4.1 Anomalies

Figure 1 serves as an example of different behaviors of log ψ and of V. We wish to stress that when studying this system with large σ, the probability distribution is smooth; nonetheless underlying structure is observed in V. This means that, for a given σ, representing the large-scale behavior with one Gaussian, as one may be tempted to do after seeing the probability distribution, is wrong as demonstrated by the structures observed in V. On the other hand, the probability function tends to a smooth limit for σ = 10, whereas the fluctuating V changes with σ; hence V may represent random fluctuations in the data. However, comparing with the raw data in Figure 1a, we can be convinced that structure of the type discovered by V exists in the data. If these are fluctuations or not, one cannot tell from a single set of data.

A generally important question is if, within changing patterns of V, there exists one (or some) which remains relatively stable as function of σ. Such a structure may be viewed as a possible anomaly in the data. It is therefore advisable to study V when looking for anomalies.
