On uniqueness of distribution of a random variable whose independent copies span a subspace in L_p

Let 1\leq p<2 and let L_p=L_p[0,1] be the classical L_p-space of all (classes of) p-integrable functions on [0,1]. It is known that a sequence of independent copies of a mean zero random variable f from L_p spans in L_p a subspace isomorphic to some Orlicz sequence space l_M. We present precise connections between M and f and establish conditions under which the distribution of a random variable f whose independent copies span l_M in L_p is essentially unique.Comment: 14 pages, submitte

Passenger-Oriented Enhanced Metrics

We report on a project building the first European ATM simulation combining flight and passenger trip data. New propagation-centric and passenger-centric performance metrics are described. The new metrics will be compared with existing, classical metrics, to compare their respective intelligibility, sensitivity and consistency. The trade-offs in performance across the metrics under a range of flight and passenger prioritisation scenarios will be examined. The corresponding regulatory and socio-political contexts are described. Complexity science techniques demonstrate the need to extend flight-centric network representations to include the passenger perspective

Delay propagation – new metrics, new insights

Network delay propagation is intimately linked with the challenges of managing passenger itineraries and corresponding connections. Airline decision-making governing these processes is driven by operational and regulatory factors. Using the first European network simulation model with explicit passenger itineraries and full delay cost estimations, we explore these factors through various flight and passenger prioritisation rules, assessing the performance impacts. Delay propagation is further characterised under the different prioritisation rules using complexity science techniques such as percolation theory and network attack. The relative effects of randomised and targeted disruption are compared

New perspectives for air transport performance

The average delays of flights and passengers are not the same. The air transport industry is lacking passenger-centric metrics; its reporting is flight-centric. We report on the first European network simulation model with explicit passenger itineraries and full delay cost estimations. Trade-offs in performance are assessed using passenger-centric and flight-centric metrics, under a range of novel flight and passenger prioritisation scenarios. The need for passenger-centric metrics is established. Delay propagation is characterised under the scenarios using, inter alia, Granger causality techniques

Topological Measure Locating the Effective Crossover between Segregation and Integration in a Modular Network

We introduce an easily computable topological measure which locates the effective crossover between segregation and integration in a modular network. Segregation corresponds to the degree of network modularity, while integration is expressed in terms of the algebraic connectivity of an associated hyper-graph. The rigorous treatment of the simplified case of cliques of equal size that are gradually rewired until they become completely merged, allows us to show that this topological crossover can be made to coincide with a dynamical crossover from cluster to global synchronization of a system of coupled phase oscillators. The dynamical crossover is signaled by a peak in the product of the measures of intra-cluster and global synchronization, which we propose as a dynamical measure of complexity. This quantity is much easier to compute than the entropy (of the average frequencies of the oscillators), and displays a behavior which closely mimics that of the dynamical complexity index based on the latter. The proposed toplogical measure simultaneously provides information on the dynamical behavior, sheds light on the interplay between modularity vs total integration and shows how this affects the capability of the network to perform both local and distributed dynamical tasks