Possibility of short-term probabilistic forecasts for large earthquakes making good use of the limitations of existing catalogs

Solar activity facilitates daily forecasts of large earthquakes

Despite the extensive literature related to earthquakes, an effective method to forecast and avoid occasional seismic hazards that cause substantial damage is lacking. The Sun has recently been identified as a potential precursor to earthquakes, although no causal relationship between its activity and the Earth's seismicity has been established. This study was aimed at investigating whether such a relationship exists and whether it can be used to improve earthquake forecasting. The edit distances between earthquake point processes were combined with delay-coordinate distances for sunspot numbers. The comparison of these two indicated the existence of unidirectional causal coupling from solar activity to seismicity on Earth, and a radial basis function regressor showed accuracy improvements in the largest magnitude prediction of next days by 2.6%-17.9% in the odds ratio when sunspot distances were included.

Two efficient calculations of edit distance between marked point processes

In this paper, we propose to use linear programming methods or a more specialized method, namely, the Hungarian method, for speeding up the exact calculation of an edit distance for marked point processes [Y. Hirata and K. Aihara, Chaos 25, 123117 (2015)]. The key observation is that the problem of calculating the edit distance reduces to a matching problem on a bipartite graph. Our preliminary numerical results show that the proposed implementations are faster than the conventional ones by a factor of 10-1000.

Prediction of flow dynamics using point processes

Describing a time series parsimoniously is the first step to study the underlying dynamics. For a time-discrete system, a generating partition provides a compact description such that a time series and a symbolic sequence are one-to-one. But, for a time-continuous system, such a compact description does not have a solid basis. Here, we propose to describe a time-continuous time series using a local cross section and the times when the orbit crosses the local cross section. We show that if such a series of crossing times and some past observations are given, we can predict the system's dynamics with fine accuracy. This reconstructability neither depends strongly on the size nor the placement of the local cross section if we have a sufficiently long database. We demonstrate the proposed method using the Lorenz model as well as the actual measurement of wind speed.

Robustness and versatility of a nonlinear interdependence method for directional coupling detection from spike trains

The detection of directional couplings between dynamics based on measured spike trains is a crucial problem in the understanding of many different systems. In particular, in neuroscience it is important to assess the connectivity between neurons. One of the approaches that can estimate directional coupling from the analysis of point processes is the nonlinear interdependence measure L. Although its efficacy has already been demonstrated, it still needs to be tested under more challenging and realistic conditions prior to an application to real data. Thus, in this paper we use the Hindmarsh-Rose model system to test the method in the presence of noise and for different spiking regimes. We also examine the influence of different parameters and spike train distances. Our results show that the measure L is versatile and robust to various types of noise, and thus suitable for application to experimental data.