63 research outputs found
Finite connected components in infinite directed and multiplex networks with arbitrary degree distributions
This work presents exact expressions for size distributions of
weak/multilayer connected components in two generalisations of the
configuration model: networks with directed edges and multiplex networks with
arbitrary number of layers. The expressions are computable in a polynomial
time, and, under some restrictions, are tractable from the asymptotic theory
point of view. If first partial moments of the degree distribution are finite,
the size distribution for two-layer connected components in multiplex networks
exhibits exponent in the critical regime, whereas the size
distribution of weakly connected components in directed networks exhibits two
critical exponents, and
Statistical Modelling of Pre-Impact Velocities in Car Crashes
The law wants to determine if any party involved in a car crash is guilty. The Dutch court invokes the expertise of the Netherlands Forensic Institute (NFI) to answer this question. We discuss the present method of the NFI to deter-
mine probabilities on pre-impact car velocities, given the evidence from the crash scene. A disadvantage of this method is that it requires a prior distribution on the velocities of the cars involved in the crash. We suggest a different approach, that of statistical significance testing, which can be carried out without a prior. We explain this method, and apply it to a toy model. Finally, a sensitivity analysis is performed on a simple two-car collision model
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