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Background: How can we compute a segregation or diversity index from a three-way or multi-way contingency table, where each variable can take on an arbitrary finite number of values and where the index takes values between zero and one? Previous methods only exist for two-way contingency tables or dichotomous variables. A prototypical three-way case is the segregation index of a set of industries or departments given multiple explanatory variables of both sex and race. This can be further extended to other variables, such as disability, number of years of education, and former military service. Methodology/Principal Findings: We extend existing segregation indices based on Euclidean distance (square of coefficient of variation) and Boltzmann/Shannon/Theil index from two-way to multi-way contingency tables by including multiple summations. We provide several biological applications, such as indices for age polyethism and linkage disequilibrium. We also provide a new heuristic conceptualization of entropy-based indices. Higher order association measures are often independent of lower order ones, hence an overall segregation or diversity index should be the arithmetic mean of the normalized association measures at all orders. These methods are applicable when individuals selfidentify as multiple races or even multiple sexes and when individuals work part-time in multiple industries. Conclusions/Significance: The policy implications of this work are enormous, allowing people to rigorously test whether employment or biological diversity has changed.

[EN] In the context of multi-hop cellular communications, user equipment devices (UEs) with relaying capabilities provide a virtual infrastructure that can enhance the cell spectral efficiency. UE relays, which are generally transparent to the destination user and lack channel state information, mainly operate in an open-loop mode. Most open-loop transmission techniques for relaying are based on orthogonal space-time block coding (OSTBC), which offers a good trade-off between performance and complexity. In this paper, we consider the concept of multi-functional multiple-input multiple-output (MIMO) transmission, which combines OSTBC with beamforming techniques. This concept is applied to networks with multiple relays, which can offer a high number of antennas to implement multi-functional MIMO techniques. The proposed schemes are shown to reduce the bit error rate of the destination user with respect to a direct transmission from the base station (BS). Furthermore, the multi-functional setup exhibits better performance than conventional OSTBC at high transmission rates. ; This work was performed in the framework of the FP7 project ICT-317669 METIS, which is partly funded by the European Union. The authors would like to acknowledge the contributions of their colleagues in METIS, although the views expressed are those of the authors and do not necessarily represent the project. ; Roger Varea, S.; Calabuig Soler, D.; Monserrat Del Río, JF.; Cardona Marcet, N. (2014). Multi-functional MIMO communication in multi-hop cellular systems. EURASIP Journal on Advances in Signal Processing. 2014(165):1-9. https://doi.org/10.1186/1687-6180-2014-165 ; S ; 1 ; 9 ; 2014 ; 165 ; Timus B, Fallgren M (Eds): In D1.1: Scenarios, requirements and KPIs for 5G mobile and wireless system. Project deliverable, ICT-317669-METIS. 2013. ; Zheng K, Fan B, Ma Z, Liu G, Shen X, Wang W: Multihop cellular networks toward LTE-advanced. IEEE Veh. Tech. Mag 2009, 4(3):40-47. ; Gozalvez J, Coll-Perales B: Experimental evaluation of multihop cellular ...