhomogeneous and are sensitive to the phase lag. When the potential is symmetric we show that efficiency of energy transduction can be maximised as a function of noise strength or temperature. However, in the case of asymmtertic potential the temperature may or may not facilitate the energy conversion but current reversals can be obtained as a function of temperature and the amplitude of the periodic drive. The reentrant behaviour of current can also be seen as a function of phase lag

Asymmetric motion in a double-well under the action of zero-mean Gaussian white noise and periodic forcing

Residence times of a particle in both the wells of a double-well system, under the action of zero-mean Gaussian white noise and zero-averaged but temporally asymmetric periodic forcings, are recorded in a numerical simulation. The difference between the relative mean residence times in the two wells shows monotonic variation as a function of asymmetry in the periodic forcing and for a given asymmetry the difference becomes largest at an optimum value of the noise strength. Moreover, the passages from one well to the other become less synchronous at small noise strength as the asymmetry parameter (defined below) differs from zero, but at relatively larger noise strengths the passages become more synchronous with asymmetry in the field sweep. We propose that asymmetric periodic forcing (with zero mean) could provide a simple but sensible physical model for unidirectional motion in a symmetric periodic system aided by a symmetric Gaussian white noise.Comment: Appeared in PRE March 1997, figures available on reques