The typical building stock was characterized from statistics of previous European projects.
According to Shapiro (2015, p. 202) the simplest assumption on the spatial distribution of seismogenic faults and criticality is that the faults are randomly distributed in space, statistically homogeneous so that the fault density fully characterizes their statistics.
Mathematical techniques and theories for characterizing the statistics of directional data with tensors are hence demanded.
In particular we focus on the dopant segregation effects due to thermosolutal convection as a function of the parameters characterizing the statistics of the stochastic force.
To illustrate the potential uses of the method we characterize the statistics of bubble velocity fluctuations in steady regimes and we characterize the transient relaxation of the buoyancy-driven pseudo-turbulence when gravity is switched-off.
We start by characterizing the statistics of the upper bound of the end-to-end SIR. Based on which, the closed-form approximations for the outage probability and the average SER are obtained.
For practical implementation of the algorithms, finding the most probable distributions that characterize the statistics in the phase space as well as effective resampling strategies is discussed to handle realizability and stability issues.
But, even in the simplest examples, characterizing spike statistics arising from the conjunction of non-linear effects, time propagation delays, synaptic noise, synaptic plasticity, and external stimuli is far from being trivial on mathematical grounds.
Thus, using the maximal entropy principle to characterize spike statistics in the gIF model by expressing constraints in terms of spike events (monomials), one can at best find an approximation which can be rather bad, especially if those constraints focus on instantaneous spike patterns ( D = 0 ) or short memory patterns.
We characterize the statistics of the trajectories through the correlation functions of the orientation angular velocity, orientation angle and the mean-squared displacement, and we find that the loss of orientational memory has significant contributions from both abrupt, large amplitude turning events and the continuous dynamics between these events.
