Inter-event Times Statistic in Stationary Processes: Nonlinear ARMA Modeling of Wind Speed Time Series

The random sequence of inter-event times of a level-crossing is a statistical tool that can be used to investigate time series from complex phenomena. Typical features of observed series as the skewed distribution and long range correlations are modeled using non linear transformations applied to Gaussian ARMA processes. We investigate the distribution of the inter-event times of the level-crossing events in ARMA processes in function of the probability corresponding to the level. For Gaussian ARMA processes we establish a representation of this indicator, prove its symmetry and that it is invariant with respect to the application of a non linear monotonic transformation. Using simulated series we provide evidence that the symmetry disappears if a non monotonic transformation is applied to an ARMA process. We estimate this indicator in wind speed time series obtained from three different databases. Data analysis provides evidence that the indicator is non symmetric, suggesting that only highly non linear transformations of ARMA processes can be used in modeling. We discuss the possible use of the inter-event times in the prediction task.

Mapping input noise to escape noise in integrate-and-fire neurons: a level-crossing approach

Noise in spiking neurons is commonly modeled by a noisy input current or by generating output spikes stochastically with a voltage-dependent hazard rate (“escape noise”). While input noise lends itself to modeling biophysical noise processes, the phenomenological escape noise is mathematically more tractable. Using the level-crossing theory for differentiable Gaussian processes, we derive an approximate mapping between colored input noise and escape noise in leaky integrate-and-fire neurons. This mapping requires the first-passage-time (FPT) density of an overdamped Brownian particle driven by colored noise with respect to an arbitrarily moving boundary. Starting from the Wiener–Rice series for the FPT density, we apply the second-order decoupling approximation of Stratonovich to the case of moving boundaries and derive a simplified hazard-rate representation that is local in time and numerically efficient. This simplification requires the calculation of the non-stationary auto-correlation function of the level-crossing process: For exponentially correlated input noise (Ornstein–Uhlenbeck process), we obtain an exact formula for the zero-lag auto-correlation as a function of noise parameters, mean membrane potential and its speed, as well as an exponential approximation of the full auto-correlation function. The theory well predicts the FPT and interspike interval densities as well as the population activities obtained from simulations with colored input noise and time-dependent stimulus or boundary. The agreement with simulations is strongly enhanced across the sub- and suprathreshold firing regime compared to a first-order decoupling approximation that neglects correlations between level crossings. The second-order approximation also improves upon a previously proposed theory in the subthreshold regime. Depending on a simplicity-accuracy trade-off, all considered approximations represent useful mappings from colored input noise to escape noise, enabling progress in the theory of neuronal population dynamics.

Mechanical Innovations Developed for the Lille Langebro Swing Bridge, Copenhagen

<p>The Lille Langebro (Little Langebro) pedestrian and cycle swing bridge opened to the public in August 2019. The bridge provides a quay-level crossing of the harbour for pedestrians and cyclists and was the outcome of an international design competition. In order to enable the passage of marine craft along the harbour the central sections of the bridge rotate. This paper gives a brief overview of the operating equipment associated with the movement of the two rotating spans before a more detailed discussion on the innovative moment connection developed to secure the joint between the two moving spans when in the bridge closed position.</p>