A bridge subjected to irregular loads will gradually be damaged. If it is not maintained, disastrous consequences will follow. It’s important, then, to know when maintenance is needed. If we know the mean number of loads within a given time interval as well as the spread around the mean number of loads, then we can identify when to work on the bridge. The loads can be viewed as zero-crossings of a stochastic process.
To understand what we mean by zero-crossings, consider a coin tossing game between two players, Sofia and Peter. When both Sofia and Peter have equal scores we say that a zero-crossing has occurred. Zero-crossings play an important role in many areas, for example, rapid DNA sequencing, edge detection in image analysis, speech recognition and machine learning. To better understand these applications we need to know how to calculate the statistics associated with the zero-crossing.
Markus Nyberg, Ludvig Lizana, and Tobias Ambjörnsson. Zero-crossing statistics for non-Markovian time series. Phys. Rev. E 97, 032114